# Mathematical Physics

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## Recent submissions

Any replacements are listed further down

[373] viXra:1504.0101 [pdf] submitted on 2015-04-14 02:53:18

### Unitarity in the Canonical Commutation Relation Does not Derive from Homogeneity of Space

Authors: Steve Faulkner

Symmetry information beneath wave mechanics is re-examined. Homogeneity of space is the symmetry, fundamental to the quantum free particle. The unitary information of the Canonical Commutation Relation is shown not to be implied by that symmetry. Keywords:quantum mechanics, wave mechanics, Canonical Commutation Relation, symmetry, homogeneity of space unitary, non-unitary.
Category: Mathematical Physics

[372] viXra:1504.0052 [pdf] submitted on 2015-04-06 16:44:13

### Before the Big Bang?

The study of the hypothetical fractal structure of the vacuum energy offers evidences that before the Big Bang existed a state where the Universe decided its geometric configuration and the nature of the matter and the quantum.
Category: Mathematical Physics

[371] viXra:1504.0045 [pdf] submitted on 2015-04-06 08:23:54

### An Examination of the Derivation of the Lagrange Equations of Motion.

Authors: Jeremy Dunning-Davies

The Lagrange equations of motion are familiar to anyone who has worked in physics. However, their range of validity is rarely, if ever, a topic for discussion. Following on an earlier examination of the consequences for these equations if the mass is not assumed constant, this note will look carefully at the other assumptions made and consider any further consequences resulting. The form of the equations applicable in electromagnetism will also be reviewed in the light of these discussions.
Category: Mathematical Physics

[370] viXra:1504.0044 [pdf] submitted on 2015-04-06 08:31:58

### Some Thoughts on the Notion of Kinetic Energy

Authors: Jeremy Dunning-Davies

The entire notion of kinetic energy seems one well and completely understood. Here, however, the topic will be examined again with special emphasis on considering the physical situation when the mass is not constant. The situation in special relativistic mechanics will also be examined in the light of these discussions.
Category: Mathematical Physics

[369] viXra:1504.0042 [pdf] submitted on 2015-04-05 23:47:13

### On the FORMAL–LOGICAL Analysis of the Foundations of Mathematics Applied to Problems in Physics

Authors: Temur Z. Kalanov

Results of the critical analysis of the standard foundations of mathematics applied to problems in physics are discussed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. The main result is as follows: the concept of “mathematical quantity” – central concept of mathematics – is meaningless, erroneous, and inadmissible one because it represents the following formal-logical and dialectical-materialistic errors: negation of the existence of the essential sign of a concept (i.e., negation the existence of the essence of the concept) and negation of the existence of measure of material object. The obtained results lead to the conclusion that the generally accepted foundations of mathematics should be reconsidered.
Category: Mathematical Physics

[368] viXra:1504.0012 [pdf] submitted on 2015-04-02 03:10:10

### Expressing the Dirac Equation as a Generalization of Maxwells Equations

Authors: Claude Michael Cassano

Using the bijective transformations between the Dirac equation and the special case of the Maxwell-Cassano equations the Dirac equation is expressed as a generalization of Maxwell's equations, via familiar field potentials and field strengths.
Category: Mathematical Physics

[367] viXra:1504.0006 [pdf] submitted on 2015-04-01 07:31:24

### The Dirac Equation is a Special Case of the Maxwell-Cassano Equations

Authors: Claude Michael Cassano

The Dirac Equation is a Special Case of the Maxwell-Cassano Equations For vector Phi of D The Klein-Gordon equation may be written (see reference (4)): Whenever Phi of D is a 2 to the M-dimensional vector, via a matrix differential operator factorization, it may be written (in the Dirac representation), as shown here: and, since these matrix operators are commutative: conformability of the matrices requires thatthese matrices are all 2×1 matrices; yielding: For symmetry purposes, let: t=ix^0 then, combining into a single matrix equation, Just as there are a number of representations of the Dirac equation, there is more than one matrix operator factorization of the Maxwell-Cassano equations (3). A matrix operator factorization of the Maxwell-Cassano equations may be compactly written, from references (1) and (3) as follows: For the stationary state the source/sink density term vanishes in the Maxwell-Cassano equations, which allows an equating of the Maxwell-Cassano equation & Dirac equation factorizations. These may imply correlations between the Dirac equation and the Maxwell-Cassano equations as the correspondences/mappings: m⇔|m| and -θ_sub_D_to_the_j = f_to_the_h. The Dirac equation may be expanded with the above notation as shown As reference (1) shows. the component pairs may be organized such that this organization exhibits the mass-generalization of Maxwell's equations, but organizing them while comparing them analogously to the Dirac equations yields the shown And, Continuing the comparison with the Maxwell-Cassano equations in the special case: m_sub_zero = -m , m_sub_1=m_sub_2=m_sub_3 = 0: So, extending the Dirac equation beyond the source/sink free case (so looking beyond just eigenvalues and eigenvectors); and writing in matrix form, and comparing: Then, viewing each matrix as a paired sum: In this form the transformations are easy to see: By the invertible matrix theorem each matrix is invertible. Thus, these transformations are oneto - bijective. From the first matrices on each side of the sum, the rest of the transformations are even more easily seen. The full set of transformations are shown, here This proves that the mass-generalized Maxwell's equations (Maxwell-Cassano equations) is a more general analysis of fundamental-elementary particle phenomena. It further proves that the Lagrangian is far simpler than that consisting of the Glashow-Salam-Weinberg + fermion + Higgs + Yukawa kludge. Also, it explains the group structure and architecture of the fermions, as shown in reference (2). It also proves that those with wealth to seek the truth choose not to do so, but with all deceivableness and unrighteousness in them they have not the love of the truth, but rather embrace strong delusion, that they profess a lie. References and further readings (1) Cassano, Claude.Michael ; "Reality is a Mathematical Model", 2010. ISBN: 1468120921 ; http://www.amazon.com/dp/1468120921 ASIN: B0049P1P4C ; http://www.amazon.com/Reality-Mathematical-Modelebook/ dp/B0049P1P4C/ref=tmm(kin(swatch(0?(encoding=UTF8&sr=&qid= (2) Cassano, Claude.Michael ; "A Mathematical Preon Foundation for the Standard Model", 2011. ISBN:1468117734 ; http://www.amazon.com/dp/1468117734 ASIN: B004IZLHI2 ; http://www.amazon.com/ Mathematical-Preon-Foundation-Standardebook/dp/B004IZLHI2/ref=tmm(kin(swatch(0?(encoding=UTF8&sr=&qid= Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 1" ; http://www.dnatube.com/video/6907/ The-Standard-Model-Architecture-and-Interactions-Part-1 http://www.scivee.tv/node/28362 Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ; http://www.youtube.com/watch?v=Mxa2u7-czmk Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ; http://www.dnatube.com/video/6908/ The-Standard-Model-Architecture-and-Interactions-Part-2 (3) Cassano, Claude.Michael ; "A Helmholtzian operator and electromagnetic-nuclear field" ; http://www.dnatube.com/video/6877/ A-Helmholtzian-operator-and-electromagnetic-nuclear-field http://www.scivee.tv/node/27991 (4) Cassano, Claude.Michael ; "A Brief Mathematical Look at the Dirac Equation" ; https://youtu.be/IcWeq6iEwFE http://www.scivee.tv/node/63581
Category: Mathematical Physics

[366] viXra:1503.0257 [pdf] submitted on 2015-03-30 06:29:25

### A Quantum Logical Understanding of Bound States

Authors: Kan Kuo-Hsiao
Comments: 6 Pages. MSC 2010: 06C15, 81P10

This short note presents the structures of lattices and continuous geometries in the energy spectrum of a quantum bound state. Quantum logic, in von Neumann's original sense, is used to construct these structures. Finally, a quantum logical understanding of the emergence of discreteness is suggested.
Category: Mathematical Physics

[365] viXra:1503.0240 [pdf] submitted on 2015-03-29 04:21:22

### Immunization Strategy Based on the Critical Node in Percolation Transition

Authors: Yang Liu, Bo Wei, Zhen Wang, Yong Deng

The problem of finding a better immunization strategy for controlling the spreading of the epidemic with limited resources has attracted much attention since its great theoretical significance and wide application. In this paper, we propose a novel and successful targeted immunization strategy based on percolation transition. Our strategy immunizes the fraction of critical nodes which lead to the emergence of giant connected component. To test the effectiveness of the proposed method, we conduct the experiments on several artificial networks and real-world networks. The results show that the proposed method outperforms the existing well-known methods with 18% to 50% fewer immunized nodes for same degree of immunization.
Category: Mathematical Physics

[364] viXra:1503.0169 [pdf] submitted on 2015-03-23 07:03:18

### New Way of Developing Information Technology and Imaginary Time for the Purpose of Building the Universe

Authors: Rodney Bartlett

Stephen Hawking writes, “In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic …” (“A Brief History of Time” by Stephen Hawking - Bantam Press, 1988, p.139) When Hawking says there are no singularities in imaginary time, can his statement relate to physics? Or is it purely mathematical, in which case it would reinforce the idea that the universe began with a singularity and a Big Bang? I believe imaginary time has physical meaning since it can be developed from space-time where parallel lines become perpendicular without any motion occurring. Such a feat depends on a particular form of General Relativity’s space-time curvature. It leads to new cosmology and quantum physics that includes deletion of distance on every scale – plus a method for cosmogenesis or creation of the universe. This author has a habit of “text recycling” or “self plagiarism”. I’ve done it in the past to present an idea in different contexts, hoping that would demonstrate the idea’s validity. In this article, sentences are added to my recycling – showing that I still believe in the basic idea I started with, but adding information (sometimes from mathematics) to support that basis.
Category: Mathematical Physics

[363] viXra:1503.0159 [pdf] submitted on 2015-03-21 12:54:48

### Simplified Calculation of Component Number in the Curvature Tensor

Authors: William O. Straub

The number of independent components in the Riemann-Christoffel curvature tensor, being composed of the metric tensor and its first and second derivatives, varies considerably with the dimension of space. Since few texts provide an explicit derivation of component number, we present here a simplified method using only the curvature tensor’s antisymmetry property and the cyclicity condition. For generality and comparison, the method for computing component number in both Riemannian and non-Riemannian space is presented.
Category: Mathematical Physics

[362] viXra:1503.0128 [pdf] submitted on 2015-03-15 19:49:29

### Variational Theory:variable-Independence and Consistency

Authors: Jian-zhong Zhao

Abstract Variational theory of elasticity is surveyed in the context of mathematical logic in the present paper. The problem of variable-independence of variational principles raised by Chien is discussed. We find that Chien’s “High-order Lagrange Multiplier Theory”, which deals with the problem of variable-independence and constraint of variational principles, is inconsistent; Luo’s system, which is involved in the problem of variable-independence, is involved in contradictions; the conventional understanding of independence of variables of variational principles connotes contradiction. In the context of mathematical logic, variational theory must be established as a mathematical system of logic, excluding vagueness and misunderstanding. By consideration of logic, variable-independence is understood as identity of variables and then formalization of variational theory is a solution to the problem of variable-independence. Two consistent systems for elasticity, the Axiomatic System of Variation and the Formal System of Variation, are suggested in this paper.
Category: Mathematical Physics

[361] viXra:1503.0063 [pdf] submitted on 2015-03-09 09:49:41

### A Discussion about Curl Equations in Mathematical Physics

Authors: LIU Changli

Usually, the numbers of unknowns are equal to the numbers of differential equations. However, there are some exceptions. One example is Maxwell equations; there are 6 unknowns and 8 equations. The other example is elasticity equations in stress form; there 6 unknowns and 9 equations. In the paper, I generalize the definition of linear correlation in algebra to the concept of differential linear correlation in differential equations, and I use this definition to explain the above problem.
Category: Mathematical Physics

[360] viXra:1503.0060 [pdf] submitted on 2015-03-09 06:50:30

### Reflecting on Numbers: A Geometry of Time, Ether, and Potential Infinity

Authors: Gerasimos T. Soldatos
Comments: 11 Pages. Published in: International Journal of Innovation in Science and Mathematics, 2015, 3(2), 48-58.

This paper is considering geometrically the smallest possible spatial displacement of the elementary mass by equating the corresponding and thereby smallest possible historical time with the unit. This time is supposed to be the travel time under smooth rectilinear motion as the motion, with the least change in the physicochemical substance of this mass, change determining the age of the mass and owing exclusively to kinematics in void space. Yet, the passage of time as recorded by physicochemical change under other types of motion towards the same terminal point and at the same arrival time, call it “age-time”, does not coincide with the arrival time. Therefore, although void space has been assumed, some other, age-shaping factor beyond kinematics is inferred to exist in this space, so that it can be held responsible for the variations in age time. It acts so as to be ensuring the uniqueness of events. The same factor should be cited as the source of motion too, given that motion is contemplated analytically with no reference to a cause of it. This factor appears to exhibit the properties of ether, with which it is identified. Ether provides momentum to mass, altering constantly the texture of the mass, that is, the age of the mass and subsequently, the velocity of it in historical time. The operation of ether is taken to be mathematically the reason for the real-world relevance of irrational numbers. The potential infinity, associated with these numbers and with the operation of ether that is filling space, becomes embedded in the actual infinite of space by itself, in this manner.
Category: Mathematical Physics

[359] viXra:1503.0022 [pdf] submitted on 2015-03-03 07:43:57

### Phase Liquid Turbulence as Novel Quantum Approach

Authors: Sergey Kamenshchikov

In this paper we consider a nonlinear stochastic approach to the description of quantum systems. It is shown that a possibility to derive quantum properties - spectrum quantization, zero point positive energy and uncertainty relations, exists in frame of Zaslavsky phase liquid. This liquid is considered as a projection of continuous turbulent medium into a Hilbert phase space. It has isotropic minimal diffusion defined by Planck constant. Areas of probability condensation may produce clustering centers – quasi stable particles-attractors which preserve boundaries and scale-free fractal transport properties. The stability of particles has been shown in frame of the first order perturbation theory. Quantum peculiarities of considered systems have been strictly derived from markovian Fokker-Planck equation. It turned out that the positive zero point energy has volumetric properties and grows for higher time resolutions. We have shown that a quasi stable attractor may be applied as a satisfactory model of an elementary quantum system. The conditions of attractor stability are defined on the basis of Nonlinear Prigogine Theorem. Finally the integrity of classical and quantum approaches is recovered: existence of particles is derived in terms of Zaslavsky quantum fluid.
Category: Mathematical Physics

[358] viXra:1503.0012 [pdf] submitted on 2015-03-01 19:44:28

### Internal and External Control in PHPR

Authors: Miguel A. Sanchez-Rey

The manuscript will lay out a few examples of computational control in PHPR.
Category: Mathematical Physics

[357] viXra:1502.0242 [pdf] submitted on 2015-02-27 09:40:01

### Conundrums Overlooked in Physics for Evermore ...

Another ... friendly and creative ... author-editor interaction is presented in which several basic conundrums in physics are mentioned, conundrums no physicist seems to care about ...
Category: Mathematical Physics

[356] viXra:1502.0225 [pdf] submitted on 2015-02-25 09:35:26

### A Mathematical Approach to Physical Realism

Authors: Carsten S.P. Spanheimer

I propose to ask mathematics itself for the possible behaviour of nature, with the focus on starting with a most simple realistic model, employing a philosophy of investigation rather than invention when looking for a unified theory of physics. Doing a 'mathematical experiment' of putting a least set of conditions on a general time-dependent manifold results in mathematics itself inducing a not too complex 4-dimensional object similar to our physical spacetime, with candidates for gravitational and electromagnetic fields emerging on the tangent bundle. This suggests that the same physics might govern spacetime not only on a macroscopic scale, but also on the microscopic scale of elementary particles, with possible junctions to quantum mechanics.
Category: Mathematical Physics

[355] viXra:1502.0221 [pdf] submitted on 2015-02-25 03:24:33

### Theoretical Computations Using PhySix

Authors: N.S. Baaklini
Comments: 15 pages, 2 references, 712 KB

We demonstrate, with simple examples from theoretical physics, the utility of doing numerical and symbolic manipulations with the aid of our computer program PhySix. The latter is a very small single-file executable application under Windows, with a code language very much (though not exactly) similar to Mathematica. A copy of the current version of PhySix is embedded in this article, and can be extracted safely, and used freely by every one.
Category: Mathematical Physics

[354] viXra:1502.0186 [pdf] submitted on 2015-02-21 08:29:20

### Foundations of a Mathematical Model of Physical Reality

Authors: J.A.J. van Leunen

This paper starts from the idea that physical reality implements a network of a small number of mathematical structures. Only in that way can be explained that observations of physical reality fit so well with mathematical methods. The mathematical structures do not contain mechanisms that ensure coherence. Thus apart from the network of mathematical structures a model of physical reality must contain mechanisms that manage coherence such that dynamical chaos is prevented. Reducing complexity appears to be the general strategy. The structures appear in chains that start with a foundation. The strategy asks that especially in the lower levels, the subsequent members of the chain emerge with inescapable self-evidence from the previous member. The chains are interrelated and in this way they enforce mutual restrictions. As a consequence the lowest levels of a corresponding mathematical model of physical reality are rather simple and can be comprehended by skilled mathematicians. In order to explain the claimed setup of physical reality, the paper selects a special foundation for the major chain. That foundation is a skeleton relational structure and it was already discovered and introduced in 1936. The paper does not touch more than the first development levels. The base model that is reached in this way puts already very strong restrictions to more extensive models. Some of the features of the base model are investigated and compared with results of contemporary physics.
Category: Mathematical Physics

[353] viXra:1502.0168 [pdf] submitted on 2015-02-20 00:49:34

### The Teq: Exploring a Link with the QCD and New Territories

Authors: Thierry PERIAT

I don’t ignore the long discussion concerning the representation of nuclei (protons and neutrons); in extenso the story of the birth of the standard model (SM). But I also know the actual difficulties and the arguments for a modest extension of the SM. Physics is actually a house containing diverse coherent theories. Some of them are logically related to the others; some are not. This still remain a modern challenge to bring all members of the family under the same roof. My attempt here is to continue the discussion around a fundamental coherent vision.
Category: Mathematical Physics

[352] viXra:1502.0147 [pdf] submitted on 2015-02-17 10:40:07

### Remarkables Properties of the Eddington Number 137 and Electric Parameter 137.036 Excluding the Multiverse Hypothesis

Authors: Francis M. Sanchez

Considering that the Large Eddington Number has correctly predicted the number of atoms in the Universe, the properties of the Eddington electric number 137 are studied. This number shows abnormal arithmetic properties, in liaison with canonic numbers of the string and superstring theories including overwhelming relations with musical canonic numbers. The liaison with the harmonic series is so tight that it seems that Egyptians was aware of them, as the architecture of the Hypostyle Karnak room reveals. The direct liaison between the mean value of two Universe radiuses and the Bohr radius through the simplest harmonic series excludes any role of chance. It is concluded that the Cosmos is a finite computer using 137 and its extension 137.036 as calculation basis.
Category: Mathematical Physics

[351] viXra:1502.0130 [pdf] submitted on 2015-02-16 06:13:26

### Computational and Mathematical Methods in the Physicalist Program

Authors: Miguel A. Sanchez-Rey

We will attempt to resolve a long-standing and important problem in gauge theory. We will also delve further into theoretical mathematics and computation.
Category: Mathematical Physics

[350] viXra:1502.0105 [pdf] submitted on 2015-02-15 02:17:51

### A Novel Bracket And Second Quantized Wave Equation Of A Photon

Authors: Ramesh Chandra Bagadi, David L Huber, Charles J Goebel

A novel kind of classical bracket of classical observables is proposed. This bracket is used directly as a derivation* of the commutator of the quantum mechanical observables that are simply obtained by Dirac quantization of the classical observables. Light bending in the presence of a massive object in Schwarzschild’s metric is considered and the above bracket is used to obtain a second quantized equation of the wave function of the photon in this situation via the Dirac quantization.
Category: Mathematical Physics

[349] viXra:1502.0072 [pdf] submitted on 2015-02-10 02:02:19

### Cross-Correlation in Cricket Data and RMT

Authors: Manu Kalia, Saugata Ghosh

We analyze cross-correlation between runs scored over a time interval in cricket matches of different teams using methods of random matrix theory (RMT). We obtain an ensemble of cross-correlation matrices $C$ from runs scored by eight cricket playing nations for (i) test cricket from 1877 -2014 (ii)one-day internationals from 1971 -2014 and (iii) seven teams participating in the Indian Premier league T20 format (2008-2014) respectively. We find that a majority of the eigenvalues of C fall within the bounds of random matrices having joint probability distribution $P(x_1\ldots,x_n)=C_{N \beta} \, \prod_{j<k}w(x_j)\left | x_j-x_k \right |^\beta$ where $w(x)=x^{N\beta a}\exp\left(-N\beta b x\right)$ and $\beta$ is the Dyson parameter. The corresponding level density gives Marchenko-Pastur (MP) distribution while fluctuations of every participating team agrees with the universal behavior of Gaussian Unitary Ensemble (GUE). We analyze the components of the deviating eigenvalues and find that the largest eigenvalue corresponds to an influence common to all matches played during these periods.
Category: Mathematical Physics

[348] viXra:1502.0048 [pdf] submitted on 2015-02-05 16:10:45

### PCT, Spin, Lagrangians

Authors: Hans Detlef Hüttenbach

In this paper I invite you to take a step aside current quantum field theory (QFT): QFT has been said to be "well-established" since the 80's of the last century by its foremost theorists), and the majority of physicists consider it to be essentially complete since the discovery of the Higgs particle. It will be interesting to see, what that really means: What are the problems left over to the younger generations? I'll show you that a.o. it fails in its Lagrangian formalism, its postulate of positivity of energy, I'll show the uselessness of the uncertainty principle as to electromagnetic fields, and we'll see that there are serious doubts as to its conception of the photonic nature of electromagnetic fields, which a simple experiment could test against.
Category: Mathematical Physics

[347] viXra:1502.0035 [pdf] submitted on 2015-02-04 14:36:56

### The Anomalous Nambu-Goldstone Theorem in Relativistic/Nonrelativistic Quantum Field Theory. II

Several aspects of the anomalous Nambu-Goldstone theorem are noted/listed and discussed.
Category: Mathematical Physics

[346] viXra:1502.0034 [pdf] submitted on 2015-02-04 14:39:00

### The Anomalous Nambu-Goldstone Theorem in Relativistic/Nonrelativistic Quantum Field Theory. III

Some mathematical aspects of holonomy in the Nambu-Goldstone theorem are discussed. A unied theorem of the normal, generalized, and anomalous Nambu-Goldstone theorems are presented.
Category: Mathematical Physics

[345] viXra:1502.0033 [pdf] submitted on 2015-02-04 14:40:41

### The Mathematical Structure of Quantum Nambu Mechanics and Neutrino Oscillations

Some Lie-algebraic structures of three-dimensional quantum Nambu mechanics are studied. From our result, we argue that the three-dimensional quantum Nambu mechanics is a natural extension of the ordinary Heisenberg quantum theory, and we give our insight that we can construct several candidates "beyond the Heisenberg quantum theory".
Category: Mathematical Physics

[344] viXra:1502.0032 [pdf] submitted on 2015-02-04 14:42:43

### A Manifestation Toward the Nambu-Goldstone Geometry

Various geometric aspects of the Nambu-Goldstone ( NG ) type symmetry breakings ( normal, generalized, and anomalous NG theorems ) are summarized, and their relations are discussed. By the viewpoint of Riemannian geometry, Laplacian, curvature and geodesics are examined. Theory of Ricci ow is investigated in complex geometry of the NG-type theorems, and its diusion and stochastic forms are derived. In our anomalous NG theorems, the structure of symplectic geometry is emphasized, Lagrangian submanifolds and mirror duality are noticed. Possible relations between the Langlands correspondence, the Riemann hypothesis and the geometric nature of NG-type theorems are given.
Category: Mathematical Physics

[343] viXra:1502.0002 [pdf] submitted on 2015-02-01 04:55:10

### Theory of the (E) Question Link with the Standard Model and with Su(5).

Authors: Thierry PERIAT

This document explores the links between the proposed “grand unified theory (GTU)” based on a SU(5) model and the theory involving extended Lie products (ELP). A special focus is given to some EM fields obtained via a Cartan-like procedure rebuilding the general theory of relativity (GTR) with the variations of the basis vectors up to the second order (the so-called GTR2 – see link in the bibliography below). The link between the GTR and the GTR2 is better understood and explained. My hope is a reconstruction of the results actually obtained by the standard model via the intervening of the ELPs for the GTR2-induced electromagnetic fields. A big part of the way in that direction has been made but the goal is not yet totally reached; thus: yet in evolution.
Category: Mathematical Physics

[342] viXra:1501.0235 [pdf] submitted on 2015-01-27 12:24:18

### A Note on the Definitions of Discrete Symmetries Operators

Authors: Valeriy V. Dvoeglazov
Comments: 11 Pages. Talk at the X Mexican School on Gravitation and Mathematical Physics, Playa del Carmen, Mexico, December 1-5, 2014. To be published in Proceedings.

On the basis of the Silagadze research[1], we investigate the question of the definitions of the discrete symmetry operators both on the classical level, and in the secondary-quantization scheme [2,3]. We studied the physical content within several bases: light-front form formulation [4], helicity basis, angular momentum basis, and so on, on several practical examples. The conclusion is that we have ambiguities in the definitions of the corresponding operators P, C; T, which lead to different physical consequences [5,6].
Category: Mathematical Physics

[341] viXra:1501.0198 [pdf] submitted on 2015-01-21 04:47:40

### Principles for the Theory and Its Agreement with Experiment

Authors: Lubomir Vlcek
Comments: 38 Pages. Physics in the past formulated at least part of the truth about the physical phenomena. Some ideas, even if they were doubtful and rejectable, are still valid today

All is building on experiments. The theory is valid if and only if it can explain everything earlier known experiments and can predict something new in physics, which will be confirmed in the future. Metrology must be paramount. All equations must be dimensionally correctly, that is, to use the correct units for each physical quantity. Correct nomenclature and correct terminology. Form of the interference field must be non-linear. Form of Intensity of the Moving Charge Electric Field must be asymmetrical. Kinetic energy of a charge moving at the velocity of v has two different values: Kinetic energy against direction of motion as wave Tkin ad = mc2[ln |1+v/c|- (v/c)/(1+v/c)] Kinetic energy in direction of motion as particle Tkin id = mc2[ln|1-v/c|+ (v/c)/(1-v/c)] Wave - particle duality as kinetic energy against and In direction of motion. Physicist must to have a healthy arrogance, do not be afraid criticize of the great physicists, if he is adamantly confident on the basis of experiments metrological and mathematically about their truth. Not afraid to speak out about errors in the theory and about their consequences. Physicist must have a flight and constantly looking partners, who can discuss with him, who can jointly develop and explore.
Category: Mathematical Physics

[340] viXra:1501.0184 [pdf] submitted on 2015-01-19 08:22:25

### New Dark Energy-Force Solves The Discrepancy Of The Proton-Radius.

Authors: Dan Visser

It is well known among physicists that two different kinds of experiments give an anomaly in the proton-radius. The anomaly is: When a muon orbits the proton the proton-radius is 4% smaller than when an electron orbits the proton. This anomaly is a puzzle in standard physics. This puzzle is solved in a new cosmological theory with a new dark energy-force. This article describes the solution. The solution is put in perspective of new physics by a combination of quantum-gravity and sub-quantum dark matter-force in one formula, within the new cosmological theory, called the Double Torus Theory for the universe.
Category: Mathematical Physics

[339] viXra:1501.0176 [pdf] submitted on 2015-01-17 04:26:38

### The Differential of the Triad and the Extended Lie Products

Authors: Thierry Periat

The document starts in examining in which way the differential of the elements of the tetrad could be extended Lie products. Because of technical difficulties we first reduce our initial exploration to the same interrogation for the triad. Provided some conditions hold true, it is demonstrated that the differential of the elements of a given triad are extended Lie products in E(3,H) where H denotes the set of quaternions.
Category: Mathematical Physics

[338] viXra:1501.0154 [pdf] submitted on 2015-01-14 11:40:56

### Polar Coordinates Satisfy Wave Equation

Authors: Louai Hassan Elzein Basheir

This paper is prepared to show that the polar coordinates satisfaction to wave equation.
Category: Mathematical Physics

[337] viXra:1501.0124 [pdf] submitted on 2015-01-12 11:31:10

### An Approximation to the Mass Ratio of the Proton to the Electron

Authors: Harry A. Watson

An Approximation to the Mass Ratio of the Proton to the Electron. The mass ratio of the proton to the electron is a dimensionless physical constant. The following expression provides a good estimate. (4π)(4π−1/π)(4π−2/π)= 1836.15 (1) The above expression is also the greatest lower bound (GLB) for a more general expression. A geometric persuasion is given and the more general expression is determined via the inversion of the spheres.
Category: Mathematical Physics

[336] viXra:1501.0105 [pdf] submitted on 2015-01-08 13:20:24

### On Some Analytical Results for 3-Cycles of the Logistic Map

Authors: Andrzej Okninski

In the present work new analytical results for the 3-cycles of the logistic map are obtained.
Category: Mathematical Physics

[335] viXra:1501.0095 [pdf] submitted on 2015-01-08 06:04:42

### Towards A Quaternionic Spacetime Calculus

Authors: Carsten S. P. Spanheimer

Introducing a special quaternionic vector calculus on the tangent bundle of a 4-dimensional space, and by forcing a condition of holomorphism, a Minkowski-type spacetime emerges, from which gravitation and also the whole Maxwell theory of electromagnetic fields arises. This is a preliminary draft.
Category: Mathematical Physics

[334] viXra:1501.0072 [pdf] submitted on 2015-01-05 21:48:02

### Conjecture of Negative Matter and Negative Internal Energy

Authors: Yuan Li, Xuhong Zou

We try to use the word“balance” to explain the energy in this universe. In chemistry, we know if a matter wants to be stable[1], the energy must be lower and lower. So we have reason to believe that if our universe is stable, then the total energy equal to zero, the perfect balance. We use coordinates to prove negative matter and negative internal energy exists and builds molds to explain the relation ship between negative matter and normal matter in our universe.
Category: Mathematical Physics

[333] viXra:1501.0053 [pdf] submitted on 2015-01-04 08:01:42

### Geography of Time in Qi Men Dun Jia

Authors: John Frederick Sweeney

One cause for the failure of western science is the assumption that Time is constant, or the reliance on such concepts as “Space – Time.” In contrast, the ancient divination method known as Qi Men Dun Jia views time as a physical entity. The QMDJ model, based on actual real physical processes, thus uses this temporal model to make accurate predictions in the real world. This paper explains the temporal mechanism, based on Hurwitz Quaternions, by which this is done. Thus Hurwitz Lattices and the 24 – Cell may describe the Geography of Time.
Category: Mathematical Physics

[332] viXra:1501.0052 [pdf] submitted on 2015-01-04 08:43:49

### The Connection Between Gravitation and the Velocity of Light

Authors: DT Froedge
Comments: 7 Pages. A bit of speculation, but interesting

It has long been known that a photon entering a gravitational potential follows a path identically to that of a photon in a variable speed of light defined by the Shapiro velocity for Minkowski flat space [1]. It is shown here that a particle having constant energy infalling a gravitational potential, and defined as a pair of trapped photons in a massless box, is accelerated by a gradient in the velocity of light exactly as a particle in a gravitational field [2], and thus, is asserted that gravitation is nothing more than a gradient in c produced by the presence of mass. It is also illustrated that QFT effects that define the total action path of trapped photons could induce an alteration in the velocity of light in the proximity of the photon paths [3], and could be the mechanism creating the effects of gravitation.
Category: Mathematical Physics

[331] viXra:1501.0019 [pdf] submitted on 2015-01-01 21:10:05

### An Exact Solution of Riccati Form of Navier-Stokes Equations with Mathematica

Authors: Victor Christianto
Comments: 4 Pages. This paper has been submitted to International Frontiers Science Letters journal. Comments are welcome

There are many obtained solutions for 2D Navier-Stokes equations. This paper discusses an exact analytical solution of Riccati form of Navier-Stokes equations with Mathematica. To our best knowledge, this solution has never been presented elsewhere before, and it is faster compared to solution of Riccati equation using Differential Transform Method (DTM).
Category: Mathematical Physics

[330] viXra:1501.0003 [pdf] submitted on 2015-01-01 00:19:09

### Explaining The Mysterious Connection Between Physics and Mathematics By Reconciling the Unified Field and Anthropic Principle

Authors: Rodney Bartlett

This is a copy of my entry in the latest essay contest conducted by the Foundational Questions Institute (FQXi). That contest restricts me to 25,000 characters, so I’ve added Notes to the end of the essay (FQXi allows the addition of notes but limits their length to much less than what I want to say). Other excellent essays in FQXi’s current contest will inform readers about the role of Fibonacci numbers and the Golden Ratio in nature, as well as referring to the book “Our Mathematical Universe” by Max Tegmark and the use of pi in a science-fiction book by astronomer Carl Sagan to show that “the universe was made on purpose”. Rather than merely repeat the other essays’ wisdom, I’ll take a different approach. I hope my approach will be novel and original, but only time will reveal where it may lead. I want to show that you can combine the topology (rubber-sheet geometry), binary digits and E=mc^2 of maths with the matter, energy and forces of physics to 1) explain dark energy and dark matter, 2) open up the whole universe and all time to human exploration and creation, 3) show that there’s an infinite, eternal cosmos (not a multiverse) beyond our observable universe, 4) unify gravitation with electromagnetism, the other fundamental forces, and the physical universe; and 5) reconcile the anthropic principle with the unified theories of physics (via a strong version of that principle - that a direct link exists between human existence and the actual form of the laws of nature). Is this an incredibly ambitious challenge for one person? Yes, and maybe you think an essay competition is not the right place for this. You might be right - but I feel ready to take on the challenge. And people tell me there’s no time like the present. An important weapon in my arsenal is R136a1 - R136a1 is a monstrous-sized star 165,000 light years away in the Large Magellanic Cloud, one of our Milky Way’s satellite galaxies. It currently has 265 times the mass of the Sun and may have been 320 solar masses when it first formed. It’s the most massive and most luminous star ever found, being 10 million times brighter than the Sun. "Owing to the rarity of these monsters, I think it is unlikely that this new record will be broken any time soon," said (English astrophysicist Paul) Crowther. It’s important to my essay because adopting a view in which everything in all space and all time (such as gravitation, electromagnetism and matter) is part of a unification says a star in the Large Magellanic Cloud and the imaginings in the human brains on Earth must indeed be connected. Instead of fantasy, the anthropic principle arises and is reconciled with the unified theories of physics. Albert Einstein showed that space-time is curved and warped, so it’s possible that our own computer science (and terraforming, and biotechnology from many centuries in the future) found its way into the remote past. In the TV program "Catalyst", Dr Graham Phillips said,“(The physicist and writer) Paul Davies thinks the universe is indeed fine-tuned for minds like ours. And who fine-tuned it? Not God, but minds from the future, perhaps even our distant descendants, that have reached back through time … and selected the very laws of physics that allow for the existence of minds in the first place. Sounds bizarre, but quantum physics actually allows that kind of thing.”
Category: Mathematical Physics

[329] viXra:1412.0278 [pdf] submitted on 2014-12-31 14:46:19

### Absolute Parallelism and New Worldview

Authors: Ivan L Zhogin
Comments: 6 Pages. essay; 2 figures (send to friedmann-2015.org)

There is a unique (compatible, second-order) 5D-equation of Absolute Parallelism (D is fixed) which solutions avoid singularities. Three of fifteen polarization modes are linearly unstable; they can carry digital information, topological charges and quasi-charges, but not the five-momentum. Phenomenological models accounting for these (quasi)charges (i.e., particles) emerge including a relativistically expanding S^3-shell cosmology and Lagrangian forth-order gravity. A radial longitudinal wave can form a shell of huge size L (in the co-moving system) along the extra-dimension. The correction to the Newton's law here behaves as 1/r on large scales, r>L, so the Dark Matter hypothesis looks unnecessary. Generation of gravitational waves (GW) in this theory differs by the factor (\lambda/L)^2 from the General Relativity result (for GW amplitude; \lambda is GW wavelength); so, short GWs should be much weaker than in GR. A new way of interpretation of Quantum Mechanics (closely relating to the huge and "undeveloped" extra-dimension) is briefly discussed.
Category: Mathematical Physics

[328] viXra:1412.0257 [pdf] submitted on 2014-12-27 22:39:47

### Quaternion Dynamics, Part 1 - Functions, Derivatives, and Integrals

Authors: Gary D. Simpson

Definitions are presented for "quaternion functions" of a quaternion. Polynomial and exponential quaternion functions are presented. Derivatives and integrals of these quaternion functions are developed. It is shown that quaternion multiplication can be represented by matrix multiplication provided the matrix has a specific type of structure. It is also shown that differentiation and integration are similar to their non-quaternion applications.
Category: Mathematical Physics

[327] viXra:1412.0227 [pdf] submitted on 2014-12-24 03:09:23

### Vedic Physics Justification for Octonions

Authors: John Frederick Sweeney
Comments: 19 Pages. Some charts and diagrams

Sir Roger Penrose, Nobel Laureate, has described them as “useless” for physics, yet the old uncle locked up in the attic, as John Baez describes them, play a fundamental role in the physics of the Universe, according to Vedic Physics theory. This paper explains why.
Category: Mathematical Physics

[326] viXra:1412.0211 [pdf] submitted on 2014-12-20 07:21:38

### Window For The Visible Matter In A Rotating Time-Torus-Universe.

Authors: Dan Visser

The subtitle of this paper is: “An overwhelming amount of evidence is available for the non-existence of the Big Bang”. Instead a new proposal for the shape and dynamic of the universe is described as an eternally rotating Time-Torus-Universe. Therein particles and observers are in orbit inside a time-density of a sub-time-torus. Such a sub-time-torus is a part of the larger Time-Torus Universe. Such a whole universe rotates forever. This is the Double Torus Universe described in the Double Torus Theory (DTT), which has no beginning or end. Such a universe is full of dark matter in synergy with new dark energy, which emerges the visible material world as we know it. The power for this synergy is capsuled in events happening by 2 dimensions of time smaller than the conformal time in the Big Bang Universe. Therefore this new theory is called ‘double’, because it uses that refined time, which is 2D-time smaller than the conformal Planck-time. However, the General Relativity Theory (GRT) and the Quantum Theory (QT) remain valid in the DTT. In the DTT a new force takes care for the torus not to expand unlimited as in the Big Bang universe. Observers inside the DTT experience a combination of quantum Newton-force and sub-quantum dark matter-force at the edge of any sub-time-torus. This leads to a sometimes shared rotating cosmological horizon in the presence. Space is no longer the issue in the DTT, but conformal and refined time are. In an overview is explained, by means of 14 handwritten sheets, how to visualize this mechanism mathematically and dimensionally. The under laying formulations are already described in former vixra-articles of mine [1]. Popular information can also be found on my website [a]. In the end a description is given of the window of visible matter (a new formula, which is independent of the cosmological constant). This formula calculates the ‘window’. In addition several examples of institutional evidence is shown to support the DTT-formulations. My opinion is: It is unbelievable how science anno 2014 wants holds on to Big Bang. Forget the Big Bang!
Category: Mathematical Physics

[325] viXra:1412.0175 [pdf] submitted on 2014-12-15 02:58:50

### Tai Xuan Jing as Vedic Literature

Authors: John Frederick Sweeney

The Tai Xuan Jing (T’ai Hsuan Ching) or Classic of the Great Mystery, although attributed to Chinese writers and preserved in China for two thousand years, probably originated in Vedic India. The Tai Xuan Jing pertains to the dynamic Raja form of 9 x 9 matter, which is a fundamental aspect of Vedic Physics. This paper argues for Vedic origins of the Tai Xuan Jing and provides supporting material for that argument, based on the mathematical argument proposed by Frank “Tony” Smith on his website.
Category: Mathematical Physics

[324] viXra:1412.0162 [pdf] submitted on 2014-12-11 03:54:38

### What Drives Reality

Authors: J.A.J. van Leunen

The dynamics of reality is well regulated. What is the mechanism that controls dynamics and what rules this mechanism? The models of contemporary physics do not answer these questions. In the realm of elementary particles the special habits of quaternions appear to play an essential role. In the past physics had a choice between the Maxwell based approach and the quaternionic based approach. That choice has a significant influence on how physics equations look. Einstein selected the Maxwell approach and in this way physics inherits the spacetime view on the universe in which we live.
Category: Mathematical Physics

[323] viXra:1412.0047 [pdf] submitted on 2014-12-03 14:37:40

### Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

Authors: Valeriy V. Dvoeglazov
Comments: 13 Pages. Prepared for the special issue of the "Adv. Appl. Clifford Algebras" - Proceedings of the ICCA10 Conference - Tartu, Estonia, Aug. 2014. Also presented by my students at the LVII Congreso Nacional de Fisica, Mazatlan, Sinaloa, Mexico, Oct. 2014

Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskii and Polubarinov, Hayashi, and Kalb and Ramond. They proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. We also proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism They are consistent with the general relativity. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Noether currents. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph. PACS number: 03.65.Pm , 04.50.-h , 11.30.Cp
Category: Mathematical Physics

[322] viXra:1412.0040 [pdf] submitted on 2014-12-02 12:28:34

### The Nature of the Fundamental Particles

Authors: Markos Georgallides
Comments: 18 Pages. The Energy Space nature of the particles

Analysing the principles of ,Mechanics and Physics, is clearly shown their common origin which is the unique essence of Space(m) and Energy (Force ,Push, Pull, Rotate) where arbitrary number ,t = time, is defined as the conversion factor between time units (second) and the length units (meter) . By contrast Inertial frame [R] is the frame of reference which describes Space-Energy homogeneously and isotropically , and in an genius manner , where arbitrary number , t = time , is defined as the conversion factor between time units (second) and length units ( meter ). The content of this article is , The Geometrical Reasoning of Planck Length being a quaternion , The Binomial nature of Monads in Monad and this because of their intrinsic property in Inner system which is , A Stationary wave on Norm of wavelength λ , and thus Poinsot's Ellipsoid becomes → Cycloidal Ellipsoid ← or Cycloidal wave motion in monads , and also the two parts of spin of particles , i.e. the plane Electromagnetic waves forming the spherical standing waves . The STPL line as the unique passage of particles from absolute [O]frame to all other [R] Inertial Frames (parallel between them) which is thus , the Navel cord (string) of galaxies , The geometrical expression of Spaces are the Geometries related to Euclidean by the Lorentz factor ,γ, and thus the common essence of Mechanics and Geometry, The isochrones motion of spaces which is shown to be the geometrical expression of Lorentz factor γ , is such that it is possible for velocities in an Affine Frame (System) or the Frame , to be the projection of one Constant Velocity of Absolute Frame [O] to the relative frames [R] where there exists Simultaneity . By considering breakages as ,masses, and also being off an absolute system [O] and under the constant velocity c as Action , then the known formulas of GR for masses and Energy are geometrically produced without any set restrictions , but from relation sec.φ = γ only. Relativity is now placed as a part of the whole Euclidean geometry , because all rotating [R] reference systems are related to the absolute system [O] which is that of Gravity Field . The Origin of Particles from the collision of Velocity vectors Breakages in common circle , The Origin of Color forces from the Retardation and the Birefringence of Spaces , The Structure of the Space-Energy universe and the boundaries in it , of General Relativity, Because breakages travel in [R] system (frame) with the constant velocity ,c, and so are in rectilinear motion between them , they occupy zero acceleration and thus can be converted to measurements in another by the simple Galilean transformations , because physical laws take the same form in all inertial systems .
Category: Mathematical Physics

[321] viXra:1411.0587 [pdf] submitted on 2014-11-28 17:17:03

### A Simple Lecture on Mubs

Authors: M. D. Sheppeard

This is a concise summary of the concept of mutually unbiased bases, including the concrete examples up to d=6.
Category: Mathematical Physics

[320] viXra:1411.0583 [pdf] submitted on 2014-11-28 00:24:59

### The Paradox in General Relativity

Authors: Cheng Tianren

This is a research paper which review the former series “From ptolemy theorem to non-Euclidean geometry”. In this paper, we introduce the geometric model basing on relativity theory of that series. We also apply the trigonometry techniques in projective geometry, to give some new estimate for field equation. And our final goal is to propose a reasonable explanation for the essential property of the 4 dimension space-time in general relativity, especially for the well-known twin and clock paradox.
Category: Mathematical Physics

[319] viXra:1411.0178 [pdf] submitted on 2014-11-15 16:11:38

### Quaternions and Hilbert Spaces

Authors: J.A.J. van Leunen

This is a compilation of quaternionic number systems, quaternionic function theory, quaternionic Hilbert spaces and Gelfand triples.
Category: Mathematical Physics

[318] viXra:1411.0175 [pdf] submitted on 2014-11-15 16:14:30

### Skeleton Relational Structures

Authors: J.A.J. van Leunen

The theory of skeleton relational structures is very useful in the investigation of the isomorphism between structures in which relations play an important role. It is an important tool for model designers. This theory is also known as lattice theory.
Category: Mathematical Physics

[317] viXra:1411.0112 [pdf] submitted on 2014-11-14 03:40:42

### Modelling and Simulation of Crowds

Authors: Shreyak Chakraborty, Salil Batabyal

In this project, we extend the work already done in [1.] to include a generalised mathematical framework for studying and explaining the dynamics and behavior of crowds of humans. The method is both analytical and numerical. The numerical methods are used to solve the differential equations of crowds that are derived analytically. The analytical and numerical solutions are compared and their relevance is shown. In this project, we study mainly two types of responses of a crowd: Position Response and Density Response. The latter is formulated using stressors using an approach similar to [2.] which also enables us to derive the General Adaptation Syndrome (GAS) Model in a very generalised form. Finally, we extend stressors to define inter-crowd and intra-crowd interactions using a parameterisation linking it directly to a generalisation of the stressdensity equation.
Category: Mathematical Physics

[316] viXra:1411.0085 [pdf] submitted on 2014-11-10 11:16:11

### About the Replacement of Metric Tensor

Authors: sangwha Yi

In the general relativity theory, study the replacement of the metric tensor in the Einstein gravity field equation.
Category: Mathematical Physics

[315] viXra:1411.0032 [pdf] submitted on 2014-11-04 08:22:08

### Metamorphoses of Resonance Curves for Two Coupled Oscillators: the Case of Small Nonlinearities in the Main Mass Frame

Authors: Jan Kyziol
Comments: 10 Pages. Under review in: Abstract and Applied Analysis, Hindawi

We study dynamics of two coupled periodically driven oscillators in general case. Periodic steady-state solutions of the system of two equations are determined within the Krylov-Bogoliubov-Mitropolsky approach. The orresponding amplitude profiles, A(omega), B(omega), which are given by two implicit equations, F(A,B,omega)=0, G(A,B,omega)=0, where omega is frequency of the driving force, are computed. These two equations, each describing a surface, define a 3D curve - intersection of these surfaces. In the present paper we carry out preliminary investigation of metamorphoses of this curve, induced by changes of control parameters. The corresponding changes of dynamics near singular points of the curve are studied. Under review in: Abstract and Applied Analysis, Hindawi
Category: Mathematical Physics

[314] viXra:1411.0015 [pdf] submitted on 2014-11-03 07:35:21

### Variational Principle of Extremum in Electromechanical and Electrodynamic Systems \\ Вариационный принцип экстремума в электромеханических и электродинамических системах

Authors: Solomon I. Khmelnik

Here we shall formulate and prove the variational optimum principle for electromechanical systems of arbitrary configuration, in which electromagnetic, mechanical, thermal, hydraulic or other processes are going on. The principle is generalized for systems described by partial differential equations, including also Maxwell equations. The presented principle permits to expand the Lagrange formalism and extend the new formalism on dissipative systems. It is shown that for such systems there exists a pair of functionals with a global saddle point. A high-speed universal algorithm for such systems calculation with any perturbations is described. This algorithm realizes a simultaneous global saddle point search on two functionals. The algorithms for solving specific mathematical and technical problems are cited. The book contains numerous examples, including those presented as M-functions of the MATLAB system and as functions of the DERIVE system. The programs in systems MATLAB and DERIVE are published as a separate annex in the form of an electronic book. Programs are not required to understand the theory. \\ Формулируется и доказывается вариационный принцип оптимума для электромеханических систем произвольной конфигурации, в которых протекают электромагнитные, механические, тепловые, гидравлические и др. процессы. Принцип обобщается на системы, описываемые уравнениями в частных производных и, в т.ч., уравнениями Максвелла. Предложенный принцип позволяет расширить лагранжев формализм и распространить новый формализм на диссипативные системы. Показывается, что для таких систем существует пара функционалов с глобальной седловой точкой. Описывается быстродействующий универсальный алгоритм расчета таких систем при любых возмущающих воздействиях. В этом алгоритме реализуется метод поиска глобальной седловой точки одновременно на двух функционалах. Приводятся алгоритмы решения конкретных математических и технических задач. Книга содержит многочисленные примеры, в т.ч. в виде М-функций системы MATLAB и в виде функций системы DERIVE. Программы в системах MATLAB и DERIVE изданы как отдельное приложение в виде электронной книги. Программы не являются обязательными для понимания теории.
Category: Mathematical Physics

[313] viXra:1410.0130 [pdf] submitted on 2014-10-22 12:27:38

### Scrutiny of Einstein’s Causality

Authors: M.E. Hassani
Comments: 6 Page; 2 Tables; 10 References.

In the present paper, the so-called Einstein’s causality is scrutinized and proven to be an illusion, a sort of mathematical fiction, and the causality as a well-established universal principle would be absolutely valid for subluminal, luminal and superluminal signals under any natural and/or artificial circumstances. It is also shown that any attempt to apply special relativity theory to superluminality of physical phenomena would be a complete waste of time since this theory has the light speed in vacuum as an upper limiting speed in its proper validity domain of applications.
Category: Mathematical Physics

[312] viXra:1410.0111 [pdf] submitted on 2014-10-19 14:09:04

### Statistics as a Dynamical Attractor.

Authors: Michail Zak

It is demonstrated that any statistics can be represented by an attractor of the solution to a corresponding system of ODE coupled with its Liouville equation. Such a non-Newtonian representation allows one to reduce foundations of statistics to better established foundations of ODE. In addition to that, evolution to the attractor reveals possible micro-mechanisms driving random events to the final distribution of the corresponding statistical law. Special attention is concentrated upon the power law and its dynamical interpretation: it is demonstrated that the underlying dynamics supports a “violent reputation” of the power-law statistics.
Category: Mathematical Physics

[311] viXra:1410.0105 [pdf] submitted on 2014-10-18 15:32:30

### A Brief Essay on Numerology of the Mass Ratio of Proton to Electron

Authors: Alexander Kritov

There are few mathematical expressions for calculation proton to electron mass ratio presented. Some of them are new and some are not. They have been analyzed in terms of their simplicity, numerical significance and precision. Expressions are listed in the structured manner with comments. The close attention should be paid to a comparison of the formula similarity via their precision. A brief review of the different attempts in similar search is given.
Category: Mathematical Physics

[310] viXra:1410.0089 [pdf] submitted on 2014-10-16 10:21:37

### Majorana-Particles Can Be Implemented In A New Cosmological Theory.

Authors: Dan Visser

This paper describes how experimentally detected Majorana-particles fit a new cosmological theory. This theory is called the rotating Double Torus Theory (DTT). It is extensively described by a cascade of articles, which are published in the vixra-archive by the author. However, although Majorana-particles will contribute very likely to the development of stable quantum-computers in the near future, they also can be implemented in this new cosmological theory. This introduces a completely new aspect of cosmology, and despite how hard it is to get acknowledgement for the DTT, it also might contribute to the understanding of evidence that is already available for the rotation of the new universe. This paper also explains why the match of the Majorana matter-force and the DTT, leads to a principle of an anti-gravitational machine based on the control of the combination Majorana-DTT-dynamics.
Category: Mathematical Physics

[309] viXra:1410.0029 [pdf] submitted on 2014-10-07 05:45:04

### Differential and Integral Calculus in Ultrapower Fields, Without the Transfer Principle of Nonstandard Analysis, or Any Topological Type Structures

Authors: Elemer E Rosinger

It has for long been been overlooked that, quite easily, infinitely many {\it ultrapower} field extensions $\mathbb{F}_{\cal U}$ can be constructed for the usual field $\mathbb{R}$ of real numbers, by using only elementary algebra. This allows a simple and direct access to the benefit of both infinitely small and infinitely large scalars, {\it without} the considerable usual technical difficulties involved in setting up and then using the Transfer Principle in Nonstandard Analysis. A natural Differential and Integral Calculus - which extends the usual one on the field $\mathbb{R}$ - is set up in these fields $\mathbb{F}_{\cal U}$ without any use of the Transfer Principle in Nonstandard Analysis, or of any topological type structure. Instead, in the case of the Riemann type integrals introduced, three simple and natural axioms in Set Theory are assumed. The case when these three axioms may be inconsistent with the Zermelo-Fraenkel Set Theory is discussed in section 5.
Category: Mathematical Physics

[308] viXra:1410.0028 [pdf] submitted on 2014-10-06 18:31:01

### Unification

Authors: Gene H. Barbee
Comments: 126 Pages. contact Gene at genebarbee@msn.com

Scientists are actively engaged in understanding new observations regarding our universe. There is agreement that achieving a new level of understanding may require an extension to what is currently known about fundamental interactions, matter and energy. This book is a summary of work by the author building on the best measurements made by physicists, astronomers and cosmologists. Historically, a culture’s cosmology was an explanation of the origin and a justification for its most significant beliefs. Understanding nature’s language goes further. With it, we can read the book of nature and participate in the unfolding of nature’s potential. A no-nonsense engineering approach is used that simplifies nature to a few simple relationships. Of specific interest are the topics of force unification, gravitational theory and the definition of space and time. It also addresses several topics at the forefront of current research like dark energy and cold dark matter. Of course these are physical matters but the author addresses what this means to life and what it is reasonable to believe regarding philosophy’s “enduring questions”. Man invented language, developed an alphabet and then used the alphabet in creative ways to communicate. As a child we learn a language. It is an extremely useful tool but we didn’t invent the language. Physics is the same way. It has a language and an alphabet that it shapes into words and a significant story. One difference, however, is that we are one of the things it shapes and if we want to understand ourselves and the things around us we must learn the language. Nature starts with the whole, separates it into parts and then fits the parts together in different ways to make the universe we observe. This is a little like a picture puzzle. The picture is cut into pieces and then re-assembled. In the process, it becomes clear that the pieces are meant to fit together and the proof is simply that the picture is once again whole. This book is written in seven sections. Sections 1-3 focus on several topics that are very basic to science but the author felt were missing or incomplete. The first goal of section 1 is to introduce a way to calculate the mass of particles like the neutron, proton and electron. The second goal is to calculate the forces that attract some of these particles to each other and understand where the forces come from. Section 4 applies fundamental relationships to one large example, the universe. In the process of understanding energy and forces, constants were discovered that are important to cosmology. Easy to understand equations are involved and again the proof of whether the contributions are correct is simply, the data. Section 5 demonstrates that the fundamentals presented in sections 1-4 apply to atomic binding energy and elemental abundance. 1-5 Section 6 and 7 are somewhat speculative but they present theory regarding perception and life. The author read about DNA but felt that the critical question “How does it construct our physical and mental reality?” was not addressed satisfactorily.
Category: Mathematical Physics

[307] viXra:1410.0005 [pdf] submitted on 2014-10-02 04:51:52

### Integral Calculus in Ultrapower Fields

Authors: Elemer E Rosinger

Infinitely many {\it ultrapower} field extensions $\mathbb{F}_{\cal U}$ are constructed for the usual field $\mathbb{R}$ of real numbers by using only elementary algebra, thus allowing for the benefit of both infinitely small and infinitely large scalars, and doing so {\it without} the considerable usual technical difficulties involved in setting up the Transfer Principle in Nonstandard Analysis. A natural Integral Calculus - which extends the usual one on the field $\mathbb{R}$ - is set up in these fields $\mathbb{F}_{\cal U}$. A separate paper presents the same for the Differential Calculus.
Category: Mathematical Physics

[306] viXra:1409.0122 [pdf] submitted on 2014-09-16 04:31:51

### The Proof of Dirichlet's Assertion on Celestial Mechanics

Authors: Reinhard Frischbier

Since the proof given by Wang Qiu-Dong on Dirichlet's assertion is based on the successive approximations objections to assumptions of the global solution of this problem have to be raised.
Category: Mathematical Physics

[305] viXra:1409.0109 [pdf] submitted on 2014-09-13 16:22:22

### Introducing Unitary Circles

Authors: Doug Jensen
Comments: 6 Pages. New math concepts introduced related to spin and imaginary numbers.

Unitary circles model the property of spin, and are based on imaginary numbers. The imaginary constant i is not a real number, and it has not been apparent how it relates to real numbers. With unitary circles, the role of imaginary numbers can be clearly understood. And the definition of i changes.
Category: Mathematical Physics

[304] viXra:1409.0105 [pdf] submitted on 2014-09-13 12:25:36

### A Proof of Nonexistence of Green's Functions for the Maxwell Equations

Authors: Zafar Turakulov

Arguments in favor of existence of Green's functions for all linear equations are analyzed. In case of equation for electromagnetic field, these arguments have been widely used through formal considerations according to which electromagnetic field equations are nothing but some non-covariant scalar equations. We criticize these considerations and show that justification of applying the method of Green's functions to equations of classical electrodynamics are invalid. Straightforward calculations are presented which show that in case of dipole radiation the method gives incorrect results.
Category: Mathematical Physics

[303] viXra:1409.0050 [pdf] submitted on 2014-09-07 16:42:14

### A Mathematical Model of Reality

Authors: J.A.J. van Leunen

It is possible to derive a model from well selected first principles that shows many similarities with what we know from observing reality. The presented model is based on first principles that formulate a recipe for modular construction and this foundation is mathematically known as an orthocomplemented weakly modular lattice. Starting from this foundation it is mathematically evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of static sub-models that each represent a static status quo of the whole model. The model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. Despite the fact that the target of the model is to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. Many of its aspects cannot be observed.
Category: Mathematical Physics

[302] viXra:1409.0047 [pdf] submitted on 2014-09-07 11:41:10

### Particle Solution to the Klein-Gordon-Dirac Equation in the Context of a Big Bang Universe

Authors: DT Froedge
Comments: 26 Pages. This is a project to crerate a Big Bang based, particle solution to the Klein Gordon

The purpose of this paper is to develop a single solution to both the Klein-Gordon & Dirac equations that expresses both the QM and the classical aspects of particles. It is found that this can be done, but only in the context of a system that has an initial event (T = 0) and is expanding at c, thus it is consistent with a big bang representation of the universe. The equations are defined in geometric algebraic, and the KGD equation will be considered a single equation factorable into linear products of the two linear Dirac expressions, with a solution defined analogously to path integrals. The solution has both amplitude, (classical), and phase, (QM) components satisfying the quadratic KG equation, and the linear Dirac expression. The equation differentials are not restricted to representing the normal QM operator replacement of p and E, applicable to the linear equation, but have a broader context in operating on the more complex function with amplitude and phase factors. The solutions represent the particle at a single event, thus the standard view of the solution being a probability amplitude field over spacetime is not applicable, but an alternate observational field is illustrated that demonstrates the connection of the solutions to the observed wave characteristics. The phase factors are as usual cyclic, but the amplitude factors exist only in the context of the entire interval. The amplitude factor of the solution is proportional to mass and thus should offer insight into particle mass ratios.
Category: Mathematical Physics

[301] viXra:1409.0038 [pdf] submitted on 2014-09-06 09:20:35

### The Origin of the Fundamental Particles in Planck  S Confinement

Authors: Markos Georgallides

This paper shows in a rigorous description, how nature is produced only from Euclidean Geometry , and that is not needed any attempt ion to establish any Philosophy or axioms as these of theories. All physical laws such as Momentum Newtons second law of gravity, Maxwells equations of fields, conservation laws, Spring from geometry logic and are common to, the Large and Short scale distances without any exclusion principles or assumptions. Existing of everything follows the only one conservation law, that of Virtual work and not any logical starting point . [STPL] line (cylinder) is a geometrical mechanism , the only passage (mould = Tensor) from, Common Circle of Space , Anti-Space (which is a Plane) to Particles (reflected evanescent waves) with real part (s) and imaginary part (± v.i) and without any assumption , that reflected waves have an unknown phase shift . Reflected wave is equal to the incident wave (the real part to the real place and the imaginary part to the imaginary place with all incident properties (spin) included) , i.e. different properties create distinct kinds of waves as these are the Fermions and Quarks of scalar magnitudes with ½ spin and Bosons of vector magnitudes with 1 spin. In Common circle circumference, the components of light waves interfere with each other to produce a ,Color , Spectrum because of Birefringence, a property of the (Centripetal) stress material with more than two indices, n, of refraction. [Retardation is the phase difference between the two light vectors through the material at different velocities (fast, slow) and determines color Bands and as Retardation and stress (σ) go up then the colors cycle through a more or less repeating Pattern and the Intensity of the colors diminishes] . In Common Circle of equilibrium Space Anti-Space with different angular velocity vector, v = w r, in the absence of applied Torques produces the Color Spectrum which is, the < Color Forces > → Gluon Red, Gluon Green, Gluon Blue and velocity of light on the circumference. Plancks length Lp in Einstein's theory of General Relativity is approximately implicated to the properties of physical Spaces instead that of Lp = e i.( - 5π / 2).10 = 8,906.10  35 m which is based on the three natural constants ,e, i, π , only . Lames stress ellipsoid represent Cauchy stress quadric of the Stress State at a point . Mohr circle can be applied to any symmetric 2x2 or 3x3 Tensor matrix and is graphically (geometrically) representing Cauchy stress Tensor. [STPL] line can be applied to any 3x3 symmetric Tensor (which are Spaces , Anti-Spaces and Sub-Spaces) and is graphically representing the passage (mould = Tensor 6x3) from , Common Circle of the Gravity Cave, in Lg = 3,969.10  62 m = 2r (a Plane) to Particles in Plancks Cave Lp , with Velocities (v = wr) that of light ,c, tending to zero . For rotations in caves Lc > Lg then exist Velocities (vc = wr) faster than that of light ,c, [vc > c ] tending to ∞. The hidden pattern of universe is ,STPL- line, which is off the Spaces and connect them ( maintain , conserve , and support all universe ) , so , it is the Navel string of galaxies.
Category: Mathematical Physics

[300] viXra:1409.0030 [pdf] submitted on 2014-09-05 06:31:52

### On Application of Green Function Method to the Solution of 3D Incompressible Navier-Stokes Equations

Authors: Algirdas Antano Maknickas

The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed into full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Velocity and outer forces densities components were expressed in form of curl for obtaining solutions satisfying continuity condition specifying divergence of velocities equality to zero. Finally, solution in 3D space for any shaped boundary was expressed in terms of 3D Green function and inverse Laplace transform accordantly.
Category: Mathematical Physics

[299] viXra:1408.0235 [pdf] submitted on 2014-08-31 13:03:31

### Theoretical Background of T.T. Brown Electro-Gravity Communication System

Authors: Algirdas Antano Maknickas

The article describes communication system working on base of gravity waves. Such system of devices should work if the electromagnetic field curves space-time. Theoretical results shows that the artificial change of gravity of space-time curvature should observes in the distance much more bigger than dimension of transmitter antenna. The article end with discussion of details of technical properties of working electro-gravity communication system.
Category: Mathematical Physics

[298] viXra:1408.0198 [pdf] submitted on 2014-08-28 17:46:38

### The Yang-Mills Theories in a Four Dimensional Space (Some Thoughts on Their Existence)

Authors: Thierry PERIAT

This exploration analyses deeply the results obtained in the 4D presentation of the theory. It confirms the existence of gauge theories for massless particles in a 4D environment. The properties of the "new" EM fields are scrutinized attentively. A link with the whirl tensor of the particle is clearly demonstrated. It asks in which way a particle can be identified with a whirl and if, by some ambivalence, some whirls are not corresponding to geometric deformations?
Category: Mathematical Physics

[297] viXra:1408.0188 [pdf] submitted on 2014-08-27 12:54:50

### Dark Matter Is Time-clock Faster Than Light In Vacuum.

Authors: Dan Visser

In this paper formulations and calculations are exposed for a new paradigm of dark matter. Dark matter does not exists of solid particles. Dark matter exists of ‘faster time-cells’ than standard-time-based-on-light-speed. These ‘cells’ may sometimes give high-energetic particles, such as e.g. neutrinos, a velocity-gain, which can violate the light-speed in vacuum. In this perspective dark matter can be detected by the ‘combination of energy per time-volume and simultaneously a small light-flash’. Therefore the focus must be on detection of clock-energy during light-flashes !! Put a clock into the dark matter detection-configuration and the energy of the ‘time energy-density’ will change the clock-period, while it also gives a light-flash per second! The ‘dark matter time-cells’ are independent on whether time is relative or not. The assumption to describe dark matter as solid particles, such as ‘wimps’, ‘axions’, or ‘dark matter being its own anti-particle’, is therefore false. The new dark matter paradigm is based on analysis and worked out in this ‘paper’ as a part of a wider framework, called the Double Torus Theory for the Universe. This is a replacement for the Big Bang theory. The wish of this paper is to contribute to the dark matter research-project-teams, who aim to detect dark matter in the up-coming period to 2017 in the UK, USA, Italy, the Netherlands and other countries. Despite all the institutional- and press-commotion of OPERA an ICARUS in 2012 I postpone neutrinos indeed can be affected by ‘dark matter faster-time-cells’. These imply the violation of General Relativity Theory (GRT) and Quantum Theory (QT). A calculation proves that e.g. 62 nanosecond velocity-gain wouldn’t be a hazardous value, but can vary depending on the intensity of the dark matter’s circular-acceleration in vacuum. This is explained in this ‘paper’. It also means not always a violation of GRT and QT will happen. Separately and consistently an additional formulation (and calculation) is given about how the vacuum-energy-density of the QT can be eliminated from its extreme too large value compared to GRT.
Category: Mathematical Physics

[296] viXra:1408.0155 [pdf] submitted on 2014-08-23 15:14:38

### The Space-Time Wormhole and Time Direction of Travelling Light

Authors: Algirdas Antano Maknickas

The investigation of Scharzschild solution using new one transform leads to the spherical solution of light path. Spherical solution forms space-time wormhole with finite throat. It was shown that wormhole throat diameter could by manipulated by changing value of Schwarzschild radius. Using symmetric formulation of Maxwell's equations one can obtain the physical time negative solution. Detailed investigation of wormhole of light for Schwarzschild radius of the earth shows that light can travel not only to the future but also to the past too.
Category: Mathematical Physics

[295] viXra:1408.0144 [pdf] submitted on 2014-08-22 00:18:25

### The Physicalist Program

Authors: Miguel A. Sanchez-Rey

We'll present the groundwork for the physicalist program and suggest it's implications.
Category: Mathematical Physics

[294] viXra:1408.0125 [pdf] submitted on 2014-08-18 15:49:57

### Reflection of Plane Electromagnetic Wave from Conducting Plane

Authors: Zafar Turakulov
Comments: 10 Pages. The work is completed with use of exterior calculus.

The phenomenon of reflection from conducting surface is considered in terms of exact solutions of Maxwell equations. Matching of waves and current density at the plane is completed. Amplitudes of reflected and transmitted waves are found as functions of incident wave and conductivity of the plane. This work is completed also for conducting plane lying between two distinct media. It is shown that in case of conducting interface waves with some certain parameters (polarization, incidence angle and frequency) and transform completely into waves of current density whereas amplitude of the reflected wave is equal to zero that is equivalent to total absorption.
Category: Mathematical Physics

[293] viXra:1408.0060 [pdf] submitted on 2014-08-10 06:44:20

### Maxwell Equations and Total Internal Reflection

Authors: Zafar Turakulov

The phenomenon of total internal reflection is considered in terms of exact solutions of Maxwell equations. Matching of plane and evanescent waves at the interface is completed. It is shown that amplitude of the reflected wave cannot be obtained from the matching alone. Since it can differ from that of incident wave due to possible energy loss which may occur in the evanescent wave zone if there is another layer of optically dense medium, this loss is to be specified via amplitude of the reflected wave. Besides, reflected wave potential has phase shift which also depends on this specification.
Category: Mathematical Physics

[292] viXra:1408.0038 [pdf] submitted on 2014-08-08 03:11:53

### X-Boson Mass Estimation Using Higgs-, W- and Z-Boson Mass in Context of the Ancient-Word-Theory

Authors: Klaus Lange
Comments: 4 Pages. main text in german language

In consideration of the Higgs-,W- and Z-Boson Mass and the fundamental results of [L1] and [L2] a mass estimation for a x-Boson like particle will made to 684 +/- 64,125 GeV/c^2.
Category: Mathematical Physics

[291] viXra:1407.0125 [pdf] submitted on 2014-07-17 07:16:32

### Stop-Squark Mass Estimation Using the Higgs-Boson in the Context of the Ancient-Word-Theory

Authors: Klaus Lange
Comments: 3 Pages. Main text in german.

In consideration of the Higgs-mass 125 – 126,5 GeV/c^2 the estimation in [L] of the STOP-squark will be adjusted to 344 +/- 86 GeV/c^2.
Category: Mathematical Physics

[290] viXra:1407.0086 [pdf] submitted on 2014-07-12 08:16:52

### The Fractal Geometry of the Quantum Vacuum

Using a simple mathematical tool and a basic properties of quantum vacuum fluctuations discover its hidden structure. The fractal dimension of the energy of fluctuations is 9, allowing you to occupy a space of nine dimensions: the three regular 6 more compacted. This special geometry of ordinary dimensions / compacted determines energy dependence of the inverse distance, allowing vacuous stability and appearance of the quantum vacuum.
Category: Mathematical Physics

[289] viXra:1407.0079 [pdf] submitted on 2014-07-11 06:50:56

### Plan B (1): Berechnung Der Zahl pi Durch Ein Ensemble Einfacher Objekte.

Authors: Stefan G. Freundt

We are surrounded by round objects. Planets, suns, stones, tree trunks and many more objects are round. Likewise, s-orbitals of electrons in atoms are spherically symmetric and thereby round. If we ascertain the surface areas, volumes, or circumferences of these objects, then we inevitably encounter the number pi. Evidently the number pi plays an important role in our environment. Accordingly, pi is included in the formulae used to describe our world. For the calculation of pi, there are an abundance of methods that can be used. In contrast, in this article we are going to pursue the goal of giving objects the simplest possible properties, and enabling these objects to calculate pi en passant. We introduce a system of equations, in which objects only interact with each other through algebraic operations (+-*/ and sqrt) and generate the number pi in a boundary case. Wir sind von runden Objekten umgeben. Planeten, Sonnen, Steine, Baumstämme und vieles mehr sind rund. S-Orbitale von Elektronen in Atomen sind ebenfalls kugelsymmetrisch und damit rund. Bestimmt man von diesen Objekten Ober fläche und Volumen oder Umfang und Flächeninhalt, begegnet man unweigerlich der Zahl pi. Offenbar nimmt die Zahl pi eine wichtige Rolle in unserer Umgebung ein. In die Formeln zur Beschreibung unserer Welt wird pi entsprechend hineingesteckt. Zur Berechnung von pi gibt es eine Menge Verfahren, die alle für einen Menschen gemacht sind, um pi zu berechnen. Im Gegensatz dazu verfolgen wir in diesem Artikel das Ziel, Objekte mit möglichst einfachen Eigenschaften auszustatten und diese Objekte in die Lage zu versetzen pi "en passant" zu berechnen. Wir stellen ein Gleichungssystem vor, in dem Objekte nur durch algebraische Operationen (+-*/ und sqrt) mit einander wechselwirken und in einem Grenzfall die Zahl pi erzeugen.
Category: Mathematical Physics

[288] viXra:1407.0068 [pdf] submitted on 2014-07-10 02:51:27

### Space-Time Sedeons and Their Application in Relativistic Quantum Mechanics and Field Theory

Authors: Victor L. Mironov, Sergey V. Mironov

This book is a systematic exposition of the algebra of sixteen-component space-time values "sedeons" and their applications to describe quantum particles and fields. The book contains the results of our several articles published in the period 2008-2014. It includes a large number of carefully selected reference material relating to the use of different multi-component algebras in physical problems and may be useful as an introduction to the application of hypercomplex numbers in physics.
Category: Mathematical Physics

[287] viXra:1406.0173 [pdf] submitted on 2014-06-28 08:11:06

### The Concept of the General Force Vector Field

Authors: Sergey G. Fedosin

A hypothesis is suggested that the classical electromagnetic and gravitational fields, acceleration field, pressure field, dissipation field, strong interaction field and weak interaction field, acting in the matter and beyond its limits are the manifestations of a single general field. With the help of generalized velocity as the 4-potential of the general field it is shown that each of these seven fields contributes linearly to the formation of the total 4-force density. However, the stress-energy tensor of the general field includes not only stress-energy tensors of these seven fields, but also the cross terms with the products of various field strengths. As a result, the energy and momentum of the system with several fields can differ from the classical energy and momentum values, not including such cross terms in the general field energy.
Category: Mathematical Physics

[286] viXra:1406.0130 [pdf] submitted on 2014-06-20 19:14:50

### Derivation of the Contour Integral Equation of the Zeta Function by the Quaternionic Analysis

Authors: Koji Sugiyama

This paper derives the contour integral equation of the zeta function by the quaternionic analysis.

Many researchers have attempted proof of Riemann hypothesis, but have not been successful. The proof of this Riemann hypothesis has been an important mathematical issue. In this paper, we attempt to derive the contour integral equation from the quaternionic analysis as preparation proving Riemann hypothesis.

We obtain a generating function of the inverse Mellin-transform. We obtain new generating function by multiplying the generating function with exponents and reversing the sign. We derive the contour integral equation from inverse Z-transform of the generating function.

We derive the summation equation, the asymptotic expansion, Faulhaber’s formula, and Nörlund–Rice integral from the contour integral equation.
Category: Mathematical Physics

[285] viXra:1406.0125 [pdf] submitted on 2014-06-19 17:56:51

### The Associahedra and Permutohedra Yet Again

Authors: M. D. Sheppeard

A concise algebraic definition of the associahedra and permutohedra polytopes is given in terms of canonical coordinates for discrete simplices.
Category: Mathematical Physics

[284] viXra:1406.0063 [pdf] submitted on 2014-06-10 10:50:27

### Plancks Length as Geometrical Exponential of Spaces

Authors: Markos Georgallides

In prior articles was shown that all Monads are Dipole , z = (a+i.v)^ n =1/w, on nth power where issues their Binomial nature and also on exponential power of the natural logarithm base ,e, as → z^n = (s +v̄ i )¹/ w = |zo| ̄ w. [cos.(φ+2kπ)/w + i.sin.(φ+2kπ)/w] = |zo| ̄ w .e^ i.(φ+2kπ) / w ← meaning that these are of wave and sinusoidal nature . This Quaternion exponential form of the quantized Spaces , Anti-Spaces , Sub-Spaces and Energy as logarithm on decimal base ,b, is the ,Monads geometrical interpretation, measured on the three natural and constant numbers e , π , i , on bases which are independent of any Space and coordinate system one of them is Planck length's Lp = 8,906.10 ^ -35 m (10 - 35 m). Moreover , Diffraction cavities are created for storing Energy of all types , and for Temperature in the Tank cavity Lt = 1,781.10 ^ -7 m (10-7m) from where is then dissipated and damped in Planck's Tank cavity Lp following the two ideal Gas equations [Λ= nRT/V] of Entropy in Thermodynamics (perfectly elastic) and the Temperature of the Black-body which is quantized and dissipated per circle ( from the Balance Tank energy ) following Stefan - Boltzmann law Wd = σ.T 4 where then the Temperature in this Ideal Tank T t = 2,213.1010 K which absorbs and emits all types of the electromagnetic radiations . Energy (Heat ) causes Monads (molecules) to vibrate . More Heat creates higher frequency vibrations and increasing also the Intensity = Pressure of the radiation . Boltzmann's constant σ = 5,67.10– 8 (W/m².K 4) = 1,38066.10– 23(J/K) is the quantized Energy [Vibration in magnitude L < 3,9698.10 – 62 m , under Heat cause] into a new monad , the Intensity . In this magnitude is emitted Graviton particle (radiation) in Gravity's Length Lg = e ^ -i.(9π/2).b = e - i.( 9π/2 ).10 = e ̄ ( 141,372 ) = 3,969.10 ̄ 62 m , and now Gravity is Incorporated into Quantum mechanics .
Category: Mathematical Physics

[283] viXra:1405.0312 [pdf] submitted on 2014-05-25 10:07:30

### Transport Catastrophe Analysis as an Alternative to a Fractal Description: Theory and Application to Financial Crisis Time Series

Authors: Sergey A. Kamenshchikov

The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for fractal Brownian processes: nondifferentiability, Brownian nature of process and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that pre-catastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. Basic conclusions of a diffusive analysis have been compared to the Lyapunov stability model. An extended Reynolds parameter has been introduces as an indicator of phase transition. A combination of diffusive and Reynolds analysis has been applied for a description of a time series of Dow Jones Industrial weekly prices for a world financial crisis of 2007-2009. Diffusive and Reynolds parameters shown an extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of short-memory and long memory shifts of a market evolution. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.
Category: Mathematical Physics

[282] viXra:1405.0306 [pdf] submitted on 2014-05-24 12:54:16

### Eternal Rotational Dark Torus Suggests Visible Big Bang in the Double Torus Universe.

Authors: Dan Visser
Comments: 10 Pages. I hope for paying attention to this article in the vixra-blog and other science magazines.

‘Spatial dark matter’ and ‘two refined time-clocks smaller than the Planck-time’ cause a CMB-dipole and concentric circles in the CMB of the universe. This proves a Double Torus Universe. Hence the universe did not start with a Big Bang. These characteristics are derived, analyzed, explained in my articles of the Double Torus Theory (DTT) and proved by current lab-experiments and astronomical observations. Furthermore three levels of accelerations are derived, which prove several dimensional characteristics, such as the accelerated space expansion in Big Bang cosmology is due to rotation of the Double Torus, or such as dimensions that show dark matter is not a mass-particle like a ‘wimp’. However, the heart of the DTT is the use of ‘time smaller than the Planck-time’ (sub-quantum-time). This is the power for events beyond quantum-gravitation, which makes events visible for just 4.45%. The rest seems to remain dark, but eventually involves in the sub-quantum-dynamics of the universe. I also give a related derivation, which uses the ‘Gaussian mathematical expression’ for accelerations related to gravitation in the DTT, instead of using the Gaussian only for CMB-temperature-variations. Thereby I introduced a new ‘duonistic-parameter’ (b=0, b=1, b=2), which describes how entangled ‘duonistic neutrinos’ involve in three levels of acceleration. These ‘duonistic neutrinos’ represent space. The acceleration-levels relate to a Newton-constant (G) for G’ < G or G=0 or G=1, or G”> G or G=2. These levels perform the dark flow, the CMB-concentric circles and the torus-rotation for the universe.
Category: Mathematical Physics

[281] viXra:1405.0298 [pdf] submitted on 2014-05-23 23:23:45

### Abstraction and Structures in Energy

Authors: Subhajit Ganguly

Zero postulation and the principles of the Theory of Abstraction are used to study structures of energy inside a black hole, which is incredibly heavy and incredibly small. We chase the questions, how matter (with various structures) is formed from energy and the energy making up matter has to be in what orientation to form the matter that we see. We arrive at the fundamental model and the equations describing the formation of structure in energy.
Category: Mathematical Physics

[280] viXra:1405.0285 [pdf] submitted on 2014-05-21 16:27:08

### Dynamics Model of Human Mind.

Authors: Michail Zak

This paper proposes a mathematical formalism for describing the machinery of human mind creativity. Since some functions of mind support discreteness of cognition, but others support its continuity, while time in physics is always continuous, an attempt to overcome the continuous/discrete duality of mind performance is implemented via utilization of special critical points: terminal attractors and repellers that act as autonomous biological clock. In this paper, attention is concentrated upon the discrete mode of the mind activity since the continuous mode was introduced and discussed in details in our previous publications. The fundamental novelty of the model is in its capability to move from disorder to order without external inputs in violation of the second law of thermodynamics; that suggests that this kind of dynamics requires extension of modern physics to include physics of life. Conceptually the discrete model links to its continuous version represented by a hypothetical particle of life that is briefly discussed prior to derivation of the discrete model. However the discrete model should be considered as the next step in study of mind dynamics since it provides a bridge to mathematical origin of self-generated novelties in such brunches as mathematical logic and linguistic, i.e. the highest level activities of human mind. The proposed model deals with rules of mind activity rather than with its content.
Category: Mathematical Physics

[279] viXra:1405.0277 [pdf] submitted on 2014-05-20 21:59:51

### Model of Hypothetical Particle of Life.

Authors: Michail Zak

The paper discusses a possible expansion of modern physics to include physics of Life since all attempts to create livings from non-living matter failed. Prior to the discussion, a life/non-life criterion is proposed: unlike physical systems, Livings can move from disorder to order without an external interference if the model of life concentrates upon the concept of intelligent behavior and does not include such “auxiliary” processes as metabolism and reproduction. A mathematical formalism suggests that a hypothetical “particle of life” (L-particle) can be represented by a quantum-classical hybrid in which the force following from the quantum potential is replaced by the information force. Besides the capability to move against the second law of thermodynamics, L-particle acquires such properties like self-image, self-awareness, self- supervision, est. that are typical for Livings. However since the L-particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of the information force that represents a bridge between non-living and living matter. It has been suggested that quantum mechanics and mechanics of livings are sub-classes of a broader physical model, and the difference between them is due to different Liouville feedbacks, i.e. in different information forces. At this stage, L-particle is introduced as an abstract mathematical concept that is satisfied only to mathematical rules and assumptions, and its physical representation is still an open problem.
Category: Mathematical Physics

[278] viXra:1405.0261 [pdf] submitted on 2014-05-18 00:55:31

### On the Physical Reality of Tachyons

Authors: S.Kalimuthu

In this work, the author attempts to show that it is not possible to generate or find tachyons
Category: Mathematical Physics

[277] viXra:1405.0226 [pdf] submitted on 2014-05-13 09:40:33

### The Derivation of the Fine Structure Constant

Authors: Bernd Ganter

Dimensions and fundamental forces in the universe, and the derivation of the fine structure constant What if we stripped away all the things we call properties … What would be left? There are at least two possible answers to this question. The first is that by stripping away all the empirical dressing … what we are left with is abstract mathematics. A second answer is that we could consider the irreducible stuff of the universe … to be information.” (Jim Baggott, Farewell to Reality, 2013, p.235) Energy and information are closely connected to each other. The strengths of the fundamental forces correspond to their information density. A comparison of the strengths of the fundamental forces shows that they follow a pattern (Ganter scheme): Information is mathematically stored in dimensions that correspond to an exponentiation level maximizing space-time volume. In a two-dimensional world information is stored according to formula W= x^(x·ln x), in a three-dimensional world according to the spherical formulae V= πr³ und O=4πr². Information can be transferred from one dimension to another, dependent on its density. The value of the fine structure constant 1/137 can be derived as result of a permanent information transfer between two- and three-dimensional worlds, corresponding to the wave-particle-dualism. And for higher energies an approximate maximum value can be predicted: 1/128.5.
Category: Mathematical Physics

[276] viXra:1405.0207 [pdf] submitted on 2014-05-10 11:29:35

### The Outside Relativity Space Energy Universe

Authors: Markos Georgallides

The position of points in Spaces presupposes Energy [22] → Point , which is nothing and has not any Position may be anywhere in Space , therefore , the Primary point A being nothing also in no Space , is the only Point and nowhere i.e. Primary Point is the only Space and from this all the others which have Position , therefore is the only Space and to exist point A at a second point B somewhere else , point A must move at point B , where then A ≡ B ← Point B is the Primary Anti-Space which Equilibrium point A in [PNS]=[A≡ B] . The position of points in [PNS] creates the infinite dipole and all quantum quantities which acquire the Potential difference and the Intrinsic moment Λ in the three Spatial dimensions (x , y , z) and on the infinite points of the ( i ) Layers at these points , which exist from the other Layers of the Primary Space Anti-Space and Sub-Space , and this because Spaces = monads = quaternion = Wave [24] . Since Primary point A is the only Space , then exists the Principle of Virtual Displacements W = ∫P.ds = 0 or [ds .(PA + P B) = 0] i.e. for any ds > 0 Impulse P = ( PA + P B ) = 0 . All points may exist with P = 0 and also with P ≠ 0 , ( P A + P B = 0 ) in ( PNS) , for all points in Spaces and Anti – Spaces , therefore [PNS] is self created , and because at each point may exist also P ≠ 0, then [PNS] is a (perfectly elastic) Field with infinite points which have a ± Charge with P = 0 → P = Λ → ∞ . Beyond Planck scale , Energy is dissipated as Temperature in this , Perfect Elastic , Configuration in individual particles with 0 < ds < 10 - 35 m as monads the units AiBi = ds- , which equilibrium by the Primary Anti–Space by an Inner Impulse (P) at edges A,B where P i A + P i B ≠ 0 , and ds = 0 → N → ∞ following the ideal Gas equation [Λ= nRT/V] of Entropy in Thermodynamics (perfectly elastic) . Monad A-B is the ENTITY and [A,B – P –A , P -B ] is the LAW , so Entities are embodied with the Laws and is quaternion A- B , and law |AB| = length of points A , B and imaginary part forces P –A , P –B . Monads = Quantum = ds = AB / ( n= ∞ → 0) = [a ± b.i] = 0 → ∞ create Spaces (S) , Anti-Spaces ( A-S) and Sub-Spaces (S-S) of AB , which Sub-Spaces are Bounded Spaces , Anti-Spaces and Sub Spaces in it and are not purely spatial because are Complex numbers which exist for all Spaces since dsn is Complex number also , in a specific number of independent moles called , Fermions and Bosons , with F = qE+qv- xB = q[ E+v- xB ] the Lorentz force in Electromagnetic crossed fields E ,B. Dipole A- B = [λ , Λ] in [PNS] are composed of the two elements λ , Λ which are created from points A , B only where Real part |AB| = λ= wavelength (dipoles ) and from the embodied Work the Imaginary part W=∫P.ds = (r.dP) = r–x p- = I.w = [λ.p] = λΛ = k2 , where momentum Λ= p and Forces dP = P –A ,P -B are the stationary sources of the Space Energy field [22-25] . EulerÁs rotation in 3D space is represented by an axis (vector) and an angle of rotation , which is a property of complex numbers and defined as z = [ s ± v-.i ] where s , |v-| are real numbers and i the imaginary part such that i² = -1. Extending imaginary part of dipole to the three dimensions v-1 i , v-2 j , v-3 k → v-.Ñi then becomes quaternion . In [24] monad [ 0,Λ ] = Energy is dissipated on points and on quantized spaces smaller < and > greater to Planck scale . The moving charges is velocity v- created from the rotating Energy momentum vector [Λ = Ω = (λ.P) = ± Spin] which creates on monads the Centrifugal force (Ff) , the equal and opposite to it Centripetal force (Fp) and acceleration ā is mapped [and because of the viscous (semi-elastic) is damped] on the ⊥ to Λ plane as → v- E||dP and v- B ^ dP ← following Kirchhoff 's circuit R ,L,C rules with circuits , the Sub-spaces of the tiny monads . The kinetic rotated energy in the viscously damped configuration ( as a Lagrange's Ray light viscously damped system ) is dissipated as Electromagnetism and when v-E- = 0 , momentum Λ- = m v- only , is exerting the velocity vector v-B to the dipole vector , λ , and the generalized mass M (the reaction to the change of velocity v-) creating component forces FE||dP -.v- and FB ^ dP – xv- in the non-viscous damped monads ( the solids ) . Energy in a vibrating System is either damped (or dissipated) into Heat which is another type of energy [Energy ,momentum vector Λ.λ is then damped on the perpendicular to Λ plane , as this is a Spring-mass System , with viscous dumping , on co variants Energy E , mass M , velocity v- or radiated away . Spin =Λ= r-.m.u- r is the rotating energy of the oscillatory system . Oscillatory motion is the simplest case of Energy dissipation of Work embodied in dipole . In any vibratory system , Energy k = λΛ is Spin of Dipole λ , and is dissipated in the three quantized Planck Spaces 0 < λ < 10 \34, (10 \ 34 < λ < 10 34 ) , λ > 10 34 m and damped as the linear momentum vector Λ = M.v̄ in them , i.e The only < Space - Energy Configuration > is a constant Sinusoidal Potential System . [28]
Category: Mathematical Physics

[275] viXra:1405.0003 [pdf] submitted on 2014-05-01 15:01:20

### P vs. NP Conceptual Graph

Authors: Andrew Nassif
Comments: 2 Pages. No rude comments please, I know the paper is short but this is just a graph

Andrew Nassif looks at the problem known as the P vs. NP and provides a conceptual graph of the problems representation through various color patterns and 3 dimensional graphs.
Category: Mathematical Physics

[274] viXra:1404.0474 [pdf] submitted on 2014-04-28 15:13:34

### Exact Form of the Physical Optics Integral

Authors: Yusuf Ziya Umul

The exact structure of the physical optics integral is obtained. With this aim, the rigorous solution of the diffraction problem of waves by a perfectly conducting half-plane is considered. The Fresnel integrals of the incident and reflected scattered fields are transformed into the physical optics integrals by defining a suitable variable transform. The relation of the obtained integral with the modified theory of physical optics is discussed.
Category: Mathematical Physics

[273] viXra:1404.0473 [pdf] submitted on 2014-04-28 15:17:49

### 3D Green’s Function for Scattering Integrals

Authors: Yusuf Ziya Umul

A three dimensional Green’s function is derived mathematically by using the two dimensional Green’s function, which is obtained as a result of the modified theory of physical optics’ algorithm. The integration of the three dimensional Green’s function leads to the two dimensional one when there spatial symmetry in the scatterer’s geometry and the incident wave. In order to obtain the three dimensional function, the two dimensional Green’s function is mathematically transformed into an infinite integral according to z. The derived Green’s function is generalized and expressed in a scattering integral for soft and hard surfaces.
Category: Mathematical Physics

[272] viXra:1404.0461 [pdf] submitted on 2014-04-25 02:20:25

### A Fundamental Hypothesis About the Speed Module of Bodies

Authors: Abel Cavaşi

A hypothesis on the motion of bodies under the action of forces perpendicular to the trajectory.
Category: Mathematical Physics

[271] viXra:1404.0290 [pdf] submitted on 2014-04-16 07:09:56

### Zeta Functions of the Riemann Hypothesis for the Sporadic Finite Simple Groups

Authors: Koji Sugiyama

This paper constructs the zeta functions of the Riemann hypothesis for the sporadic finite simple groups.

Although many researchers have tried the proof of the Riemann hypothesis, they have not resulted in the success. The proof of this Riemann hypothesis has been an important issue of mathematics. In this paper, we construct zeta functions for the sporadic finite simple groups as preparation proving the Riemann hypothesis.

We define the polynomial ring of a group in order to add groups and to add the members of a group.

The argument of a zeta function is a complex number. We can interpret a complex number as the subgroup of a quaternion. Therefore, we can expand the argument of a zeta function to a quaternion. On the other hand, a complex number is one-dimensional complex general linear group. And the sporadic finite simple groups are high dimensional complex general linear groups. Therefore, we can expand the argument of a zeta function to sporadic finite simple groups.

We define the product of groups the direct product. We interpret the cyclic groups of prime order as prime groups. We construct the natural groups of natural order with products of prime groups. Sporadic finite simple groups become subgroups of natural groups because arbitrary finite groups become subgroups of natural groups. We can express arbitrary finite groups by zeta function of prime groups. And we can express arbitrary noncommutative finite groups by zeta function of sporadic finite simple groups.
Category: Mathematical Physics

[270] viXra:1404.0280 [pdf] submitted on 2014-04-16 08:17:13

### Zeta Function Regularization of the Sum of All Natural Numbers by Damped Oscillation Summation Method

Authors: Koji Sugiyama

This paper let the sum of all natural numbers by damped oscillation summation method of a new zeta function regularization. The zeta function regularization is a method to assign finite values to divergent integration or sums. One method of the regularization is the analytic continuation. The integral representation of the zeta function converges by the analytic continuation. On the other hand, the zeta function also has a series representation. One of the representation is the sum of all natural numbers. The sum does not converges by the regularization. It diverges. This paper let the sum converge by damped oscillation summation method of the new regularization. Both the integral representation and the series representation have same value for mathematical consistency. One method to let divergent series converge is Abel summation method. The method let the divergent series converge by multiplying convergence factor exp(-εk). However, the sum of all natural numbers does not converge by the medhod. Therefore it is an important issue to find a new summation method. We define new "sum of all natural numbers" by damped oscillation summation method. The method let the divergent series converge by multiplying convergence factor exp(-εk)cos(εk). The factor is damped and oscillating very slowly. The tradional sum divers for infinite terms. On the other hand, the new "sum" equals the traditional sum for the finite term. And the "sum" converges -1/12.
Category: Mathematical Physics

[269] viXra:1404.0116 [pdf] submitted on 2014-04-13 19:03:13

### A Derivation of GravitoElectroMagnetic (GEM) Proca-type Equations in Fractional Space

Authors: Victor Christianto
Comments: 8 Pages. This paper has been submitted to Prespacetime Journal. Comments are welcome

In a recent paper, M. Zubair et al. described a novel approach for fractional space generalization of the differential electromagnetic equations. A new form of vector differential operator Del, and its related differential operators, is formulated in fractional space. Using these modified vector differential operators, the classical Maxwell equations have been worked out for fractal media. In the meantime, there are other papers discussing fractional Maxwell equations. However, so far there is no derivation of Proca equations and Proca-type equations for GEM in fractional space. Therefore in this paper I present for the first time a derivation of GravitoElectroMagnetic (GEM) Proca-type equations in fractional space. Considering that Proca equations may be used to explain some electromagnetic effect in superconductor, then fractional GEM Proca-type equations may be expected to explain some gravitomagnetic effects of superconductor for fractal media. It is our hope, that this paper may stimulate further investigation and experiments in particular with respect to gravitomagnetic effects.
Category: Mathematical Physics

[268] viXra:1404.0104 [pdf] submitted on 2014-04-12 12:24:45

### Chaotic Probabilities and Unpredictability in Phys

Authors: Michail Zak

A new class of dynamical systems that have random solutions with chaotic probability densities is discovered.
Category: Mathematical Physics

[267] viXra:1404.0088 [pdf] submitted on 2014-04-11 11:47:03

### The Emergence Mechanism and Calculation Method of Turbulent Flows // Механизм возникновения и метод расчета турбулентных течений.

Authors: Solomon I. Khmelnik

An explanation is offered of the mechanism of turbulent flows emergence, based of the Maxwell-like gravitation equations, updated after some known experiments. It is shown that the moving molecules of flowing liquid interact like electrical charges. The forces of such interaction can be calculated and included to the Navier-Stokes equations as mass forces. Navier-Stocks equations complemented by these forcesbecome equations of hydrodynamics for turbulent flow. For the calculations of turbulent flows the known methods of Navier-Stokes equations solution may be used. // Предлагается объяснение механизма возникновения турбулентных течений, которое основано на максвеллоподобных уравнениях гравитации, уточненных на основе известных экспериментов. Показывается, что движущиеся молекулы текущей жидкости взаимодействуют между собой аналогично движущимся электрическим зарядам. Силы такого взаимодействия могут быть расчитаны и включены в уравнения Навье-Стокса как массовые силы. Уравнения Навье-Стокса, дополненные такими силами, становятся уравнениями гидродинамики для турбулентного течения. При этом для расчета турбулентных течений можно использовать известные методы решения уравнений Навье-Стокса.
Category: Mathematical Physics

[266] viXra:1404.0068 [pdf] submitted on 2014-04-08 18:23:33

### An Alternative Scenario for the Supraconduction in Graphene?

Authors: Thierry PERIAT

A scenario building a link between a gauge approach and a special feature of one of the Ginsburg-Landau fundamental equation is proposed.
Category: Mathematical Physics

[265] viXra:1404.0034 [pdf] submitted on 2014-04-05 00:13:33

### A Corollary of the Theorem of Recurrence

Authors: Abel Cavaşi

A corollary of the reccurence theorem of the Frenet formulas: the darbuzian of any order depends only on variations of the lancretians of lower order.
Category: Mathematical Physics

[264] viXra:1404.0030 [pdf] submitted on 2014-04-04 07:43:10

### Sudies on Vortex

Authors: Arm Boris Nima

We check that the relation between the angle and the radius of the movement of an object following a logarithm spiral of p p SO(2) is constant.
Category: Mathematical Physics

[263] viXra:1404.0023 [pdf] submitted on 2014-04-03 09:19:10

### The Wave Nature of the Geometry Primary Dipole

Authors: Marcos Georgallides

In prior articles , the position of points in Spaces creates Momentum [Λ] which is bounded in the three constant Energy Layer States k1,2,3 [10] . This rotating energy E = Λ λ is transformed into the Acceleration al and Rotational Ellipsoid , and radiated away ,by loosing angular momentum E = r.m.vr and conserved as momentum E = M.v where emission of linear momentum creates vector v of generalized mass M . When vector v = 0 , this rotating Energy is generalized mass M which is mapped on the perpendicular to Λ plane as velocity v̄r which creates Newton smallest equilibrium accelerations (a f + a p = 0) from Centrifugal (Ff) and Centripetal (Fp) forces . On the infinite points of [PNS] and on the infinite dipole AiBi this acceleration vectors create the Wave motion of the infinite dipole AiBi which dipole are composed of the wavelength λ and the rotating Energy Λ . From this Position , Time enters in equations of motion as the meter of changes only .This rotating Energy is interchanged on dipole A  B = (λ , Λ= mv) in the Configuration of co variants λ , m , v̄ as ellipsoid in the two perpendicular fields E = [(/x) + (/dy) + (/z)] . Λ and B = [(/x) + (/dy) + (/z)] xΛ following conservation laws only. Classical theories are confined in Space -Time and Planck-time (which are not assessing the outer reality of Spaces ) , with Time , which is only a meter of changes , and not existing differently . Spaces are composed of infinite points which are related each other with a quantum of Work ( Energy ) .The Norm is the Equation of Total Energy State of Monads equal to → ET = •[(k/ λv) .vE ²] ² + [Λ.vB +ΛxvB ] ² = • [(k/λv) .vE.² ]² + T ² ← which is completely refining Time and leaving only λ Λ = k which indicates a Space Energy Universe . Energy in a Vibrating system is either dissipated into Heat (temperature) which is another type of energy { Energy E as momentum vector Λλ is damped on the perpendicular to Λ plane , as it is like a < Spring-mass System with viscous dumping > , on the basic three co-variants of , Energy E , Lagranges generalized mass M = m , and velocity v̄ with Norm the wavelength λ , and secondly on the rotating Energy Λ= r̄.M.ūr } or radiated away. Newton's laws have a Universal application in all Configuration Systems instead of the referred as the Inertial ones . Even also to the smallest circular motion , ( anywhere that exists momentum ) , exists also Centrifugal and Centripetal forces which create acceleration and the Oscillatory motion . Since also velocity v maybe equal to 0 → c → ∞ then the velocity of light is not the faster in universe . In Black Holes Configuration a new Type of light is needed with a greater velocity than that of light to see what is happening . Light which is a quaternion is travelling either as wave ( photon Λ) either as particle (E =Mv̄= r.m.v̄r ) and in both cases as , a travelling Energy λ.Λ = k interchanged in the two perpendicular forced fields E = . Λ and B =  x Λ ( Electromagnetic fields ) following conservation laws . Gauss laws spring from this property. Oscillatory motion is the simplest case of Energy dissipation of Work embodied in dipole . In the vibratory system , Energy k = λΛ is Spin of Dipole , dissipated on ⊥ to Λ plane and damped as momentum vector λ.mv̄ . Monad ĀB is the ENTITY and [ A ,B – PA  , P B  ] is the LAW , so Entities are embodied with the Laws . Entity is quaternion A B , and law |AB| = length of points A,B and imaginary part forces PA , P B  . Dipole A  B = [ λ , Λ ] in [PNS] are composed of the two elements λ , Λ which are created from points A ,B only where Real part |AB| = λ = wavelength (dipoles ) and from the embodied work , λ Λ , the Imaginary part W = ∫ P.ds =(r.dP) = r̄xp = I.w = [λ.p] = λ.Λ = k2 , where momentum Λ = p= m.v and Forces dP = P B –P A are the stationary sources of the Space Energy field . The moving charges is velocity v created from the rotating Energy momentum vector [ Ω = (λ.P) = ± Spin ] which creates the Centrifugal force (Ff) , the equal and opposite to it Centripetal force (Fp) and the acceleration ā mapped (damped ) on the perpendicular to Λ plane as → v E||dP and v B  dP. F = q.E + q.v̄ x B = q.[ E + v̄ x B ] is Lorentz force in Electromagnetic crossed fields E and B . Since (dP  ± Λ ) the work occurring from momentum p = mv = Λ acting on force dP is zero so when v E =0 , momentum Λ  = mv only , is exerting the velocity vector v B to the dipole , , λ , and the generalized mass M ( the reaction to the change of velocity v̄ ) which creates the component forces , FE || dP .v and FB  dP x v .
Category: Mathematical Physics

[262] viXra:1404.0017 [pdf] submitted on 2014-04-02 22:35:49

### The Generalized Helix

Authors: Abel Cavaşi
Comments: 3 Pages. Contains an English translation from Romanian

We define the generalized helix of order k, then we make a link with movement on the generalized helix.
Category: Mathematical Physics

[261] viXra:1403.0925 [pdf] submitted on 2014-03-24 12:25:15

### Do the Two Operations Addition and Multiplication Commute with Each Other?

We use the validity of Addition and Multiplication. We provide an example that the two operations Addition and Multiplication do not commute with each other. All analyses are performed in a finite set of natural numbers.
Category: Mathematical Physics

[260] viXra:1403.0286 [pdf] submitted on 2014-03-17 06:04:56

### The Arm Theory

Authors: Arm Boris Nima

Did you ever wondered what is the Taylor formula for an arbitrary chosen basis ? The answer of this question is the Arm theory introduced in this article.
Category: Mathematical Physics

[259] viXra:1403.0285 [pdf] submitted on 2014-03-17 06:10:06

### The p-Arm Theory

Authors: Arm Boris Nima

We introduce the p-Arm theory which give rise to a new mathematical object that we call the "p-exponential" which is invariant under p derivation. We calculate its derivate and we use this new function to solve dierential equations. Next, we dene its real and imaginary part which are the p-cosinus and the p-sinus respectively.
Category: Mathematical Physics

[258] viXra:1403.0284 [pdf] submitted on 2014-03-17 06:11:48

### The Arm Prime Factor Decomposition

Authors: Arm Boris Nima

We introduce the Arm prime factors decomposition which is the equivalent of the Taylor formula for decomposition of integers on the basis of prime numbers. We make the link between this decomposition and the p-adic norm known in the p-adic numbers theory. To see how it works, we give examples of these two formulas.
Category: Mathematical Physics

[257] viXra:1403.0283 [pdf] submitted on 2014-03-17 06:13:24

### The Arm Factorization

Authors: Arm Boris Nima

We construct the equivalent of the Taylor formula in the basis of all roots fx kgK when K is Z iZ, Q iQ and C.
Category: Mathematical Physics

[256] viXra:1403.0282 [pdf] submitted on 2014-03-17 06:15:09

### The Arm Fourier Theory

Authors: Arm Boris Nima

We give the developpment of functions in C[z] C[z 1 ] with a scalar product which involves an integral and a residue calculus. Then we give some examples of those developpments and nd new 'representations' of the exponential and the logarithm function . We draw those representations and we see that there are similar to their original representations
Category: Mathematical Physics

[255] viXra:1403.0281 [pdf] submitted on 2014-03-17 06:17:47

### The Arm Lie Group Theory

Authors: Arm Boris Nima

We developp the Arm-Lie group theory which is a theory based onthe exponential of a changing of matrix variable u(X). We dene a corresponding u-adjoint action, the corresponding commutation relations in the Arm-Lie algebra and the u-Jacobi identity. Throught the exponentiation, Arm-Lie algebras become Arm-Lie groups. We give the example of pp so(2) and pp su(2).
Category: Mathematical Physics

[254] viXra:1403.0280 [pdf] submitted on 2014-03-17 06:19:35

### Remarks Around Lorentz Transformation

Authors: Arm Boris Nima

After diagonalizing the Lorentz Matrix, we nd the frame where the Dirac equation is one derivation and we calculate the 'speed' of the Schwarschild metric
Category: Mathematical Physics

[253] viXra:1403.0279 [pdf] submitted on 2014-03-17 06:20:51

### Some Poisson Lie sigma Models

Authors: Arm Boris Nima

We calculate the Poisson-Lie sigma model for every 4-dimensional Manin triples (function of its structure constant) and we give the 6-dimensional models for the Manin triples (sl(2; C) sl(2; C) ; sl(2; C); sl(2; C) ), (sl(2; C) sl(2; C) ; sl(2; C) ); sl(2; C), (sl(2; C); su(2; C); sb(2; C)) and (sl(2; C); sb(2; C); su(2; C))
Category: Mathematical Physics

[252] viXra:1403.0278 [pdf] submitted on 2014-03-17 06:22:13

### Noncommutative_ricci_curvature_and_dirac_operator_on_b_qsu_2_at_the_fourth_root_of_unity

Authors: Arm Boris Nima

We calculate the torsion free spin connection on the quantum group Bq[SU2] at the fourth root of unity. From this we deduce the covariant derivative and the Riemann curvature. Next we compute the Dirac operator of this quantum group and we give numerical approximations of its eigenvalues.
Category: Mathematical Physics

[251] viXra:1403.0277 [pdf] submitted on 2014-03-17 06:24:03

### Noncommutative_geometry_on_d6.

Authors: Arm Boris Nima

We study the noncommutative geometry of the dihedral group D6 using the tools of quantum group theory. We explicit the torsion free regular spin connection and the corresponding 'Levi-Civita' connection. Next, we nd the Riemann curvature and its Ricci tensor. The main result is the Dirac operator of a representation of the group which we nd the eigenvalues and the eigenmodes
Category: Mathematical Physics

[250] viXra:1403.0276 [pdf] submitted on 2014-03-17 06:25:21

### Non_commutative_geometry_on_usb2

Authors: Arm Boris Nima

We study the Borel algebra dene by [xa; xb] = 2a;1xb as a noncommutative manifold R 3 . We calculate its noncommutative dierential form relations. We deduce its partial derivative relations and the derivative of a plane wave. After calculating its de Rham cohomology, we deduce the wave operator and its corresponding magnetic solution
Category: Mathematical Physics

[249] viXra:1403.0271 [pdf] submitted on 2014-03-16 10:54:34

### The Triangular Properties of Associated Legendre Functions Using the Vectorial Addition Theorem for Spherical Harmonics

Authors: Rami Mehrem
Comments: 7 pages including 1 figure

Triangular properties of associated Legendre functions are derived using the Vectorial Addition Theorem of spherical harmonics
Category: Mathematical Physics

[248] viXra:1403.0059 [pdf] submitted on 2014-03-09 10:41:32

### Navier-Stokes Equations. on the Existence and the Search Method. // Уравнения Навье-Стокса. Существование и метод поиска глобального решения.

Authors: Solomon I. Khmelnik
Comments: 108 Pages. Book. The rules Clay Mathematics Institute written as follows: "In the case of … the Navier-Stokes problem, the SAB will consider the award of the Millennium Prize for deciding the question in either direction." I suggest my decision of this problem.

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence. Then we consider the so-called closed systems. We prove that for them the necessary and sufficient conditions of global extremum for the named functional always exist. Accordingly, the search for global extremum is always successful, and so the unique solution of Naviet-Stokes is found. We contend that the systems described by Navier-Stokes equations with determined boundary solutions (pressure or speed) on all the boundaries, are closed systems. We show that such type of systems include systems bounded by impermeable walls, by free space under a known pressure, by movable walls under known pressure, by the so-called generating surfaces, through which the fluid flow passes with a known speed. The book is supplemented by open code programs in the MATLAB system – functions realizing the calculation method and test programs. Links on test programs are given in the text of the book when the examples are described. // Формулируется и доказывается вариационный принцип экстремума для вязкой несжимаемой и сжимаемой жидкости, из которого следует, что уравнения Навье-Стокса являются условиями экстремума некоторого функционала. Описывается метод поиска решения этих уравнений, который состоит в движении по градиенту к экстремуму этого функционала. Формулируются условия достижения этого экстремума, которые являются одновременно необходимыми и достаточными условиями существования глобального экстремума этого функционала. Книга дополняется открытыми кодами программам в системе MATLAB – функциями, реализующими расчетный метод, и тестовыми программами.
Category: Mathematical Physics

[247] viXra:1403.0004 [pdf] submitted on 2014-03-01 09:50:38

### Matrices and Quaternions

Authors: Gary D. Simpson

A possibly novel mathematical structure is presented. The structure is a matrix whose elements are quaternions. The structure is distinct from a tensor.
Category: Mathematical Physics

[246] viXra:1403.0002 [pdf] submitted on 2014-03-01 01:01:17

### The Description of the Physical Field with Spin 1/3.

Authors: Vyacheslav Telnin

viXra.org 1402.0167 gives general description of raising vector space W in the power M/L. The result is the new vector space V. In this paper we take W - the 8 – dimensional generalization of our 4 – dimensional vector space. Then we raise W in the power 1/3. The result is the 2 – dimensional vector space V. The metric and algebraic tensors for V are the same as in viXra.org 1402.0176. After that we take some vector from V and use it for construction of Lagrangian. And for simplicity we restrict us by only first 4 dimensions of W. Then, from the principle of minimal action, we get the equations for our vector. And we derive that vector from these equations. Then we define the tensor and vector of energy – momentum for this Lagrangian. And also we find the density of spin tensor and (with the help of the algebraic tensor) the density of spin vector. The numerical cofactor in them is 1/3. So we consider that spin of this vector is 1/3. It coincides with the power of W for V (vector space we took our vector from).
Category: Mathematical Physics

[245] viXra:1402.0176 [pdf] submitted on 2014-02-28 05:27:31

### Raising Our 4-Dimensional Uncurved Space W to the Power ½.

Authors: Vyacheslav Telnin

The application of the (1402.0167, 1402.0170 viXra.org) to our 4 – dimensional vector space W when M = 1, L = 2. Cobasics are chosen so that V has simple algebraic and metric tensors.
Category: Mathematical Physics

[244] viXra:1402.0171 [pdf] submitted on 2014-02-27 06:57:14

### Explorations in Physics

Authors: Anamitra Palit
Comments: 14 Pages. This paper is of a Composite nature.I have included it in the Mathematical Physics Category

The article seeks to investigate several issues concerning the topics: Relativity, Quantum Mechanics and classical physics. The following issues have been investigated:1)Relativity suggesting virtual particles 2) Lorentz Transformations Suggestive of a Bypass route 3)Space getting Curved 4) On Higg’s Mechanism 5)On Tensor Equations of a Composite Nature 6) General Covariance and Tensor Equations 7) On rocket motion 8) Newton’s Law of Gravitation in the Light of GR
Category: Mathematical Physics

[243] viXra:1402.0170 [pdf] submitted on 2014-02-27 07:00:01

### Metric and Algebraic Tensors for 4-Dimensional Uncurved Space.

Authors: Vyacheslav Telnin

The definition of the algebraic tensor for vector space by using the vector product of vectors from it’s basis. And application it to the our 4 – dimensional space.
Category: Mathematical Physics

[242] viXra:1402.0166 [pdf] submitted on 2014-02-26 19:05:56

### Euler's Equation and Quaternions

Authors: Gary D. Simpson

The objective of this text is to present a method of using vectors and quaternions to produce Euler's Equation. The method presented uses the cross product of vectors in the j-k plane to produce the isine portion of Euler's Equation. The cosine portion of Euler's Equation is produced by the dot product of the same vectors. The method is then generalized to apply to quaternions.
Category: Mathematical Physics

[241] viXra:1402.0151 [pdf] submitted on 2014-02-22 23:59:56

### Some Observations on Schrödinger's Affine Connection

Authors: William O. Straub

In a series of papers written over the period 1944-1948, the great Austrian physicist Erwin Schrödinger presented his ideas on symmetric and non-symmetric affine connections and their possible application to general relativity. Several of these ideas were subsequently presented in his notable 1950 book Space-Time Structure, in which Schrödinger outlined the case for both metric and general connections, symmetric and otherwise. In the following discussion we focus on one particular connection presented by Schrödinger in that book and its relationship with the non-metricity tensor. We also discuss how this connection overcomes a problem that Hermann Weyl experienced with the connection he proposed in his failed 1918 theory of the combined gravitational-electromagnetic field. A simple physical argument is then presented demonstrating that Schrödingers’s formalism accommodates electromagnetism in a more natural way than Weyl’s theory.
Category: Mathematical Physics

[240] viXra:1402.0090 [pdf] submitted on 2014-02-13 19:58:42

### Proceedings of the First International Conference on Superluminal Physics and Instantaneous Physics as New Fields of Research

Authors: editor Florentin Smarandache

In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we can pass from Subluminal Physics to Superluminal Physics, and further to Instantaneous Physics (instantaneous traveling). In the lights of two consecutive successful CERN experiments with superluminal particles in the Fall of 2011, we believe these two new fields of research should begin developing. A physical law has a form in Newtonian physics, another form in the Relativity Theory, and different form at Superluminal theory, or at Instantaneous (infinite) speeds –according to the S-Denying Theory spectrum. First, we extend physical laws and formulas to superluminal traveling and to instantaneous traveling. Afterwards, we should extend existing classical physical theories from subluminal to superluminal and instantaneous traveling. And lately we need to find a general theory that unites all theories at: law speeds, relativistic speeds, superluminal speeds, and instantaneous speeds –as in the S-Multispace Theory. The First International Conference on Superluminal Physics as New Fields of Research was hold at the University of New Mexico, Gallup Campus, NM 87301, USA, as an electronic conference on 2-4 July 2012. There were seven papers selected for this volume by the following authors and coauthors: KAIZHE GUO, CHONGWU GUO, CHEN JIANGUO, DONG JINGFENG, MI HAIJIANG, CHANGWEI HU, YANG SHIJIA, GULI, and FU YUHUA.
Category: Mathematical Physics

[239] viXra:1402.0054 [pdf] submitted on 2014-02-07 23:50:24

### The Critical Analysis of the Mathematical Formalism of Theoretical Physics. Iv. the Foundations of Trigonometry

Authors: Temur Z. Kalanov

Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
Category: Mathematical Physics

[238] viXra:1402.0050 [pdf] submitted on 2014-02-07 07:40:17

### The Cubic Equation and 137.036

Authors: J. S. Markovitch

A special case of the cubic equation, distinguished by having an unusually economical solution, is shown to relate to both the fine structure constant inverse (approximately 137.036) and the sines squared of the quark and lepton mixing angles.
Category: Mathematical Physics

[237] viXra:1401.0215 [pdf] submitted on 2014-01-29 09:25:00

### Exploring Gravitational Phenomena in a Riemann-Minkowski Spacetime

Authors: Carsten S.P. Spanheimer

After the concept of a locally scale-invariant spacetime has been introduced in the companion document, now physical experiments on mathematical entities will be performed to find out implications of that model. With regard to earlier solutions by others, an unbiased inspection of different gravitational scenarios under local scale-invariance in comparison with physical reality is undertaken. This gives five results at once: A suspected locality condition, a promising gravitational ansatz, a static solution for the gravitational potential in the subjective picture together with a possible static cosmic redshift, and a set of candidate terms for governing field equations of physical spacetime.
Category: Mathematical Physics

[236] viXra:1401.0162 [pdf] submitted on 2014-01-24 05:45:27

### Associative Space Time Sedenions

Authors: V.L.Mironov, S.V.Mironov

We present an alternative type of sixteen-component hypercomplex scalar-vector values "space-time sedenions", generating associative noncommutative space-time Clifford algebra.
Category: Mathematical Physics

[235] viXra:1401.0153 [pdf] submitted on 2014-01-22 16:41:37

### An Explanation of the Entropic Nature of the Mass Using Classical Physics

Authors: Nicolas Poupart

This paper presents a theory of the relativistic gravitational field by simply applying Carnot's principle to the gravitation and by reinforcing as inviolable the mass-energy equivalence law and the equivalence of the inertial mass and the heavy mass. It will be shown that this theory can explain easily the origin of dark matter and dark energy. In addition, it will also be shown that this theory is not distinguishable from general relativity at our experimental scale.
Category: Mathematical Physics

[234] viXra:1401.0152 [pdf] submitted on 2014-01-22 16:47:29

### Une Explication de la Nature Entropique de la Masse Utilisant la Physique Classique

Authors: Nicolas Poupart
Comments: 7 Pages. Original french version of "An explanation of the entropic nature of the mass using classical physics"

Cet article expose une théorie du champ gravitationnel relativiste en appliquant simplement le principe de Carnot à la gravitation et en considérant la loi d'équivalence masse-énergie ainsi que l'équivalence masse inertielle et masse pesante comme inviolable. Il sera démontré que cette théorie permet d'expliquer aisément l'origine de la matière noire ainsi que de l'énergie noire. De plus, il sera également démontré que cette théorie n'est pas différenciable de la relativité générale à notre échelle expérimentale.
Category: Mathematical Physics

[233] viXra:1401.0145 [pdf] submitted on 2014-01-20 16:15:01

### Proof For A Rotational Double Torus Universe.

Authors: Dan Visser
Comments: 5 Pages. I hope Proffessor P. Coles , University Sussex UK, takes notice.

The Universe rotates. We live in a Double Torus Universe. A dark matter torus rotates in a larger time torus of refined time smaller than the Planck-time. The Planck-satellite showed a more detailed picture of the CMB related to Big Bang cosmology. However, I have put that in perspective of a new set of equations that belong to the framework of the Double Torus Theory. That shows my proof for a rotational dark matter Flow by warm and cold areas in the CMB. I also explain why the accelerated space-expansion in the Big Bang cosmology is an illusion.
Category: Mathematical Physics

[232] viXra:1401.0140 [pdf] submitted on 2014-01-20 03:08:23

### Extended Fokker Planck Model: Properties and Solutions

Authors: Sergey Kamenshchikov

In the current paper Fokker Planck model of random walks has been extended to non conservative cases characterized by explicit dependence of diffusion and energy on time. A given generalization allows describing of such non equilibrium processes as Levy flights in a classical differential form without use of fractal PDE. Besides it takes into account mixing properties that are obligatory for a certain class of chaotic systems, such as Kolmogorov K – system. It was shown that an abnormal transport is a consequence of the equilibrium distortion and not stationary diffusion. The particular case of fixed boundaries was considered. According to the received solutions it was shown that a system structure can resist a weak disturbance in the vicinity of the discrete regimes, defined by a system scale and its nonlinear properties. These regimes correspond to the exponential increase of quasi regular structure fluctuations. Only fast disruption of regime is possible for other states of the system. It leads to an immediate transition to the chaos.
Category: Mathematical Physics

[231] viXra:1401.0107 [pdf] submitted on 2014-01-15 09:15:08

### The Features For Dark Matter And Dark Flow Found.

Authors: Dan Visser
Comments: 9 Pages. I hope the press takes notice!

Fly-By- and GPS-satellites reveal an earth-dark matter-halo is affecting the orbit-velocities of satellites. After analysis by a new set of equations, which describe dark matter, dark matter-force and quantum-gravity combined in a new dark energy force-formula, the new formulations match a percentage whereof satellites feel extra gravity. Also the dark matter-density has been calculated. The analysis confirms dark matter exists as a halo around the earth. Secondly it shows what dark matter really is. It also shows what a dark flow is. The dark matter-features are presented in a Double Torus Cosmology, a new model for the universe, which replaces Big Bang cosmology and enables to understand dark matter better!
Category: Mathematical Physics

[230] viXra:1401.0062 [pdf] submitted on 2014-01-08 10:06:09

### Gravity as the Intrinsic Vorticity of Points

Authors: Markos Georgallides

Primary Dipole dš = ĀB =[a ± b.i] as complex number, and z̄o =[ s, v̄n.i] = [λ ,±Λ .i ] = [λ , Λ] as quaternion in [PNS] is the ENTITY with the embodied LAW [A , B - PA , PB  ],is composed of the two only elements λ , Λ which are created from points A and B , |AB| = λ = wavelength (dipoles ) and from work W = ∫A-B [ P.ds ] = 0 = (dP.r̄) = r̄xp = I.w = [λ.p] = λ.Λ = k2 , the momentum Λ = p = k2/ λ. and Forces dP = P B –P A) ,which are the sources of Space field . Forces dP parallel to the parallel of Space Anti-Space lines [S]≡ [AS], create a Static force field E in (dP, λ) plane , and Forces dP perpendicular to the parallel of Space Anti-Space lines [S]≡[AS] , create a Static force field B which is perpendicular to E and  to ( dP,λ) plane . Motion occurs from the moving charges exerted as velocity v ,created from dipole momentum ± Λ  when is mapped in force field B as v E|| dP and v B  dP with the generalized mass m (the reaction to the motion) which creates the component forces FE = (λm).E , FB = (λm) .v̄ x B. Velocity vector v\ (v\ E , v\ B) is in [ v \. B \ ] plane forming an angle θ < 180° to the field B , and total force F= FE + F B = (λm). E + (λm). v̄ x B which combination of the two types result in a helical motion, with the stability demand → E = - (v̄xB) = - (v̄.B)  which is the alternative conservation of momentum [ k 2 = Λ²/2λm ] in the two perpendicular fields E , B and in case (λm) = q then force F = FE + FB = q.E + q.v̄ xB = q.[ E + v̄ x B ] → which is Lorentz force . Since Spin ( vortices) Λ , - Λ  , are in inverted order of rotation and vice-versa , then even function f(Λ) = f(-Λ) and odd function is - f(Λ) = f(-Λ) and their sum f(Λ)+f(-Λ)=0 and so, Mapping (graph) of Even function f(Λ),is always symmetrical about Λ axis or a mirror and of Odd symmetrical about the origin and is the interpretation of the Wave nature of spaces i.e. The Physical Universe behaves as a simple harmonic oscillator . Conjugating quaternion of the differential time operator and 3D angular speed vector w̄ with negation truth eo = [- λ,xΛ] = 0 then ( ∂/∂t ,
Category: Mathematical Physics

[229] viXra:1401.0056 [pdf] submitted on 2014-01-07 22:27:20

### Is Fine Structure Constant Related to Shannon Information Entropy?

Authors: Victor Christianto

Here I describe what I can recall from a seminar held in Moscow State University, December 2008. The lecture was given by Prof. Anosov, and the title is relation between fundamental constants. In essence, he tried to describe fine structure constant from Shannon entropy. My note book on his lecture was lost since several years ago, so this is a derivation out of my memory on that lecture. I am not aware that until now there is a paper discussing link between fine structure constant and Shannon entropy, so I hope that this short article will stimulate further discussion.
Category: Mathematical Physics

[228] viXra:1401.0017 [pdf] submitted on 2014-01-02 11:07:08

### Electric Field Thermokinetic Spectroscopy

Authors: F. F. Mende

Is proposed the new method of investigating the thermophysical and structural characteristics of materials and models, based on the measurement of electrostatic pour on, appearing with the heating or mechanical loads.
Category: Mathematical Physics

[227] viXra:1401.0016 [pdf] submitted on 2014-01-02 11:17:59

### Analog Realization of a Fractional-Order Element on 0.35 um CMOS Technology

Authors: Alexander C. Abad, Emmanuel A. Gonzalez, Roderick Y. Yap, L'ubomir Dorcak

In this short note, we present the analog realization of a fractional-order differentiator of order alpha=1/2 in 0.35um CMOS technology.
Category: Mathematical Physics

[226] viXra:1312.0241 [pdf] submitted on 2013-12-31 00:02:28

### Expressions For The Fine Structure Constant and Boltzman's Constant

Authors: Claude Michael Cassano

The Fine Structure Constant and Boltzman's Constant may be expressed in terms of a small number of notable irrational numbers and integers.
Category: Mathematical Physics

[225] viXra:1312.0226 [pdf] submitted on 2013-12-28 15:51:23

### A General Relativity Primer

Authors: Salvish Goomanee

In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
Category: Mathematical Physics

[224] viXra:1312.0152 [pdf] submitted on 2013-12-20 08:10:34

### Трехмерность бытия и теоремы Ферма и Пифагора (Three-Dimensional Being and the Theorem Fermat's and Pythagorean)

Authors: Putenikhin P.V.

The logical relationship of the theorems the Fermat’s and the Pythagorean allow to draw conclusions that multidimensional worlds do not exist.
Путенихин П.В. Логическая взаимосвязь теорем Пифагора и Ферма позволяет сделать вывод о том, что многомерные миры не существуют.
Category: Mathematical Physics

[223] viXra:1311.0196 [pdf] submitted on 2013-11-28 21:19:11

### Sphere Geometry of Forces & Fundamental Particles of the Universe

Authors: S.C. Gaudie
Comments: 11 pages; mostly font 11; A4 paper; UK English; Freelance scientist.

This answers fundamental questions from Wikipedia about Generations of Matter [**web 1] and related properties. Why are there three generations of quarks and leptons? Why are the ratios of masses of quarks and leptons as they are? Also, is the ratio of fundamental force strengths related to the size of the universe and why are the ratios as they are? This theory defines a “fundamental sub-structure" that is a tetrahedron with the further “sub-structure" of spheres. The 1, 3, 6 “quantum numbers” ratios in this theory show why the relative masses & radii of quarks and the “large leptons” are their “known values”. The ratios for each of these “fundamental sub-structure", “quantum numbers” are 1, 3 & 6; simple integer values. Another geometrical possibility, with the same values, is based on the spatial axes. The big picture could be the arrangement of the “fundamental spheres” along the axes of space. This theory suggests the “fundamental sub-structure" is behind the relative masses of the quarks& “heavy leptons”. The cube root of the mass was used to calculate a diameter ratio parameter. These ratios are also applied to other basic properties of the universe. This “fundamental sub-structure" has also been applied to the relative strengths of the fundamental forces determining the size of the universe at the time of their creation. There seems to be a universal “template” for the properties of the universe. The ratio numbers can be thought of as "quantum numbers". The universe is believed to have gone through creation of forces, inflation stages & must, of necessity, have gone through “phase changes". These could be interconnected. This “theory” combines the above items into ONE overall “theory”.
Category: Mathematical Physics

[222] viXra:1311.0189 [pdf] submitted on 2013-11-28 10:08:45

### Quantum-Gravity Can Be Recalculated By Refined Time Smaller Than The Planck-Time In A Rotational Double Torus Universe.

Authors: Dan Visser
Comments: 5 Pages. I hope the press will take notice, especially E. Verlinde of the UvA-NL

In particular calculations have been made for the detection of extraterrestrial high energy neutrinos. Additional the rest-energy of a neutrino is calculated (equivalent to its rest mass). But both calculations are not standard. The calculations are made from the perspective of a new model for the universe: The Double Torus hypothesis. The alternative calculation shows that the result matches a neutrino-incident in the ICECUBE-project in Antartica for a value of 250 TeV energy. Moreover, an extra calculation is made for the expected neutrino rest-energy by the Standard Model (equivalent for its rest-mass). This shows that time roughly 100 times smaller than the Planck-time can generate a neutrino-rest-energy of 2.2 eV. This delivers evidence for the existence of a sub-quantum-domain of refined time that affects dark vacuum-particles; this is dark matter described in the Double Torus-framework. That generates visible quantum-gravitational particles. Such a calculation could also be performed for an electron or a quark. But that is not (yet) performed in this paper. But one of the conclusions is that the detection of high energy neutrinos could turn out to be additional evidence for the existence of rotational Double Torus Universe.
Category: Mathematical Physics

[221] viXra:1311.0182 [pdf] submitted on 2013-11-27 22:43:06

### All Fermion Masses and Charges Are Determined By Two Calculated Numbers

Authors: Claude Michael Cassano

All the fermion masses may be determined from merely two numbers dependent on π , e , and a few rational fractions, and all the fermion charges thereafter., In this, now, dimension independent revision; the electron mass and the ratio of the muon mass to the electron mass are shown calculable from simple quadratic functions of π , e , and a few rational fractions. All the remaining masses may be determined from from these constants and their indexes determined by the mass-generalized Maxwell's equations. These calculated masses are all well within current specs as of this publication. In fact, more recent neutrino measurements and estimates have put their values into a rather tight range which the computed values in this update fall within.
Category: Mathematical Physics

[220] viXra:1311.0170 [pdf] submitted on 2013-11-25 14:36:42

### The Reverse Side of Helmholtz Paradox: Flow with Zero Laplacian Generates a Constant Vortex

Authors: Sergey V. Ershkov

The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time. In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids). Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is turned to be ideal (unviscid) due to zero Laplacian.
Category: Mathematical Physics

[219] viXra:1311.0164 [pdf] submitted on 2013-11-25 03:17:10

### On Global Solution of Incompressible Navier-Stokes Equations

Authors: Algirdas Antano Maknickas

Using equality of full and covariant time derivatives and partial solutions of Helmholtz equation analytical solution of 1D, 2D and 3D Navier-Stokes equations was obtained
Category: Mathematical Physics

[218] viXra:1311.0152 [pdf] submitted on 2013-11-22 10:14:30

### The New DAN-energy, The Rotational Dark Vacuum-particle, A Particular Calculation And The Rotational Universe.

Authors: Dan Visser
Comments: 5 Pages. I hope the press wil take notice and will publish about the Double Torus framework.

The title of this article presents evidence-based insight of the manner entropy-gravity might work in detail. Entropy-gravity stands in the picture while simultaneously the Double Torus hypothesis posits the universe can no longer be maintained as the Big Bang cosmology. So from the point of view of the Double Torus hypothesis both hypotheses could be theoretically related. The Double Torus hypothesis is point-particle related, but entropy-gravity used string-mathematics. However, entropy-gravity also used the Holographic Principle. So only the string-mathematics seem to be useful and not an expectable physics model; besides it is limited to Big Bang cosmology. Therefore it might be unexpectedly true that the Universe is Double Torus-shaped with dynamics that carry dark vacuum-particles with the same dynamics, namely: A Double Torus sub-quantum generated quantum-gravity whereof optical reality is a part of.
Category: Mathematical Physics

[217] viXra:1311.0121 [pdf] submitted on 2013-11-17 06:39:16

### Einstein’s Energy Is Connected To A New Dark Energy In A Rotational Double Torus Universe While Accelerated Space-expansion in Big Bang Cosmology Is An Optical Illusion.

Authors: Dan Visser
Comments: 13 Pages. I hope the press will take notice of the Double Torus hypothesis and in particular this paper.

Einstein’s energy is connected to a new dark energy force, refined-time, the fundamental constants of Planck and Newton and prove the universe is a rotational Double Torus Universe. Also is proven that an accelerated space-expansion in a stand-alone Big Bang cosmology is an optical illusion. This paper presents a new energy-equation connecting Einstein’s relativistic-energy to a new dark matter-force in a new dark energy force. This new equation is the result of combining a rather new energy-formula of E. Verlinde (UvA-NL) with my new dark energy force-formula of my Double Torus hypothesis. The Double Torus hypothesis is a new model for the universe and against Big Bang Cosmology. A second new equation proves indeed the accelerated space-time expansion is an optical illusion. The new dark energy force uses refined time, which is smaller than the Planck-time. Such causes a cyclic refined time-process from a sub-quantum scale recalculating dark matter towards the quantum scale, but in a rotational Double Torus Universe. This has consequences for the philosophy of past and future.
Category: Mathematical Physics

[216] viXra:1311.0108 [pdf] submitted on 2013-11-16 01:26:45

### The Inner Structure of Basis Spinors.

Authors: Vyacheslav Telnin

At first the 4-dimensional real basis spinors are set in accordance to usual 2-dimensional complex basis spinors. This is the first step. Then the 4-dimensional space of real basis spinors represents as the tensor product of two 2-demensional spaces. Further the sum of these two 2-dimensional spaces represents as the tensor product of two new 2-dimensional spaces. And this operation repeats infinitely.The metric tensor defines for each of derived in this process spaces (as for 2- dimensional, so for 4-dimensional). The shortage of data at this process compensates by the simplicity principle.
Category: Mathematical Physics

[215] viXra:1311.0099 [pdf] submitted on 2013-11-14 12:53:12

### Superluminal Spatio-Temporal Transformations:first Basic Step Toward the Superluminal Relativistic Mechanics

Authors: M.E. Hassani

The paper provides a crucial elementary derivation of new superluminal spatio-temporal transformations based on the idea that, conceptually and kinematically, each subluminal, luminal and/or superluminal inertial reference frame has,in addition to its relative velocity, its proper specific kinematical parameter,which having the physical dimensions of a constant speed. Consequently,the relativity principle and causality principle are coherently extended to superluminal velocities and, more importantly, this original approach constitutes the first basic step toward the formulation of superluminal relativistic mechanics in which the standard special relativity theory should be a particular case.
Category: Mathematical Physics

[214] viXra:1311.0090 [pdf] submitted on 2013-11-12 04:08:29

### Increasing of Dimention of Our Space from 4 to 16 Through Spinors.

Authors: Vyacheslav Telnin

From the fact, that 2-dimensional basis spinors are complex, there are made two conclusions. The first is that it is possible to change them by 4-dimensional real basis spinors. The second is that it is possible to enter 12 more dimensions in addition to 4 ordinary dimensions of our space. There is found connection of the basis of that 16-dimensional space with the basis of 4-dimensional space of real basis spinors.
Category: Mathematical Physics

[213] viXra:1311.0045 [pdf] submitted on 2013-11-06 08:00:28

### Entropy of Real Pendulum

Authors: Dmitri Martila

Mustiness basement of Science were blown up, in time of rising Einstein. He has not taken any of the Newtonian principles (three dimensional World with absolute time) into General Relativity. The beam of starlight passing in Sun's low gravity, showed, that even in weak field limit the General Relativity empirically contradicts the Newton's theory. Nowadays the Science is slow. I propose to critically examine its foundations once again. Because there are experiences, which contradict the Science. And the entropy, as it not being sold on market, is mystical enough.
Category: Mathematical Physics

[212] viXra:1311.0025 [pdf] submitted on 2013-11-04 09:17:55

### The Emergence Mechanism and Calculation Method of Turbulent Flows

Authors: Solomon I. Khmelnik

An explanation is offered of the mechanism of turbulent flows emergence, based of the Maxwell-like gravitation equations, updated after some known experiments. It is shown that the moving molecules of flowing liquid interact like electrical charges. The forces of such interaction can be calculated and included to the Navier-Stokes equations as mass forces. Navier-Stocks equations complemented by these forcesbecome equations of hydrodynamics for turbulent flow. For the calculations of turbulent flows the known methods of Navier-Stokes equations solution may be used.
Category: Mathematical Physics

[211] viXra:1311.0011 [pdf] submitted on 2013-11-02 07:17:21

### The Theory of the (E) Question - Presentation in any 4D space

Authors: Thierry PERIAT

The motivations for introducing a “new” mathematical tool within the general theory of relativity (A. Einstein’s work - GTR) have been intensively exposed in a first paper [vixra.org; 1311.0004]. This “companion” paper develops an argumentation allowing the intervening of the same tool in a pure 4D space. So far we know, it is one of the first theoretical works connecting the GTR and the Quantum Theory in a plausible manner at the Planckian limit.
Category: Mathematical Physics

[210] viXra:1311.0004 [pdf] submitted on 2013-11-01 12:11:05

### The Theory of the (E) Question - Presentation in any 3D space

Authors: Thierry PERIAT

This article is the first part of a research connecting the A. Einstein's general relativity and the Quantum Theory. The connection is realized via the canonical 3 + 1 ADM procedure and the introduction of a mathematical tool which is nothing but just a kind of inner product.
Category: Mathematical Physics

[209] viXra:1310.0235 [pdf] submitted on 2013-10-26 10:57:34

### Scale-Invariant Embeddings in a Riemannian Spacetime

Authors: Carsten S.P. Spanheimer

A framework for calculations in a semi-Riemannian space with the typical metric connection and curvature expressions is developed, with an emphasis on deriving them from an embedding function as a more fundamental object than the metric tensor. The scale-invariant and 'linearizing' logarithmic nature of an 'infinitesimal embedding' of a tangent space into its neighbourhood is observed, and a composition scheme of spacetime scenarios from 'outer' non-invariant and 'inner' scale-invariant embeddings is briefly outlined.
Category: Mathematical Physics

[208] viXra:1310.0234 [pdf] submitted on 2013-10-26 11:40:40

### Navier-Stokes Equations. On the Existence and the Search Method for Global Solutions.

Authors: Solomon I. Khmelnik
Comments: Pages. The rules Clay Mathematics Institute written as follows: "In the case of … the Navier-Stokes problem, the SAB will consider the award of the Millennium Prize for deciding the question in either direction." I suggest my decision of this problem.

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence. Then we consider the so-called closed systems. We prove that for them the necessary and sufficient conditions of global extremum for the named functional always exist. Accordingly, the search for global extremum is always successful, and so the unique solution of Naviet-Stokes is found. We contend that the systems described by Navier-Stokes equations with determined boundary solutions (pressure or speed) on all the boundaries, are closed systems. We show that such type of systems include systems bounded by impermeable walls, by free space under a known pressure, by movable walls under known pressure, by the so-called generating surfaces, through which the fluid flow passes with a known speed. The book is supplemented by open code programs in the MATLAB system – functions realizing the calculation method and test programs. Links on test programs are given in the text of the book when the examples are described. The programs may be obtained from the author by request at solik@netvision.net.il
Category: Mathematical Physics

[207] viXra:1310.0231 [pdf] submitted on 2013-10-25 21:29:54

### Saint-Venant's Principle: Experimental and Analytical

Authors: Jian-zhong Zhao

Mathematical provability , then classification, of Saint-Venant's Principle are discussed. Beginning with the simplest case of Saint-Venant's Principle, four problems of elasticity are discussed mathematically. It is concluded that there exist two categories of elastic problems concerning Saint-Venant's Principle: Experimental Problems, whose Saint-Venant's Principle is established in virtue of supporting experiment, and Analytical Problems, whose Saint-Venant's decay is proved or disproved mathematically, based on fundamental equations of linear elasticity. The boundary-value problems whose stress boundary condition consists of Dirac measure, a "singular distribution ", can not be dealt with by the mathematics of elasticity for " proof " or "disproof " of their Saint-Venant's decay, in terms of mathematical coverage.
Category: Mathematical Physics

[206] viXra:1310.0191 [pdf] submitted on 2013-10-22 11:40:05

### Time, Dark Energy and the Black-hole White-hole Universe

Authors: Malcolm Macleod

In this essay I propose an expanding black-hole universe (ours) with a contracting white-hole universe twin. Units of Planck momentum are transferred discretely from the white-hole to the black-hole thereby giving a rationale for the expansion of the universe, time, the arrow of time, dark energy and dark matter.
Category: Mathematical Physics

[205] viXra:1310.0165 [pdf] submitted on 2013-10-17 04:11:02

### A Soliton Solution to the Klein-Gordon Equation

Authors: Claude Michael Cassano

A soliton solution of the Klein-Gordon equation, ke^{-|m⋅r|} , consistent with the mass-generalized Maxwell's equations and the preon foundation for the fermions is presented, proved and discussed.
Category: Mathematical Physics

[204] viXra:1310.0146 [pdf] submitted on 2013-10-16 11:16:19

### Quaternions , Spaces , and The Parallel Postulate

Authors: Marcos Georgallides

Lagrange equation of motion for a single point ( Primary Point A is the only Space ) , states that this point must move from the Initial Position A to another position say B . This Equilibrium for points A and B , presupposes in Mechanics the Principle of Virtual Displacements and the work done is W = ∫ P.ds = 0 , or when ds = distance AB then → [ ds .( PA + P B ) = 0 ] ...(1).. From Equation (1) are self created all the Spaces [S] the equilibrium Anti-Spaces [AS] and the Sub-Spaces [SS] with infinite points in them and with a finite work on it . Monad dš (dipole AB) is a complex number of type [ dš = z = x+i.y ] ..(1a) representing the real part (x) , the distance AB , and imaginary parts (i.y) which is the work of …(1) . Complex number , z , the first dimentional unit AB , is such that either repeated by itself as monad ( z• = z.z.z.z. w-times ) or repeated times itself in monad ( ⁿ√z = z /ⁿ = z• , z/ⁿ.z/ⁿ.z/ⁿ….w = 1/n-times , or the nth roots of z equal to w = 1/n ) remains unaltered forming Spaces ( z•) , Anti-spaces( - z•) and the inversing Sub-spaces (ⁿ•z) , meaning that , unit circle is mapped on itself simultaneously on the two bases , 1 and n=1/w , where w.n = 1. This duality of coexistance on AB [ the w.th power and the n.th root of z where w.n =1 ] presupposes a common base ,m, which creates this unit polynomial exponentiation . Analysing this exponentiation according to one of the four basic properties of logs then becomes → log.w(1= w.n) = log.w(w)+log.w(n=1/w) = 1+1/w = 1+ n and it is the base of natural logarithms e and since 1= w.n then → ( 1+ n )• = (1+1/w)• = constant = m = e ← ....(2) Since the first dimentional unit AB is a complex number with many imaginary parts (and this because of the infinite variables) then this unit has the general type of quaternion .i.e. m^±(ª+₫.i) = q• = (Tq)•.[cos.wφ + ε.sin.wφ] ……where m = lim(1+1/w)• for w = 1→ ∞ , q = z = ± ( x+y.i ) sinφ = y/•x²+y² , cosφ = x/•x²+y² , |z| = •x²+y², Tq = • x²+y1²+y2²+ ….yn² , Ty = • y1²+y2²+ ….yn² ε = (y.i/Ty)=[y.i ] / [Ty]=(y1.a1+y2.a2+.)/(• y1²+y2²+yn²) [PNS] ↔ quaternion ↔ [ dŝ = x+i.y ] is a Vector with two components , the one x is the only Space with Scalar Potential field Φo , which is only half lengths of Space , Anti-Space , ( the longitudinal position ) , (x) → (-x) straight line connecting Space [S] , Anti-Space [AS] in [PNS] and in it exist , the initial Work , or Impulse , bounded on points which cannot be created or destroyed which is analogous to the (x) magnitude , and the other one y is the infinite local curl fields So , due to the Spin which is the intrinsic rotation of the Space and Anti-Space . Because in [S] and [AS] forces PA - PB are acting in the same straight line so moment lever is zero ( 0 ) , therefore Primary [S] and [AS] are ir-rotational and so it is possible to express this Primary field as a scalar function (Φo). This shows that [PNS] is a Space Work or Space- Spin or < Space Energy Existence > , where Time is not existing , because Φo and So are not time-varying . The same is holding also for the infinite dipole AiBi which are also complex numbers with all their properties , that of quaternions . Because quaternion properties are wrapped in lower and higher dimensions only by rotation , this is the property of spaces , so all dipole AnBn may have commons , which may bleed off in any Space , a very useful device for Quantum-mechanics . Geometrically states that , this property of commons allows to the dipole AnBn or to Spaces ↔ [ dŝ = xn+i.yn ] , to be also a Space -Time existence wrapped in the , Space-Energy Existence because of , Operation ↔ Quaternion → Notation m^±(ª+₫.i) = q• → = (Tq)•. [cos.wφ + ε.sin.wφ] Scatters , Part or all Content of the quaternion q , in all Spaces and Sub-Spaces as q• [ i.e. The duality of coexistence ↔ of the content of dŝ , from w.th power to the n.th root of q , where w.n =1 , is the measuring of , drag areas and other trapped accumulator , and by rotation to convert them in Spaces ]. An extend analysis of this unification follows in [23]
Category: Mathematical Physics

[203] viXra:1310.0082 [pdf] submitted on 2013-10-13 07:52:44

### The Complete Classification of Self-Similar Solutions of the Navier-Stokes Equations for Incompressible Flow

Authors: Sergey V. Ershkov
Comments: 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow

A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here. The equation of momentum has been split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one. The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity (potential of which should be a harmonic function). ¬¬¬Then we consider equation for solenoidal (divergence-free) field of flow velocity in the proper rotating co-ordinate system. Such a transition transforms the equation of motion to the Helmholtz vector differential equation. The inverse transformation from the rotating system to ordinary Cartesian coordinate system is possible only in case of constant angular velocity of rotation of such a system. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations.
Category: Mathematical Physics

[202] viXra:1310.0081 [pdf] submitted on 2013-10-12 16:06:14

### Vortex Theory of Electromagnetism

By examining the theory of relativity, as originally proposed by Lorentz and Poincaré, the fundamental relationship between space-time and matter is discovered, thus completing the theory of relativity and electrodynamics. As a result, the four-dimensional theory of general motion and the four-dimensional vortex theory of interaction are developed. It is seen that the electromagnetic four-vector potential and strength fields are the four-dimensional velocity and vorticity fields, respectively. Furthermore, the four-vector electric current density is proportional to the four-dimensional mean curvature of the four-vector potential field. This is the fundamental geometrical theory of electromagnetism, which determines the origin of electromagnetic interaction and clarifies some of the existing ambiguities. Interestingly, the governing geometry of motion and interaction is non-Euclidean.
Category: Mathematical Physics

[201] viXra:1310.0021 [pdf] submitted on 2013-10-03 14:27:31

### A New Exact Solution of EINSTEIN’S Equations

Authors: Thomas Günther

This article presents a new exact solution of Einstein’s equations with cosmological constant, which includes de Sitter’s metric as a special case. The generalized solution admits a nonzero stress energy momentum tensor. The second section is concerned with a transformation of the line element into a spherical symmetric but anisotropic form.
Category: Mathematical Physics

[200] viXra:1309.0212 [pdf] submitted on 2013-09-30 16:38:40

### Some Further Problems with Analytical Mechanics.

Authors: Jeremy Dunning-Davies
Comments: 4 Pages. Again it is hoped this short note will provoke more examination of this topic.

Here two derivations of Hamilton’s equations of motion are examined and found to depend crucially on both the system being conservative and the mass being constant. It is speculated that these derivations might be extended to the case where, as well as the system being conservative, the mass varies purely with time. However, at this stage, other generalisations seem unlikely and, if that is so, the usefulness of the Hamilton approach in mechanics would appear to be limited.
Category: Mathematical Physics

[199] viXra:1309.0210 [pdf] submitted on 2013-09-30 14:46:09

### Some Results in Classical Mechanics for the Case of a Variable Mass.

Authors: Jeremy Dunning-Davies
Comments: 6 Pages. It is hoped this short note will provoke further examination of the topic discussed.

In most, if not all, introductions to classical mechanics, the mass is assumed to be constant. Usually this is mentioned and often attention is drawn to such systems as rocket motion to indicate that, in practice, the mass is not always a constant. In truth, many students actually meet a varying mass for the first time when introduced to the Special Theory of Relativity. However, varying masses do occur in nature when relativistic effects are not important. Here an attempt is made to draw together some common results of classical mechanics with a variable mass taken into account. Particular attention will be drawn to a perceived change in the expression for the kinetic energy and to crucial changes in the basic form of Lagrange’s equations of motion.
Category: Mathematical Physics

[198] viXra:1309.0141 [pdf] submitted on 2013-09-19 10:13:47

### Sedenion Space

Authors: John Frederick Sweeney
Comments: 37 Pages. De – Constructing De Marrais Series

The late Robert Marrais wrote of 3 distinct aspects of Sedenion Space: one belonging to the E8 x E8 Super – Symmetry of the embattled Super String Theory, one belonging to Icosahedral Rotation Groups or H3, and a third belonging to O. V. Lyashko. In addition, this paper discusses methods to classify and to categorize the Sedenions.
Category: Mathematical Physics

[197] viXra:1309.0116 [pdf] submitted on 2013-09-17 10:54:11

### Sedenions, Lissajous Figures and the Exceptional Lie Algebra G2

Authors: John Frederick Sweeney

This paper examines a point of intersection between the work of the late Robert de Marrais and Vedic Physics. Specifically, de Marrais discussed the concept of Lissajous Figures in relation to Sedenions and his 42 Assessors, in his first paper about Box Kites. Later, John Baez took up a related subject, the problem of epicycloids, apparently without having read the work of de Marrais. This paper examines this intersection between leading - edge mathematical physics and Vedic Physics in order to further illuminate the higher algebras - the Octonions, Sedenions and Trigintaduonions.
Category: Mathematical Physics

[196] viXra:1309.0008 [pdf] submitted on 2013-09-03 12:10:52

### Yang-Mills Gauge Invariant Theory for Space Curved Electromagnetic Field

Authors: Maknickas Algirdas Antano

It was proposed new gauge invariant Lagrangian, where the gauge field interact with the charged electromagnetic fields. Gauge invariance was archived by replacing of particle mass with new one invariant of the field $F_{\mu\nu}F^{\mu\nu}$ multiplied with calibration constant $\alpha_g$. It was shown that new proposed Lagrangian generates similar Dirac and electromagnetic field equations. Solution of Dirac equations for a free no massless particle answers to the 'question of the age' why free particle deal in experiments like a de Broil wave. Resulting wave functions of the new proposed Lagrangian will describe quantized list of bespinor particles of different masses. Finally, it was shown that renormalization of the new proposed Lagrangian is similar to QED in case similarity of new proposed Lagrangian to classic QED.
Category: Mathematical Physics

[195] viXra:1309.0002 [pdf] submitted on 2013-09-02 05:33:45

### Waves and Special Relativity

Authors: José Francisco García Juliá

The existence of the waves proves the existence of the special relativity.
Category: Mathematical Physics

[194] viXra:1308.0140 [pdf] submitted on 2013-08-27 09:54:56

### Unified Field; Gravity, Electric, Strong Forces as Standing Wave Orbitals

Authors: Malcolm Macleod

A set of formulas for gravity, atomic orbitals and the nucleus based on the Bohr model of the atom for n-orbitals are given. The formulas differ only in orbital velocity implying a common geometrical link. Analysis of the Rydberg formula suggests a mechanism whereby standing wave energy-wells form physical orbitals in the empty space between particles. These orbitals are anti-photons; photons albeit of opposite phase. Via a simple wave addition/subtraction, an incoming photon replaces the original orbital with the new orbital. The electron itself does not move. Gravitational waves become standing wave orbitals that are essentially extensions of atomic orbitals, they are both the orbital path and the orbital momentum. Potential and kinetic gravitational energies simply reflect the ratio of alignment of their motion vectors. Nucleus mass deficit and quantum entanglement may also be explained via this mechanism.
Category: Mathematical Physics

[193] viXra:1308.0125 [pdf] submitted on 2013-08-23 07:54:00

### Nonstandard Ultra-logic-systems Applied to the GGU-model

Authors: Robert A. Herrmann

In this paper, a mathematical model for instruction-information, via instruction-sets, is presented and used as a fundamental aspect of the General Grand Unification Model (GGU-model), the only known mathematical cosmogony. A modern and differentiating nonstandard structure is employed to model this cosmogony, where a standardizing process produces a physical cosmology.
Category: Mathematical Physics

[192] viXra:1308.0118 [pdf] submitted on 2013-08-22 03:52:44

### Planck Unit Theory: Fine Structure Constant and Sqrt of Planck Momentum

Authors: Malcolm Macleod

A geometrical relationship between the charge constants, the fine structure constant alpha and the sqrt of Planck momentum is used to define G, h, e and electron mass me in terms of the 4 most accurate natural constants c, alpha, R and mu0 the vacuum permeability. As c and mu0 have exact values and the Rydberg constant R is precise to 12 digits, the accuracy of the calculated values for G, h, e and me is limited only by the precision of alpha. Results consistent with CODATA 2010 and suggest a digital Planck unit theory.
Category: Mathematical Physics

[191] viXra:1308.0080 [pdf] submitted on 2013-08-16 12:59:44

### Improving Koide Formula

Authors: Branko Zivlak

Abstract. Based on the methods, author used in previously published articles at viXra.org, Koide formula is corrected, to the results 2/3. The mass of tau lepton is also calculated.
Category: Mathematical Physics

[190] viXra:1308.0069 [pdf] submitted on 2013-08-13 09:56:13

### Abel Resummation , Regularization, Renormalization and Infinite Series

Authors: Jose Javier Garcia Moreta

ABSTRACT: We Study the use of Abel summation applied to the evaluation of infinite series and infinite (divergent) integrals , we give several examples of how we can obtain a regularization for sums in the form and for divergent integrals in one and more variables
Category: Mathematical Physics

[189] viXra:1308.0034 [pdf] submitted on 2013-08-06 07:04:55

### Riemann Hypothesis Solved Through Physics-Math In New Cosmological Model: The Double Torus Hypothesis.

Authors: Dan Visser
Comments: 20 Pages. A copy has been send to the Clay Mathematics Institute.

The Double Torus Hypothesis is a newly proposed cosmological model. It reaches further than quantum-dynamics. It are ‘sub-quantum dynamics’ in the Double Torus, which show how new insights lead to the solution of the Riemann hypothesis. The secret is the existence of the continuous recalculation by two additional time-clocks from below the Planck-scale. Several of my papers describe this additional time in a new dark energy-force formula. This formula shows that a quantum-Newton-force and a sub-quantum dark matter-space-force perform extreme small accelerations that function as the exponent of the number ‘e’, where it enables sub-quantum-vacuum to expand or contract. The clue to the solution of the Riemann hypothesis is, that these physics sub-quantum-accelerations connect with ’π’ for surfaces below the elementary quantum-surface. I show how the famous Euler-formula e^iπ +1=0 is related to that process and I also show this Euler-formula can be related to the Riemann hypothesis by expressing the prime-numbers in the inverse Riemann hypothesis. I relate that configuration to the divided structure of an elementary quantum-surface. This leads to a configuration that solves the Riemann hypothesis. So, now is the moment to announce how I did that. I realize this might be experienced as shocking, because I am an outsider: I’m an independent cosmologist. Hopefully my solution awards me with the 1 million USD-price by the Clay Mathematics Institute (this dated pdf-file has been send to the Clay Mathematics Institute).
Category: Mathematical Physics

[188] viXra:1308.0018 [pdf] submitted on 2013-08-04 10:05:46

### G2 Root System and 28 Nakshastra

Authors: John Frederick Sweeney

The G2 Root system is the only root system in which the angle of pi / 6 appears between two roots. This is made necessary in nature by the demand for circular objects which can be divided by six or twelve, according to Vedic literature concerning the 28 Nakshastra or astrological houses. In addition, G2 provides the key linkage between the Sedenions, which curiously contain properties related to the number 29 and the Octonions. G2 is key to the transformation from Binary to Trinary,Fano Plane to Tetrahedron and the Sedenions, mixing the 8 x 8 to 9 x 9 aspects of matter, or the Satwa and Raja aspects. Finally, from the Sedenions this paper develops toward the Hopf Fibration and the Boerdijk-Coxeter Helix, which is composed of Sedenions in the form of tetrahedra. Along the way we travel all the way back to the Osiris Temple of Abydos, Egypt, where G2 appears.
Category: Mathematical Physics

[187] viXra:1307.0113 [pdf] submitted on 2013-07-23 08:40:13

### The Proof

Authors: Andrej Rehak
Comments: 9 Pages. The essay can be rated at FQXi's 2013 Essay Contest at http://fqxi.org/community/forum/topic/1876

If the result of the product of zero and infinity is not defined then the system located within dimensions of their ideas has no definition. On a scale between zero and infinity, we establish the system. Universally valid definition of its geometry of motion proves its validity. We prove that the system is. We establish a platform for its unification.
Category: Mathematical Physics

[186] viXra:1307.0101 [pdf] submitted on 2013-07-20 20:40:42

### Clifford Clock and the Complex Spaces of the Qi Men Dun Jia Model

Authors: John Frederick Sweeney

The concept of the Clifford Clock, which demonstrates the relationships between real, complex, quarternions and octonions, has become established in math physics. Less well-known are the spaces in which the algebras dwell. Space consists of an infinite number of tiny invisible cubes. Under the rubric of the Clifford Clock, these spaces take on significance, since the spaces themselves take on periodic aspects, and are directly related to Supersymmetry and the Super Brauer group of Lie Algebras. In addition, the Clifford Clock of Complex Spaces bears relevance to octagonal cuspid newforms, which are related to the Riemann Zeta Function.
Category: Mathematical Physics

[185] viXra:1307.0100 [pdf] submitted on 2013-07-20 14:31:05

### Description on the P vs. NP; A Guide to its Mathematics

Authors: Andrew Nassif

Most people when thinking of the P vs. NP thinks of it as unsolved or unsolvable although it goes with a simple algorithmic proof in which I have written in my previous paper. Now as you may know, the P vs. NP can lead to some of the greatest breakthroughs in computer science, and mathematical physics. The question however asks you to use a method to figure out the complexity vs. non-complexity of a problem, which I have demonstrated in my last paper as the example of someone removing 100 possible students from a group of 400 and then coming up with the different combinations in which the 300 can’t be picked. This problem can be used in example with probability and solved through the complex equation where there is a solution for P equaling NP and you would then get ((400!)-(100!*3)). I gave this example using set theory and logic as well. This number would then be more than the number of atoms in the known planet in which we live on. However this is just one of the examples. My next example was an example of how some computers show through algorithms and polynomials that P does equal NP.
Category: Mathematical Physics

[184] viXra:1307.0098 [pdf] submitted on 2013-07-20 08:15:30

### On The OPERA Problem and Its Consequences

Authors: M. H. Hassani
Comments: 10 Pages; 17 References. This work is accepted for publication in Galilean Electrodynamics Journal

Since OPERA is a very carefully designed experiment thus the sobering importance of its result, coupled with decades of some successful tests of special relativity theory (SRT) requires certain adjustment in our usual manner of thinking, and seriously prompts us to consider alternatives which should be consistent with both. To this end, we propose an alternative model as an explanation to the observed neutrino superluminality based on the universality of the well-known rest mass energy formula, and the idea that, at superluminal level, the velocity of a particle with real mass may be simultaneously dependent on its energy ratio and the kinematical attainability parameter. By raising this idea to the status of a hypothesis, we show that not only the OPERA result is very realistic but also is perfectly consistent with supernova SN1987a measurement. Consequently, SRT is not violated by the existence of superluminal particles since it is conceptually, physically and exclusively valid at subluminal level for relativistic velocities. As a direct consequence, the Minkowski space-time and Lorentz transformations are coherently extended to superluminal velocities.
Category: Mathematical Physics

[183] viXra:1307.0045 [pdf] submitted on 2013-07-08 12:34:00

### Estudio de las Matrices de Barut, Muzinich y Williams para Espin 1

Authors: Maria de Guadalupe Caldera Cabral
Comments: 65 Pages. Thesis in Spanish

In this Thesis the formulae are presented for the relativistic products of the matrices gamma_{\mu\nu} of Barut,Muzinich and Williams for the spin 1. They are analogs of the Dirac matrices for the spin 1/2. They are found in the 2(2S+1) relativistic equations of Weinberg, Tucker and Hammer. Moreover, it was proven that the mapping exists between the Proca vector-tensor formalism and the 2(2S+1) formalism. The formulae of the relativistic products can be useful in the calculations of the scattering amplitudes, cross-sections and the energy spectra of the bound states for bosons.
Category: Mathematical Physics

[182] viXra:1307.0030 [pdf] submitted on 2013-07-06 05:17:19

### From the Heim-Droescher Dimensions Formular to a Topological Structure Formular of Ancient-Word-Theory

Authors: Klaus Lange

Using the Heim-Droescher dimensions formular it will be shown that the number pair {p;n} = {57; 420} exist. With Heim QFT alone no meaning for this number pair is given. But with the delta-extended Ancient-Word-Matrix it is shown that for all number pairs {1;2}, {2;2}, {4;6}, {6;12} and {57;420} topological classification numbers are given.
Category: Mathematical Physics

[181] viXra:1307.0025 [pdf] submitted on 2013-07-05 03:27:55

### Structural Supersymmetry and Other Particle Properties Within the Framework of Ancient-Word-Theory

Authors: Klaus Lange

This paper shows that the prime number Apeiron according to Hedwig Cornad-Martius and Burkhard Heim is only a special case of parallel number sets. Based on the Ancient-Word-Matrix from Michael König this leads to a structural supersymmetry and to other exotic particle properties. A calculation of the fine structure constant, the Weinberg angle and the mass of the stop-squark to 688+/-43 GeV/c^2 will be given.
Category: Mathematical Physics

[180] viXra:1307.0024 [pdf] submitted on 2013-07-04 20:19:45

### Modified Saint-Venant’s Principe With Example

Authors: Jian-zhong Zhao

The Statement of Modified Saint-Venant’s Principle is suggested. The axisymmetrical deformation of the infinite circular cylinder loaded by an equilibrium system of forces on its near end is discussed and its formulation of Modified Saint-Venant’s Principle is established. It is evident that finding solutions of boundary-value problems is a precise and pertinent approach to establish Saint-Venant type decay of elastic problems.
Category: Mathematical Physics

[179] viXra:1307.0022 [pdf] submitted on 2013-07-04 09:33:19

### Dimensions Strucure, Fine Structure Constant and The Ancient-Word-Matrix

Authors: Klaus Lange

Based on the Ancient-Word-matrix, developed by Michael König, this paper shows how the entire 12 dimensional strucure according to Burkhard Heim theory is embedded into the G4 space matrix. The strucuture properties of complex relativity by Jean Emile Charon will be revealed using the Heim prime number space. A very good estimation of the fine structure constant will be made.
Category: Mathematical Physics

[178] viXra:1306.0236 [pdf] submitted on 2013-06-30 20:22:18

### The Orthogonal Real Representations of the Poincare Group

Authors: Leonardo Pedro

The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We show that the projective representation of the Poincare group on the Majorana spinor field is orthogonal and irreducible. Using the Bargmann-Wigner equations, we study all orthogonal irreducible projective real representations of the Poincare group, with finite or null mass and discrete spin.
Category: Mathematical Physics

[177] viXra:1306.0231 [pdf] submitted on 2013-06-28 19:36:33

### Self/anti-Self Charge Conjugate States in the Helicity Basis

Authors: V. V.Dvoeglazov
Comments: 4 Pages. Presented in the DGFM-SMF School. December 2012. Puerto Vallarta, Mexico.

We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2,0)+(0,1/2)$representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. Particular attention has been paid to the question of (anti)commutation of the Charge conjugation operator and the Parity in the helicity basis. Dynamical equations have also been presented. In the (1/2,0)+(0,1/2) representation they obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The chirality and the helicity (two concepts which are frequently confused in the literature) for Dirac and Majorana states have been discussed. Category: Mathematical Physics [176] viXra:1306.0050 [pdf] submitted on 2013-06-07 17:37:51 ### The Universe Rotates And Is No Big Bang Authors: Dan Visser Comments: 4 Pages. I found a ‘quadruple image’ of ‘Hot and Cold Spots’ in the CMB-image, published by the gathered data of the Planck-satellite in 2013, and analyzed by me in the context of the (new) Double Torus cosmology. The ‘quadruple image’ proves the Universe rotates!! The ‘quadruple image’ follows the logic of a ‘dark flow’ in the Double Torus. This ‘dark flow’ is expressed in my (new) dark energy force-formula and astronomically determined. Hence, the Double Torus (until now a hypothesis), is changing into “hitting the right spot”, or in other words: “starts being a real model” !! The new cosmology is extensively described in a series of papers of mine, hosted in the vixra-archive in the category Mathematical Physics. Category: Mathematical Physics [175] viXra:1306.0026 [pdf] submitted on 2013-06-06 05:33:35 ### Extended Prigozhin Theorem: Method for Universal Characterization of Complex System Evolution Authors: Sergey Kamenshchikov Comments: 7 pages. Author is looking for postdoc position. kamphys@gmail.com Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, injected into system and power of energy, dissipated through internal nonlinear mechanisms. It was found out that basic phase parameter as control parameter must be delimited for two types of system - accelerator and decelerator. It was suggested to select zero state entropy on through condition of zero value for entropy production. Zero state introduces universal principle of disorder characterization. On basis of self organization S – theorem we have derived relations for entropy production behavior in the vicinity stationary state of system. Advantage of these relations in comparison to classical Prigozhin theorem is versatility of their application to arbitrary nonlinear systems. It was found out that extended Prigozhin theorem introduces two relations for accelerator and decelerator correspondingly, which remarks their quantitative difference. At the same time classic Prigozhin theorem makes possible description of linear decelerator only. For unstable motion it corresponds to strange attractor. Category: Mathematical Physics [174] viXra:1305.0202 [pdf] submitted on 2013-05-31 12:24:22 ### Newtonian Gravitational N-Body Spherical Simplification Algorithm in Riemannian Dual Space-Time Authors: Nathan O. Schmidt Comments: 22 pages; 6 figures; published in The Hadronic Journal, Volume 36, Number 1, February 2013 We propose a preliminary algorithm which is designed to reduce aspects of the n-body problem to a 2-body problem for holographic principle compliance. The objective is to share an alternative view-point on the n-body problem to try and generate a simple solution in the near future. The algorithm operates complex and triplex data structures to encode the chaotic dynamical system equipped with order parameter fields in both 3D and 4D versions of the Riemannian dual (fractional quantum Hall superfluidic) space-time topology. For the algorithm, we arbitrarily select one point-mass to be the origin and, from that reference frame, we subsequently engage a series of instructions to consolidate the residual (n-1)-bodies to a time-effective spherical surface. Through a step-by-step example, we demonstrate that the algorithm yields time-effective net-quantities that authorize us to define a time-effective potential, kinetic, and Lagrangian. Category: Mathematical Physics [173] viXra:1305.0201 [pdf] submitted on 2013-05-31 06:16:18 ### The Orthogonal Representation of the Poincare Group on the Majorana Spinor Field Authors: Leonardo Pedro Comments: 14 Pages. The irreducibility of a representation of a real Lie algebra may depend on whether the representation space is a real or complex Hilbert space. The unitary projective representations of the Poincare group on complex Hilbert spaces were studied by Wigner and many others. Although the Poincare group has a real Lie algebra, we do not know of any study of the orthogonal projective representations of the Poincare group on real Hilbert spaces. The Majorana spinor field, a space-time dependent element of a 4 dimensional real vector space, is a solution of the free Dirac equation. Our goal is to study the projective representation of the Poincare group on the real Hilbert space of Majorana spinor fields. The Majorana-Fourier and Majorana-Hankel orthogonal transforms of Majorana spinor fields are defined and related to the linear and angular momentums of a spin one-half projective representation of the Poincare group. Then we show that the projective representation of the Poincare group on the Majorana spinor field, whether we include the parity and time reversal or not, is orthogonal and irreducible. This contrasts with the unitary projective representations of the Poincare group on the Dirac and Weyl spinor fields, whose properties change when including or excluding the parity and time reversal transformations. Category: Mathematical Physics [172] viXra:1305.0173 [pdf] submitted on 2013-05-29 00:07:18 ### Qi Men Dun Jia a Mathematical Physics Model Authors: John Frederick Sweeney Comments: 5 Pages. Copyright John Frederick Sweeney 2013 Qi Men Dun Jia is an ancient form of divination from China which is still employed to make accurate predictions, and thus meets the definition of a scientific model based on scientific theory. This paper introduces a series of books which engages in "reverse engineering," using the concepts of contemporary mathematical physics to explain how this ancient model works. Specifically, we address Clifford Algebras, Bott Periodicity, Exceptional Lie Algebras, icosians, octonions and sedenions, as well as the Fano Plane and isometric relationships to Leptons and Baryons. The introduction concludes with reference to extremely ancient and superior science from 12,000 years ago, ancient Vedic culture and extremely ancient Egyptian culture. Category: Mathematical Physics [171] viXra:1305.0171 [pdf] submitted on 2013-05-29 04:29:28 ### Zeta Regularization Method Applied to the Calculation of Divergent Divergent Integrals Authors: Jose Javier Garcia Moreta Comments: 15 Pages. •ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization •Keywords: = Riemann Zeta function, Functional determinant, Zeta regularization, divergent series . Category: Mathematical Physics [170] viXra:1305.0145 [pdf] submitted on 2013-05-23 10:52:34 ### Calculate Universe 3 – Planck Units Authors: Branko Zivlak Comments: 5 Pages. 1 Table, 1 Appendix This article is about relations between fundamental physical constants. The mass, radius and cycle of the universe are the basis for calculating Planck units. Category: Mathematical Physics [169] viXra:1305.0137 [pdf] submitted on 2013-05-22 22:25:06 ### Zanaboni Theory and Saint-Venant's Principle: Updated Authors: Jian-zhong Zhao Comments: 14 Pages. Zanaboni Theory is mathematically analyzed in this paper. The conclusion is that Zanaboni Theorem is invalid and not a proof of Saint-Venant's Principle; Discrete Zanaboni Theorem and Zanaboni's energy decay are inconsistent with Saint-Venant's decay; the inconsistency, discussed here, between Zanaboni Theory and Saint-Venant's Principle provides more proofs that Saint-Venant's Principle is not generally true. Category: Mathematical Physics [168] viXra:1305.0136 [pdf] submitted on 2013-05-22 22:34:09 ### Saint-Venant's Principle: Rationalized and Rational Authors: Jian-zhong Zhao Comments: 8 Pages. The problem of statement of Saint-Venant's Principle is concerned. Statement of Boussinesq or Love is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of Saint-Venant’s Principle of elasticity is suggested to rule out the ambiguity of Statements of Boussinesq and Love. Rational Saint-Venant's Principle is suggested to fit and guide applications of the principle to fields of continuum physics and cover the analogical case as well as the non-analogical case discovered and discussed in this paper .  Constraint-free " problems are suggested and  Constraint-free " Rational Saint-Venant's Principle or Rational Saint-Venant's Principle with Relaxed Boundary Condition is developed to generalize the principle and promote its applications to fields of continuum physics . Applications of Analogical Rational Saint-Venant's Principle and  Constraint-free " Rational Saint-Venant's Principle are exemplified, emphasizing  properness " of the boundary-value problems. Three kinds of properly posed boundary-value problems, i.e., the boundary-value problem with the undetermined boundary function, the boundary-value problem with the implicit boundary condition and the boundary-value problem with the explicit boundary condition, are suggested for both  constrained " and  constraint-free " problems. Category: Mathematical Physics [167] viXra:1305.0132 [pdf] submitted on 2013-05-21 05:51:06 ### New Formula for Dark Energy Force Gives New Connection to Quantum-Gravity and Topology for Electron-Spin. Authors: Dan Visser Comments: 6 Pages. This article is about a new formula for dark energy force. This has already been published in a series of my articles in the archive vixra, but gets little attention. The new formula is part of a larger universe than the Big Bang, called the Double Torus hypothesis. The new dark energy force is different from dark energy in the Big Bang, because it uses the extension of time. This article emphases the extra time relating gravity and a new topology of quantum-spin of point particles, such as electrons. This article describes that cohesion by my dark energy force formula in a Double Torus Universe. Category: Mathematical Physics [166] viXra:1305.0124 [pdf] submitted on 2013-05-19 07:49:32 ### Virtual Presentations for the Icm 2 Conference in Prague: Poster 1 Authors: Andrew Beckwith Comments: 4 Pages. 1st of six posters for the ICM 2 conference in Prague. The following questions are raised in this document. First, can@@ there be a stable (massive) graviton? If so, does this massive graviton, as modeled by KK DM, with a modification of slight 4 dimensional space mass, contribute to DE, at least in terms of re acceleration ? The answer, if one assumes that the square of a frequency for graviton mass is real valued and greater than zero appears to be affirmative. The author, when considering a joint DM – DE model finds evidence that re acceleration of the universe one billion years ago in a higher dimensional setting can be justified in terms of a slight modification of standard KK DM models, if one considers how an information exchange between present to prior universes occurs, which the author thinks mandates more than four dimensional space time geometry Category: Mathematical Physics [165] viXra:1305.0123 [pdf] submitted on 2013-05-19 07:52:54 ### Poster 2, for Icm2 Conference, Cz Authors: Andrew Beckwith Comments: 4 Pages. Poster or virtual paper for the ICM 2 conference This paper uses the “Fjortoft theorem” for defining necessary conditions for instability. The point is that it does not apply in the vicinity of the big bang. We apply this theorem to what is called by T. Padmanabhan a thermodynamic potential which becomes would be unstable if conditions for the applications of “Fjortoft’s theorem” hold. In our case, there is no instability, so a different mechanism has to be appealed to. In the case of vacuum nucleation, we argue that conditions exist for the nucleation of particles as of the electroweak regime. Due to injecting material from a node point, in spacetime. This regime of early universe creation, coexits with the failure of applications of “Fjortoft” theorem in such a way as to give necessary and sufficient conditions for matter creation, in a way similar to the Higgs Boson Category: Mathematical Physics [164] viXra:1305.0122 [pdf] submitted on 2013-05-19 07:54:46 ### Poster 3 for the Icm 2 Conference, Cz Authors: Andrew Beckwith Comments: 4 Pages. When initial radius R approaches zero if we use Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of the initial radius approaching zero are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to entanglement entropy implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto , and show that there are consequences due to initial entanged entropy for a time dependent horizon radius in cosmology, with for flat space conditions r(H)=conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time except with in line with the conformal time being almost zero. . The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the initial radial length gets, then for initial cosmological entropy if it is entanglement entropy, initial cosmological entropy will not go to zero. Category: Mathematical Physics [163] viXra:1305.0121 [pdf] submitted on 2013-05-19 07:56:51 ### Poster 4 for the Icm 2 Conference, Cz Authors: Andrew Beckwith Comments: 4 Pages. First, we show through a numerical simulation that the massive Schwinger model used to formulate solutions to CDW transport is insufficient for transport of solitons (anti-solitons) through a pinning gap model of CDW transport. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits formation of solitons (anti- solitons) which could be used to transport CDW through a potential barrier. We argue that there are analogies between this construction and the false vacuum hypothesis used for showing a necessary and sufficient condition for formation of CDW soliton – anti - soliton (S-S’) pairs in wave functionals presented in a prior publication Category: Mathematical Physics [162] viXra:1305.0120 [pdf] submitted on 2013-05-19 07:58:57 ### Poster 5, for the Icm 2 Conference, Cz Authors: Andrew Beckwith Comments: 4 Pages. The author asks if octonion quantum gravity is relevant near the Planck scale. Furthermore, the question is raised if gravitational waves would be generated during the initial phase, , of the universe when an increase in degrees of freedom have in setting , so that the result can be observed by a gravitational detector.. The well appreciated .quantum gravity problem that the notion of a quantum state, representing the structure of spacetime at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having the initial octonion geometry embedded in a larger, non linear “pilot model” (semi classical) embedding structure. The Penrose suggestion of re cycled space time avoiding a ‘big crunch’ is picked as the embedding structure, so as to avoid the ‘instants’ of time issue. In addition the favored idea is to avoid the well known string theory trap known as the dimensionality problem of an equation of motion (consistency condition) which is the reason why string theory dimensionality is either (10 or 26) depending upon if super symmetry is imposed. Getting octonion gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the lunacy of then afterwards ‘Schrodinger equation ‘ states of the universe, forevermore afterwards. Setting , in a GW detector due to appropriate measurement procedures may allow the opportunity to find experimental clues as to this embedding structure in which octonion gravity may emerge in the Planckian regime.of evolutionary cosmology Category: Mathematical Physics [161] viXra:1305.0118 [pdf] submitted on 2013-05-19 08:00:58 ### Poster 6 for the Icm 2 Conference, CZ Authors: Andrew Beckwith Comments: 4 Pages. The following questions is asked, If one takes the covariant derivative of a Stress-energy representation of early universe massive gravitons, is the derivative of the Graviton stress tensor equal to zero ? If so, then in what range of astrophysics does this occur, and when does this formalism break down? Lavenda and Davies argued that the derivative of a generalized GR stress energy tensor being zero in itself is insufficient to show that the 1st law of thermodynamics alone holds. If the full Stress-Energy tensor expression for GR is written out, there is a stress energy tensor component involving GW alone which we highlight. The problem as to this test is if the derivative of the Stress energy tensor, for gravitons as written by Visser is brought up. This Visser stress energy tensor for massive gravitons will not even satisfy the 1st thermodynamic law. We bring this up as a counter point to an article written by Lavenda and Davies purporting to claim that the Tolman test for a first law of thermodynamics which they generalize to first and second law of thermodynamics for inflationary cosmology. We show a breakdown of a zero value for the derivative of the Stress energy tensor for early universe massive gravitons and this derivative of the massive Graviton Stress energy tensor (Visser) will not even satisfy the first law of thermodynamics according to the Tolman criteria. Note that if the Visser Massive Graviton Stress energy tensor scenario does not hold then the Lavenda and Davies objection to inflation is upheld. Category: Mathematical Physics [160] viXra:1305.0100 [pdf] submitted on 2013-05-17 03:47:11 ### Orbital Averages and the Secular Variation of the Orbits Authors: Maurizio M. D'Eliseo Comments: 13 Pages. Orbital averages are employed to compute the secular variation of the elliptical planetary elements in the orbital plane in presence of perturbing forces of various kinds. They are also useful as an aid in the computation of certain complex integrals. An extensive list of computed integrals is given. Category: Mathematical Physics [159] viXra:1305.0099 [pdf] submitted on 2013-05-16 08:37:03 ### Amending Maxwell’s Equations for Real and Complex Gauge Groups in Non-Abelian Form Authors: Richard L. Amoroso, Elizabeth A. Rauscher Comments: 6 Pages. We have analyzed, calculated and extended the modification of Maxwell’s equations in a complex Minkowski metric, M4 in a C2 space using the SU2 gauge, SL(2,c) and other gauge groups, such as SUn for n >2 expanding the U1 gauge theories of Weyl. This work yields additional predictions beyond the electroweak unification scheme. Some of these are: 1) modified gauge invariant conditions, 2) short range non-Abelian force terms and Abelian long range force terms in Maxwell’s equations, 3) finite but small rest of the photon, and 4) a magnetic monopole like term and 5) longitudinal as well as transverse magnetic and electromagnetic field components in a complex Minkowski metric M4 in a C4 space. Category: Mathematical Physics [158] viXra:1305.0085 [pdf] submitted on 2013-05-14 14:42:59 ### A Complex and Triplex Framework for Encoding the Riemannian Dual Space-Time Topology Equipped with Order Parameter Fields Authors: Nathan O. Schmidt Comments: 16 pages, 2 figures, published in the Hadronic Journal In this work, we forge a powerful, easy-to-visualize, flexible, consistent, and disciplined abstract vector framework for particle and astro physics that is compliant with the holographic principle. We demonstrate that the structural properties of the complex number and the sphere enable us to introduce and define the triplex number---an influential information structure that is similar to the 3D hyper-complex number by D. White and P. Nylander---which identifies a 3D analogue of (2D) complex space. Consequently, we engage the complex and triplex numbers as abstract vectors to systematically encode the state space of the Riemannian dual 3D and 4D space-time topologies, where space and time are dual and interconnected; we use the triplex numbers (with triplex multiplication) to extend 1D and 2D algebraic systems to 3D and 4D configurations. In doing so, we equip space-time with order parameter fields for topological deformations. Finally, to exemplify our motivation, we provide three example applications for this framework. Category: Mathematical Physics [157] viXra:1305.0071 [pdf] submitted on 2013-05-12 06:33:07 ### Time for New Cosmology Authors: Dan Visser Comments: 2 Pages. The Higgs-particle could be a dark matter particle! It is not enough to confirm spin 0 and + parity for the Higgs-like particle to let it be the Higgs-particle. The Double Torus hypothesis should be involved. A dark matter particle in this new framework could also have spin 0 and + parity under condition it contributes to gravity, but its properties can also contribute as negative mass to anti-gravity. Category: Mathematical Physics [156] viXra:1305.0056 [pdf] submitted on 2013-05-08 15:06:47 ### The Schrödinger Equation in Complex Minkowski Space, Nonlocality and Anticipatory Systems Authors: Richard L. Amoroso, Elizabeth A. Rauscher Comments: 19 Pages. We develop a formalism for the Schrödinger equation in an eight dimensional complex Minkowski space and discuss its relation to the Dirac equation, properties of nonlocality, remote connectedness, Young’s double slit experiment, Bell’s Theorem, the EPR paradox and anticipatory parameters of spacetime; and also identify an imaginary temporal component as a small nonlinear term and find soliton or solitary wave solutions. These coherent solutions can carry information over long distances, are consistent with Lorentz invariance and appear to provide a fundamental methodology for describing the issue of quantum measurement and a new context for the basis of quantum theory. In the Copenhagen view models of reality are not desirable. However our new approach may enable the redefinition of concepts of reality from a new nonlocal anticipatory quantum theory. Certainly the most desirable consequence of scientific discovery is the ability to redefine our concepts of reality. Category: Mathematical Physics [155] viXra:1305.0055 [pdf] submitted on 2013-05-08 15:09:12 ### Relativistic Physics in Complex Minkowski Space, Nonlocality, Aether Model and Quantum Physics Authors: Richard L. Amoroso, Elizabeth A. Rauscher Comments: 25 Pages. Many naturally occurring phenomena require theoretical treatment utilizing complex analysis by methods such as the Cauchy-Riemann relations using hyper-geometrical spaces which treat inherently nonlinear, non-dispersive, collective nonlocal resonant states of a quantum system, so as to be consistent with the nonlinearity inherent in General Relativity. Typical quantum approaches form linear approximations limiting the ability to formulate a quantum consistent Relativity Theory. Category: Mathematical Physics [154] viXra:1305.0049 [pdf] submitted on 2013-05-08 06:04:29 ### The Genesis of Circle Authors: Andrej Rehak Comments: 4 Pages. Geometric demonstration of free fall and rotation reveals space-time nature of the genesis of circle. We show that the operations with radius are equivalent to operations with velocity. Consequently, conventional spatial unit for radius (m), becomes equivalent to dynamic space-time unit for speed (m/s). We prove that the velocity is a physical equivalence of geometric idea of radius. Category: Mathematical Physics [153] viXra:1305.0048 [pdf] submitted on 2013-05-08 06:10:03 ### The Period of a Pendulum Authors: Andrej Rehak Comments: 8 Pages. Geometric demonstration located in v, t diagram explains the nature of the period of a pendulum, i.e. the universal connection of time with velocity (radius) and acceleration. Conceptual nature of the principles proof points to its universal validity. In other words, if it is valid for a circle, it is valid. Through the geometry of free fall we describe physical nature of irrational numbers π and √2. We demonstrate physical matrix of scale √2nπ. Through the relationship between the variables of space, time and velocity, using the principle of the pendulum, we illustrate the foundation of the law of conservation of energy. Analyzing its motion we point to nature of distortion of Euclidean geometry. Category: Mathematical Physics [152] viXra:1305.0033 [pdf] submitted on 2013-05-05 00:05:04 ### Critical Analysis of the Mathematical Formalism of Theoretical Physics. I. Foundations of Differential and Integral Calculus Authors: Temur Z. Kalanov Comments: 8 Pages. Critical analysis of the generally accepted (standard) foundations of differential and integral calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that the generally accepted foundations are based on the logically and practically erroneous concepts “infinitesimal quantity (uninterruptedly diminishing quantity)”, “derivative”, “derivative as function of variable quantity” and, consequently, represent incorrect basis of mathematics and of theoretical physics. Category: Mathematical Physics [151] viXra:1305.0032 [pdf] submitted on 2013-05-05 00:09:30 ### Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Pythagorean Theorem Authors: Temur Z. Kalanov Comments: 10 Pages. The critical analysis of the Pythagorean theorem and of the problem of irrational numbers is proposed. Methodological basis for the analysis is the unity of formal logic and of rational dialectics. It is shown that: 1) the Pythagorean theorem represents a conventional (conditional) theoretical proposition because, in some cases, the theorem contradicts the formal-logical laws and leads to the appearance of irrational numbers; 2) the standard theoretical proposition on the existence of incommensurable segments is a mathematical fiction, a consequence of violation of the two formal-logical laws: the law of identity of geometrical forms and the law of lack of contradiction of geometrical forms; 3) the concept of irrational numbers is the result of violation of the dialectical unity of the qualitative aspect (i.e. form) and quantitative aspect (i.e. content: length, area) of geometric objects. Irrational numbers represent a calculation process and, therefore, do not exist on the number scale. There are only rational numbers. Category: Mathematical Physics [150] viXra:1305.0031 [pdf] submitted on 2013-05-05 00:13:38 ### On the Natural-Science Foundations of Geometry Authors: Temur Z. Kalanov Comments: 11 Pages. The work is devoted to solution of an actual problem – the problem of relation between geometry and natural sciences. Methodological basis of the method of attack is the unity of formal logic and of rational dialectics. It is shown within the framework of this basis that geometry represents field of natural sciences. Definitions of the basic concepts "point", "line", "straight line", "surface", "plane surface", and “triangle” of the elementary (Euclidean) geometry are formulated. The natural-scientific proof of the parallel axiom (Euclid’s fifth postulate), classification of triangles on the basis of a qualitative (essential) sign, and also material interpretation of Euclid’s, Lobachevski’s, and Riemann’s geometries are proposed. Category: Mathematical Physics [149] viXra:1305.0010 [pdf] submitted on 2013-05-01 19:19:35 ### "Hidden" Parameters Describing Internal Motion Within Extended Particle Elements Authors: R.L. Amoroso, L.H. Kauffman, E.A. Rauscher, P. Rowlands J-P Vigier Comments: 27 Pages. Recent attempts to consider isolated particles and real constitutive wave elements as localized, extended spacetime structures (i.e., moving within time-like hypertubes or branes are developed within a causal extension of the Feynman-Gell-Mann electron model. These extended structures contain real internal motions, (i.e., internal hidden parameters) locally correlated with the "hidden parameters" describing the local collective motions of the corresponding pilot-waves. Recent experimental evidence is briefly discussed. Category: Mathematical Physics [148] viXra:1305.0009 [pdf] submitted on 2013-05-01 19:35:02 ### Empirical Protocol for Measuring Virtual Tachyon / Tardon Interactions in a Dirac Vacuum Authors: Richard L. Amoroso, Elizabeth A. Rauscher Comments: 18 Pages. Here we present discussion for the utility of resonant interference in Calabi-Yau mirror symmetry as a putative empirical test of the existence of virtual tachyon / tardon interactions in a covariant Dirac polarized vacuum Category: Mathematical Physics [147] viXra:1304.0163 [pdf] submitted on 2013-04-29 14:51:49 ### P vs. NP and Riemann Hypothesis Solution (Revised) Authors: Andrew Nassif Comments: 2 Pages. This problem has been solved by me over a year ago, and published. Today I am posting a more complex and complicated version, yet put in Layman terms. I hope by doing this it will garner the attention of Clay Mathematics as well as show logical input on its mathematical endeavors. Category: Mathematical Physics [146] viXra:1304.0152 [pdf] submitted on 2013-04-26 14:13:20 ### Some Thoughts on Special Relativity Authors: Jeremy Dunning-Davies. Comments: 6 Pages. Here an introduction to Wesley’s neomechanics is presented. It is shown to produce some of the same results as Special Relativity but without both the mathematical and philosophical basis of that subject. As with other work in which results associated with General Relativity are obtained without recourse to the fundamental bases of that subject, so here too the pre-eminent place afforded Special Relativity in modern science is called into question. The opportunity is taken to extend Wesley’s ideas to the case where the mass of the body when at rest is not constant. Category: Mathematical Physics [145] viXra:1304.0106 [pdf] submitted on 2013-04-21 22:33:04 ### The Generalizations of the First Noether Theorem. Authors: Vyacheslav Telnin Comments: 6 Pages. This paper deals with the generalizations of the First Noether theorem. It takes into account not only the first derivatives of the fields by the coordinates in Lagrangian, but also the second. And this theorem is generalized on the curved spaces. And also it's generalized on asymmetric metric tensors. Category: Mathematical Physics [144] viXra:1304.0051 [pdf] submitted on 2013-04-10 15:49:46 ### Calculate Universe 2 Authors: Branko Zivlak Comments: 4 Pages. 1 Table This article is about relations between fundamental physical constants. Category: Mathematical Physics [143] viXra:1304.0010 [pdf] submitted on 2013-04-03 02:57:32 ### New Cosmological Hypothesis Match Observations by New Dark Energy-Time Applied to Dark Matter for the Existence of a Double Torus Universe. Authors: Dan Visser Comments: 13 Pages. The Double Torus hypothesis stands for a new architecture for the Universe, which means another dark energy as dynamics and no Big Bang. New dark energy-time is applied to dark matter. It is ‘extra time’ originated from a time-scale smaller than the Planck-time. The implication is a Double Torus of the dark energy-time enclosing and intertwining an inner dark matter torus. It might sound controversial, but a new ‘dark energy-force formula’ in the hypothesis enables to make calculations, which match the observed dark matter-accelerations in galaxies and the Pioneer satellites 1 and 2. This new formula relates to Newton quantum-gravity force and dark matter-force both implemented in one product. The dark matter force could be gravitational (+) and anti-gravitational (-). The formula also sets the laboratory acceleration-limit for Newton-gravity, 5 x 10^-14 m/s^2, to a theoretically lower value of 2.8659 x10^-14 m/s^2. There is no other formula, or theory, to do that. The hypothesis-dynamic is developed by DAN Visser, Almere, the Netherlands, an independent cosmologist. Additional evidence comes from astronomical observations: Such as the asymmetry in the Cosmic Microwave Background (CMB) and a ‘Dark Flow’, which pleads for a cyclic-curved torus-shape of the universe. This also could explain the observed ‘cold spot’ in the CMB by to imagine dark matter is disappearing in the far end of the curved torus-shape. Hence, also a ‘hot spot’ in the CMB should exist. This should correspond to the approaching dark flow coming from the other curved torus far-end. Category: Mathematical Physics [142] viXra:1303.0209 [pdf] submitted on 2013-03-28 04:10:29 ### Calculate Universe 1 Authors: Branko Zivlak Comments: 8 Pages. 11 relations, 1 figure This paper is about relations between the mass of universe and mass of some elementary particles. Important is only the diagram in Figure 1, which you can understand in any language if you know the language of mathematics and physics. Category: Mathematical Physics [141] viXra:1303.0167 [pdf] submitted on 2013-03-22 15:28:17 ### Quantum Perturbation Theory in Stock Trading Authors: Yingqiong Gu Comments: 3 Pages. It is a hot topic about how to trade a stock/group of stocks in a non-news day. Author tries to design safe, profitable automated stock trading agents using evolutionary algorithms[2]. In quantum mechanics, perturbation theory[4] is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and Eigen states) can, from considerations of continuity, be expressed as 'corrections' to those of the simple system. These corrections, being 'small' compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In Stock Market, for a non-news trading day, stock prices will mostly depend on the initial price at given time, and bid-ask spread. Category: Mathematical Physics [140] viXra:1303.0152 [pdf] submitted on 2013-03-21 04:22:55 ### Quantization of Points and Energy on Dipole Vectors and on Spin Authors: Markos Georgallides Comments: 22 Pages. Point , which is nothing and has not any Position , may be anywhere in Space , therefore the Primary point A , being nothing also in no Space , is the only Point and nowhere i.e. Primary Point is the only Space and from this all the others , so then this primary point A to exist at a second point B somewhere else , point A must move at point B , where then A ≡ B . Presupposition for Unit AB = ds means an Impulse P removes point A to B and since in each Restrained System (S) the Work done ( W ) by Impulse P on a Virtual displacement ( ds > 0) is zero , and then W = ∫ A-B [ P.ds ] = 0 → [ ds .( PA+P B ) = 0 ] and Point A is in Space [S] and point B is in Anti-Space [aS] which are self created and are Property and Essence from the same Unit AB, therefore these are also a Restrained System(S). Since the only two Elements of Universe are ds and P and are connected by Virtual Work Principle and since Unit AB = ds is a quantized dimension,so Impulse is also quantized.Quantization of Points becomes through Vector Unit dš = ÃB which is the first dimensional Unit [ Zenon Paradox 13]and this because Vector has Position and Direction .Quantization of Energy is done in bound States ( loops ) because bound states [11-16] withhold diffusion ( flow ) .The two fundamental dimensions ( quanta of Points (ds) and quanta of Energy (dP) , are connected on Primary dipole and on any dipole AiBi . [PNS] is self created and consists a space (x,y,z) Scalar field Sp which constructs a vector field Sa = Ñ.Sp . The position of dipole in the equilibrium Space Anti-Space keeps charge = momentum ( Energy→ the difference of primary Work which is bounded on edge points ) and Angular momentum ( Spin → angular momentum is the intrinsic twist of Space , Anti-Space ) which inextricably unify geometry of Space and motion . On any Dipole AB of [PNS] with dš = ( [J,E,B] and content © ) ,where motion occurs only as (+) → (-) Source (+) → Drain (-) ,Conservation State of Work exists on magnitude |dš| = √ J² + E² + B² of vector ř ( J,E, B ) ( which is the Sub-Space of AB ) and on the two perpendicular Fields Ê = Ñx J , B = Ñx Ê ( which are the two diffused equilibrium Spaces and Anti -Spaces of AB , Ñx Ê = 0 , Ñ x B = 0 ) . Since,Source (+) →Drain (-) , in [PNS] is the equilibrium of Space [S] and Anti-Space [aS] , therefore the only magnitude for motion is J , while E and B are produced , as this happens in the Magnetic fields where lines ( loops ) close in themselves and this because no sources exist ↑→ ® for magnetic fields B and so the two models [ the B-field Pole and Amperian loop ] are explained. Solving equation ds.( PA+ PB ) = 0 then ds.PA = - ds.PB and since , dš , is constant for Primary dipole , so the Work conserved on every point in Spaces is constant and equal to [ dš .Impulse P = constant ] . i.e. The applied Work [ Wi → 1 → ∞ ] = ( charge ± P ) on every point of the three , Spaces , Anti–Spaces and Sub–Spaces , which coexist in [PNS] is conserved on Points , meaning that every point of [PNS] consist the fundamental ± Scalar Field with variables the Constraint Forces and Angular momentum [ Spin = Wij →1→ ∞] , and is conserved always in [PS] , [ PaS] or, The two elements [Vector dš = AB (matter) , ± dP ,Work p , Spin = momentum ] of the Infinite Dipole Vectors [AB] = [ ĀB – PA , PB ] build Particles with Identity Card , the Constant Product → dš . p = constant …(k) ← so , the Possible Energy Range (m) Scales , of the two fundamental and quantized dimensions [ ds , - P , + P ] are the three Layers , (- i ) ↔ (0 ) = - P → [ ds , - P , ] → Black Holes Scale = k 1 → ds 1. dP 1 = k 1 (-i ) ↔ (+i) = 7 P → [ ds , - P , + P ] → Planck Scale Matter = k 2 → ds 2. dP 2 = k 2 (+i ) ↔ (0 ) = + P → [ ds , + P , ] → Dark Matter Scale = k 3 → ds 3. dP 3 = k 3 For any single particle of wavelength λ = ds and dP = Charge → momentum ( p ) exists : dš.dP = λ . p = constant = h → is the reduced Planck constant in Planck Scale Matter . For ds near zero and P = ∞ , is needed a new Type of Light to see what is happening below Planck length Level , Layer 10¯35 m .Primary Vector monad and Vector monads are , either Static ( equilibrium ) or Dynamic ( are moving ) , and keep their Conservation of State ( The Total work is equal to zero ) in the three equilibrium and perpendicular monads [ J , E , B ] which are in Subspaces , Spaces , Anti-Spaces ( and thus , not turn to non-existence ) and are interchanged by Pythagoras conservation law of Volume. The geometric concepts of [PNS] as two dimensional field is that , the third dimension represents the amplitude of the potential S . Considering x-y Plane as the base and the vertical (z) is the potential S , then contours of constant potential altitudes of [PNS] are Cylindrical or Solenoidal and for Position 0 ( which is the equilibrium Horizon of Space and anti-Space) is Sphere , therefore [PNS] with the included Space [S] and Anti-Space [aS] may be Sphere and Solenoidal simultaneously. Category: Mathematical Physics [139] viXra:1303.0134 [pdf] submitted on 2013-03-18 12:13:37 ### New Gravity-Physics and Mathematics Calculate Dark Matter-Accelerations and Prove a Recalculated Double Torus Universe. Authors: Dan Visser Comments: 8 Pages. New gravity-physics and -mathematics produce calculations of dark matter-accelerations and prove we live in a Double Torus Universe, which recalculates Quantum Gravity in vacuum. The set of equations to do that, prove the (new) dark energy force formula in the Double Torus Hypothesis is correct. The formula has been developed step by step and described in my Vixra-papers. It is an alternative for still unknown dark energy used in Big Bang cosmology. It is a tool for the awareness that the universe is not a universe that started with a Big Bang. The universe is a Double Torus, which uses + and - dark matter force to change quantum-gravity. The formula shows clearly a new view on the universe to be necessary. This paper shows theoretical predictions through calculations that match the experimental values of dark matter-accelerations in galaxies, the Pioneer-satellites (1 and 2) and produces the lowest limit for Newton-gravitational force. This Newton limit-acceleration matches the laboratory-experiments and moreover sets the limit to a slightly theoretical lower limit-acceleration of 2.8659 x 10^-14 [m/s2]. There is no other theory that predicts this limit. The conditions of the formula show, that quantum-gravity is related to a dark matter force. Dark energy-time from below the Planck-time is applied to the dark matter. Category: Mathematical Physics [138] viXra:1303.0090 [pdf] submitted on 2013-03-12 08:23:19 ### Gravitational Forces Are not Conservative Authors: Florentino Muñiz Ania Comments: 2 Pages. Spanish. This article shows how the gravitational force is conservative only in ideal models of small size. It is shown as strictly mathematical generally is not conservative. From it you can get energy by asymmetric systems. Spanish: En este artículo se muestra como la fuerza gravitatoria sólo es conservativa en modelos ideales de pequeño tamaño. Se demuestra con rigor matemático como, en general, no es conservativa. De ella se puede obtener energía mediante sistemas asimétricos. Category: Mathematical Physics [137] viXra:1303.0008 [pdf] submitted on 2013-03-02 12:49:28 ### On the Söllinger, Weizsäcker Relations and Bošković’s Curve of Force (English Version) Authors: Branko Zivlak Comments: 7 Pages. 15 relations, 1 table, 1 figure Abstract. In "The Code of Nature" [1] Helmut Söllinger gives his and Carl Friedrich von Weizsacker's (1912-2007) relationships between the fundamental physical constants. The first section examines Sollinger's the relationship between the masses of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory. Category: Mathematical Physics [136] viXra:1303.0003 [pdf] submitted on 2013-03-01 15:56:25 ### Exact Solution of the Reduced Version of Pwe (Paraxial Wave Equation) in Bipolar Coordinate System Authors: Sergey V. Ershkov Comments: 5 Pages. Keywords: Helmholtz equation, PWE, paraxial approximation, bipolar coordinates A new type of exact solution of the reduced 3 dimensional spatial PWE (paraxial wave equation) for the case of bipolar coordinates is presented here. First, we consider a self-similar representation of the solution in a bipolar coordinate system, the second we additionally reduce PWE under a proper paraxial assumption. Analyzing the structure of the final equation, we obtain the simple exact solution which is proved to satisfy to such an equation in bipolar coordinates. Besides, there is a limitation of the components of self-similar solution of a new type. Category: Mathematical Physics [135] viXra:1302.0154 [pdf] submitted on 2013-02-24 10:16:15 ### On the Söllinger, Weizsäcker Relations and Bošković’s Curve of Force Authors: Branko Zivlak Comments: pages 7+7, language Serbian+Italian, 15 formulas, 1Table, 1 picture Abstract. In "The Code of Nature" [1] Helmut Söllinger gives his and Carl Friedrich von Weizsäcker's (1912-2007) the relationship between the fundamental physical constants. The first section examines the relationship between the mass of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory. This version is written, in the lenguages, Bošković’s father and mother. Category: Mathematical Physics [134] viXra:1302.0132 [pdf] submitted on 2013-02-19 21:26:30 ### On the Orbits of the Magnetized Kepler Problems in Dimension$2k+1$Authors: Zhanqiang Bai, Guowu Meng, Erxiao Wang Comments: 13 Pages. It is demonstrated that, for the recently introduced classical magnetized Kepler problems in dimension$2k+1$, the non-colliding orbits in the external configuration space"$\mathbb R^{2k+1}\setminus\{\mathbf 0\}$are all conics, moreover, a conic orbit is an ellipse, a parabola, and a branch of a hyperbola according as the total energy is negative, zero, and positive. It is also demonstrated that the Lie group${\mr {SO}}^+(1,2k+1)\times {\bb R}_+$acts transitively on both the set of oriented elliptic orbits and the set of oriented parabolic orbits. Category: Mathematical Physics [133] viXra:1302.0112 [pdf] submitted on 2013-02-17 02:09:57 ### Robert Kiehn's Ideas About Falaco Solitons and Generation of Turbulent Wake from TGD Perspective Authors: M. Pitkanen Comments: 7 Pages. I have been reading two highly interesting articles by Robert Kiehn. There are very many contacts on TGD inspired vision and its open interpretational problems. The notion of Falaco soliton has surprisingly close resemblance with K\"ahler magnetic flux tubes defining fundamental structures in TGD Universe. Fermionic strings are also fundamental structures of TGD accompanying magnetic flux tubes and this supports the vision that these string like objects could allow reduction of various condensed matter phenomena such as sound waves -usually regarded as emergent phenomena allowing only highly phenomenological description - to the fundamental microscopic level in TGD framework. This can be seen as the basic outcome of this article. Kiehn proposed a new description for the generation of various instability patterns of hydrodynamics flows (Kelvin-Helmholtz and Rayleigh-Taylor instabilities) in terms of hyperbolic dynamics so that a connection with wave phenomena like interference and diffraction would emerge. The role of characteristic surfaces as surfaces of tangential and also normal discontinuities is central for the approach. In TGD framework the characteristic surfaces have as analogs light-like wormhole throats at which the signature of the induced 4-metric changes and these surfaces indeed define boundaries of two phases and of material objects in general. This inspires a more detailed comparison of Kiehn's approach with TGD. Category: Mathematical Physics [132] viXra:1302.0110 [pdf] submitted on 2013-02-17 02:17:26 ### What P-Adic Icosahedron Could Mean? and What About P-Adic Manifold? Authors: M. Pitkanen Comments: 40 Pages. The original focus of this article was p-adic icosahedron. The discussion of attempt to define this notion however leads to the challenge of defining the concept of p-adic sphere, and more generally, that of p-adic manifold, and this problem soon became the main target of attention since it is one of the key challenges of also TGD. There exists two basic philosophies concerning the construction of both real and p-adic manifolds: algebraic and topological approach. Also in TGD these approaches have been competing: algebraic approach relates real and p-adic space-time points by identifying the common rationals. Finite pinary cutoff is however required to achieve continuity and has interpretation in terms of finite measurement resolution. Canonical identification maps p-adics to reals and vice versa in a continuous manner but is not consistent with p-adic analyticity nor field equations unless one poses a pinary cutoff. It seems that pinary cutoff reflecting the notion of finite measurement resolution is necessary in both approaches. This represents a new notion from the point of view of mathematics. a) One can try to generalize the theory of real manifolds to p-adic context. The basic problem is that p-adic balls are either disjoint or nested so that the usual construction by gluing partially overlapping spheres fails. This leads to the notion of Berkovich disk obtained as a completion of p-adic disk having path connected topology (non-ultrametric) and containing p-adic disk as a dense subset. This plus the complexity of the construction is heavy price to be paid for path-connectedness. A related notion is Bruhat-Tits tree defining kind of skeleton making p-adic manifold path connected. The notion makes sense for the p-adic counterparts of projective spaces, which suggests that p-adic projective spaces (S2 and CP2 in TGD framework) are physically very special. b) Second approach is algebraic and restricts the consideration to algebraic varieties for which also topological invariants have algebraic counterparts. This approach looks very natural in TGD framework - at least for imbedding space. Preferred extremals of Kähler action can be characterized purely algebraically - even in a manner independent of the action principle - so that they might make sense also p-adically. Number theoretical universality is central element of TGD. Physical considerations force to generalize the number concept by gluing reals and various p-adic number fields along rationals and possible common algebraic numbers. This idea makes sense also at the level of space-time and of "world of classical worlds" (WCW). Algebraic continuation between different number fields is the key notion. Algebraic continuation between real and p-adic sectors takes place along their intersection which at the level of WCW correspond to surfaces allowing interpretation both as real and p-adic surfaces for some value(s) of prime p. The algebraic continuation from the intersection of real and p-adic WCWs is not possible for all p-adic number fields. For instance, real integrals as functions of parameters need not make sense for all p-adic number fields. This apparent mathematical weakness can be however turned to physical strength: real space-time surfaces assignable to elementary particles can correspond only some particular p-adic primes. This would explain why elementary particles are characterized by preferred p-adic primes. The p-adic prime determining the mass scale of the elementary particle could be fixed number theoretically rather than by some dynamical principle formulated in real context (number theoretic anatomy of rational number does not depend smoothly on its real magnitude!). Although Berkovich construction of p-adic disk does not look promising in TGD framework, it suggests that the difficulty posed by the total disconnectedness of p-adic topology is real. TGD in turn suggests that the difficulty could be overcome without the completion to a non-ultrametric topology. Two approaches emerge, which ought to be equivalent. a) The TGD inspired solution to the construction of path connected effective p-adic topology is based on the notion of canonical identification mapping reals to p-adics and vice versa in a continuous manner. The trivial but striking observation was that canonical identification satisfies triangle inequality and thus defines an Archimedean norm allowing to induce real topology to p-adic context. Canonical identification with finite measurement resolution defines chart maps from p-adics to reals and vice versa and preferred extremal property allows to complete the discrete image to hopefully space-time surface unique within finite measurement resolution so that topological and algebraic approach are combined. Finite resolution would become part of the manifold theory. p-Adic manifold theory would also have interpretation in terms of cognitive representations as maps between realities and p-adicities. b) One can ask whether the physical content of path connectedness could be also formulated as a quantum physical rather than primarily topological notion, and could boil down to the non-triviality of correlation functions for second quantized induced spinor fields essential for the formulation of WCW spinor structure. Fermion fields and their n-point functions could become part of a number theoretically universal definition of manifold in accordance with the TGD inspired vision that WCW geometry - and perhaps even space-time geometry - allow a formulation in terms of fermions. This option is a mere conjecture whereas the first one is on rigorous basis. Category: Mathematical Physics [131] viXra:1302.0059 [pdf] submitted on 2013-02-09 17:05:12 ### Exact Solution of Helmholtz Equation for the Case of Non-Paraxial Gaussian Beams Authors: Sergey V. Ershkov Comments: 7 Pages. Keywords: Helmholtz equation, paraxial approximation, Gaussian beam A new type of exact solution of the full 3 dimensional spatial Helmholtz equation for the case of non-paraxial Gaussian beams is presented here. We consider appropriate representation of the solution for Gaussian beams in a spherical coordinate system, then implement it in the full 3 dimensional Helmholtz Eq. Analyzing the structure of the final equation, we obtain one of the simple exact solutions which is proved to satisfy to such an equation for Gaussian beams. Also the proper examples of implementing of the paraxial approximation for Gaussian beam could easily be obtained for a new type of exact solution of Helmholtz equation. Category: Mathematical Physics [130] viXra:1302.0020 [pdf] submitted on 2013-02-04 05:20:58 ### New Periodic Table of Elements 1-92 Authors: Chun-Xuan Jiang Comments: 13 Pages. We make the new periodic table of elements 1-92 Category: Mathematical Physics [129] viXra:1301.0158 [pdf] submitted on 2013-01-26 07:14:47 ### Double Torus Hypothesis For The Universe In Perspective. Authors: Dan Visser Comments: 6 Pages. The Double Torus, a new hypothesis for the universe, has been put in perspective and related to other theories and hypotheses. This ‘paper’ could be used by the press. The Double Torus hypothesis is theoretically and mathematically-physics-based. Examples of evidence might be available already. Category: Mathematical Physics [128] viXra:1301.0139 [pdf] submitted on 2013-01-22 05:11:06 ### Fine Structure Constant And Relations Between Dimensionless Constants Authors: Branko Zivlak Comments: 9 Pages. 25 relations Abstract. The aim of this article is to determine dimensionless physical constants through mathematical constants and other dimensionless physical constants. Category: Mathematical Physics [127] viXra:1301.0110 [pdf] submitted on 2013-01-18 10:51:52 ### The Code of Nature Authors: Helmut Söllinger Comments: Pages. e-mail adress of the author: 64.soellinger@aon.at The scope of the work described in this paper is a systematic investigation as to whether or not the mass of the proton and the electron can be represented by other fundamental constants. The author arrives at the conclusion that the mass of the proton and the electron can be expressed by a combination of five constants that occur in nature; namely, e, εo, h, c, G, plus a time-variable parameter. In this context, the author has studied more than 37,000 options using electronic support and powering the fundamental constants with natural numbers only. The simplest and most convincing formula the author has found is: me3 x mp3 = (e2 h/4p εo c G R)2 This equation results in the exact value of the mass of the proton and the electron. The beauty and simplicity of this equation give rise to the following question: What, if not this formula, is able to represent the mass of the two most important particles? The author’s conclusion is that either the electron and proton masses themselves are natural constants that cannot be represented by other constants of nature, or that – as shown in this paper – they can be perfectly well represented by five other fundamental constants, in addition to a time-variable parameter. Category: Mathematical Physics [126] viXra:1301.0082 [pdf] submitted on 2013-01-14 09:26:09 ### Pauli Matrices and Dirac Matrices in Geometric Algebra of Quarks Authors: Martin Erik Horn Comments: 8 Pages. It is a historical accident that we describe Pauli matrices as (2 x 2) matrices and Dirac matrices as (4 x 4) matrices. As it will be shown in this paper we can use (3 x 3) matrices or (9 x 9) matrices for this purpose as well. This hopefully will enable us one day to construct a unified geometric algebra picture which includes Gell-Mann matrices in an appropriate manner. Category: Mathematical Physics [125] viXra:1301.0078 [pdf] submitted on 2013-01-14 04:30:47 ### Riemann Zeros Quantum Chaos Functional Determinants and Trace Formulae Authors: Jose Javier garcia Moreta Comments: 10 Pages. ABSTRACT: We study the relation between the Guzwiller Trace for a dynamical system and the Riemann-Weil trace formula for the Riemann zeros, using the Bohr-Sommerfeld quantization condition and the fractional calculus we obtain a method to define implicitly a potential , we apply this method to define a Hamiltonian whose energies are the square of the Riemann zeros (imaginary part) , also we show that for big ‘x’ the potential is very close to an exponential function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, WKB semiclassical approximation, Gutzwiller trace formula, Bohr-Sommerfeld quantization,exponential potential. Category: Mathematical Physics [124] viXra:1301.0076 [pdf] submitted on 2013-01-14 03:05:17 ### Universal Principles of Perfect Chaos Authors: S. Kamenshchikov Comments: 12 Pages. contact e-mail: kamphys@gmail.com. Author is looking for postdoc position. The purpose of this work was to introduce strict, comprehensive definition of perfect chaos, to find out its basic properties in terms of phase transitions and give connections for uncertainties, lying in base of perfect chaos concept. Concept of perfect chaos as undetermined description was introduced basing on two formalized necessary and sufficient conditions: finite phase space resolution and instability of phase space trajectories. Properties of Kolmogorov system, including phase mixing, turned out to be consequences of chaotic state but not its comprehensive and sufficient conditions. Description relativity was defined as mandatory property of perfect chaos – the same areas of phase space may show regular and chaotic properties depending on description space - time accuracy. Herewith evolution of physical system in given generalized phase space can be represented by consequence of regular states and intermediate transitions. For chaotic state with uniform diffusion it was found out that nonlinear dispersion law is mandatory property. One in its turn necessarily leads to space – time instability of probability density and appearance of probability cavities in phase space - phase space attractors where particles density grows up. Case of chaotic state with fixed boundary and diffusion was considered. It turned out that Fourier decomposition allows to derive relations between coordinate – momentum and time - energy definition uncertainties. It was shown that chaos diffusion factor is the only parameter, limiting product of corresponding uncertainties. Category: Mathematical Physics [123] viXra:1301.0065 [pdf] submitted on 2013-01-12 06:19:36 ### The Mathematics Behind a New Dark Energy Force Related to Gravity and Anti-Gravity by Negative Mass Through a Dark Matter Force in Another Cosmology Named the ‘Double Torus Hypothesis’. Authors: Dan Visser Comments: 6 Pages. I present the mathematics of a new ‘Dark Energy Force’ in replay with my former ‘papers’. The reason is particles that feel small gravity, and anti-particles that maybe feel anti-gravity, and the particle-cosmology I use, with negative mass, never have been exposed experimentally to General Relativity, in order to prove that a real anti-gravity exists. However, the mathematics in my frame work theoretically prove, that only dark matter-mass could have negative mass. This is in contradiction with a new theory of Entropy-Gravity, which theoretically proved gravity is not fundamental, but caused by entropy. My framework is also in contradiction with the Elementary Process theory, which also predicts gravity is not fundamental, but will cause anti-gravity by anti-matter with positive mass. Both these frameworks consider their theory in a Big Bang cosmology. So I replayed my mathematics to highlight again, that a new dark matter-force, embedded in a new cosmology named Double Torus Universe, is the only one that could cause real anti-gravity. My framework is independently developed from institutions and based on two extra-time arrows from below the Planck-scale. Additionally, and for the first time, I used a Feynman-diagram to express this dark matter-force in order to illustrate the existence of real anti-gravity theoretically. Category: Mathematical Physics [122] viXra:1301.0040 [pdf] submitted on 2013-01-08 00:47:32 ### Basic Blueprint for Making This Universe Authors: Rodney Bartlett Comments: 5 Pages. Over 30 years of thinking, plus the insights and mistakes in my viXra articles, reveal the basic blueprint for making this universe. This article continues from where previous articles finished (throughout, I’ve provided links to prior contributions). I begin with explanation of quantum particles, forces and spin in terms of positioning of Mobius loops and the flow of the loops’ binary digits accounting for the interference between gravitation and electromagnetism – together with a link supporting the idea of an electronics-based universe and addressing the topics of hidden variables, quantum fluctuation and virtual particles. The next link speaks of the inverse-square law and infinity. I give Dr. Carl Sagan credit where credit is due - and conclude that, being years ahead of his time, he saw a fundamental truth about the universe’s nature which he decided to include in his book “Contact”. Then time travel into the past (via matrices and the figure-8 Klein bottle), before putting it all together and indulging in some speculation about how to make this universe we’re living in. I think it’s too simple to say “We don’t need to make the universe … it’s already here”. That statement relies on time being strictly linear (like a straight line, rectilinear). We know it isn’t, but is curvilinear and warped. It’s better to say the universe is here now because our future civilization did the following in the past – Category: Mathematical Physics [121] viXra:1212.0167 [pdf] submitted on 2012-12-31 09:45:17 ### Nonperturbational "Continued-Fraction" Spin-offs of Quantum Theory's Standard Perturbation Methods Authors: Steven Kenneth Kauffmann Comments: 8 Pages. The inherently homogeneous stationary-state and time-dependent Schroedinger equations are often recast into inhomogeneous form in order to resolve their solution nonuniqueness. The inhomogeneous term can impose an initial condition or, for scattering, the preferred permitted asymptotic behavior. For bound states it provides sufficient focus to exclude all but one of the homogeneous version's solutions. Because of their unique solutions, such inhomogeneous versions of Schroedinger equations have long been the indispensable basis for a solution scheme of successive perturbational corrections which are anchored by their inhomogeneous term. Here it is noted that every such perturbational solution scheme for an inhomogeneous linear vector equation spins off a nonperturbational continued-fraction scheme. Unlike its representation-independent antecedent, the spin-off scheme only works in representations where all components of the equation's inhomogeneous term are nonzero. But that requirement seems to confer theoretical physics robustness heretofore unknown: for quantum fields the order of the perturbation places a bound on unperturbed particle number, the spin-off scheme contrariwise has only basis elements of unbounded unperturbed particle number. It furthermore is difficult to visualize such a continued-fraction spin-off scheme generating infinities, since its successive iterations always go into denominators. Category: Mathematical Physics [120] viXra:1212.0164 [pdf] submitted on 2012-12-31 04:19:39 ### Discrete Structure of Spacetime Authors: Nicola D'Alfonso Comments: 4 Pages. In this paper, I introduce a particular discrete spacetime that should be seriously considered as part of physics because it allows to explain the characteristics of the motion properly, contrary to what happens with the continuous spacetime of the common conception. Category: Mathematical Physics [119] viXra:1212.0159 [pdf] submitted on 2012-12-29 08:34:36 ### The Force of Gravity Belongs to Another Cosmology. Authors: Dan Visser Comments: 4 Pages. This article summarizes theoretical based evidence related to practice for the prediction the universe is not originated from a Big Bang. Instead cosmology could be based on a Double Torus Universe, as is published in my papers in the Vixra-archive. In a few website-articles I also express my vision on the revision of physics and cosmology within this framework. This paper in particular highlights how Gravity could violate General Relativity by a (new) dark energy force in the new Cosmology. This framework contains the connection of the Newton-Gravity force for tiny matter-particles to a dark matter force, producing “+” and “–“ mass-generation, both at scales of about 10^-22 meter. This can cause repulsive gravity in nature. This can open-up a new energy-source for travelling through space by non-relativistic scaling. Category: Mathematical Physics [118] viXra:1212.0147 [pdf] submitted on 2012-12-25 15:49:22 ### Mathematical Theory of Magnetic Field Authors: Zafar Turakulov Comments: 9 Pages. no comments The study of magnetic fields produced by steady currents is a full-valued physical theory which like any other physical theory employs a certain mathematics. This theory has two limiting cases in which source of the field is confined on a surface or a curve. It turns out that mathematical methods to be used in these cases are completely different and differ from from that of the main of the main part of this theory, so, magnetostatics actually consists of three distinct theories. In this work, these three theories are discussed with special attention to the case current carried by a curve. In this case the source serves as a model of thin wire carrying direct current, therefore this theory can be termed magnetostatics of thin wires. The only mathematical method used in this theory till now, is the method of Green's functions. Critical analysis of this method completed in this work, shows that application of this method to the equation for vector potential of a given current density has no foundation and application of this method yields erroneous results Category: Mathematical Physics [117] viXra:1212.0128 [pdf] submitted on 2012-12-21 00:50:41 ### Symmetry-Nondependent Self-Gravitational Upper Bound on Static Local Energy from Use of a Nonperturbative Iteration Method for Lippmann-Schwinger Equations Authors: Steven Kenneth Kauffmann Comments: 5 Pages. It has recently been shown that self-gravitation reduces static spherically-symmetric cumulative energy distributions below the value of their radii times the "Planck force", which is the inverse of G times the fourth power of c. In this article quantitative treatment of self-gravitation is extended to any static energy density that is nonnegative, smooth and globally integrable. The resulting dimensionless local gravitational energy-reduction factor (namely the inverse of the local gravitational time-dilation factor) is shown to satisfy the zero-momentum nonrelativistic Lippmann-Schwinger quantum scattering equation for a repulsive potential which is proportional (with a known coefficient) to that static energy density. Standard perturbative Born-type iteration of Lippmann-Schwinger equations can diverge for sufficiently strong potentials, which in the gravitational case correspond to sufficiently large static energy densities. We have been able, however, to devise an alternate, completely nonperturbative iteration method for Lippmann-Schwinger equations in coordinate representation. Every one of this nonperturbative method's successive approximations to the local gravitational energy-reduction factor turns out to be positive and less than or equal to unity. In consequence, the self-gravitationally corrected static energy contained in any sphere is bounded by that sphere's diameter times the "Planck force". Category: Mathematical Physics [116] viXra:1212.0068 [pdf] submitted on 2012-12-10 05:06:49 ### Mathematical Derivation of the Fine Structure Constant from Fundamental Properties of Natural Numbers Authors: Otto G. Piringer Comments: 12 Pages Recent publications discussed a possible change with time of Sommerfeld's fine structure constant alpha, in which several of the fundamental constants of Nature are combined. The problem of a changing nature of alpha raises the question whether its value is ultimately a result of chance or reveals an objective law of nature. If the value of alpha is independent of human reason, a derivation of it may be possible from basic numbers, like e and pi, which appear in the logical development of mathematics[1]. In the following investigation a pure mathematical derivation of the fine structure constant is described, starting from a fundamental property of natural numbers. The constant alpha results as a limit value in an algorithm with exponential structures. Category: Mathematical Physics [115] viXra:1211.0143 [pdf] submitted on 2012-11-25 05:08:12 ### Riemann Zeros and an Exponential Potential Authors: Jose Javier Garcia Moreta Comments: 5 Pages. ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We study also how we could use the WKB method to recover the potential from the Eigenvalue Staircase for the Riemann Category: Mathematical Physics [114] viXra:1211.0140 [pdf] submitted on 2012-11-24 02:12:29 ### The Poisson Realization of$\mathfrak{so}(2, 2k+2)$on Magnetic Leave Authors: Guowu Meng Comments: 13 Pages. Let${\mathbb R}^{2k+1}_*={\mathbb R}^{2k+1}\setminus\{\vec 0\}$($k\ge 1$) and$\pi$:${\mathbb R}^{2k+1}_*\to \mathrm{S}^{2k}$be the map sending$\vec r\in {\mathbb R}^{2k+1}_*$to${\vec r\over |\vec r|}\in \mathrm{S}^{2k}$. Denote by$P\to {\mathbb R}^{2k+1}_*$the pullback by$\pi$of the canonical principal$\mathrm{SO}(2k)$-bundle$\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $. Let$E_\sharp\to {\mathbb R}^{2k+1}_*$be the associated co-adjoint bundle and$E^\sharp\to T^*{\mathbb R}^{2k+1}_*$be the pullback bundle under projection map$T^*{\mathbb R}^{2k+1}_*\to {\mathbb R}^{2k+1}_*$. The canonical connection on$\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $turns$E^\sharp$into a Poisson manifold. The main result here is that the real Lie algebra$\mathfrak{so}(2, 2k+2)$can be realized as a Lie subalgebra of the Poisson algebra$(C^\infty(\mathcal O^\sharp), \{, \})$, where$\mathcal O^\sharp$is a symplectic leave of$E^\sharp$of special kind. Consequently, in view of the earlier result of the author, an extension of the classical MICZ Kepler problems to dimension$2k+1$is obtained. The hamiltonian, the angular momentum, the Lenz vector and the equation of motion for this extension are all explicitly worked out. Category: Mathematical Physics [113] viXra:1211.0048 [pdf] submitted on 2012-11-10 00:53:16 ### Zanaboni Theorem and Saint-Venant's Principle Authors: Jian-zhong Zhao Comments: 10 Pages. Violating the law of energy conservation, Zanaboni Theorem is invalid and Zanaboni's proof is wrong. Zanaboni's mistake of " proof " is analyzed. Energy Theorem for Zanaboni Problem is suggested and proved. Equations and conditions are established in this paper for Zanaboni Problem, which are consistent with , equivalent or identical to each other. Zanaboni Theorem is, for its invalidity , not a mathematical formulation or proof of Saint-Venant's Principle. AMS Subject Classifications: 74-02, 74G50 Category: Mathematical Physics [112] viXra:1210.0132 [pdf] submitted on 2012-10-23 14:58:23 ### Inconsistency of Magnetic Monopole Authors: Ali R. Hadjesfandiari Comments: 8 pages, 1 figure It is simply proved that the Hamiltonian for an electric point charge interacting with a fixed magnetic monopole does not exist. This shows that the concept of magnetic monopole is inconsistent within the theory of electrodynamics. Category: Mathematical Physics [111] viXra:1210.0123 [pdf] submitted on 2012-10-22 15:46:18 ### The Symmetry Groups of Light Authors: John A. Gowan Comments: 4 Pages. In the mathematical terms of Evariste Galois' "Group Theory", the "Tetrahedron Model" is a description of the symmetry group of light, including its destruction by asymmetric weak force decays (producing our matter-only Cosmos), and its on-going restoration in obedience to Noether's Theorem of symmetry conservation (as in the conversion of bound to free energy in stars). The usual symmetry group identified with light is that of local phase transformations, and it is designated as either SO(2) or U(1). However, I am suggesting here that light contains a very much larger (and more interesting) symmetry group associated with its transformation into particle-antiparticle pairs (and back again into light). I don't know what the formal designation of this group might be. For an expert's explanation of the formal aspects of symmetry and group theory, See: Keith Devlin The Language of Mathematics Chapt. 5 "The Mathematics of Beauty", 1998 W. H. Freeman & Co. (Holt Paperbacks); see also: Ian Stewart Why Beauty is Truth Chapt. 13 "The Five Dimensional Man", Basic Books 2007. Category: Mathematical Physics [110] viXra:1210.0114 [pdf] submitted on 2012-10-21 15:02:39 ### The Cuantifiplane (1) Authors: Jose Miguel Hernandez Perez Comments: 4 Pages. sorry for the grammatical errors this text can explain where it all started Category: Mathematical Physics [109] viXra:1209.0097 [pdf] submitted on 2012-09-27 05:05:24 ### An Algebraic Approach to Systems with Dynamical Constraints Authors: Jerzy Hanckowiak Comments: 15 Pages. Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's theorem is obtained and constraints are also considered in the phase space. Category: Mathematical Physics [108] viXra:1209.0081 [pdf] submitted on 2012-09-24 09:00:38 ### Higgs Boson and Geometry Authors: Markos Georgallides Comments: 12 Pages. This article explains how Geometry and geometrical constructions , [ Spaces , Anti-Spaces , Sub-Spaces ] are able to connect Properties , such as Mass , Energy , and the conservation laws of Physics with only one substance , that of Vector ds , which is ds = AB > 0 → < ∞ with Impulses P A + P B = 0 or ≠ 0 at edge points A , B . Since neutrinos may travel faster than light and also gravity instantly affects , a new explanation is needed . The present article < The Higgs Boson ( Particle ) and the Euclidean Geometry > describes the motion of one of the infinite Sub-Spaces in [ PNS ] , which are moving in Primary Neutral Space . It has been shown that , 1.. Primary point A , having not Position and consequently not any Space existing , therefore is the only Space , and to exist at a second point B somewhere else , point A must move at point B , where then A ≡ B . Point B is the Primary Anti-Space which Equilibrium point A [ PNS ] = [ A ≡ B ] . Since Primary point A is the only Space , then on it exists Principle of Virtual Displacements W = ∫ P.ds = 0 , or [ ds . ( PA + P B ) = 0 ] , i.e. for any ds > 0 Impulse P = ( PA + P B ) = 0 . All points may exist with P = 0 → ( PNS ) and also with P ≠ 0 , [ P A + P B = 0 for points in Spaces and Anti - Spaces ] , therefore [ PNS ] is self created , and because at each point may exist also P ≠ 0 , then [ PNS ] is a Field with infinite points which have a ± Charge with P = 0 → P → ∞ . Primary Neutral - Space [ PNS ] exists with the infinite Points N with three Spatial dimensions ( Xo , Yo , Zo ) and the infinite Impulses P , ( P xi , Pyi , Pzi ) , and i = 0 → ∞ . 2.. Since points A , B of [ PNS ] coincide with the infinite Points , of the infinite Spaces , Anti-Spaces and Sub-Spaces of [ PNS] , and since Motion may occur at all Bounded Sub-Spaces , then this Relative motion is happening between all points belonging to [ PNS ] and to those points belonging to the other Sub-Spaces ( A ≡ B ) . The Infinite points in [ PNS ] form infinite Units AiBi = ds , which equilibrium by Primary Anti – Space by an Inner Impulse ( P ) at edges A , B where PiA + Pi B ≠ 0 , and ds = 0 → N = ∞ . 3 .. Monads = Quantum = ds = AB / ( n = ∞ → 0 ) = [ a ± b.i ] = 0 → ∞ create Spaces ( S ) , Anti -Spaces ( A-S ) , and Sub-Spaces ( S-S ) of AB , which Sub-Spaces are Bounded Spaces , Anti-Spaces and Sub Spaces in it , and are not purely spatial because are Complex numbers which exist for all Spaces , since binomial dsⁿ is Complex number also . 4.. Monads ds ( dipole AB ) and according to their position in S , A-S , S-S , make the four types of matter , and the Combination of the four types of matter , creates all gauge magnitudes which is Mass and Energy , and so all types of Particles and Fields in universe .The 15 possible types of matter correspond to the , Visible , Invisible , Real and Imaginary Universes ( Visible and Invisible Dark matter and Energy ) . Dipole AB is composed of the two Elements → the [ Dipole AB = matter ≡ is the communicator] , and the Impulse [ P ] with the Bounded Impulses ( PA , P B ) . 5.. The difference of Impulses dP = P B – PA > = < 0 of Dipole AB (mass) , creates ± charge . For very small ds ( near zero) which happens at the boundaries of Spaces , ± charge may be point charge ( Spaces form open Strings while Sub-Spaces form closed Strings . Cosmic rays is a Quantum field from a , near zero ds Sub-Space ) , and in very large scales ds , is of ± charge and of the same Field , ( This because Particles , wave like , do not enter a Space smaller than their wavelength ) . 6.. A ray , say M - Ray , interact on the infinite Monads of [PNS] with infinite velocity and zero frequency . This Motion is Continuous and occurs on Dimensional Bounded Units , ds , and not on Points ( this happens only for very small ds near zero and at boundaries of the Spaces ) which are dimensionless . The difference of Impulse dP = P B-PA on points A , B and on points Pi A , Pi B is ± charge . All particles act as wave ( wave-particle duality ) because of the Total energy conservation law of Pythagoras in 2,3 Dim . 7.. The four Interaction of particles or Fields occur directly or Indirectly . Category: Mathematical Physics [107] viXra:1208.0237 [pdf] submitted on 2012-08-30 04:32:08 ### Can Differentiable Description of Physical Reality be Considered Complete? :toward a Complete Theory of Relativity Authors: Xiong Wang Comments: 15 Pages. How to relate the physical \emph{real} reality with the logical \emph{true} abstract mathematics concepts is nothing but pure postulate. The most basic postulates of physics are by using what kind of mathematics to describe the most fundamental concepts of physics. Main point of relativity theories is to remove incorrect and simplify the assumptions about the nature of space-time. There are plentiful bonus of doing so, for example gravity emerges as natural consequence of curvature of spacetime. We argue that the Einstein version of general relativity is not complete, since it can't explain quantum phenomenon. If we want to reconcile quantum, we should give up one implicit assumption we tend to forget: the differentiability. What would be the benefits of these changes? It has many surprising consequences. We show that the weird uncertainty principle and non-commutativity become straightforward in the circumstances of non-differentiable functions. It's just the result of the divergence of usual definition of \emph{velocity}. All weirdness of quantum mechanics are due to we are trying to making sense of nonsense. Finally, we proposed a complete relativity theory in which the spacetime are non-differentiable manifold, and physical law takes the same mathematical form in all coordinate systems, under arbitrary differentiable or non-differentiable coordinate transformations. Quantum phenomenon emerges as natural consequence of non-differentiability of spacetime. Category: Mathematical Physics [106] viXra:1208.0071 [pdf] submitted on 2012-08-16 15:43:12 ### The Mass of the Electron-Neutrino Expressed by Known Physical Constants Authors: Laszlo I. Orban Comments: 5 Pages. Many trials attempted to understand the neutrinos ever since Pauli theoretically concluded its existence from the conservation of energy calculations. The present paper demonstrates that commencing from two appropriately chosen measurement systems, the mass of the electron-neutrino can be calculated from the mass of the electron and the fine-structure constant. The mass of the neutrino can be determined by the theoretically derived expression (m_k=\alpha^3 m_e) (m_k￼ is the mass of the neutrino, m_e is the mass of electron, alpha is the fine-structure constant). Category: Mathematical Physics [105] viXra:1208.0048 [pdf] submitted on 2012-08-12 02:37:48 ### What is Mass? Chapter One: Mass in Newtonian Mechanics and Lagrangian Mechanics Authors: Xiong Wang Comments: 13 Pages. author name: Xiong WANG Email:wangxiong8686@gmail.com To see a World in a Grain of Sand, And a Heaven in a Wild'' We will try to see the development and the whole picture of theoretical physic through the evolution of the very fundamental concept of mass. 1The inertial mass in Newtonian mechanics 2 The Newtonian gravitational mass 3 Mass in Lagrangian formulism 4 Mass in the special theory of relativity 5$E = MC^2$6 Mass in quantum mechanics 7 Principle of equivalence and general relativity 8 The energy momentum tensor in general relativity 9 Mass in the standard model of particle physics 10 The higgs mechanism Category: Mathematical Physics [104] viXra:1208.0036 [pdf] submitted on 2012-08-08 17:19:13 ### Mathematical Follow-up for Dark Energy and Dark Matter in the Double Torus Universe. Authors: Dan Visser Comments: 7 Pages. The main issue in this paper is my mathematics to be presented about the maximum of dark energy depending on the information-differences on the wall of any volume in the Double Torus. Secondly the expressions must be worked out further by invitation to them how are triggered by my ideas the universe has a Double Torus geometry. Thirdly I go deeper into details with dark matter, not only stating dark matter is a spatial particle that spins and gets its energy from its acceleration into a dark matter torus, but also pretending dark matter gets its mass from the vacuum energy. I lay out the conditions for understanding why the Big Bang dynamics is therefore a part of the Double Torus and how the dark flow in the universe emerge from the Double Torus dark energy equation. Fourthly I refer to the pretention neutrinos should be sensitive for the flow of dark matter particles expressed in the set of equations in a former paper. But extensively this paper amplifies this theoretical neutrino-evidence, despite all the confusion around the truth of neutrinos-faster-than-light. Fifthly I observe some dark energy and dark matter issues from some of my former papers. Category: Mathematical Physics [103] viXra:1207.0059 [pdf] submitted on 2012-07-16 02:49:37 ### Fractional Circuit Elements: Memristors, Memcapacitors, Meminductors and Beyond Authors: Xiong Wang Comments: 2 Pages. Memristor was postulated by Chua in 1971 by analyzing mathematical relations between pairs of fundamental circuit variables and realized by HP laboratory in 2008. This relation can be generalized to include any class of two-terminal devices whose properties depend on the state and history of the system. These are called memristive systems, including current-voltage for the memristor, charge-voltage for the memcapacitor, and current-flux for the meminductor. This paper further enlarge the family of elementary circuit elements, in order to model many irregular and exotic nondifferentiable phenomena which are common and dominant to the nonlinear dynamics of many biological, molecular and nanodevices. Category: Mathematical Physics [102] viXra:1207.0036 [pdf] submitted on 2012-07-11 00:23:09 ### The Conceptual Basis for Multidimensional Physics Authors: Alexander Egoyan Comments: 10 Pages. In this work a conceptual basis for multidimensional physics (MD physics) is proposed. The new physics is based on the elastic model of multidimensional geometry [1]. Reality may be considered as the process of time evolution of holistic macro objects - elastic membranes. An embedded membrane in this multidimensional world will look different for the external and internal observers: from the outside it will look like a material object with smooth infinitesimal geometry, while from the inside our Universe-like space-time fabric. When interacting with elementary particles and other membranes, a membrane will transform their energy into its elastic energy (a new form of energy) - the energy of stretching of the infinitesimal segments. For example, living organisms play the role of internal observers of the Universe, and at the same time they serve as external observers for 2D membranes embedded into our Universe. A new explanation of gravity and cosmological aspects are also discussed. Category: Mathematical Physics [101] viXra:1207.0032 [pdf] submitted on 2012-07-09 04:04:07 ### Uncertainty Principle of Mathematics Authors: Mourici Shachter Comments: 5 Pages. This short paper prove that mathematically, Reality is not real . This short paper is not about Heisenberg's uncertainty principle of quantum physics. There is another uncertainty principle that depends solely on mathematical arguments and explains why our world can't be easily equated. Or more accurately can be describe in infinitely different ways all of those representations are mathematically correct. Which mean that the representation of any physical phenomena is not unique. . Given an example how to use it to solve complicate problems in engineering Category: Mathematical Physics [100] viXra:1206.0078 [pdf] submitted on 2012-06-22 02:10:33 ### The Unified Theory of Electrical Machines Authors: Shachter Mourici Comments: 23 Pages. In this paper an entirely new approach is used to solve the old problem known as "The Unified Theory of Electrical Machines" Instead of solving an electric circuit with time dependent resistors and coils. I spent a lot of time in finding the appropriate coordinate system in which the problem becomes very simple. Instead of mathematical reasoning with innumerous number of mathematical equation I used pictorial reasoning This Unified Theory of Electrical Machines is the shortest and therefore can be used to teach student the principles of electrical machines in a one semester course The systematic procedure introduced in this paper is not limited to machine theory and can be applied in many physic and engineering problems. Category: Mathematical Physics [99] viXra:1206.0069 [pdf] submitted on 2012-06-19 15:01:49 ### A Functional Determinant Expression for the Riemann XI-Function Authors: Jose Javier Garcia Moreta Comments: 9 Pages. • ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law, Quantum chaos. Category: Mathematical Physics [98] viXra:1206.0066 [pdf] submitted on 2012-06-19 05:22:29 ### Unified Theory of Electrical Machines, a Philosophical Explanation to How a Universe Can be Created Just from Nothing Authors: Mourici Shachter Comments: 16 Pages. It is well known that physics explains natural phenomena using mathematics, But what happens if we derive from a good physical experiment a wrong mathematical equation, use it for more than 100 years without knowing it is wrong. In this paper I develop again the equation of energy conversion in a general electrical machine and prove that the equations we use are wrong. One of Professor Einstein statements was that the laws of physics are the same for every observer so I made the electrical equation of the machine to look like the mechanical equation. What I found was astonishing and is valid for all other area in physics. It is found that in general any constant in physic can be represented by a superposition of time and phase dependent sinusoidal function. So may be what we think about speed of light and other physical constant is entirely wrong. In the last part of this issue, I use the consequences of that article to create a virtual universe. Category: Mathematical Physics [97] viXra:1206.0049 [pdf] submitted on 2012-06-12 15:23:28 ### A Technique for Cataloging Types of Particles and Types of Stuff Authors: Thomas J. Buckholtz Comments: 11 Pages. We develop theory leading to an ability to catalog types of elementary particles. The resulting catalog provides for known interaction-mediating bosons, non-traditional interaction-carrying bosons, and fermions. Ratios of theoretical numbers of analogs of various types of particles match observed ratios of densities for baryonic matter, dark matter, and dark energy. Category: Mathematical Physics [96] viXra:1206.0028 [pdf] submitted on 2012-06-07 15:07:57 ### New Dark Matter Cosmology Authors: Dan Visser Comments: 10 Pages. This paper presents a set of equations, as well as further derivations and calculations, to present dark matter in an alternative cosmology. The alternative is: The Universe did not start with the Big Bang, but is a recalculated Double Torus Universe of dark energy and dark matter. The calculations within this framework show a dark matter-particle, which has the shape of a smallest possible Double Torus, and has a constant diameter of R ≈ 0.712 x 10^-22 [m] at where it exists. At this length the lowest acceleration for Newton gravity becomes a dark matter-acceleration; the Newton force then changes into a lowest dark matter force. This paper shows both forces are embedded in a united ‘new dark energy force’. In the transition of Newton gravity to dark matter gravity, the new dark energy force has a value of 10^-116 kg^4s^2. Accordingly another calculation reveals this force is a ‘force to recalculate space-time itself’. Further calculations also enable to mark dark matter mass with a value of ≈ 2.8 keV/c^2. Again accordingly the dark matter-density (in kg/m) is ≈ 71 gram per 1 million-km (≈1/149 the distance to the sun, or more than three times the distance from Earth to Moon). The dark energy force uses extra time-arrows from an under-laying time-domain of conventional space-time’. This directly gives evidence to the perception gravity is not fundamental. In general this paper relates dark matter mass, new dark energy force and the level where Newton gravity and dark matter meet each other; specifically in that level space-time is recalculated. Moreover an alternative perception of the Higgs-field is given, related to this recalculation. Category: Mathematical Physics [95] viXra:1206.0026 [pdf] submitted on 2012-06-07 08:44:08 ### Metaphysics of the Free Fock Space with Local and Global Information Authors: Jerzy Hanckowiak Comments: 24 Pages. A new interpretation of the basic vector of the free Fock space (FFS) and the FFS is proposed. The approximations to various equations with additional parameters, for n-point information (n-pi), are also considered in the case of non-polynomial nonlinearities. Key words: basic, generating and state vectors, local and global, Cuntz relations, perturbation and closure principles, homotopy analysis method, Axiom of Choice, consilience. Category: Mathematical Physics [94] viXra:1206.0021 [pdf] submitted on 2012-06-06 08:33:46 ### A Simple and Compact Approach to Hydrodynamic Using Geometric Algebra Authors: Xiong Wang Comments: 8 Pages. A new simple and compact approach to hydrodynamic is presented using the formalism of geometric algebra (GA). Category: Mathematical Physics [93] viXra:1205.0102 [pdf] submitted on 2012-05-25 22:01:25 ### Saint-Venant's Principe of the " Cavity in Cylinder " Problem Authors: Jian-zhong Zhao Comments: 16 Pages. The problem of a cylinder with a small spherical cavity loaded by an equilibrium system of forces is suggested and discussed and its formulation of Saint-Venant's Principle is established. It is evident that finding solutions of boundary-value problems is a precise and pertinent approach to establish Saint-Venant type decay of elastic problems. Keywords : Saint-Venant’s Principe, proof, provability, solution, decay, formulation, cavity AMS Subject Classifications: 74-02, 74G50 Category: Mathematical Physics [92] viXra:1205.0089 [pdf] submitted on 2012-05-22 21:05:18 ### Saint-Venant's Principe of the Problem of the Cylinder Authors: Jian-zhong Zhao Comments: 9 Pages. The Statement of Modified Saint-Venant's Principle is suggested. The axisymmetrical deformation of the infinite circular cylinder loaded by an equilibrium system of forces on its near end is discussed and its formulation of Modified Saint-Venant's Principle is established. It is evident that finding solutions of boundary-value problems is a precise and pertinent approach to establish Saint-Venant type decay of elastic problems. AMS Subject Classifications: 74-02, 74G50 Category: Mathematical Physics [91] viXra:1205.0017 [pdf] submitted on 2012-05-03 17:23:45 [90] viXra:1205.0010 [pdf] submitted on 2012-05-03 09:04:50 ### Memresistors and Non-Memristive Zero-Crossing Hysteresis Curves Authors: Blaise Mouttet Comments: 6 Pages. It has been erroneously asserted by the circuit theorist Leon Chua that all zero-crossing pinched hysteresis curves define memristors. This claim has been used by Stan Williams of HPLabs to assert that all forms of RRAM and phase change memory are memristors. This paper demonstrates several examples of dynamic systems which fall outside of the constraints of memristive systems and yet also produce the same type of zero-crossing hysteresis curves claimed as a fingerprint for a memristor. This establishes that zero-crossing hysteresis serves as insufficient evidence for a memristor. Keywords- non-linear dynamic systems, memresistor, phase change memory, RRAM, ReRAM Category: Mathematical Physics [89] viXra:1205.0009 [pdf] submitted on 2012-05-03 09:13:44 ### Response to “Pinched Hysteresis Loops is the Fingerprint of Memristive Devices” Authors: Blaise Mouttet Comments: 2 Pages. This is a short response to a recent paper by Kim et al. [1] which correctly notes that the zero-crossing pinched hysteresis loop of a memristor or memristive system must hold for all amplitudes, for all frequencies, and for all initial conditions, of any periodic testing waveform, such as sinusoidal or triangular signals, which assumes both positive and negative values over each period of the waveform. An example is noted from the literature indicating that TiO2 memory resistors might not be considered either memristors or memristive systems given this constraint. Keywords- non-linear dynamic systems, memresistor, RRAM, ReRAM Category: Mathematical Physics [88] viXra:1205.0008 [pdf] submitted on 2012-05-03 09:22:18 ### Pinched Hysteresis Loops Are a Fingerprint of Square Law Capacitors Authors: Blaise Mouttet Comments: 5 Pages. It has been claimed that pinched hysteresis curves are the fingerprint of memristors. This paper demonstrates that a linear resistor in parallel with a nonlinear, square law capacitor also produces pinched hysteresis curves. Spice simulations are performed examining the current vs. voltage behavior of this circuitry under different amplitudes and frequencies of an input signal. Based on this finding a more generalized dynamic systems model is suggested for ReRAM and neuromorphic modeling to cover a broader range of pinched hysteresis curves. Keywords- non-linear circuit theory, RRAM, ReRAM, memristor, memristive systems, memadmittance systems, memresistor Category: Mathematical Physics [87] viXra:1204.0094 [pdf] submitted on 2012-04-27 06:21:14 ### About Material Equilibrium Authors: Etkin V.A. Comments: 9 Pages. English It is shown, that change of image of heat and work in open systems entails necessity to revise of conditions of material equilibrium, found by Gibbs. Thus the chemical potential gives way to other potentials in conformity with conditions of unambiguity of researched processes. Category: Mathematical Physics [86] viXra:1204.0051 [pdf] submitted on 2012-04-14 12:23:30 ### The Resurfacing of Rindler's Coordinate Theory Authors: sangwha Yi Comments: 11 Pages. Thank you. In the general relativity theory, in the Rindler’s coordinate theory, find the present accelerated theory’s problem, resurface Rindler’s coordinate theory that used the tetrad on the new method.The theory’s concept is that save Rindler’s coordinate transformation in the other way. Category: Mathematical Physics [85] viXra:1204.0043 [pdf] submitted on 2012-04-11 11:01:42 ### Duonistic Neutrinos Violate Relativity Authors: Dan Visser Comments: 10 Pages. Neutrinos-faster-than-light? The science-battle is not yet over! ‘Yes’, said the OPERA-team in September 22 2011. ‘No’, said the ICARUS-team in February 23 2012. But this paper carries on that it is undoubtedly correct that neutrinos can go faster-than-light. Neutrinos can only do that in neutrino-pairs: I call these pairs Duonistic Neutrinos! This paper presents the set of equations to prove that. The smallest gravity-acceleration g’ appears to be prior to the trajectory of single packaged neutrinos. OPERA and ICARUS might be right both in the end. Category: Mathematical Physics [84] viXra:1203.0089 [pdf] submitted on 2012-03-24 11:31:41 ### "Physical Intuition" : What Is Wrong with It ? Authors: Elemer E Rosinger Comments: 13 Pages. It appears not to be known that subjecting the axioms to certain conditions, such as for instance to be physically meaningful, may interfere with the logical essence of axiomatic systems, and do so in unforeseen ways, ways that should be carefully considered and accounted for. Consequently, the use of "physical intuition" in building up axiomatic systems for various theories of Physics may lead to situations which have so far not been carefully considered. Category: Mathematical Physics [83] viXra:1203.0087 [pdf] submitted on 2012-03-22 09:37:31 ### A Discinnect : Limitations of the Axiomatic Method in Physics Authors: Elemer E Rosinger Comments: 16 Pages. This paper presents the phenomenon of disconnect in the axiomatic approach to theories of Physics, a phenomenon which appears due to the insistence on axioms which have a physical meaning. This insistence introduces a restriction which is foreign to the abstract nature of axiomatic systems as such. Consequently, it turns out to introduce as well the mentioned disconnect. The axiomatic approach in Physics has a longer tradition. It is there already in Newton's Principia. Recently for instance, a number of axiomatic approaches have been proposed in the literature related to Quantum Mechanics. Special Relativity, [2], had from its beginning in 1905 been built upon two axioms, namely, the Galilean Relativity and the Constancy of the Speed of Light in inertial reference frames. Hardly noticed in wider circles, the independence of these two axioms had quite early been subjected to scrutiny, [5,3], and that issue has on occasion been addressed ever since, see [8,4,24] and the literature cited there. Recently, [24], related to these two axioms in Special Relativity, the following phenomenon of wider importance in Physics was noted. As the example of axiomatization of Special Relativity shows it, it is possible to face a disconnect between a system of physically meaningful axioms, and on the other hand, one or another of the mathematical models used in the study of the axiomatized physical theory. The consequence is that, seemingly unknown so far, one faces in Physics the possibility that the axiomatic method has deeper, less obvious, and in fact not considered, or simply overlooked limitations. As there is no reason to believe that the system of the usual two axioms of Special Relativity is the only one subjected to such a disconnect, the various foundational ventures in modern Physics, related for instance to gravitation, quanta, or their bringing together in an overarching theory, may benefit from the study of the possible sources and reasons for such a disconnect. An attempt of such study is presented in this paper. Category: Mathematical Physics [82] viXra:1203.0059 [pdf] submitted on 2012-03-16 03:56:23 ### Quantum Adeles Authors: Matti Pitkänen Comments: 41 Pages. A generalization of number concept is proposed. One can replace integer n with n-dimensional Hilbert space and sum + and product × with direct sum ⊕ and tensor product ⊗ and introduce their co-operations, the definition of which is highly non-trivial. This procedure yields also Hilbert space variants of rationals, algebraic numbers, p-adic number fields, and even complex, quaternionic and octonionic algebraics. Also adeles can be replaced with their Hilbert space counterparts. Even more, one can replace the points of Hilbert spaces with Hilbert spaces and repeat this process, which is very similar to the construction of infinite primes having interpretation in terms of repeated second quantization. This process could be the counterpart for construction of nth order logics and one might speak of Hilbert or quantum mathematics. The construction would also generalize the notion of algebraic holography and provide self-referential cognitive representation of mathematics. This vision emerged from the connections with generalized Feynman diagrams, braids, and with the hierarchy of Planck constants realized in terms of coverings of the imbedding space. Hilbert space generalization of number concept seems to be extremely well suited for the purposes of TGD. For instance, generalized Feynman diagrams could be identifiable as arithmetic Feynman diagrams describing sequences of arithmetic operations and their co-operations. One could interpret ×q and +q and their co-algebra operations as 3-vertices for number theoretical Feynman diagrams describing algebraic identities X=Y having natural interpretation in zero energy ontology. The two vertices have direct counterparts as two kinds of basic topological vertices in quantum TGD (stringy vertices and vertices of Feynman diagrams). The definition of co-operations would characterize quantum dynamics. Physical states would correspond to the Hilbert space states assignable to numbers. One prediction is that all loops can be eliminated from generalized Feynman diagrams and diagrams are in projective sense invariant under permutations of incoming (outgoing legs). Category: Mathematical Physics [81] viXra:1203.0058 [pdf] submitted on 2012-03-16 03:58:04 ### About Absolute Galois Group Authors: Matti Pitkänen Comments: 18 Pages. Absolute Galois Group defined as Galois group of algebraic numbers regarded as extension of rationals is very difficult concept to define. The goal of classical Langlands program is to understand the Galois group of algebraic numbers as algebraic extension of rationals - Absolute Galois Group (AGG) - through its representations. Invertible adeles -ideles - define Gl1 which can be shown to be isomorphic with the Galois group of maximal Abelian extension of rationals (MAGG) and the Langlands conjecture is that the representations for algebraic groups with matrix elements replaced with adeles provide information about AGG and algebraic geometry. I have asked already earlier whether AGG could act is symmetries of quantum TGD. The basis idea was that AGG could be identified as a permutation group for a braid having infinite number of strands. The notion of quantum adele leads to the interpretation of the analog of Galois group for quantum adeles in terms of permutation groups assignable to finite l braids. One can also assign to infinite primes braid structures and Galois groups have lift to braid groups. Objects known as dessins d'enfant provide a geometric representation for AGG in terms of action on algebraic Riemann surfaces allowing interpretation also as algebraic surfaces in finite fields. This representation would make sense for algebraic partonic 2-surfaces, and could be important in the intersection of real and p-adic worlds assigned with living matter in TGD inspired quantum biology, and would allow to regard the quantum states of living matter as representations of AGG. Adeles would make these representations very concrete by bringing in cognition represented in terms of p-adics and there is also a generalization to Hilbert adeles. Category: Mathematical Physics [80] viXra:1203.0007 [pdf] submitted on 2012-03-03 03:23:21 ### The Universe Has 5 Dimensions Authors: Jake Vlastos Comments: 16 Pages. our universe has 5 dimensions adn this project is the proof for this theory Category: Mathematical Physics [79] viXra:1203.0005 [pdf] submitted on 2012-03-02 04:06:06 ### Evidence for a Closed-Curved and Cyclic Double Torus Universe Authors: Dan Visser Comments: 7 Pages. The evidence comes from an alternative calculation of deviations in the dipole fine-structure constant (α). The alternative calculation reveals α deviations spatially and timely connected to a curved dark flow that fits a closed-curved and cyclic Double Torus Universe. This opens-up a new perception the Big Bang is spinning inside another cosmological model. In reality this means the deviation in the dipole α represents the recalculation of the electromagnetic force. Hence, in terms of a cosmological completeness, with also the other forces involved, one could say reality is recalculated by new features of the Double Torus Universe. The features are described earlier in papers posted in the Vixra-archive. Specifically this paper gives the derivations and calculations to show the evidence α deviations are spatially and timely connected in the Double Torus Universe. Category: Mathematical Physics [78] viXra:1202.0075 [pdf] submitted on 2012-02-25 01:52:59 ### Is Indeed Information Physical ? Authors: Elemer E Rosinger Comments: 29 Pages. Information being a relatively new concept in science, the likelihood is pointed out that we do not yet have a good enough grasp of its nature and relevance. This likelihood is further enhanced by the ubiquitous use of information which creates the perception of a manifest, yet in fact, rather superficial familiarity. The paper suggests several aspects which may be essential features of information, or on the contrary, may not be so. In this regard, further studies are obviously needed, studies which may have to avoid with care various temptations to reductionism, like for instance the one claiming that information is physical". Category: Mathematical Physics [77] viXra:1202.0001 [pdf] submitted on 2012-02-01 02:19:14 ### Comparison of Infinitely Large and Infinitely Small Quantities. Authors: Victor Katyushchik Comments: 4 Pages. The three-dimensional space formatting allows to operate on infinitely large and infinitely small quantities confidently, without any contradictions, paradoxes and uncertainties. Category: Mathematical Physics [76] viXra:1201.0119 [pdf] submitted on 2012-01-30 04:01:12 ### Monopole Positioning in Closed Space, Trefoil Conversion & Energy Calculation. Authors: Prakhar bhatnagar Comments: 5 Pages. Magnetic monopole is a hypothetical particle with a single pole. In this paper a new mathematical structure for Dirac string has been proposed .Quantitative aspects and qualitative aspects of a monopole represented as a Dirac string have been highlighted. Magnetic bundle has been defined in a complex form and pole has been defined as composition of that bundle for single pole the pole variable is single. The pole can be considered as a group of threads or a point lying on a monopole magnet bundle for one pole the thread is single and one dimensional. The function is in complex form and defines magnetic bundle. Category: Mathematical Physics [75] viXra:1201.0117 [pdf] submitted on 2012-01-29 07:51:38 ### New Dark Energy and Letter to the Nobel Committee. Authors: Dan Visser Comments: 10 Pages. This paper describes what New Dark Energy is, as well as my comment “Nobel Nominations in a New World” to the Nobel Committee. These seemingly different looking subjects are importantly connected in a plead to change the way Nobel-nominations are performed in a changing world with internet and alternative archives, such as viXra. The point is, that institutional established physics and cosmology block new ideas from the public domain. Therefore an appendix has been added to this paper to summarize in a nutshell, relativity, space-expansion, accelerated space-expansion and the one time-direction in the Big Bang Cosmology, in order to explain better what new dark energy is and what its meaning is for physics and new cosmology. That message is meant for the Nobel Committee. Furthermore three-why’s are answered: Why are two extra time-directions needed in a new cosmology? Why is the introduction of dark mass, squared? Why would there be a Double Torus for New Cosmology? Also the basic-formulas are summarized, referring to my papers, such as the dark energy force formula from my thought-experiment, followed by its transformed-version: the force smaller than the smallest gravity. In the end New Dark Energy is formulated as a product of new dark mass (squared) and two extra time-directions from below the Planck scale. This marks that New Dark Energy could recalculate the established dual unitary-entangled quantum-spaces faster backwards in time than time goes forward in the Big Bang Cosmology ! This affects the established quantum dynamics and classical reality towards the past and future differently than Einstein’s General Relativity is prescribing. The letter to the Nobel Committee is send by me, because no other institutions is doing that for me. Category: Mathematical Physics [74] viXra:1201.0065 [pdf] submitted on 2012-01-16 10:48:52 ### Superluminal Physics & Instantaneous Physics as New Trends in Research Authors: Florentin Smarandache Comments: 4 Pages. In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we can pass from Subluminal Physics to Superluminal Physics, and further to Instantaneous Physics. In the lights of two consecutive successful CERN experiments with superluminal particles in the Fall of 2011, we believe that these two new fields of research should begin developing. Category: Mathematical Physics [73] viXra:1112.0094 [pdf] submitted on 2011-12-31 14:02:34 ### Particle Mass Ratios Authors: DT Froedge Comments: 12 Pages. This paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios. Category: Mathematical Physics [72] viXra:1112.0055 [pdf] submitted on 2011-12-18 14:01:31 ### Higgs-Limited Boson Surface (Higgs-LBS) is a Mass-Surface – Thus not a Singular Higgs-Boson and is Related to Faster-Than-Light-Neutrinos. Authors: Dan Visser Comments: 4 Pages. Avalable only for arXiv and informing me by email. In this paper I give a formulation for why a new Higgs-mass is considered otherwise than is usually done. This leads to an additional explanation of my earlier posted papers about neutrinos-faster-than-light-in-vacuum; I also refer to my earlier calculated new Higgs-mass. The addition is a deeper analysis, which does not change the result in the former paper. It is extending the Higgs-energy. The first prediction is the Higgs-particle is a Limited Boson-Surface, or Higgs-LBS. This means: It is not a singular Higgs-mass boson. The second prediction is: The occurrence of an Higgs-LBS may be about 60 nanoseconds before a proton-proton collision in an accelerator, such as the LHC in CERN. This is possible because the Higgs-energy is related to a new dark energy force squared. These predictions are supposed to fit in a new cosmological hypothesis, called the Double Torus of dark energy and dark matter, wherein a new dark energy force is defined as a force smaller than the smallest gravity, which could act beyond General Relativity. Category: Mathematical Physics [71] viXra:1111.0106 [pdf] submitted on 28 Nov 2011 ### A New Force Smaller Than The Smallest Gravity. Authors: Dan Visser Comments: 7 Pages. In the formulations of this 'paper' speaks the existence of a force smaller than the smallest gravity. This is a new dark energy force, which affects neutrinos differently than is assumed according to current physics. The formulations also imply a different look on the Higgs-mass and dark matter-mass. The 'paper' is also is an overview of recent 'papers' [1] , which already described these issues, but a deeper analysis became important, because a new cosmological hypothesis is involved. The CERN-experiments on these issues are the falsification for my formulations, but until now my formulations withstand several experimental results, and in this case the match with the latest neutrino-faster-than-light experiments is very convincing (more attention might be given to this 'paper' towards institutional disciplines by the Arxiv or Nature). Category: Mathematical Physics [70] viXra:1111.0091 [pdf] submitted on 1 Nov 2011 ### Langlands Conjectures in TGD Framework Authors: Matti Pitkänen Comments: 24 pages. The arguments of this article support the view that in TGD Universe number theoretic and geometric Langlands conjectures could be understood very naturally. The basic notions are following. 1. Zero energy ontology (ZEO) and the related notion of causal diamond CD (CD is short hand for the cartesian product of causal diamond of M4 and of CP2). ZEO leads to the notion of partonic 2-surfaces at the light-like boundaries of CD and to the notion of string world sheet. These notions are central in the recent view about TGD. One can assign to the partonic 2-surfaces a conformal moduli space having as additional coordinates the positions of braid strand ends (punctures). By electric-magnetic duality this moduli space must correspond closely to the moduli space of string world sheets. 2. Electric-magnetic duality realized in terms of string world sheets and partonic 2-surfaces. The group G and its Langlands dual LG would correspond to the time-like and space-like braidings. Duality predicts that the moduli space of string world sheets is very closely related to that for the partonic 2-surfaces. The strong form of 4-D general coordinate invariance implying electric-magnetic duality and S-duality as well as strong form of holography indeed predicts that the collection of string world sheets is fixed once the collection of partonic 2-surfaces at light-like boundaries of CD and its sub-CDs is known. 3. The proposal is that finite measurement resolution is realized in terms of inclusions of hyperfinite factors of type II1 at quantum level and represented in terms of confining effective gauge group. This effective gauge group could be some associate of G: gauge group, Kac-Moody group or its quantum counterpart, or so called twisted quantum Yangian strongly suggested by twistor considerations. At space-time level the finite measurement resolution would be represented in terms of braids at space-time level which come in two varieties correspond to braids assignable to space-like surfaces at the two light-like boundaries of CD and with light-like 3-surfaces at which the signature of the induced metric changes and which are identified as orbits of partonic 2-surfaces connecting the future and past boundaries of CDs. There are several steps leading from G to its twisted quantum Yangian. The first step replaces point like particles with partonic 2-surfaces: this brings in Kac-Moody character. The second step brings in finite measurement resolution meaning that Kac-Moody type algebra is replaced with its quantum version. The third step brings in zero energy ontology: one cannot treat single partonic surface or string world sheet as independent unit: always the collection of partonic 2-surfaces and corresponding string worlds sheets defines the geometric structure so that multilocality and therefore quantum Yangian algebra with multilocal generators is unavoidable. In finite measurement resolution geometric Langlands duality and number theoretic Langlands duality are very closely related since partonic 2-surface is effectively replaced with the punctures representing the ends of braid strands and the orbit of this set under a discrete subgroup of G defines effectively a collection of "rational" 2-surfaces. The number of the "rational" surfaces in geometric Langlands conjecture replaces the number of rational points of partonic 2-surface in its number theoretic variant. The ability to compute both these numbers is very relevant for quantum TGD. 4. The natural identification of the associate of G is as quantum Yangian of Kac-Moody type group associated with Minkowskian open string model assignable to string world sheet representing a string moving in the moduli space of partonic 2-surface. The dual group corresponds to Euclidian string model with partonic 2-surface representing string orbit in the moduli space of the string world sheets. The Kac-Moody algebra assigned with simply laced G is obtained using the standard tachyonic free field representation obtained as ordered exponentials of Cartan algebra generators identified as transversal parts of M4 coordinates for the braid strands. The importance of the free field representation generalizing to the case of non-simply laced groups in the realization of finite measurement resolution in terms of Kac-Moody algebra cannot be over-emphasized. 5. Langlands duality involves besides harmonic analysis side also the number theoretic side. Galois groups (collections of them) defined by infinite primes and integers having representation as symplectic flows defining braidings. I have earlier proposed that the hierarchy of these Galois groups define what might be regarded as a non-commutative homology and cohomology. Also G has this kind of representation which explains why the representations of these two kinds of groups are so intimately related. This relationship could be seen as a generalization of the MacKay correspondence between finite subgroups of SU(2) and simply laced Lie groups. 6. Symplectic group of the light-cone boundary acting as isometries of the WCW geometry kenociteallb/compl1 allowing to represent projectively both Galois groups and symmetry groups as symplectic flows so that the non-commutative cohomology would have braided representation. This leads to braided counterparts for both Galois group and effective symmetry group. 7. The moduli space for Higgs bundle playing central role in the approach of Witten and Kapustin to geometric Landlands program is in TGD framework replaced with the conformal moduli space for partonic 2-surfaces. It is not however possible to speak about Higgs field although moduli defined the analog of Higgs vacuum expectation value. Note that in TGD Universe the most natural assumption is that all Higgs like states are "eaten" by gauge bosons so that also photon and gluons become massive. This mechanism would be very general and mean that massless representations of Poincare group organize to massive ones via the formation of bound states. It might be however possible to see the contribution of p-adic thermodynamics depending on genus as analogous to Higgs contribution since the conformal moduli are analogous to vacuum expectation of Higgs field. Category: Mathematical Physics [69] viXra:1111.0090 [pdf] submitted on 1 Nov 2011 ### How Infinite Primes Relate to Other Views About Mathematical Infinity? Authors: Matti Pitkänen Comments: 18 pages. Infinite primes is a purely TGD inspired notion. The notion of infinity is number theoretical and infinite primes have well defined divisibility properties. One can partially order them by the real norm. p-Adic norms of infinite primes are well defined and finite. The construction of infinite primes is a hierarchical procedure structurally equivalent to a repeated second quantization of a supersymmetric arithmetic quantum field theory. At the lowest level bosons and fermions are labelled by ordinary primes. At the next level one obtains free Fock states plus states having interpretation as bound many particle states. The many particle states of a given level become the single particle states of the next level and one can repeat the construction ad infinitum. The analogy with quantum theory is intriguing and I have proposed that the quantum states in TGD Universe correspond to octonionic generalizations of infinite primes. It is interesting to compare infinite primes (and integers) to the Cantorian view about infinite ordinals and cardinals. The basic problems of Cantor's approach which relate to the axiom of choice, continuum hypothesis, and Russell's antinomy: all these problems relate to the definition of ordinals as sets. In TGD framework infinite primes, integers, and rationals are defined purely algebraically so that these problems are avoided. It is not surprising that these approaches are not equivalent. For instance, sum and product for Cantorian ordinals are not commutative unlike for infinite integers defined in terms of infinite primes. Set theory defines the foundations of modern mathematics. Set theory relies strongly on classical physics, and the obvious question is whether one should reconsider the foundations of mathematics in light of quantum physics. Is set theory really the correct approach to axiomatization? 1. Quantum view about consciousness and cognition leads to a proposal that p-adic physics serves as a correlate for cognition. Together with the notion of infinite primes this suggests that number theory should play a key role in the axiomatics. 2. Algebraic geometry allows algebraization of the set theory and this kind of approach suggests itself strongly in physics inspired approach to the foundations of mathematics. This means powerful limitations on the notion of set. 3. Finite measurement resolution and finite resolution of cognition could have implications also for the foundations of mathematics and relate directly to the fact that all numerical approaches reduce to an approximation using rationals with a cutoff on the number of binary digits. 4. The TGD inspired vision about consciousness implies evolution by quantum jumps meaning that also evolution of mathematics so that no fixed system of axioms can ever catch all the mathematical truths for the simple reason that mathematicians themselves evolve with mathematics. I will discuss possible impact of these observations on the foundations of physical mathematics assuming that one accepts the TGD inspired view about infinity, about the notion of number, and the restrictions on the notion of set suggested by classical TGD. Category: Mathematical Physics [68] viXra:1111.0089 [pdf] submitted on 1 Nov 2011 ### Motives and Infinite Primes Authors: Matti Pitkänen Comments: 79 pages. In this article the goal is to find whether the general mathematical structures associated with twistor approach, superstring models and M-theory could have a generalization or a modification in TGD framework. The contents of the chapter is an outcome of a rather spontaneous process, and represents rather unexpected new insights about TGD resulting as outcome of the comparisons. 1. Infinite primes, Galois groups, algebraic geometry, and TGD In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and cohomology groups for them. The notion of cohomology giving rise also to homology if Poincare duality holds true is central. The number of various cohomology theories has inflated and one of the basic challenges to find a sufficiently general approach allowing to interpret various cohomology theories as variations of the same motive as Grothendieck, who is the pioneer of the field responsible for many of the basic notions and visions, expressed it. Cohomology requires a definition of integral for forms for all number fields. In p-adic context the lack of well-ordering of p-adic numbers implies difficulties both in homology and cohomology since the notion of boundary does not exist in topological sense. The notion of definite integral is problematic for the same reason. This has led to a proposal of reducing integration to Fourier analysis working for symmetric spaces but requiring algebraic extensions of p-adic numbers and an appropriate definition of the p-adic symmetric space. The definition is not unique and the interpretation is in terms of the varying measurement resolution. The notion of infinite has gradually turned out to be more and more important for quantum TGD. Infinite primes, integers, and rationals form a hierarchy completely analogous to a hierarchy of second quantization for a super-symmetric arithmetic quantum field theory. The simplest infinite primes representing elementary particles at given level are in one-one correspondence with many-particle states of the previous level. More complex infinite primes have interpretation in terms of bound states. 1. What makes infinite primes interesting from the point of view of algebraic geometry is that infinite primes, integers and rationals at the n:th level of the hierarchy are in 1-1 correspondence with rational functions of n arguments. One can solve the roots of associated polynomials and perform a root decomposition of infinite primes at various levels of the hierarchy and assign to them Galois groups acting as automorphisms of the field extensions of polynomials defined by the roots coming as restrictions of the basic polynomial to planes xn=0, xn=xn-1=0, etc... 2. These Galois groups are suggested to define non-commutative generalization of homotopy and homology theories and non-linear boundary operation for which a geometric interpretation in terms of the restriction to lower-dimensional plane is proposed. The Galois group Gk would be analogous to the relative homology group relative to the plane xk-1=0 representing boundary and makes sense for all number fields also geometrically. One can ask whether the invariance of the complex of groups under the permutations of the orders of variables in the reduction process is necessary. Physical interpretation suggests that this is not the case and that all the groups obtained by the permutations are needed for a full description. 3. The algebraic counterpart of boundary map would map the elements of Gk identified as analog of homotopy group to the commutator group [Gk-2,Gk-2] and therefore to the unit element of the abelianized group defining cohomology group. In order to obtains something analogous to the ordinary homology and cohomology groups one must however replaces Galois groups by their group algebras with values in some field or ring. This allows to define the analogs of homotopy and homology groups as their abelianizations. Cohomotopy, and cohomology would emerge as duals of homotopy and homology in the dual of the group algebra. 4. That the algebraic representation of the boundary operation is not expected to be unique turns into blessing when on keeps the TGD as almost topological QFT vision as the guide line. One can include all boundary homomorphisms subject to the condition that the anticommutator δikδjk-1jkδik-1 maps to the group algebra of the commutator group [Gk-2,Gk-2]. By adding dual generators one obtains what looks like a generalization of anticommutative fermionic algebra and what comes in mind is the spectrum of quantum states of a SUSY algebra spanned by bosonic states realized as group algebra elements and fermionic states realized in terms of homotopy and cohomotopy and in abelianized version in terms of homology and cohomology. Galois group action allows to organize quantum states into multiplets of Galois groups acting as symmetry groups of physics. Poincare duality would map the analogs of fermionic creation operators to annihilation operators and vice versa and the counterpart of pairing of k:th and n-k:th homology groups would be inner product analogous to that given by Grassmann integration. The interpretation in terms of fermions turns however to be wrong and the more appropriate interpretation is in terms of Dolbeault cohomology applying to forms with homomorphic and antiholomorphic indices. 5. The intuitive idea that the Galois group is analogous to 1-D homotopy group which is the only non-commutative homotopy group, the structure of infinite primes analogous to the braids of braids of braids of ... structure, the fact that Galois group is a subgroup of permutation group, and the possibility to lift permutation group to a braid group suggests a representation as flows of 2-D plane with punctures giving a direct connection with topological quantum field theories for braids, knots and links. The natural assumption is that the flows are induced from transformations of the symplectic group acting on δ M2+/-× CP2 representing quantum fluctuating degrees of freedom associated with WCW ("world of classical worlds"). Discretization of WCW and cutoff in the number of modes would be due to the finite measurement resolution. The outcome would be rather far reaching: finite measurement resolution would allow to construct WCW spinor fields explicitly using the machinery of number theory and algebraic geometry. 6. A connection with operads is highly suggestive. What is nice from TGD perspective is that the non-commutative generalization homology and homotopy has direct connection to the basic structure of quantum TGD almost topological quantum theory where braids are basic objects and also to hyper-finite factors of type II1. This notion of Galois group makes sense only for the algebraic varieties for which coefficient field is algebraic extension of some number field. Braid group approach however allows to generalize the approach to completely general polynomials since the braid group make sense also when the ends points for the braid are not algebraic points (roots of the polynomial). This construction would realize the number theoretical, algebraic geometrical, and topological content in the construction of quantum states in TGD framework in accordance with TGD as almost TQFT philosophy, TGD as infinite-D geometry, and TGD as generalized number theory visions. 2. p-Adic integration and cohomology This picture leads also to a proposal how p-adic integrals could be defined in TGD framework. 1. The calculation of twistorial amplitudes reduces to multi-dimensional residue calculus. Motivic integration gives excellent hopes for the p-adic existence of this calculus and braid representation would give space-time representation for the residue integrals in terms of the braid points representing poles of the integrand: this would conform with quantum classical correspondence. The power of 2π appearing in multiple residue integral is problematic unless it disappears from scattering amplitudes. Otherwise one must allow an extension of p-adic numbers to a ring containing powers of 2π. 2. Weak form of electric-magnetic duality and the general solution ansatz for preferred extremals reduce the Kähler action defining the Kähler function for WCW to the integral of Chern-Simons 3-form. Hence the reduction to cohomology takes places at space-time level and since p-adic cohomology exists there are excellent hopes about the existence of p-adic variant of Kähler action. The existence of the exponent of Kähler gives additional powerful constraints on the value of the Kähler fuction in the intersection of real and p-adic worlds consisting of algebraic partonic 2-surfaces and allows to guess the general form of the Kähler action in p-adic context. 3. One also should define p-adic integration for vacuum functional at the level of WCW. p-Adic thermodynamics serves as a guideline leading to the condition that in p-adic sector exponent of Kähler action is of form (m/n)r, where m/n is divisible by a positive power of p-adic prime p. This implies that one has sum over contributions coming as powers of p and the challenge is to calculate the integral for K= constant surfaces using the integration measure defined by an infinite power of Kähler form of WCW reducing the integral to cohomology which should make sense also p-adically. The p-adicization of the WCW integrals has been discussed already earlier using an approach based on harmonic analysis in symmetric spaces and these two approaches should be equivalent. One could also consider a more general quantization of Kähler action as sum K=K1+K2 where K1=rlog(m/n) and K2=n, with n divisible by p since exp(n) exists in this case and one has exp(K)= (m/n)r × exp(n). Also transcendental extensions of p-adic numbers involving n+p-2 powers of e1/n can be considered. 4. If the Galois group algebras indeed define a representation for WCW spinor fields in finite measurement resolution, also WCW integration would reduce to summations over the Galois groups involved so that integrals would be well-defined in all number fields. 3. Floer homology, Gromov-Witten invariants, and TGD Floer homology defines a generalization of Morse theory allowing to deduce symplectic homology groups by studying Morse theory in loop space of the symplectic manifold. Since the symplectic transformations of the boundary of δ M4+/-× CP2 define isometry group of WCW, it is very natural to expect that Kähler action defines a generalization of the Floer homology allowing to understand the symplectic aspects of quantum TGD. The hierarchy of Planck constants implied by the one-to-many correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates leads naturally to singular coverings of the imbedding space and the resulting symplectic Morse theory could characterize the homology of these coverings. One ends up to a more precise definition of vacuum functional: Kähler action reduces Chern-Simons terms (imaginary in Minkowskian regions and real in Euclidian regions) so that it has both phase and real exponent which makes the functional integral well-defined. Both the phase factor and its conjugate must be allowed and the resulting degeneracy of ground state could allow to understand qualitatively the delicacies of CP breaking and its sensitivity to the parameters of the system. The critical points with respect to zero modes correspond to those for Kähler function. The critical points with respect to complex coordinates associated with quantum fluctuating degrees of freedom are not allowed by the positive definiteness of Kähler metric of WCW. One can say that Kähler and Morse functions define the real and imaginary parts of the exponent of vacuum functional. The generalization of Floer homology inspires several new insights. In particular, space-time surface as hyper-quaternionic surface could define the 4-D counterpart for pseudo-holomorphic 2-surfaces in Floer homology. Holomorphic partonic 2-surfaces could in turn correspond to the extrema of Kähler function with respect to zero modes and holomorphy would be accompanied by super-symmetry. Gromov-Witten invariants appear in Floer homology and topological string theories and this inspires the attempt to build an overall view about their role in TGD. Generalization of topological string theories of type A and B to TGD framework is proposed. The TGD counterpart of the mirror symmetry would be the equivalence of formulations of TGD in H=M4× CP2 and in CP3× CP3 with space-time surfaces replaced with 6-D sphere bundles. 4. K-theory, branes, and TGD K-theory and its generalizations play a fundamental role in super-string models and M-theory since they allow a topological classification of branes. After representing some physical objections against the notion of brane more technical problems of this approach are discussed briefly and it is proposed how TGD allows to overcome these problems. A more precise formulation of the weak form of electric-magnetic duality emerges: the original formulation was not quite correct for space-time regions with Euclidian signature of the induced metric. The question about possible TGD counterparts of R-R and NS-NS fields and S, T, and U dualities is discussed. 5. p-Adic space-time sheets as correlates for Boolean cognition p-Adic physics is interpreted as physical correlate for cognition. The so called Stone spaces are in one-one correspondence with Boolean algebras and have typically 2-adic topologies. A generalization to p-adic case with the interpretation of p pinary digits as physically representable Boolean statements of a Boolean algebra with 2n>p>pn-1 statements is encouraged by p-adic length scale hypothesis. Stone spaces are synonymous with profinite spaces about which both finite and infinite Galois groups represent basic examples. This provides a strong support for the connection between Boolean cognition and p-adic space-time physics. The Stone space character of Galois groups suggests also a deep connection between number theory and cognition and some arguments providing support for this vision are discussed. Category: Mathematical Physics [67] viXra:1111.0088 [pdf] submitted on 1 Nov 2011 ### Could One Generalize Braid Invariant Defined by Vacuum Expecation of Wilson Loop to and Invariant of Braid Cobordisms and of 2-Knots? Authors: Matti Pitkänen Comments: 17 pages. Witten was awarded by Fields medal from a construction recipe of Jones polynomial based on topological QFT assigned with braids and based on Chern-Simons action. Recently Witten has been working with an attempt to understand in terms of quantum theory the so called Khovanov polynomial associated with a much more abstract link invariant whose interpretation and real understanding remains still open. The attempts to understand Witten's thoughts lead to a series of questions unavoidably culminating to the frustrating "Why I do not have the brain of Witten making perhaps possible to answer these questions?". This one must just accept. In this article I summarize some thoughts inspired by the associations of the talk of Witten with quantum TGD and with the model of DNA as topological quantum computer. In my own childish manner I dare believe that these associations are interesting and dare also hope that some more brainy individual might take them seriously. An idea inspired by TGD approach which also main streamer might find interesting is that the Jones invariant defined as vacuum expectation for a Wilson loop in 2+1-D space-time generalizes to a vacuum expectation for a collection of Wilson loops in 2+2-D space-time and could define an invariant for 2-D knots and for cobordisms of braids analogous to Jones polynomial. As a matter fact, it turns out that a generalization of gauge field known as gerbe is needed and that in TGD framework classical color gauge fields defined the gauge potentials of this field. Also topological string theory in 4-D space-time could define this kind of invariants. Of course, it might well be that this kind of ideas have been already discussed in literature. Category: Mathematical Physics [66] viXra:1111.0087 [pdf] submitted on 1 Nov 2011 ### Could the Notion of Hyperdeterminant be Useful in TGD Framework? Authors: Matti Pitkänen Comments: 4 pages. The vanishing of ordinary determinant tells that a group of linear equations possesses non-trivial solutions. Hyperdeterminant generalizes this notion to a situation in which one has homogenous multilinear equations. The notion has applications to the description of quantum entanglement and has stimulated interest in physics blogs. Hyperdeterminant applies to hyper-matrices with n matrix indices defined for an n-fold tensor power of vector space - or more generally - for a tensor product of vector spaces with varying dimensions. Hyper determinant is an n-linear function of the arguments in the tensor factors with the property that all partial derivatives of the hyper determinant vanish at the point, which corresponds to a non-trivial solution of the equation. A simple example is potential function of n arguments linear in each argument. Why the notion of hyperdeterminant- or rather its infinite-dimensional generalization- might be interesting in TGD framework relates to the quantum criticality of TGD stating that TGD Universe involves a fractal hierarchy of criticalities: phase transitions inside phase transitions inside... At classical level the lowest order criticality means that the extremal of Kähler action possesses non-trivial second variations for which the action is not affected. The system is critical. In QFT context one speaks about zero modes. The vanishing of the so called Gaussian (of functional) determinant associated with second variations is the condition for the existence of critical deformations. In QFT context this situation corresponds to the presence of zero modes. The simplest physical model for a critical system is cusp catastrophe defined by a potential function V(x) which is fourth order polynomial. At the edges of cusp two extrema of potential function stable and unstable extrema co-incide and the rank of the matrix defined by the potential function vanishes. This means vanishing of its determinant. At the tip of the cusp the also the third derivative vanishes of potential function vanishes. This situation is however not describable in terms of hyperdeterminant since it is genuinely non-linear rather than only multilinear. In a complete analogy, one can consider also the vanishing of n:th variations in TGD framework as higher order criticality so that the vanishing of hyperdeterminant might serve as a criterion for the higher order critical point and occurrence of phase transition. Why multilinearity might replace non-linearity in TGD framework could be due to the non-locality. Multilinearty with respect to imbedding space-coordinates at different space-time points would imply also the vanishing of the standard local divergences of quantum field theory known to be absent in TGD framework on basis of very general arguments. In this article an attempt to concretize this idea is made. The challenge is highly non-trivial since in finite measurement resolution one must work with infinite-dimensional system. Category: Mathematical Physics [65] viXra:1111.0086 [pdf] submitted on 1 Nov 2011 ### What Could be the Generalization of Yangian Symmetry of N=4 Susy in TGD Framework? Authors: Matti Pitkänen Comments: 45 pages. There have been impressive steps in the understanding of N=4 maximally sypersymmetric YM theory possessing 4-D super-conformal symmetry. This theory is related by AdS/CFT duality to certain string theory in AdS5× S5 background. Second stringy representation was discovered by Witten and is based on 6-D Calabi-Yau manifold defined by twistors. The unifying proposal is that so called Yangian symmetry is behind the mathematical miracles involved. In the following I will discuss briefly the notion of Yangian symmetry and suggest its generalization in TGD framework by replacing conformal algebra with appropriate super-conformal algebras. Also a possible realization of twistor approach and the construction of scattering amplitudes in terms of Yangian invariants defined by Grassmannian integrals is considered in TGD framework and based on the idea that in zero energy ontology one can represent massive states as bound states of massless particles. There is also a proposal for a physical interpretation of the Cartan algebra of Yangian algebra allowing to understand at the fundamental level how the mass spectrum of n-particle bound states could be understood in terms of the n-local charges of the Yangian algebra. Twistors were originally introduced by Penrose to characterize the solutions of Maxwell's equations. Kähler action is Maxwell action for the induced Kähler form of CP2. The preferred extremals allow a very concrete interpretation in terms of modes of massless non-linear field. Both conformally compactified Minkowski space identifiable as so called causal diamond and CP2 allow a description in terms of twistors. These observations inspire the proposal that a generalization of Witten's twistor string theory relying on the identification of twistor string world sheets with certain holomorphic surfaces assigned with Feynman diagrams could allow a formulation of quantum TGD in terms of 3-dimensional holomorphic surfaces of CP3× CP3 mapped to 6-surfaces dual CP3× CP3, which are sphere bundles so that they are projected in a natural manner to 4-D space-time surfaces. Very general physical and mathematical arguments lead to a highly unique proposal for the holomorphic differential equations defining the complex 3-surfaces conjectured to correspond to the preferred extremals of Kähler action. Category: Mathematical Physics [64] viXra:1111.0085 [pdf] submitted on 1 Nov 2011 ### A Possible Explanation for Shnoll Effect Authors: Matti Pitkänen Comments: 17 pages. Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction. These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics. The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II1 (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λi) for a positive integer valued variable n characterized by rational-valued parameters λi is obtained by replacing n and the integers characterizing λi with so called quantum integers depending on the quantum phase qm=exp(i2π/m). Quantum integer nq must be defined as the product of quantum counterparts pq of the primes p appearing in the prime decomposition of n. One has pq= sin(2π p/m)/sin(2π/m) for p≠ P and pq=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p. The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers Pn to P-n and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ Pn)=∑ I(Pn). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n+n-, n+q>0 with fixed n-q<0, are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct. The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ kpΔ R/R and Δ m/m≈ kmΔ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P. Category: Mathematical Physics [63] viXra:1110.0030 [pdf] submitted on 9 Oct 2011 ### A New Dark Energy Force Theoretically Calculates Faster-than-light-neutrinos. Authors: Dan Visser Comments: 7 pages A theoretical calculation with a new dark energy force formula discloses the correctness of the experimental faster-than-light-neutrinos in the CERN-San Grasso experiment. The formulation in this paper theoretically confirms that Einstein's Relativity could be violated. This introduces the obligation to accept a new cosmological model, called the Double Torus hypothesis . The theoretical calculation in this paper is based on a new momentum of dark energy force, formulated by its new force and two extra time dimensions below the Planck scale. In detail this completely new perspective shows that the dark energy force starts to dominate the lowest limit of the Newton-force-acceleration under specific conditions of neutrino-oscillations. This paper theoretically calculates 62.8 nanosecond for the experimental detected early-arrival of muon-neutrinos related to how light-in-vacuum would have arrived. This is a marvelous close match compared to the ((60.7 ± 6.9 (stat.) ± 7.4 (sys.)) nanosecond found during the 'neutrino-flight path' from CERN to San Grasso. Category: Mathematical Physics [62] viXra:1109.0038 [pdf] submitted on 18 Sep 2011 ### Zeno's Paradoxe and the Nature of Points in Quantized Euclidean Universe Authors: Markos Georgallides Comments: 9 pages This article explains the correlation between Euclidean Geometry , Complex Numbers and Physics . A Straight line AB is continuous in Points between A and B [ i.e. all points between AB are the elements which fill AB ] , which Points are also , Nothing , Everything , and maybe Anywhere , without any Dimension , and one has to pass the infinite points between A and B . A point C is on line AB only when exists CA+ CB = AB , or the whole AB is equal to the parts CA , CB , and this is an equation , which differentiates geometries . Since points have not any dimension and since only AB has dimension ( the length AB and for ÃC the length AC ) and since on ÃB exist infinite AC → AB , which have infinite Spaces , Anti-Spaces and Sub-Spaces , then 1. Straight line AB is continuous with points as filling ( Infinitively divisible ) . 2. Straight line AB is discontinuous (discrete) with dimensional Units , ds =AB as filling ( that is made up of finite divisible or indivisible parts the Monads ds ) or ds → AB / n , where n = 1 , 2 , → ∞ ) , and for n = ∞ then ds = 0 . 3. Straight line AB is discontinuous (discrete) with dimensional Units ds , or ds = quantum = AB / n [ where n = 1,2,3 → ∞ , = ( a + b.i ) / n , Infinitively divisible and keeping always the conservation of properties at end points A , B ] as filling , and continuous with points as filling ( for n = ∞ then ds = 0 i.e. a point ) . This is the Vector relation of Monads , ds , ( or , as Complex Numbers in their general form , ds = a + b. i ) , which is the Dual Nature of lines AB , ( discrete and continuous ) . So travelling on Points ( ds = 0 ) between AB one never comes to B , on the contrary travelling with ds > 0 one comes in finite time . 4 . Achilles has to pass every point of line AB which is then as passing from the starting point A , ds =0 , where Velocity of Achilles is v(A) = ds/dt = 0 . The same happens for Tortoise at point B where Velocity v(T) = ds/dt = 0 . On the contrary , Achilles passing AB on dimensional Units , ds , then Achilles velocity v(A) = ds/dt(A) is greater than that of Tortoise v(T) = ds / dt(T) . Since in PNS , v = ∞ , T = 0 , meaning infinite velocity and Time not existing , then Arrow AB in [PNS] is constant because AB = ds = Constant = u . 0 = ∞ . 0 Straight line AB is discontinuous (discrete) with dimensional Units ds = AB / n where n = 1 → ∞ and continuous with points [ n = ∞ ] . Continuously on AB happens also with all discrete ds , ( This is the Dual Nature of lines ( Geometry ), discrete and continuous ) . Monads ds = 0 → ∞ are Simultaneously , actual infinite ( because for n = ∞ then ds = [ AB / n = ∞ ] = 0 i.e. a point ) , and potential infinite , ( because for n = 0 then ds = [ AB / n=0 ] = ∞ i.e. the straight line through AB . Category: Mathematical Physics [61] viXra:1109.0034 [pdf] submitted on 16 Sep 2011 ### Can Electromagnetic Scalar Waves be Radiated by a Metal Sphere? Authors: Giuliano Bettini Comments: 24 pages. There is a lot of chattering on the Internet about Tesla waves, vacuum energy, scalar waves and so on. Professor Meyl says he has a complete theory, experimental evidence and apparatus on these waves. In a theoretical paper Van Vlaenderen introduced a generalization of classical electrodynamics for the prediction of scalar field effects. It is said the Monstein has demonstrated the physical existence of such scalar waves. NASA in a report seems to consider such waves as a promising item to be studied. Some other papers appeared in arXiv. I've already showed that such waves are a consequence of "generalized" Maxwell fields which simply mean space time analytic functions not limited by the Lorenz gauge condition, but accepted instead in a wide sense. In this paper I remember my ideas on these waves, together with my doubts about their physical existence. In fact, the deduction of the scalar waves equations, together with their physical interpretation, in my opinion demonstrates nothing about the physical existence of scalar waves. I discuss the experiment of Monstein, and suggest some other experiment. Obviously I think that the lack of demonstration of the existence doesn't mean the demonstration of inexistence. Category: Mathematical Physics [60] viXra:1108.0048 [pdf] submitted on 29 Aug 2011 ### New Value for the Higgs Mass. Authors: Dan Visser Comments: 4 pages. Publication is free for any institute or magazine The Higgs mass is approximately 0.5 TeV/c2 . This is a new predicted value. This mass value for Higgs is calculated with a new dark energy force formula, which is performing in the hypothesis of the Double Torus, a new cosmological "model" for the universe. This "model" embeds the Big Bang framework. The new Higgs mass is theoretically disclosed by implementing the dimensional features of relativistic spacetime into the dimensions of the dark energy force formula and an equalization to the lowest limit for acceleration in Newton force, being a transition where Newton breaks down and the dark energy force takes over. The dark energy force generates gravitational movement and thus mass. This enables to calculate a Higgs mass differently than in currently used theories. Category: Mathematical Physics [59] viXra:1108.0047 [pdf] submitted on 27 Aug 2011 ### Electrostatics and Fluid Flow with 3D Analytic Functions Authors: Giuliano Bettini Comments: 21 pages. I present examples of applications of 3-dimensional analytic functions to electrostatics and potential flows, mainly devoted to engineers and physicists. Of course, the paper only suggests areas of future development, despite that a persistent idea, from Sommerfeld on, seems to be "The powerful tool of the theory of complex functions cannot be used in three-dimensional potential theory" (Sommerfeld, "Mechanics of Deformable Bodies", Academic Press, 1950) I summarize here unpublished manuscripts dated 1994. Category: Mathematical Physics [58] viXra:1108.0042 [pdf] submitted on 26 Aug 2011 ### Majorana Neutrino: Chirality and Helicity Authors: Valeriy V. Dvoeglazov Comments: 19 Pages We introduce the Majorana spinors in the momentum representation. They obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). Particular attention has been paid to the questions of chirality and helicity (two concepts which frequently are confused in the literature) for Dirac and Majorana states. Category: Mathematical Physics [57] viXra:1108.0005 [pdf] submitted on 2 Aug 2011 ### Black Hole vs. Variable Rest Mass Neutron Star Authors: D.T. Froedge Comments: 14 pages In a previous paper we have discussed the conjecture of a variable particle rest mass, as a function of gravitational potential (Scalar Gravitational Theory with Variable Rest Mass) This paper discuses the implications of that theory in regard to a large neutron star, and contrast the difference between the predicted phenomena, and Black Hole theory as put fourth by standard GR. The validity of this theory would be established by the finding of a neutron star having a mass greater than allowed by Black Hole theory. Category: Mathematical Physics [56] viXra:1107.0062 [pdf] submitted on 31 Jul 2011 ### Scalar Gravitational Theory with Variable Rest Mass Authors: D.T. Froedge Comments: 16 pages The purpose of this paper is to present a non-tensor theory of gravitation that provides the equivalent equations of motion, but does not result in the issue of black holes, non-localizable energy, or spacetime singularities. The prime assumption is the notion that the rest mass of a particle entering a gravitational potential is reduced in proportion to the energy gained by the velocity increases. One could designate this development as a "catalytic" theory in that gravitation is a vector catalyst, that converts rest energy into kinetic energy. The total mass energy will be considered localized with the individual mass particles, and defined relative to a given observer. No energy will be ascribed to the field, thus there is no stress energy tensor. We will develop the energy mass relation, and show that it can result in the proper orbital precession as demonstrated by GR. The rest mass is not significantly different from that of a particle defined in a stationary asymptotically flat GR space-time, when the defining point particles via the Komar mass. Since rest mass of a particle goes to zero on approaching a Schwarzschild boundary, the formation of black holes becomes problematic. Category: Mathematical Physics [55] viXra:1107.0042 [pdf] submitted on 21 Jul 2011 ### Matter Over Anti-Matter Explained in a Double Torus. Authors: Dan Visser Comments: 4 pages September 1 2009 a new cosmological hypothesis was proposed to imagine the universe otherwise. Many institutional scientists still try to implement their results into the commonly accepted Big Bang theory. I am one of the two scientists who propose a Double Torus as a new shape for the universe. Several 'papers' are hosted at 'vixra' about this subject. This paper adds an explanaition to these afore published papers and in particular explains the 'dominance of matter over anti-matter', deduced from the earlier derived 'dark energy force formula' and the perspective of the Double Torus. Category: Mathematical Physics [54] viXra:1107.0017 [pdf] submitted on 10 Jul 2011 ### Recalculation-mechanism of the Big Bang in a Double Torus Universe. Authors: Dan Visser Comments: 5 pages Here in this 'paper' a deeper analysis of the 'dark energy force formula' in the Double Torus Cosmology is made. Earlier 'papers' were posted as 'pre-papers' in the vixra-archive. These are subject to a new cosmological hypothesis, being further described in higher order mathematics in the near future by Christopher Forbes. I have found evidence through an unexpected interpretation of CMB results, that the 'dark energy force formula' appears to be a functional 'recalculation-mechanism' for quantum gravity. Category: Mathematical Physics [53] viXra:1106.0059 [pdf] submitted on 27 Jun 2011 ### The Gauge Theory's Expansion in the Electro-Magnetic Field Authors: Sangwha Yi Comments: 6 pages. In the special relativity theory, study the gauge theory in the Electro-magnetic field theory.Using that the Electro-magnetic potential is 4-vector, treat invariant potential. And the Electro-Magnetic field theory's the gauge theory expand. Category: Mathematical Physics [52] viXra:1106.0018 [pdf] submitted on 11 Jun 2011 ### Exact Solution of Viscous-Plastic Flow Equations for Glacier Dynamics in 2-Dimensional Case. Authors: Sergey V. Ershkov Comments: 6 pages Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D solution of Ice dynamics could be classified as Riccati's type. Due to a very special character of Riccati's type equation, it's general solution is proved to have a proper gap of components of such a solution. Category: Mathematical Physics [51] viXra:1105.0033 [pdf] submitted on 23 May 2011 ### Discussion Needed About Three (New) Cosmological Models Based on Mathematics and Physics Authors: Dan Visser Comments: 5 pages Three new cosmological models are 'circling' the science-community: a 'Bouncing Universe', a 'Conformal Cyclic Cosmology and a 'Double Torus Cosmology'. All new ideas, commented anonymously and discussed institutionally. This paper wants more cosmologists and physicists to involve the discussion openly in the media, without walking save roads. The authors and readers are invited to involve this discussion. Which model is true and can the mathematics be matched? Category: Mathematical Physics [50] viXra:1105.0022 [pdf] submitted on 15 May 2011 ### Hard Theoretical Evidence for the Dark Energy Force Formula in a Double Torus Universe. Authors: Dan Visser Comments: 6 pages This paper shows how a 'dark energy force formula' emerges five more space- and two more time-dimensions in nature. The 'formula' is earlier described in vixra-papers, announcing the universe is a double torus of dark energy and dark matter. The 'formula' is a completely different force than the cosmological constant of Einstein used to explain accelerated expansion in the big bang. With this in mind, two independent experimental investigations has given additional proof, that the 'dark energy force formula' correlates the independent investigations, because: 1) Five extra space-dimensions have to exist, according to how electrons behave in graphene-experiments. 2) Computer-simulation shows a double torus geometry, that emerges from two colliding blackholes involving a third torus during pulsation. These results match with the postulate that the universe exists of a double torus of dark energy and dark matter, including a 'dark energy force formula'. Category: Mathematical Physics [49] viXra:1105.0016 [pdf] submitted on 12 May 2011 ### A Few Implications of the Laws of Transactions, from the Abstraction Theory. Authors: Subhajit Ganguly Comments: 10 pages. Considering transport of light through space-time, following the laws of physical transactions (viXra:1101.0035) it may be said that there must be a spreading effect on it. Over suitable distances from a source of light, an observer's perception is bound to be affected due to this spreading. In the following paper, these effects on the reception of a signal, due to the spreading of light are studied. Experimental set-ups are desired to verify the actual angles of spread with their theoretical values. An experiment regarding the minimum distance between two disturbances for them to be distinguishable is also carried out. The energy quantum is also studied in a new light. Category: Mathematical Physics [48] viXra:1104.0085 [pdf] submitted on 28 Apr 2011 ### Dark Matter Formula For Fundamental Calculation Of Satelite Flybys In Hyperbolic Orbits. Authors: Dan Visser Comments: 8 pages For the first time an announcement is made in this paper to have found fundamental evidence for the flyby-anomalies of six satelites earlier investigated by John Anderson and coworkers of the Jet Propulsion Laboratory (JPL) in Pasadena USA. The central part of this theoretical evidence exists of a 'dark matter impuls flow' being the cause of a velocity-change for satelites during their 'flyby' along the earth. A formula is given to calculate the velocity-change caused by dark matter. Also a dark matter constant is suggested. The origin of the evidence is related to a 'dark energy force formula', which is a new force in a new proposed cosmological model describing dark energy and dark matter in a double torus geometry (TTM). Originally the 'dark energy force formula' is discovered by an independent cosmologist and E-ingenieur, Dan Visser from Almere, the Netherlands. Then afterwards a few 'papers' have been published in the vixra-archive since September 1 2009 in colaboration with mathematician and physicist Christopher Forbes (UK). These 'papers' could be considered as 'pre-exercises' in awaiting for a more robust mathematical framework for the new proposed double torus cosmological model. Category: Mathematical Physics [47] viXra:1103.0115 [pdf] submitted on 30 Mar 2011 ### A Note on the Action at a Distance Authors: José Francisco García Juliá Comments: 3 pages We consider that the action at a distance is carried out by virtual carriers of the force, which are created and annihilated in the vacuum by the field in a time less than that of the Heisenberg's uncertainty. Category: Mathematical Physics [46] viXra:1103.0114 [pdf] submitted on 30 Mar 2011 ### The Finite Element Method (Fem)to Finding the Reverberation Times of Irregular Rooms Authors: Jalil Olia, Vahid Afshinmehr Comments: 20 pages In this paper we applied a finite element method to finding the effects on the reverberation times of common irregularities like curved surfaces, non-parallel walls and large open-walled ante-rooms, found in auditoria. The number of modes having a reverberation time in a specified time interval is expressed as a function of the total allowed degrees of freedom and it is shown that even when the number of degrees of freedom of the model is large there is, in general, no one dominant group. Curved surfaces in particular lead to a situation where some modes have very long reverberation times, leading to bad acoustics. In such situations a knowledge of the offending mode shapes give an indication on where to position absorptive material for optimum effect. Category: Mathematical Physics [45] viXra:1103.0012 [pdf] submitted on 3 Mar 2011 ### Double Torus Cosmology Reveals Cosmic Backround to Measure Dark Energy. Authors: Dan Visser, Chris Forbes Comments: 7 pages. Particularly this paper announces dark energy could be measured as a cosmic backround (CMB)-frame related to a specific quantumstate of dark energy and dark matter conform a double torus cosmology (TTM[1,2,3,4,5,6,7]). In addition this paper also refers to a planned dark energy interferometerproject expected to be operational in 2014[8]. Both aspects can be combined in order to get a better expectation and interpretation of the detection of dark energy. This paper shows dark energy to interact differently than in the planned experiments of the dark energy interferometer-project. That is the motive to publish this paper. Benchmark is dark energy and dark matter are not considered in a big bang cosmology, but in a double torus universe of one torus of dark energy, which encloses and intertwines a second torus of dark matter (TTM-cosmology). In derivations is shown that dark energy will affect falling (super positioned) Cesium atoms in the dark energy interferometerproject unexpectedly: 1. It will touch the super-positioned atoms twice! ; the cause will be the torus-geometry of the TTM-derived CMB-frame. 2. The 'Twice-touching' will vary subsequently; the cause will be a dependency on 'expansion or contraction' of the CMB-torus geometry through dynamics that are caused by the "+" and "-" strength of the dark energy force in the TTM and which is produced by the dark energy torus. This has motivated me to calculate a specific value for TTM-dark energy on about 4 x 10-114 [X.s] in 6.4 x 10-48 [m2] as a new sort of spin-quantumstate [X.s], which drives the expansion of big bang cosmology analogue to how elementary spin is a 'generator for rotation' in conventional quantumphysics. Probably this paper might be of interest to the dark energy interferometer-project at least. Category: Mathematical Physics [44] viXra:1102.0037 [pdf] submitted on 21 Feb 2011 ### A Beautiful Theory of Everything: How Simplexity Leads to Reality! Authors: Ayind T Mahamba Comments: 8 Pages. Submissions for FQXi essay contest. The quest to explain the true nature of reality is one of the great scientific goals. In fact, this essay contest asks: is Nature fundamentally continuous or discrete and how can these two different but very useful concepts be fully reconciled? Physical science is vast, complex and remains mysterious [10]. Since long ago, the great thinkers and scholars have dedicated their lives to the attempted comprehension1 of this reality that has become so abstract. Throughout the centuries and through experimentation, they have established numerous laws, concepts, theories, and principles concerning the fundamental notions of reality (centered on matter-energy and spacetime). I propose a central theory (MIT), based on the information of, and compatible with, the contemporary scientific knowledge; the existing fundamental relation between the "physical entities" passes through the determined quantitative transmission (quantity) of this preserved transcendent greatness (quality). In addition to a "formal" relationship (existence) which creates an informal description of what is real, there is a causal relationship between "phenomena" (relativity). My informational approach has been productive in several domains where many enigma persist; solutions for these problems must be envisaged globally, using ideas and concepts from numerous different fields, with a coherent schema... The "Theory of Universal Relativity" (TUR as a ToE) proposed here lays bridges between domains which, at first glance, have nothing to do with each other; it also provides insight into how we can improve our knowledge by understanding the interplay of complexity and simplicity. Therefore emerging from simplexity (contraction of simplicity and complexity), reality is both digital and analogue (and between) and also more! We know there is a strange and mysterious world that surrounds us, a world largely hidden from our senses with extra dimensions and as a mathematical concept of reality, MIT may confirm that we are part of a cosmic hologram (a paradigm shift). My theory has the advantage of being extremely simple, not limited to scientists because everyone can understand it (I = 1 ± i). So, in this essay, I will try to explain why and how [1][13][48][51]. Category: Mathematical Physics [43] viXra:1102.0032 [pdf] submitted on 19 Feb 2011 ### Quintessence-Momentum as Link Between Mass and Charge Authors: Malcolm Macleod Comments: 3 pages. This paper suggests a 'quantity of momentum', a square root of Planck momentum, here referred to as Quintessence-momentum, as a natural unit that is common to both mass and charge. In terms of this Quintessence momentum Q, alpha (Sommerfeld fine structure constant) and c; geometrical formulas for the natural physical constants and the electron mass are proposed. Results are consistent with CODATA 2006. Category: Mathematical Physics [42] viXra:1102.0027 [pdf] submitted on 17 Feb 2011 ### Scale Dimension as the Fifth Dimension of Spacetime Authors: Sergey G. Fedosin Comments: 5 pages. In Russian The scale dimension which is discovered in the theory of infinite nesting of matter is studied from the perspective of the physical implementation of well-studied four-and n-dimensional geometric objects. Adding of the scale dimension to Minkowski space means the need to use the five-dimensional spacetime. Category: Mathematical Physics [41] viXra:1102.0009 [pdf] submitted on 7 Feb 2011 ### On the Stability of Linear Systems Authors: Daniele Sasso Comments: 7 pages, 5 figures. The criteria of stability defined in the standard theory of linear systems aren't exhaustive and show some inconsistencies. In this article we define new criteria of stability more consistent with real physical situations. In particular we distinguish between static stability and dynamic stability in order to analyse the stability of systems in the time domain and in Laplace's equivalent domain. Let introduce then the frequency stability in order to analyse the stability of systems in the Fourier domain. Category: Mathematical Physics [40] viXra:1101.0096 [pdf] submitted on 29 Jan 2011 ### Entanglement Related to Cosmology-TTM Authors: Dan Visser, Christopher Forbes Comments: 10 pages This paper postulates a theoretical structure within entangled photons. The postulate is introduced within the framework of the cosmological Twin-Tori Model (TTM). Related papers are to be found in viXra[1,2,3,4,5,6]. After generally derived equations and interpretations, a mass (mt) per 2π is calculated on ~ 2.6 x 10-34 [(J.s) m2 / s]. Such a tiny spinning-forward surface per second (torus geometry) has an energy much smaller than the Planckenergy in Joule, suggesting a subdivision of 1043 surfaces below the Planckscale: If one photon changes spin, the entangled photon could follow by means of the spinning-forward tiny surface-structure within the torus geometry (per 2π), being an information-flux for entanglement in general below the Planckscale. Category: Mathematical Physics [39] viXra:1101.0052 [pdf] submitted on 16 Jan 2011 ### Hidden Mathematical Symmetries in the 32 Crystal Point Groups? Authors: Giuliano Bettini Comments: 10 pages In a preceding paper we introduced a conjecture: the classification of the 32 crystal classes with 5 bits. In the present paper we will review our preceding result, and continue showing some further interesting issues. In the paper, it is argued that bits should be identified with five basic unknown symmetries generating these 32 groups. Probably it is not merely a coincidence that 32 means 5 bits. And probably is it not merely a coincidence that each complete subset of bits (properties) means the holohedry of a crystal system; and each new bit means a new crystal system. The purpose of this article was of course not to draw a conclusive theory, but to suggest ideas that, we hope, will be useful for researchers in mathematics, group theory and crystallography. Category: Mathematical Physics [38] viXra:1101.0037 [pdf] submitted on 11 Jan 2011 ### Fine Structure Constant α ~ 1/137.036 and Blackbody Radiation Constant αR ~ 1/157.555 Authors: Ke Xiao Comments: 5 pages The fine structure constant α = e2/hc ~ 1/137.036 and the blackbody radiation constant αR = e2(aR/k4B)1/3 ~ 1/157.555 are linked by prime numbers. The blackbody radiation constant is a new method to measure the fine structure constant. It also links the fine structure constant to the Boltzmann constant. Category: Mathematical Physics [37] viXra:1101.0035 [pdf] submitted on 10 Jan 2011 ### Abstraction In Theory - Laws of Physical Transactions Authors: Subhajit Ganguly Comments: 15 pages Considering transport or tendency ... (see paper) Category: Mathematical Physics [36] viXra:1012.0052 [pdf] submitted on 29 Dec 2010 ### 32 Point Groups of Three Dimensional Crystal Cells Described by 5 Bits Authors: Giuliano Bettini Comments: 9 pages, in Italian There are 32 possible combinations of symmetry operations that define the external symmetry of crystals. These 32 possible combinations result in the 32 crystal classes. But for a radar engineer it is inevitable to associate "32" to "5 bits". I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with a (tentative) physical meaning of each bit. Each bit means a physical property. Category: Mathematical Physics [35] viXra:1012.0031 [pdf] submitted on 14 Dec 2010 ### Further on Non-Cartesian Systems Authors: Elemér E Rosinger Comments: 9 pages A class of non-Cartesian physical systems, [7], are those whose composite state spaces are given by significantly extended tensor products. A more detailed presentation of the way such extended tensor products are constructed is offered, based on a step by step comparison with the construction of usual tensor products. This presentation clarifies the extent to which the extended tensor products are indeed more general than the usual ones. Category: Mathematical Physics [34] viXra:1012.0020 [pdf] submitted on 8 Dec 2010 ### Non-Cartesian Systems : an Open Problem Authors: Elemer E Rosinger Comments: 6 pages The following open problem is presented and motivated : Are there physical systems whose state spaces do not compose according to either the Cartesian product, as classical systems do, or the usual tensor product, as quantum systems do ? Category: Mathematical Physics [33] viXra:1012.0014 [pdf] submitted on 4 Dec 2010 ### Four Departures in Mathematics and Physics Authors: Elemer E Rosinger Comments: 28 pages Much of Mathematics, and therefore Physics as well, have been limited by four rather consequential restrictions. Two of them are ancient taboos, one is an ancient and no longer felt as such bondage, and the fourth is a surprising omission in Algebra. The paper brings to the attention of those interested these four restrictions, as well as the fact that each of them has by now ways, even if hardly yet known ones, to overcome them. Category: Mathematical Physics [32] viXra:1012.0002 [pdf] submitted on 1 Dec 2010 ### Some Comments on Projective Quadrics Subordinate to Pseudo-Hermitian Spaces Authors: Arkadiusz Jadczyk Comments: 7 pages, To appear in Advances in Applied Clifford Algebras We study in some detail the structure of the projective quadric Q' obtained by taking the quotient of the isotropic cone in a standard pseudohermitian space Hp,q with respect to the positive real numbers R+ and, further, by taking the quotient ~Q = Q'/U(1). The case of signature (1. 1) serves as an illustration. ~Q is studied as a compactification of RxHp-1,q-1 Category: Mathematical Physics [31] viXra:1011.0039 [pdf] submitted on 17 Nov 2010 ### Some Orbital and Other Properties of the 'Special Gravitating Annulus' Authors: Guy Moore, Richard Moore Comments: 40 pages Our obtaining the analytical equations for the gravitation of a particular type of mathematical annulus, which we called a 'Special Gravitating Annulus' (SGA), greatly facilitates studying its orbital properties by computer programming. This includes isomorphism, periodic and chaotic polar orbits, and orbits in three dimensions. We provide further insights into the gravitational properties of this annulus and describe our computer algorithms and programs. We study a number of periodic orbits, giving them names to aid identification. 'Ellipses extraordinaires' which are bisected by the annulus, have no gravitating matter at either focus and represent a fundamental departure from the normal association of elliptical orbits with Keplerian motion. We describe how we came across this type of orbit and the analysis we performed. We present the simultaneous differential equations of motion of 'ellipses extraordinaires' and other orbits as a mathematical challenge. The 'St.Louis Gateway Arch' orbit contains two 'instantaneous static points' (ISP). Polar elliptical orbits can wander considerably without tending to form other kinds of orbit. If this type of orbit is favoured then this gives a similarity to spiral galaxies containing polar orbiting material. Annular oscillatory orbits and rotating polar elliptical orbits are computed in isometric projection. A 'daisy' orbit is computed in stereo-isometric projection. The singularity at the centre of the SGA is discussed in relation to mechanics and computing, and it appears mathematically different from a black hole. In the Appendix, we prove by a mathematical method that a thin plane self-gravitating Newtonian annulus, free from external influence, exhibiting radial gravitation that varies inversely with the radius in the annular plane, must have an area mass density which also varies inversely with the radius and this exact solution is the only exact solution. Category: Mathematical Physics [30] viXra:1010.0063 [pdf] submitted on 29 Oct 2010 ### Dark Matter and Visible Matter Fundamentally Related in New Cosmological Model and Recalculated. Authors: Dan Visser Comments: 7 pages A new surface energy-value for dark matter is calculated, derivated from a perspective of a "higher order universe". A universe of dark energy, dark- and visible matter, and a dark energy force. A fundamental connection between dark matter and visible matter is related to dark energy (viXra-paper 1010.0014 in particular is the reference for this novum [5]. The surface energy-density of dark matter seems to be a factor 5 to 20 times higher than earlier predicted value-ranges by the CDMS-project and the Fermi-satelite. Also the produced energies through particle-collissions by LHC CERN will not be enough to achieve the dark matter surface energy-value. The "fact" some of these projects have announced some vaque "bliebs" might be due to a new phenomenon in the search of dark matter. It could be caused by "three dimensional time", which is embedded as a "new duality" in the new model, the "Twin-Tori cosmological Model (TTM)"[1,2,3,4]. The "three dimensional time" might cause dark matter taking unknown paths before detection. This paper has calculated the surface energy-density value for dark matter on 1 TeV in a surface of 6.4 x 10 -48 [m2]. Category: Mathematical Physics [29] viXra:1010.0036 [pdf] submitted on 24 Oct 2010 ### On Using Quaternion Operators in Quantum and Microphysics. Authors: Debayan Dasgupta Comments: 10 pages The main purpose of this paper is to show the application of mathematical system of quaternions in physics. We show a basic way of generating a quaternion operator and a method of obtaining the Schrodinger's equation using this operator matrix. Then we investigate the various probable uses of the coefficient matrix to scale relativity and spacetime quantization. Category: Mathematical Physics [28] viXra:1010.0014 [pdf] submitted on 7 Oct 2010 ### Deeper Properties Through Dark and Visible-Matter in a New Cosmological Twin-Tori Model (TTM). Authors: Dan Visser Comments: 5 pages A new cosmological model, named the Twin-Tori Model (TTM)[1], postulates a dark energy force Fde , which empowers the dynamic of a lower order universe, well known as the big bang. In this paper I introduce the 1st derivative F'de of this dark energy force to reveal deeper properties of the TTM, such as: why quantummechanics exists in the big bang, why dark matter and visible matter are equally responsible for gravity in galaxies for 1/4 of the density of dark matter at a specific length, why the big bang universe is recalculated by subquantumlevel-information below the Plancklength, and why the impression of space-expansion is due to the higher order cosmological model TTM. Category: Mathematical Physics [27] viXra:1009.0007 [pdf] submitted on 3 Sep 2010 ### A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations Authors: D.T. Froedge Comments: 16 pages 38 equations 98kb The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an interacting atomic system, eigenvalues represent particle energies in an interacting system of particles. An equation is proposed that has vector solutions defined in Dirac, or Clifford algebra, that treats a collection of particles as a single system..The proposed solution is a descriptor of a symmetric, light speed expanding group of interacting particles having real, as well as the familiar QM constituents. Category: Mathematical Physics [26] viXra:1007.0031 [pdf] submitted on 19 Jul 2010 ### A New Generic Class of Beltrami "Force-Free" Fields. Part-I: Theoretical Considerations Authors: T. E. Raptis Comments: 13 pages. We report on a new general class of solutions of the Beltrami equation, with special characteristics. We also provide examples of solutions that also satisfy Maxwell equations. A subset of these solutions can be isolated which corresponds to "gauge" fields. A special projective geometry of vacuum fields is also revealed and discussed. Category: Mathematical Physics [25] viXra:1006.0070 [pdf] submitted on 30 Jun 2010 ### Causal Set Theory and the Origin of Mass-ratio Authors: Carey R Carlson Comments: 16 pages. Quantum theory is reconstructed using standalone causal sets. The frequency ratios inherent in causal sets are used to define energy-ratios, implicating the causal link as the quantum of action. Space-time and its particle-like sequences are then constructed from causal links. A 4-D time-lattice structure is defined and then used to model neutrinos and electron clouds, which together constitute a 4-D manifold. A 6-D time-lattice is used to model the nucleons. The integration of the nucleus with its electron cloud affords calculation of the mass-ratio of the proton (or the neutron) with respect to the electron. Arrow diagrams, along with several ball-and-stick models, are used to streamline the presentation. Category: Mathematical Physics [24] viXra:1006.0052 [pdf] submitted on 21 Jun 2010 ### Handbook of Functions Errata Authors: Fredy Zypman Comments: 2 pages Formulas connecting toroidal functions and elliptical functions are useful in various areas of physics. In solving a problem in electrostatics we run across an error in the Handbook of mathematical functions of Abramowitz and Stegun. In this paper we report the details. Category: Mathematical Physics [23] viXra:1006.0042 [pdf] submitted on 16 Jun 2010 ### The Geometry of CP2 and its Relationship to Standard Model Authors: Matti Pitkänen Comments: 13 Pages. This appendix contains basic facts about CP2 as a symmetric space and Kähler manifold. The coding of the standard model symmetries to the geometry of CP2, the physical interpretation of the induced spinor connection in terms of electro-weak gauge potentials, and basic facts about induced gauge fields are discussed Category: Mathematical Physics [22] viXra:1006.0041 [pdf] submitted on 16 Jun 2010 ### Could the Dynamics of Kähler Action Predict the Hierarchy of Planck Constants? Authors: Matti Pitkänen Comments: 5 Pages. The original justification for the hierarchy of Planck constants came from the indications that Planck constant could have large values in both astrophysical systems involving dark matter and also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also factor spaces of CD and CP2 emerged from consistency conditions. It however seems that TGD actually predicts this hierarchy of covering spaces. The extreme non-linearity of the field equations defined by Kähler action means that the correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates is 1-to-many. This leads naturally to the introduction of the covering space of CD x CP2, where CD denotes causal diamond defined as intersection of future and past directed light-cones. Category: Mathematical Physics [21] viXra:1006.0040 [pdf] submitted on 16 Jun 2010 ### Weak Form of Electric-Magnetic Duality, Electroweak Massivation, and Color Confinement Authors: Matti Pitkänen Comments: 13 Pages. The notion of electric magnetic duality emerged already two decades ago in the attempts to formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable step of progress took place in the understanding of this notion. This concept leads to the identification of the physical particles as string like objects defined by magnetic charged wormhole throats connected by magnetic ux tubes. The second end of the string contains particle having electroweak isospin neutralizing that of elementary fermion and the size scale of the string is electro-weak scale would be in question. Hence the screening of electro-weak force takes place via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic duality leads also to a detailed understanding of how TGD reduces to almost topological quantum field theory. A surprising outcome is the necessity to replace CP2 Kähler form in Kähler action with its sum with S2 Kähler form. Category: Mathematical Physics [20] viXra:1006.0039 [pdf] submitted on 16 Jun 2010 ### How to Define Generalized Feynman Diagrams? Authors: Matti Pitkänen Comments: 16 Pages. Generalized Feynman diagrams have become the central notion of quantum TGD and one might even say that space-time surfaces can be identified as generalized Feynman diagrams. The challenge is to assign a precise mathematical content for this notion, show their mathematical existence, and develop a machinery for calculating them. Zero energy ontology has led to a dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially from the basic identifications as does also unitarity and non-trivial coupling constant evolution. There are however several formidable looking challenges left. 1. One should perform the functional integral over WCW degrees of freedom for fixed values of on mass shell momenta appearing in the internal lines. After this one must perform integral or summation over loop momenta. 2. One must define the functional integral also in the p-adic context. p-Adic Fourier analysis relying on algebraic continuation raises hopes in this respect. p-Adicity suggests strongly that the loop momenta are discretized and ZEO predicts this kind of discretization naturally. In this article a proposal giving excellent hopes for achieving these challenges is discussed. Category: Mathematical Physics [19] viXra:1006.0038 [pdf] submitted on 16 Jun 2010 ### Physics as Generalized Number Theory: Infinite Primes Authors: Matti Pitkänen Comments: 37 Pages. Physics as a generalized number theory program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields, and infinite primes discussed in this article. The construction of infinite primes is formally analogous to a repeated second quantization of an arithmetic quantum field theory by taking the many particle states of previous level elementary particles at the new level. Besides free many particle states also the analogs of bound states appear. In the representation in terms of polynomials the free states correspond to products of first order polynomials with rational zeros. Bound states correspond to nth order polynomials with non-rational but algebraic zeros. The construction can be generalized to classical number fields and their complexifications obtained by adding a commuting imaginary unit. Special class corresponds to hyper-octonionic primes for which the imaginary part of ordinary octonion is multiplied by the commuting imaginary unit so that one obtains a sub-space M8 with Minkowski signature of metric. Also in this case the basic construction reduces to that for rational or complex rational primes and more complex primes are obtained by acting using elements of the octonionic automorphism group which preserve the complex octonionic integer property. Can one map infinite primes/integers/rationals to quantum states? Do they have space-time surfaces as correlates? Quantum classical correspondence realized in terms of modified Dirac operator implies that if infinite rationals can be mapped to quantum states then the mapping of quantum states to space-time surfaces automatically gives the map to space-time surfaces. The question is therefore whether the mapping to quantum states defined by WCW spinor fields is possible. A natural hypothesis is that number theoretic fermions can be mapped to real fermions and number theoretic bosons to WCW ("world of classical worlds") Hamiltonians. The crucial observation is that one can construct infinite hierarchy of hyper-octonionic units by forming ratios of infinite integers such that their ratio equals to one in real sense: the integers have interpretation as positive and negative energy parts of zero energy states. One can construct also sums of these units with complex coefficients using commuting imaginary unit and these sums can be normalized to unity and have interpretation as states in Hilbert space. These units can be assumed to possess well defined standard model quantum numbers. It is possible to map the quantum number combinations of WCW spinor fields to these states. Hence the points of M8 can be said to have infinitely complex number theoretic anatomy so that quantum states of the universe can be mapped to this anatomy. One could talk about algebraic holography or number theoretic Brahman=Atman identity. One can also ask how infinite primes relate to the p-adicization program and to the hierarchy of Planck constants. The key observation is that infinite primes are in one-one correspondence with rational numbers at the lower level of hierarchy. At the first level of hierarchy the p-adic norm with respect to p-adic prime for this rational gives power p-n so that one has two powers of p - pn+ and pn- since two infinite primes corresponding to fermionic vacua X±1, where X is the product of all primes at given level of hierarchy, characterize the partonic 2-surface. The proposal inspired by the p-adicization program is that Δφ = 2π/pn defines angle measurement resolution crucial in the construction of p-adic variants of WCW ("world of classical world") as a union of symmetric coset spaces by starting from discrete variants of the real counterpart of symmetric space having common points with tis p-adic variant. The two measurement resolutions correspond to CD and CP2 degrees of freedom. The hierarchy of Planck constants generalizes imbedding space to a book like structure with pages identified in terms of singular coverings and factor spaces of CD and CP2. There are good arguments suggesting that only coverings characterized by integers na and nbare realized. The identifications na = n+ and nb = n- lead to highly non-trivial physical predictions and allow sharpen the view about the hierarchy of Planck constants. Therefore the notion of finite measurement resolution becomes the common denominator for the three threads of the number theoretic vision and give also a connection with the physics as infinite-dimensional geometry program and with the inclusions of hyper-finite factors defined by WCW spinor fields and proposed to characterize finite measurement resolution at quantum level. Category: Mathematical Physics [18] viXra:1006.0037 [pdf] submitted on 16 Jun 2010 ### Physics as Generalized Number Theory: Classical Number Fields Authors: Matti Pitkänen Comments: 28 Pages. Physics as a generalized number theory program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields discussed in this article, and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article the connection between standard model symmetries and classical number fields is discussed. The basis vision is that the geometry of the infinite-dimensional WCW ("world of classical worlds") is unique from its mere existence. This leads to its identification as union of symmetric spaces whose Kähler geometries are fixed by generalized conformal symmetries. This fixes space-time dimension and the decomposition M4 x S and the idea is that the symmetries of the Kähler manifold S make it somehow unique. The motivating observations are that the dimensions of classical number fields are the dimensions of partonic 2-surfaces, space-time surfaces, and imbedding space and M8 can be identified as hyper-octonions- a sub-space of complexified octonions obtained by adding a commuting imaginary unit. This stimulates some questions. Could one understand S = CP2 number theoretically in the sense that M8 and H = M4 x CP2 be in some deep sense equivalent ("number theoretical compactification" or M8 - H duality)? Could associativity define the fundamental dynamical principle so that space-time surfaces could be regarded as associative or co-associative (defined properly) sub-manifolds of M8 or equivalently of H. One can indeed define the associativite (co-associative) 4-surfaces using octonionic representation of gamma matrices of 8-D spaces as surfaces for which the modified gamma matrices span an associate (co-associative) sub-space at each point of space-time surface. Also M8 - H duality holds true if one assumes that this associative sub-space at each point contains preferred plane of M8 identifiable as a preferred commutative or co-commutative plane (this condition generalizes to an integral distribution of commutative planes in M8). These planes are parametrized by CP2 and this leads to M8 - H duality. WCW itself can be identified as the space of 4-D local sub-algebras of the local Clifford algebra of M8 or H which are associative or co-associative. An open conjecture is that this characterization of the space-time surfaces is equivalent with the preferred extremal property of Kähler action with preferred extremal identified as a critical extremal allowing infinite-dimensional algebra of vanishing second variations. Category: Mathematical Physics [17] viXra:1006.0036 [pdf] submitted on 16 Jun 2010 ### Physics as Generalized Number Theory: P-Adic Physics and Number Theoretic Universality Authors: Matti Pitkänen Comments: 51 Pages. Physics as a generalized number theory program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields (in particular, identifying associativity condition as the basic dynamical principle), and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article p-adic physics and the technical problems relates to the fusion of p-adic physics and real physics to a larger structure are discussed. The basic technical problems relate to the notion of definite integral both at space-time level, imbedding space level and the level of WCW (the "world of classical worlds"). The expressibility of WCW as a union of symmetric spacesleads to a proposal that harmonic analysis of symmetric spaces can be used to define various integrals as sums over Fourier components. This leads to the proposal the p-adic variant of symmetric space is obtained by a algebraic continuation through a common intersection of these spaces, which basically reduces to an algebraic variant of coset space involving algebraic extension of rationals by roots of unity. This brings in the notion of angle measurement resolution coming as Δφ = 2π/pn for given p-adic prime p. Also a proposal how one can complete the discrete version of symmetric space to a continuous p-adic versions emerges and means that each point is effectively replaced with the p-adic variant of the symmetric space identifiable as a p-adic counterpart of the real discretization volume so that a fractal p-adic variant of symmetric space results. If the Kähler geometry of WCW is expressible in terms of rational or algebraic functions, it can in principle be continued the p-adic context. One can however consider the possibility that that the integrals over partonic 2-surfaces defining ux Hamiltonians exist p-adically as Riemann sums. This requires that the geometries of the partonic 2-surfaces effectively reduce to finite sub-manifold geometries in the discretized version of δM+4. If Kähler action is required to exist p-adically same kind of condition applies to the space-time surfaces themselves. These strong conditions might make sense in the intersection of the real and p-adic worlds assumed to characterized living matter. Category: Mathematical Physics [16] viXra:1006.0035 [pdf] submitted on 16 Jun 2010 ### Construction of Configuration Space Spinor Structure Authors: Matti Pitkänen Comments: 34 Pages. There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first approach relies on a direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach discussed in this article relies on the construction of spinor structure based on the hypothesis that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for the second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of spinor structure. This implies a geometrization of fermionic statistics. The basic philosophy is that at fundamental level the construction of WCW geometry reduces to the second quantization of the induced spinor fields using Dirac action. This assumption is parallel with the bosonic emergence stating that all gauge bosons are pairs of fermion and antifermion at opposite throats of wormhole contact. Vacuum function is identified as Dirac determinant and the conjecture is that it reduces to the exponent of Kähler function. In order to achieve internal consistency induced gamma matrices appearing in Dirac operator must be replaced by the modified gamma matrices defined uniquely by Kähler action and one must also assume that extremals of Kähler action are in question so that the classical space-time dynamics reduces to a consistency condition. This implies also super-symmetries and the fermionic oscillator algebra at partonic 2-surfaces has intepretation as N = 1 generalization of space-time supersymmetry algebra different however from standard SUSY algebra in that Majorana spinors are not needed. This algebra serves as a building brick of various super-conformal algebras involved. The requirement that there exist deformations giving rise to conserved Noether charges requires that the preferred extremals are critical in the sense that the second variation of the Kähler action vanishes for these deformations. Thus Bohr orbit property could correspond to criticality or at least involve it. Quantum classical correspondence demands that quantum numbers are coded to the properties of the preferred extremals given by the Dirac determinant and this requires a linear coupling to the conserved quantum charges in Cartan algebra. Effective 2-dimensionality allows a measurement interaction term only in 3-D Chern-Simons Dirac action assignable to the wormhole throats and the ends of the space-time surfaces at the boundaries of CD. This allows also to have physical propagators reducing to Dirac propagator not possible without the measurement interaction term. An essential point is that the measurement interaction corresponds formally to a gauge transformation for the induced Kähler gauge potential. If one accepts the weak form of electric-magnetic duality Kähler function reduces to a generalized Chern-Simons term and the effect of measurement interaction term to Kähler function reduces effectively to the same gauge transformation. The basic vision is that WCW gamma matrices are expressible as super-symplectic charges at the boundaries of CD. The basic building brick of WCW is the product of infinite-D symmetric spaces assignable to the ends of the propagator line of the generalized Feynman diagram. WCW Kähler metric has in this case "kinetic" parts associated with the ends and "interaction" part between the ends. General expressions for the super-counterparts of WCW ux Hamiltoniansand for the matrix elements of WCW metric in terms of their anticommutators are proposed on basis of this picture. Category: Mathematical Physics [15] viXra:1006.0034 [pdf] submitted on 16 Jun 2010 ### Construction of Configuration Space Geometry from Symmetry Principles Authors: Matti Pitkänen Comments: 26 Pages. There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first one relies on a direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach relies on the construction of spinor structure assuming that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for the second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of spinor structure. In this article the construction of Kähler form and metric based on symmetries is discussed. The basic vision is that WCW can be regarded as the space of generalized Feynman diagrams with lines thickned to light-like 3-surfaces and vertices identified as partonic 2-surfaces. In zero energy ontology the strong form of General Coordinate Invariance (GCI) implies effective 2-dimensionality and the basic objects are pairs partonic 2-surfaces X2 at opposite light-like boundaries of causal diamonds (CDs). The hypothesis is that WCW can be regarded as a union of infinite-dimensional symmetric spaces G/H labeled by zero modes having an interpretation as classical, non-quantum uctuating variables. A crucial role is played by the metric 2-dimensionality of the light-cone boundary δM+4 + and of light-like 3-surfaces implying a generalization of conformal invariance. The group G acting as isometries of WCW is tentatively identified as the symplectic group of δM+4 x CP2 localized with respect to X2. H is identified as Kac-Moody type group associated with isometries of H = M+4 x CP2 acting on light-like 3-surfaces and thus on X2. An explicit construction for the Hamiltonians of WCW isometry algebra as so called ux Hamiltonians is proposed and also the elements of Kähler form can be constructed in terms of these. Explicit expressions for WCW ux Hamiltonians as functionals of complex coordinates of the Cartesisian product of the infinite-dimensional symmetric spaces having as points the partonic 2-surfaces defining the ends of the the light 3-surface (line of generalized Feynman diagram) are proposed. Category: Mathematical Physics [14] viXra:1006.0033 [pdf] submitted on 16 Jun 2010 ### Identification of the Configuration Space Kähler Function Authors: Matti Pitkänen Comments: 38 Pages. There are two basic approaches to quantum TGD. The first approach, which is discussed in this article, is a generalization of Einstein's geometrization program of physics to an infinitedimensional context. Second approach is based on the identification of physics as a generalized number theory. The first approach relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of classical worlds" (WCW) identified as the space of 3-surfaces in in certain 8-dimensional space. There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first approach relies on direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach relies on the construction of spinor structure based on the hypothesis that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of WCW spinor structure. In this article the proposal for Kähler function based on the requirement of 4-dimensional General Coordinate Invariance implying that its definition must assign to a given 3-surface a unique space-time surface. Quantum classical correspondence requires that this surface is a preferred extremal of some some general coordinate invariant action, and so called Kähler action is a unique candidate in this respect. The preferred extremal has intepretation as an analog of Bohr orbit so that classical physics becomes and exact part of WCW geometry and therefore also quantum physics. The basic challenge is the explicit identification of WCW Kähler function K. Two assumptions lead to the identification of K as a sum of Chern-Simons type terms associated with the ends of causal diamond and with the light-like wormhole throats at which the signature of the induced metric changes. The first assumption is the weak form of electric magnetic duality. Second assumption is that the Kähler current for preferred extremals satisfies the condition jK ^ djK = 0 implying that the ow parameter of the ow lines of jK defines a global space-time coordinate. This would mean that the vision about reduction to almost topological QFT would be realized. Second challenge is the understanding of the space-time correlates of quantum criticality. Electric-magnetic duality helps considerably here. The realization that the hierarchy of Planck constant realized in terms of coverings of the imbedding space follows from basic quantum TGD leads to a further understanding. The extreme non-linearity of canonical momentum densities as functions of time derivatives of the imbedding space coordinates implies that the correspondence between these two variables is not 1-1 so that it is natural to introduce coverings of CD x CP2. This leads also to a precise geometric characterization of the criticality of the preferred extremals. Category: Mathematical Physics [13] viXra:1006.0032 [pdf] submitted on 16 Jun 2010 ### Physics as Infinite-dimensional Geometry and Generalized Number Theory: Basic Visions Authors: Matti Pitkänen Comments: 32 Pages. There are two basic approaches to the construction of quantum TGD. The first approach relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of classical worlds" identified as the space of 3-surfaces in in certain 8-dimensional space. Essentially a generalization of the Einstein's geometrization of physics program is in question. The second vision is the identification of physics as a generalized number theory. This program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields (in particular, identifying associativity condition as the basic dynamical principle), and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article brief summaries of physics as infinite-dimensional geometry and generalized number theory are given to be followed by more detailed articles. Category: Mathematical Physics [12] viXra:1003.0027 [pdf] submitted on 6 Mar 2010 ### Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and Other Areas of Science Authors: Florentin Smarandache, V. Christianto, Fu Yuhua, Radi I. Khrapko, J. Hutchison Comments: 147 pages The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. Revealing the secrets of Nature, so that we truly see 'the sunlit plains extended, and at night the wondrous glory of the everlasting stars', requires far more than mere technical ability and mechanical dexterity learnt form books and consensus. The dustbin of scientific history is replete with discredited consensus and the grand reputations of erudite reactionaries. Only by boldly asking questions, fearlessly, despite opposition, and searching for answers where most have not looked for want of courage and independence of thought, can one hope to discover for one's self. From nothing else can creativity blossom and grow, and without which the garden of science can only aspire to an overpopulation of weeds. Category: Mathematical Physics [11] viXra:1001.0044 [pdf] submitted on 28 Jan 2010 ### A 'Planck-like' Characterization of Exponential Function Authors: Constantinos Ragazas Comments: 8 pages We derive a characterization of simple exponential functions that has the exact mathematical form to Planck's Formula for blackbody radiation in Quantum Physics. Category: Mathematical Physics [10] viXra:1001.0002 [pdf] submitted on 6 Jan 2010 ### Mathematical Model of Information Authors: Elemér E Rosinger Comments: 17 pages. A simple and rather general mathematical model of the phenomenon of information is presented, followed by several examples and comments. Category: Mathematical Physics [9] viXra:0910.0069 [pdf] submitted on 31 Oct 2009 ### Invariants Relative to Change of Value of the Independent Variable and Their Role in the Physics. Authors: Vladimir I. Smirnov Comments: 34 pages, Russian and English versions included It is identified the new class of invariants which values are constant at change of value of an inde-pendent variable. Their properties and a deriving method are shown on already known and still un-known instances, concerning to various areas of physics. In particular, new invariants (50), (55) and (57) for the straight lines intersected in one point on a plane have been discovered. Besides, the re-quest for detection of the third (not dependent on two already known) an invariant (31) electromag-netic fields for a special case of the special theory of relativity is made. Category: Mathematical Physics [8] viXra:0910.0016 [pdf] submitted on 11 Oct 2009 ### Mathematical and Phenomenological Elements of the Twin-Tori Model of Physics and Cosmology. Authors: Chris Forbes Comments: 10 pages In this, a follow up to a previous paper 'A Short Article On A Newly Proposed Model Of Cosmology' (viXra:0909.0005), some of the basic mathematical structures to be used in the formulation of the model are shown, and several advantages are discussed. The paper then takes a more phenomenological approach and several simple (1+1) dimensional models are explored. Category: Mathematical Physics [7] viXra:0909.0026 [pdf] submitted on 9 Sep 2009 ### A First Order Singular Perturbation Solution to a Simple One-Phase Stefan Problem with Finite Neumann Boundary Conditions Authors: Bruce Rout Comments: 13 pages This paper examines the difference between infinite and finite domains of a Stefan Problem. It is pointed out that attributes of solutions to the Diffusion Equation suggest assumptions of an infinite domain are invalid during initial times for finite domain Stefan Problems. The paper provides a solution for initial and early times from an analytical approach using a perturbation. This solution can then easily be applied to numerical models for later times. The differences of the two domains are examined and discussed. Category: Mathematical Physics [6] viXra:0908.0045 [pdf] submitted on 10 Aug 2009 ### Cylindrical Wave, Wave Equation, and Method of Separation of Variables Authors: Hamid V. Ansari Comments: 7 pages It is shown that the wave equation cannot be solved for the general spreading of the cylindrical wave using the method of separation of variables. But an equation is presented in case of its solving the above act will have occurred. Also using this equation the above-mentioned general spreading of the cylindrical wave for large distances is obtained which contrary to what is believed consists of arbitrary functions. Category: Mathematical Physics [5] viXra:0908.0001 [pdf] submitted on 1 Aug 2009 ### New Calculuses Authors: Vladislav Konovalov Comments: 12 pages In the article the new calculuses are offered similar differential and integral, but differing, that in them the analysis of the previous and subsequent values of a function is made. The new calculuses allow to decide problems, the solution which one with usage customary differential and integral calculus is impossible. Category: Mathematical Physics [4] viXra:0907.0002 [pdf] submitted on 9 Jul 2009 ### 3x3 Unitary to Magic Matrix Transformations Authors: Philip Gibbs Comments: 5 pages, published in Prespacetime Journal, V5 We prove that any 3x3 unitary matrix can be transformed to a magic matrix by multiplying its rows and columns by phase factors. A magic matrix is defined as one for which the sum of the elements in any row or column add to the same value. This result is relevant to recent observations on particle mixing matrices. Category: Mathematical Physics [3] viXra:0812.0008 [pdf] submitted on 21 Dec 2008 ### Topological Maxwell Field Theory and Symmetry Breaking. Authors: R. M. Kiehn Comments: recovered from sciprint.org Finally, I have found time to think about, and the incentive to study, how the field theory of Topological thermodynamics, electrodynamics, and hydrodynamics can be compared to field theory concepts that have been developed by Lagrangian methods, for both the classic and quantum mechanical varieties. For more than 30 years I have known that Cartan's topological methods could be applied to dissipative systems; the methods based on diffeomorphic-invariant Lagrangian field theories can not. The incentive came when I realized that the topological methods of Cartan gave dynamical results that can explain "symmetry breaking" and quantization in terms of continuous topological evolution. Category: Mathematical Physics [2] viXra:0703.0021 [pdf] submitted on 18 Mar 2007 ### Quantization in Dynamic Smarandache Multi-Space Authors: Fu Yuhua Comments: recovered from sciprint.org Discussing the applications of Dynamic Smarandache Multi-Space (DSMS) Theory. Supposing for the n different dynamic spaces (n is a dynamic positive integer and the function of time) the different equations have been established, as these n different dynamic spaces synthesize the DSMS, and they are mutually affected, some new coupled equations need to establish in the DSMS to replace some equations in the original dynamic spaces, as well as supply other equations to process the contact, boundary conditions and so on. For the unified processing of all equations in the DSMS, this paper proposes to run the quantization processing to all the variables and all the equations and establish the unified variational principle of quantization with the collocation method based on the method of weighted residuals, and simultaneously solve all the equations in the DSMS with the optimization method. Thus by using the unified variational principle of quantization in the DSMS and the fractal quantization method, will pave the way for the unified processing of the theory of relativity and the quantum mechanics, and the unified processing of the four foundational interactions. Finally the coupled solution for the problem of relativity and quantum mechanics is discussed. Category: Mathematical Physics [1] viXra:0703.0020 [pdf] submitted on 18 Mar 2007 ### Smarandache Stepped Functions Authors: Mircea Eugen Selariu Comments: recovered from sciprint.org The discovery of mathematical complements, assembled under the name of the eccentric mathematics, gave the opportunity for a series of applications, amongst which, in this article, are presented the impulse, step, and unitary ramp functions. The difference, in comparison with the same classic functions, from the distributions theory, is that those eccentric are periodical with a 2π period. By combining these between them, new mathematical functions have been defined; united under the name Smarandache stepped functions. Category: Mathematical Physics ## Replacements of recent Submissions [281] viXra:1503.0169 [pdf] replaced on 2015-03-31 03:04:32 ### New Way of Developing Information Technology and Imaginary Time for the Purpose of Building the Universe Authors: Rodney Bartlett Comments: 14 Pages. Stephen Hawking writes, “In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic …” (“A Brief History of Time” by Stephen Hawking - Bantam Press, 1988, p.139) When Hawking says there are no singularities in imaginary time, can his statement relate to physics? Or is it purely mathematical, in which case it would reinforce the idea that the universe began with a singularity and a Big Bang? I believe imaginary time has physical meaning since it can be developed from space-time where parallel lines become perpendicular without any motion occurring. Such a feat depends on a particular form of General Relativity’s space-time curvature. It leads to new cosmology and quantum physics that includes deletion of distance on every scale – plus a method for cosmogenesis or creation of the universe. This author has a habit of copying and pasting. I’ve done it in the past to present an idea in different contexts, hoping that would demonstrate the idea’s validity. In this article, sentences are added to my recycling – showing that I still believe in the basic idea I started with, but adding information (sometimes from mathematics) to support that basis. In addition, I’ve included a 600-word summary at the start that was inspired by a reply I gave to HarryT in the vixra forums (where I write as rodney1956) as well as by the 2012 Nature Letter “Quantum teleportation over 143 kilometres using active feed-forward “ (http://www.nature.com/nature/journal/v489/n7415/full/nature11472.html). The summary uses strings to unite fields and matter. I've decided to call the strings bits (Binary digITS) that aren't only regarded as units of information, but also as quantum-size pulses of energy. Category: Mathematical Physics [280] viXra:1503.0063 [pdf] replaced on 2015-03-12 08:48:44 ### A Discussion on Curl Equations in Mathematical Physics Authors: LIU Changli Comments: 5 Pages. The paper is written in English and Chinese. Usually, the numbers of unknowns are equal to the numbers of differential equations. However, there are some exceptions. One example is Maxwell equations; there are 6 unknowns and 8 equations. The other example is elasticity equations in stress form; there 6 unknowns and 9 equations. In the paper, I generalize the definition of linearly dependent in algebra to the concept of differential linearly dependent in differential equations, and I use this definition to explain the above problem. Category: Mathematical Physics [279] viXra:1503.0045 [pdf] replaced on 2015-03-11 15:24:26 ### Variation of a Scheme Authors: Miguel A. Sanchez-Rey Comments: 5 Pages. A short explanation of the holographic interface of PHPR will be stated. Category: Mathematical Physics [278] viXra:1503.0022 [pdf] replaced on 2015-03-10 12:09:38 ### Phase Liquid Condensate as Novel Quantum Approach Authors: Sergey Kamenshchikov Comments: 6 Pages. In this paper we consider a nonlinear stochastic approach to the description of quantum systems. It is shown that a possibility to derive quantum properties - spectrum quantization, zero point positive energy and uncertainty relations, exists in frame of Zaslavsky phase liquid. This liquid is considered as a projection of continuous medium into a Hilbert phase space. It has isotropic minimal diffusion defined by Planck constant. Areas of probability condensation, formed by phase liquid turbulence, may produce clustering centers–particles, which preserve boundaries. These areas are described as strange attractors with fractal transport properties. The stability of attractors has been shown in frame of the first order perturbation theory. Quantum peculiarities of considered systems have been strictly derived from markovian Fokker-Planck equation. It turned out that the positive zero point energy has volumetric properties and grows for higher time resolutions. We have shown that a quasi stable condensate may be applied as a satisfactory model of an elementary quantum system. The conditions of attractor stability are defined on the basis of Nonlinear Prigogine Theorem. It is shown that the integrity of classical and quantum approaches is recovered while existence of particles is derived in terms of mechanical model. Category: Mathematical Physics [277] viXra:1502.0241 [pdf] replaced on 2015-04-07 17:00:07 ### Concept of Smallest Length Having a Physical Sense: Theorem Authors: Emmanuel Kanambaye Comments: 9 Pages. The document is in french In this document, after presented that we mean by "smallest length having physical sense",we propose the theorem resulting. Category: Mathematical Physics [276] viXra:1502.0186 [pdf] replaced on 2015-04-20 04:14:09 ### Foundations of a Mathematical Model of Physical Reality Authors: J.A.J. van Leunen Comments: 39 Pages. This paper starts from the idea that physical reality implements a network of a small number of mathematical structures. Only in that way can be explained that observations of physical reality fit so well with mathematical methods. The mathematical structures do not contain mechanisms that ensure coherence. Thus apart from the network of mathematical structures a model of physical reality must contain mechanisms that manage coherence such that dynamical chaos is prevented. Reducing complexity appears to be the general strategy. The structures appear in chains that start with a foundation. The strategy asks that especially in the lower levels, the subsequent members of the chain emerge with inescapable self-evidence from the previous member. The chains are interrelated and in this way they enforce mutual restrictions. As a consequence the lowest levels of a corresponding mathematical model of physical reality are rather simple and can be comprehended by skilled mathematicians. In order to explain the claimed setup of physical reality, the paper selects a special foundation for the major chain. That foundation is a skeleton relational structure and it was already discovered and introduced in 1936. The paper does not touch more than the first development levels. The base model that is reached in this way puts already very strong restrictions to more extensive models. Some of the features of the base model are investigated and compared with results of contemporary physics. Category: Mathematical Physics [275] viXra:1502.0186 [pdf] replaced on 2015-03-28 06:13:53 ### Foundations of a Mathematical Model of Physical Reality Authors: J.A.J. van Leunen Comments: 35 Pages. This paper starts from the idea that physical reality implements a network of a small number of mathematical structures. Only in that way can be explained that observations of physical reality fit so well with mathematical methods. The mathematical structures do not contain mechanisms that ensure coherence. Thus apart from the network of mathematical structures a model of physical reality must contain mechanisms that manage coherence such that dynamical chaos is prevented. Reducing complexity appears to be the general strategy. The structures appear in chains that start with a foundation. The strategy asks that especially in the lower levels, the subsequent members of the chain emerge with inescapable self-evidence from the previous member. The chains are interrelated and in this way they enforce mutual restrictions. As a consequence the lowest levels of a corresponding mathematical model of physical reality are rather simple and can be comprehended by skilled mathematicians. In order to explain the claimed setup of physical reality, the paper selects a special foundation for the major chain. That foundation is a skeleton relational structure and it was already discovered and introduced in 1936. The paper does not touch more than the first development levels. The base model that is reached in this way puts already very strong restrictions to more extensive models. Some of the features of the base model are investigated and compared with results of contemporary physics. Category: Mathematical Physics [274] viXra:1502.0186 [pdf] replaced on 2015-03-14 05:43:03 ### Foundations of a Mathematical Model of Physical Reality Authors: J.A.J. van Leunen Comments: 33 Pages. This paper starts from the idea that physical reality implements a network of a small number of mathematical structures. Only in that way can be explained that observations of physical reality fit so well with mathematical methods. The mathematical structures do not contain mechanisms that ensure coherence. Thus apart from the network of mathematical structures a model of physical reality must contain mechanisms that manage coherence such that dynamical chaos is prevented. Reducing complexity appears to be the general strategy. The structures appear in chains that start with a foundation. The strategy asks that especially in the lower levels, the subsequent members of the chain emerge with inescapable self-evidence from the previous member. The chains are interrelated and in this way they enforce mutual restrictions. As a consequence the lowest levels of a corresponding mathematical model of physical reality are rather simple and can be comprehended by skilled mathematicians. In order to explain the claimed setup of physical reality, the paper selects a special foundation for the major chain. That foundation is a skeleton relational structure and it was already discovered and introduced in 1936. The paper does not touch more than the first development levels. The base model that is reached in this way puts already very strong restrictions to more extensive models. Some of the features of the base model are investigated and compared with results of contemporary physics. Category: Mathematical Physics [273] viXra:1502.0186 [pdf] replaced on 2015-03-05 06:27:29 ### Foundations of a Mathematical Model of Physical Reality Authors: J.A.J. van Leunen Comments: 32 Pages. This paper starts from the idea that physical reality implements a network of a small number of mathematical structures. Only in that way can be explained that observations of physical reality fit so well with mathematical methods. The mathematical structures do not contain mechanisms that ensure coherence. Thus apart from the network of mathematical structures a model of physical reality must contain mechanisms that manage coherence such that dynamical chaos is prevented. Reducing complexity appears to be the general strategy. The structures appear in chains that start with a foundation. The strategy asks that especially in the lower levels, the subsequent members of the chain emerge with inescapable self-evidence from the previous member. The chains are interrelated and in this way they enforce mutual restrictions. As a consequence the lowest levels of a corresponding mathematical model of physical reality are rather simple and can be comprehended by skilled mathematicians. In order to explain the claimed setup of physical reality, the paper selects a special foundation for the major chain. That foundation is a skeleton relational structure and it was already discovered and introduced in 1936. The paper does not touch more than the first development levels. The base model that is reached in this way puts already very strong restrictions to more extensive models. Some of the features of the base model are investigated and compared with results of contemporary physics. Category: Mathematical Physics [272] viXra:1502.0168 [pdf] replaced on 2015-02-24 16:38:03 ### The TEQ: Exploring a Link with the QCD and New Territories - v2 Authors: Thierry PERIAT Comments: 16 Pages. First attempt of a GUT in a 4D space I don’t ignore the long discussion concerning the representation of nuclei (protons and neutrons); in extenso the story of the birth of the standard model (SM). But I also know the actual difficulties and the arguments for a modest extension of the SM. Physics is actually a house containing diverse coherent theories. Some of them are logically related to the others; some are not. This still remain a modern challenge to bring all members of the family under the same roof. My attempt here is to continue the discussion around a fundamental coherent vision. Starting with general considerations concerning the QCD, I reexamine the notion of equation of motion via the Lorentz-Einstein Law, introduce a new paradigm, explain the type I supraconduction and finally make a junction with the old Wong’s work for basic situations. All this is obtained in staying in a four dimensional world. I don’t pretend to have discovered the holy “Grail”. Category: Mathematical Physics [271] viXra:1502.0147 [pdf] replaced on 2015-02-23 20:34:18 ### Remarkable Properties of the Eddington Number 137 and Electric Parameter 137.036 Excluding the Multiverse Hypothesis Authors: Francis M. Sanchez Comments: 10 Pages. Considering that the Large Eddington Number has correctly predicted the number of atoms in the Universe, the properties of the Eddington electric number 137 are studied. This number shows abnormal arithmetic properties, in liaison with the 5th harmonic number 137/60. It seems that Egyptians was aware of this, as the architecture of the Hypostyle Karnak room reveals, as well as the Ptolemaic approximation p ≈ 2 + 137/120, together with a specific mention in the Bible, and overhelming connexions with musical canonic numbers. The SO(32) characteristic superstring number 496, the third perfect number, connects directly with the three main interaction parameters, and is very close to the square root of the Higgs boson-electron mass ratio, so the Higgs boson discovery excludes the Multiverse, favoring rather a unique Cosmos being a finite computer using 137 and its extension 137.036 as calculation basis. The direct liaison between the mean value of the two main cosmic radiuses and the Bohr radius through the simplest harmonic series excludes any role of chance. Precise symmetric relations involving the Lyuty-Kotov non-Doppler period permit to propose precise (100 ppb) values for the weak and strong interaction constants, as well as G ≈ 6.6754635 × 10-11 kg-1 m3 s-2, at 2s the tabulated value. Category: Mathematical Physics [270] viXra:1502.0147 [pdf] replaced on 2015-02-23 01:14:02 ### Remarkable Properties of the Eddington Number 137 and Electric Parameter 137.036 Excluding the Multiverse Hypothesis Authors: Francis M. Sanchez Comments: 9 Pages. Considering that the Large Eddington Number has correctly predicted the number of atoms in the Universe, the properties of the Eddington electric number 137 are studied. This number shows abnormal arithmetic properties, in liaison with canonic numbers of the string and superstring theories including overwhelming relations with musical canonic numbers. The liaison with the 5th harmonic number 137/60 is so tight that it seems that Egyptians was aware of them, as the architecture of the Hypostyle Karnak room reveals, as well as the Ptolemaic approximation for p ≈ 2 + 137/120, together with a specific mention in the Bible. The direct liaison between the mean value of the two main cosmic radiuses and the Bohr radius through the simplest harmonic series excludes any role of chance. The SO(32) characteristic superstring number 496, the third perfect number, connects directly with the three main interaction parameters, and is very close to the square root of the Higgs boson-electron mass ratio, so the Higgs boson discovery excludes the Multiverse, favoring rather a unique Cosmos being a finite computer using 137 and its extension 137.036 as calculation basis. Category: Mathematical Physics [269] viXra:1502.0147 [pdf] replaced on 2015-02-21 08:23:10 ### Remarkable Properties of the Eddington Number 137 and Electric Parameter 137.036 Excluding the Multiverse Hypothesis Authors: Francis M. Sanchez Comments: 8 Pages. Considering that the Large Eddington Number has correctly predicted the number of atoms in the Universe, the properties of the Eddington electric number 137 are studied. This number shows abnormal arithmetic properties, in liaison with canonic numbers of the string and superstring theories including overwhelming relations with musical canonic numbers. The liaison with the harmonic series is so tight that it seems that Egyptians was aware of them, as the architecture of the Hypostyle Karnak room reveals. The direct liaison between the mean value of two Universe radiuses and the Bohr radius through the simplest harmonic series excludes any role of chance. It is concluded that the Cosmos is a finite computer using 137 and its extension 137.036 as calculation basis. Category: Mathematical Physics [268] viXra:1502.0147 [pdf] replaced on 2015-02-20 00:04:27 ### Remarkable Properties of the Eddington Number 137 and Electric Parameter 137.036 Excluding the Multiverse Hypothesis Authors: Francis M. Sanchez, Valery Kotov Comments: 8 Pages. Considering that the Large Eddington Number has correctly predicted the number of atoms in the Universe, the properties of the Eddington electric number 137 are studied. This number shows abnormal arithmetic properties, in liaison with canonic numbers of the string and superstring theories including overwhelming relations with musical canonic numbers. The liaison with the harmonic series is so tight that it seems that Egyptians was aware of them, as the architecture of the Hypostyle Karnak room reveals. The direct liaison between the mean value of two Universe radiuses and the Bohr radius through the simplest harmonic series excludes any role of chance. It is concluded that the Cosmos is a finite computer using 137 and its extension 137.036 as calculation basis. Category: Mathematical Physics [267] viXra:1502.0048 [pdf] replaced on 2015-02-15 14:07:41 ### PCT, Spin, Lagrangians Authors: Hans Detlef Hüttenbach Comments: 18 Pages. Some orthrographical corrections. In this paper I invite you to take a step aside current quantum field theory (QFT): QFT has been said to be "well-established" since the 80's of the last century by its foremost theorists), and the majority of physicists consider it to be essentially complete since the discovery of the Higgs particle. It will be interesting to see, what that really means: What are the problems left over to the younger generations? I'll show you that a.o. it fails in its Lagrangian formalism, its postulate of positivity of energy, I'll show the uselessness of the uncertainty principle as to electromagnetic fields, and we'll see that there are serious doubts as to its conception of the photonic nature of electromagnetic fields, which a simple experiment could test against. Category: Mathematical Physics [266] viXra:1502.0048 [pdf] replaced on 2015-02-07 14:10:49 ### PCT, Spin, Lagrangians Authors: Hans Detlef Hüttenbach Comments: 18 Pages. Smoothed two sentences, one misspelling.. In this paper I invite you to take a step aside current quantum field theory (QFT): QFT has been said to be "well-established" since the 80's of the last century by its foremost theorists), and the majority of physicists consider it to be essentially complete since the discovery of the Higgs particle. It will be interesting to see, what that really means: What are the problems left over to the younger generations? I'll show you that a.o. it fails in its Lagrangian formalism, its postulate of positivity of energy, I'll show the uselessness of the uncertainty principle as to electromagnetic fields, and we'll see that there are serious doubts as to its conception of the photonic nature of electromagnetic fields, which a simple experiment could test against. Category: Mathematical Physics [265] viXra:1501.0202 [pdf] replaced on 2015-01-22 03:24:00 ### Solving Formally the Magnetic Reconnection Problem Authors: Thierry Periat Comments: 5 Pages. No change in the text - Administrative modifications In that short note, I demonstrate formally the existence of a logical path implying the automatic resolution of the magnetic reconnection problem. The latter has been the motivation for numerous articles and is actually explored by the ARTEMIS mission. Category: Mathematical Physics [264] viXra:1501.0184 [pdf] replaced on 2015-02-09 15:39:21 ### New Dark Energy-Force Solves The Discrepancy Of The Proton-Radius. Authors: Dan Visser Comments: 8 Pages. It is well known among physicists that two different kinds of experiments give an anomaly in the proton-radius. The anomaly is: When a muon orbits the proton the proton-radius is 4% smaller than when an electron orbits the proton. This anomaly is a puzzle in standard physics. This puzzle is solved in a new cosmological theory with a new dark energy-force. This article describes the solution. The solution is put in perspective of new physics by a combination of quantum-gravity and sub-quantum dark matter-force in one formula, within the new cosmological theory, called the Double Torus Theory for the universe. Additionally the principle for an anti-gravitational machine is shown based on the use of a dark matter force. Category: Mathematical Physics [263] viXra:1501.0184 [pdf] replaced on 2015-01-21 08:52:22 ### New Dark Energy-Force Solves The Discrepancy Of The Proton-Radius. Authors: Dan Visser Comments: 6 Pages. It is well known among physicists that two different kinds of experiments give an anomaly in the proton-radius. The anomaly is: When a muon orbits the proton the proton-radius is 4% smaller than when an electron orbits the proton. This anomaly is a puzzle in standard physics. This puzzle is solved in a new cosmological theory with a new dark energy-force. This article describes the solution. The solution is put in perspective of new physics by a combination of quantum-gravity and sub-quantum dark matter-force in one formula, within the new cosmological theory, called the Double Torus Theory for the universe. Category: Mathematical Physics [262] viXra:1501.0124 [pdf] replaced on 2015-03-20 03:15:53 ### An Approximation to the Mass Ratio of the Proton to the Electron Authors: Harry A. Watson Comments: 5 Pages. An Approximation to the Mass Ratio of the Proton to the Electron. The mass ratio of the proton to the electron is a dimensionless physical constant. The following expression provides a good estimate. (4π)(4π−1/π)(4π−2/π)= 1836.15 (1) The above expression is also the greatest lower bound (GLB) for a more general expression. A geometric persuasion is given and the more general expression is determined via the inversion of the spheres. Category: Mathematical Physics [261] viXra:1501.0124 [pdf] replaced on 2015-03-03 11:50:02 ### An Approximation to the Mass Ratio of the Proton to the Electron Authors: Harry A. Watson Comments: 4 Pages. An Approximation to the Mass Ratio of the Proton to the Electron. The mass ratio of the proton to the electron is a dimensionless physical constant. The following expression provides a good estimate. (4π)(4π−1/π)(4π−2/π)= 1836.15 (1) The above expression is also the greatest lower bound (GLB) for a more general expression. A geometric persuasion is given and the more general expression is determined via the inversion of the spheres. Category: Mathematical Physics [260] viXra:1501.0124 [pdf] replaced on 2015-02-24 08:09:21 ### An Approximation to the Mass Ratio of the Proton to the Electron Authors: Harry A. Watson Comments: 5 Pages. An Approximation to the Mass Ratio of the Proton to the Electron. The mass ratio of the proton to the electron is a dimensionless physical constant. The following expression provides a good estimate. (4π)(4π−1/π)(4π−2/π)= 1836.15 (1) The above expression is also the greatest lower bound (GLB) for a more general expression. A geometric persuasion is given and the more general expression is determined via the inversion of the spheres. Category: Mathematical Physics [259] viXra:1501.0105 [pdf] replaced on 2015-01-09 16:38:15 ### On Some Analytical Results for 3-Cycles of the Logistic Map Authors: Andrzej Okninski Comments: 4 Pages. A comment has been added (end of Section2). In the present work new analytical results for the 3-cycles of the logistic map are obtained. Category: Mathematical Physics [258] viXra:1501.0105 [pdf] replaced on 2015-01-09 05:26:55 ### On Some Analytical Results for 3-Cycles of the Logistic Map Authors: Andrzej Okninski Comments: 4 Pages. One reference added. In the present work new analytical results for the 3-cycles of the logistic map are obtained. Category: Mathematical Physics [257] viXra:1501.0105 [pdf] replaced on 2015-01-08 18:29:30 ### On Some Analytical Results for 3-Cycles of the Logistic Map Authors: Andrzej Okninski Comments: 4 Pages. Mistake in caption of Fig. 1 has been corrected. In the present work new analytical results for the 3-cycles of the logistic map are obtained. Category: Mathematical Physics [256] viXra:1501.0095 [pdf] replaced on 2015-03-02 09:05:50 ### Towards A Quaternionic Spacetime Tensor Calculus Authors: Carsten S.P. Spanheimer Comments: 38 Pages. Introducing a special quaternionic vector calculus on the tangent bundle of a 4-dimensional space, and by forcing a condition of holomorphism, a Minkowski-type spacetime emerges, from which special relativity, gravitation and also the whole Maxwell theory of electromagnetic fields arises. Category: Mathematical Physics [255] viXra:1501.0095 [pdf] replaced on 2015-02-02 09:30:48 ### Towards A Quaternionic Spacetime Calculus Authors: Carsten S. P. Spanheimer Comments: 38 Pages. Introducing a special quaternionic vector calculus on the tangent bundle of a 4-dimensional space, and by forcing a condition of holomorphism, a Minkowski-type spacetime emerges, from which gravitation and also the whole Maxwell theory of electromagnetic fields arises. This is a preliminary draft. Category: Mathematical Physics [254] viXra:1501.0095 [pdf] replaced on 2015-01-12 12:48:08 ### Towards A Quaternionic Spacetime Calculus Authors: Carsten S. P. Spanheimer Comments: 38 Pages. Introducing a special quaternionic vector calculus on the tangent bundle of a 4-dimensional space, and by forcing a condition of holomorphism, a Minkowski-type spacetime emerges, from which gravitation and also the whole Maxwell theory of electromagnetic fields arises. This is a preliminary draft. Category: Mathematical Physics [253] viXra:1501.0052 [pdf] replaced on 2015-03-25 12:13:11 ### Gravitation is a Gradient in the Velocity of Light Authors: DT Froedge Comments: 12 Pages. Ongoing Development It has long been known that a photon entering a gravitational potential follows a path identical to that of a photon in a variable speed of light defined by the Shapiro velocity for Minkowski flat space [1]. It is shown here that a particle defined as a pair of trapped photons in a massless box, having constant energy infalling a conservative gravitational field, is accelerated by a gradient in the velocity of light exactly as a particle in a gravitational potential [2], It is asserted that gravitation is a gradient in c produced by the presence of mass. The symmetry of the Lorentz transform between the change in velocity and the change in c is demonstrated as the mechanism for gravitational acceleration . Also discussed are the QFT effects that define the total action path of photons which could induce an alteration in the velocity of light in the proximity of a photon path [3], and thus the mechanism for creating the effects of gravitation. Category: Mathematical Physics [252] viXra:1501.0052 [pdf] replaced on 2015-01-16 16:08:59 ### A Connection Between Gravitation, the Velocity of Light, and Quantum Field Effects Authors: DT Froedge Comments: 9 Pages. It has long been known that a photon entering a gravitational potential follows a path identical to that of a photon in a variable speed of light defined by the Shapiro velocity for Minkowski flat space [1]. It is shown here that a particle having constant energy infalling a gravitational potential, and defined as a pair of trapped photons in a massless box, is accelerated by a gradient in the velocity of light exactly as a particle in a gravitational field [2], and thus, is asserted that gravitation is nothing more than a gradient in c produced by the presence of mass. It is also illustrated that QFT effects that define the total action path of photons could induce an alteration in the velocity of light in the proximity of a photon path [3], and could be the mechanism creating the effects of gravitation. Category: Mathematical Physics [251] viXra:1412.0162 [pdf] replaced on 2014-12-16 15:08:54 ### What Drives Reality Authors: J.A.J. van Leunen Comments: 11 Pages. The dynamics of reality is well regulated. What is the mechanism that controls dynamics and what rules this mechanism? The models of contemporary physics do not answer these questions. In the realm of elementary particles the special habits of quaternions appear to play an essential role. In the past physics had a choice between the Maxwell based approach and the quaternionic based approach. That choice has a significant influence on how physics equations look. Einstein selected the Maxwell approach and in this way physics inherits the spacetime view on the universe in which we live. Category: Mathematical Physics [250] viXra:1411.0178 [pdf] replaced on 2014-11-25 06:28:41 ### Quaternions and Hilbert Spaces Authors: J.A.J. van Leunen Comments: 30 Pages. This is a compilation of quaternionic number systems, quaternionic function theory, quaternionic Hilbert spaces and Gelfand triples. Category: Mathematical Physics [249] viXra:1411.0032 [pdf] replaced on 2014-12-09 08:41:56 ### Metamorphoses of Resonance Curves for Two Coupled Oscillators: the Case of Small Nonlinearities in the Main Mass Frame Authors: Jan Kyziol Comments: 10 pages We study dynamics of two coupled periodically driven oscillators in general case. Periodic steady-state solutions of the system of two equations are determined within the Krylov-Bogoliubov-Mitropolsky approach. The orresponding amplitude profiles, A(omega), B(omega), which are given by two implicit equations, F(A,B,omega)=0, G(A,B,omega)=0, where omega is frequency of the driving force, are computed. These two equations, each describing a surface, define a 3D curve - intersection of these surfaces. In the present paper we carry out preliminary investigation of metamorphoses of this curve, induced by changes of control parameters. The corresponding changes of dynamics near singular points of the curve are studied. Category: Mathematical Physics [248] viXra:1411.0015 [pdf] replaced on 2014-11-10 05:51:44 ### Variational Principle of Extremum in Electromechanical and Electrodynamic Systems \\ Вариационный принцип экстремума в электромеханических и электродинамических системах Authors: Solomon I. Khmelnik Comments: 360 Pages. Here we shall formulate and prove the variational optimum principle for electromechanical systems of arbitrary configuration, in which electromagnetic, mechanical, thermal, hydraulic or other processes are going on. The principle is generalized for systems described by partial differential equations, including also Maxwell equations. The presented principle permits to expand the Lagrange formalism and extend the new formalism on dissipative systems. It is shown that for such systems there exists a pair of functionals with a global saddle point. A high-speed universal algorithm for such systems calculation with any perturbations is described. This algorithm realizes a simultaneous global saddle point search on two functionals. The algorithms for solving specific mathematical and technical problems are cited. The book contains numerous examples, including those presented as M-functions of the MATLAB system and as functions of the DERIVE system. The programs in systems MATLAB and DERIVE are published as a separate annex in the form of an electronic book. Programs are not required to understand the theory. \\ Формулируется и доказывается вариационный принцип оптимума для электромеханических систем произвольной конфигурации, в которых протекают электромагнитные, механические, тепловые, гидравлические и др. процессы. Принцип обобщается на системы, описываемые уравнениями в частных производных и, в т.ч., уравнениями Максвелла. Предложенный принцип позволяет расширить лагранжев формализм и распространить новый формализм на диссипативные системы. Показывается, что для таких систем существует пара функционалов с глобальной седловой точкой. Описывается быстродействующий универсальный алгоритм расчета таких систем при любых возмущающих воздействиях. В этом алгоритме реализуется метод поиска глобальной седловой точки одновременно на двух функционалах. Приводятся алгоритмы решения конкретных математических и технических задач. Книга содержит многочисленные примеры, в т.ч. в виде М-функций системы MATLAB и в виде функций системы DERIVE. Программы в системах MATLAB и DERIVE изданы как отдельное приложение в виде электронной книги. Программы не являются обязательными для понимания теории. Category: Mathematical Physics [247] viXra:1409.0122 [pdf] replaced on 2015-02-03 01:11:41 ### The Proof of Dirichlet's Assertion on Celestial Mechanics Authors: Reinhard Frischbier Comments: 7 Pages. A typo had to be fixed in Eq (1). I am very sorry for causing so much work and I promise that this version will be final. Since the proof given by Wang Qiu-Dong on Dirichlet's assertion is based on the successive approximations objections to assumptions of the global solution of this problem have to be raised. Category: Mathematical Physics [246] viXra:1409.0122 [pdf] replaced on 2015-02-02 05:34:40 ### The Proof of Dirichlet's Assertion on Celestial Mechanics Authors: Reinhard Frischbier Comments: 7 Pages. we have corrected two minor typesetting mistakes Since the proof given by Wang Qiu-Dong on Dirichlet's assertion is based on the successive approximations objections to assumptions of the global solution of this problem have to be raised. Category: Mathematical Physics [245] viXra:1409.0122 [pdf] replaced on 2015-01-07 06:43:41 ### The Proof of Dirichlet's Assertion on Celestial Mechanics Authors: Reinhard Frischbier Comments: 7 Pages. Since the proof given by Wang Qiu-Dong on Dirichlet's assertion is based on the successive approximations objections to assumptions of the global solution of this problem have to be raised. Category: Mathematical Physics [244] viXra:1409.0122 [pdf] replaced on 2014-09-16 07:36:10 ### The Proof of Dirichlet's Assertion on Celestial Mechanics Authors: Reinhard Frischbier Comments: 7 Pages. Since the proof given by Wang Qiu-Dong on Dirichlet's assertion is based on the successive approximations objections to assumptions of the global solution of this problem have to be raised. Category: Mathematical Physics [243] viXra:1409.0109 [pdf] replaced on 2014-12-25 20:57:06 ### Introducing Spin Authors: Doug Jensen Comments: 13 Pages. The property of spin is introduced. Two types of spin (real and imaginary) are integrated with a complex spin equation that is over 200 years old. This material changes our view of imaginary numbers, and the definition of the constant i has changed. Category: Mathematical Physics [242] viXra:1409.0109 [pdf] replaced on 2014-10-15 08:14:28 ### Introducing Unitary Circles Authors: Doug Jensen Comments: 8 Pages. Unitary circles are introduced. These circles model the property of spin and are based on imaginary numbers. A new definition for the constant i is implied. The mathematical evidence supporting these circles includes the introduction of an elegant pi formula. Category: Mathematical Physics [241] viXra:1409.0050 [pdf] replaced on 2015-01-11 06:55:05 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 45 Pages. It is possible to derive a model from a set of well selected first principles. After a series of extensions of this foundation the model shows many similarities with what we know from observing reality. The first principles formulate a skeleton relational structure that is mathematically known as an orthocomplemented weakly modular lattice. It can be considered as part of a recipe for modular construction. When starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of sub-models that each represent a static status quo of the whole model. This base model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based sub model that embeds the discrete objects. The discrete part of the model keeps its data in an infinite dimensional separable Hilbert space. The continuum part stores its data in a corresponding non-separable Hilbert space. An extra mechanism that controls the coherence and the scheduling of dynamics applies the recurrent embedding of the discrete objects into appropriate continuums. Despite the fact that the target of the model is planned to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. The reason for this restriction is that many of its aspects cannot be observed and will never become observable. Physicists tend to deny completely or largely deduced models. The deduced model appears to own built-in restrictions that guard against uncontrolled growth of the complexity of the model. Category: Mathematical Physics [240] viXra:1409.0050 [pdf] replaced on 2014-12-18 16:02:46 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 44 Pages. It is possible to derive a model from a set of well selected first principles. After a series of extensions of this foundation the model shows many similarities with what we know from observing reality. The first principles formulate a skeleton relational structure that is mathematically known as an orthocomplemented weakly modular lattice. It can be considered as part of a recipe for modular construction. When starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of sub-models that each represent a static status quo of the whole model. This base model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. The discrete part of the model keeps its data in an infinite dimensional separable Hilbert space. The continuum part stores its data in a corresponding non-separable Hilbert space. An extra mechanism that controls the coherence and the scheduling of dynamics applies the recurrent embedding of the discrete objects into appropriate continuums. Despite the fact that the target of the model is planned to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. The reason for this restriction is that many of its aspects cannot be observed and will never become observable. Physicists tend to deny completely or largely deduced models. Category: Mathematical Physics [239] viXra:1409.0050 [pdf] replaced on 2014-12-13 05:48:50 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 11 Pages. It is possible to derive a model from a set of well selected first principles. After a series of extensions of this foundation the model shows many similarities with what we know from observing reality. The first principles formulate a skeleton relational structure that is mathematically known as an orthocomplemented weakly modular lattice. It can be considered as part of a recipe for modular construction. When starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of sub-models that each represent a static status quo of the whole model. This base model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. The discrete part of the model keeps its data in an infinite dimensional separable Hilbert space. The continuum part stores its data in a corresponding non-separable Hilbert space. An extra mechanism that controls the coherence and the scheduling of dynamics applies the recurrent embedding of the discrete objects into appropriate continuums. Despite the fact that the target of the model is planned to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. The reason for this restriction is that many of its aspects cannot be observed and will never become observable. Physicists tend to deny completely or largely deduced models. Category: Mathematical Physics [238] viXra:1409.0050 [pdf] replaced on 2014-11-25 06:13:48 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 43 Pages. It is possible to derive a model from a set of well selected first principles. After a series of extensions of this foundation the model shows many similarities with what we know from observing reality. The first principles formulate a skeleton relational structure that is mathematically known as an orthocomplemented weakly modular lattice. It can be considered as part of a recipe for modular construction. When starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of sub-models that each represent a static status quo of the whole model. This base model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. The discrete part of the model keeps its data in an infinite dimensional separable Hilbert space. The continuum part stores its data in a corresponding non-separable Hilbert space. An extra mechanism that controls the coherence and the scheduling of dynamics applies the recurrent embedding of the discrete objects into appropriate continuums. Despite the fact that the target of the model is planned to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. The reason for this restriction is that many of its aspects cannot be observed and will never become observable. Physicists tend to deny completely or largely deduced models. Category: Mathematical Physics [237] viXra:1409.0050 [pdf] replaced on 2014-11-16 09:27:30 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 40 Pages. It is possible to derive a model from a set of well selected first principles. After a series of extensions of this foundation the model shows many similarities with what we know from observing reality. The first principles formulate a skeleton relational structure that is mathematically known as an orthocomplemented weakly modular lattice. It can be considered as part of a recipe for modular construction. When starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of sub-models that each represent a static status quo of the whole model. This base model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. The discrete part of the model keeps its data in an infinite dimensional separable Hilbert space. The continuum part stores its data in a corresponding non-separable Hilbert space. An extra mechanism that controls the coherence and the scheduling of dynamics applies the recurrent embedding of the discrete objects into appropriate continuums. Despite the fact that the target of the model is planned to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. The reason for this restriction is that many of its aspects cannot be observed and will never become observable. Physicists tend to deny completely or largely deduced models. Category: Mathematical Physics [236] viXra:1409.0050 [pdf] replaced on 2014-10-25 13:29:49 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 30 Pages. It is possible to derive a model from well selected first principles that shows many similarities with what we know from observing reality. The presented model is based on first principles that formulate a recipe for modular construction and this foundation is mathematically known as an orthocomplemented weakly modular lattice. When starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of static sub-models that each represent a static status quo of the whole model. The model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. The discrete part of the model keeps its data in an infinite dimensional separable Hilbert space. The continuum part stores its data in a corresponding non-separable Hilbert space. Despite the fact that the target of the model is to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. The reason for this restriction is that many of its aspects cannot be observed and will never become observable. Physicists tend to deny completely or largely deduced models. Category: Mathematical Physics [235] viXra:1409.0050 [pdf] replaced on 2014-10-15 05:24:43 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 29 Pages. It is possible to derive a model from well selected first principles that shows many similarities with what we know from observing reality. The presented model is based on first principles that formulate a recipe for modular construction and this foundation is mathematically known as an orthocomplemented weakly modular lattice. Starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of static sub-models that each represent a static status quo of the whole model. The model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. Despite the fact that the target of the model is to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. Many of its aspects cannot be observed. Category: Mathematical Physics [234] viXra:1409.0050 [pdf] replaced on 2014-10-09 16:23:24 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 26 Pages. It is possible to derive a model from well selected first principles that shows many similarities with what we know from observing reality. The presented model is based on first principles that formulate a recipe for modular construction and this foundation is mathematically known as an orthocomplemented weakly modular lattice. Starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of static sub-models that each represent a static status quo of the whole model. The model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. Despite the fact that the target of the model is to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. Many of its aspects cannot be observed. Category: Mathematical Physics [233] viXra:1409.0050 [pdf] replaced on 2014-09-25 16:34:38 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 26 Pages. It is possible to derive a model from well selected first principles that shows many similarities with what we know from observing reality. The presented model is based on first principles that formulate a recipe for modular construction and this foundation is mathematically known as an orthocomplemented weakly modular lattice. Starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of static sub-models that each represent a static status quo of the whole model. The model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. Despite the fact that the target of the model is to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. Many of its aspects cannot be observed. Category: Mathematical Physics [232] viXra:1409.0050 [pdf] replaced on 2014-09-22 09:44:18 ### A Mathematical Model of Reality Authors: J.A.J. van Leunen Comments: 26 Pages. It is possible to derive a model from well selected first principles that shows many similarities with what we know from observing reality. The presented model is based on first principles that formulate a recipe for modular construction and this foundation is mathematically known as an orthocomplemented weakly modular lattice. Starting from this foundation it is mathematically evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of static sub-models that each represent a static status quo of the whole model. The model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based model that embeds the discrete objects. Despite the fact that the target of the model is to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. Many of its aspects cannot be observed. Category: Mathematical Physics [231] viXra:1409.0030 [pdf] replaced on 2015-01-02 06:40:47 ### On Application of Green Function Method to the Solution of 3D Incompressible Navier-Stokes Equations Authors: Algirdas Antano Maknickas Comments: 4 Pages. The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed into full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Velocity and outer forces densities components were expressed in form of curl for obtaining solutions satisfying continuity condition specifying divergence of velocities equality to zero. Finally, solution in 3D space for any shaped boundary was expressed in terms of 3D Green function and inverse Laplace transform accordantly. Category: Mathematical Physics [230] viXra:1409.0020 [pdf] replaced on 2014-12-22 13:27:22 ### The Concept of Mass as Interfering Photons, and the Originating Mechanism of Gravitation Authors: DT Froedge Comments: 10 Pages. For most purposes in physics the concept of mass particles and photons are treated as though they are completely separate and distinct entities having little connection accept through collision interactions. This paper explores the concept of a mass particle being viewed as a pair of trapped photons in a mass-less box demonstrating proper relativistic dynamics, Lorentz covariance, and gravitational properties. The mechanism of trapping of the photons in the particle is not herein defined; however the lack of sufficient spin to properly constitute a photon would be a containment factor. Although this presentation is primarily focused on electrons, presumably it would be applicable to any particle with primary constituents consisting of particles that travel at light speed along null vectors. This illustrates the concept of the equivalence of mass and energy, and why mass velocity cannot exceed the speed of light. It is asserted and illustrated; that the gravitational effect on particles and photons can be can be effectuated by a simple gradient in the speed of light. This allows the assertion that gravitation is a local alteration of c generated by the presence of matter and could be a QFT effect. Category: Mathematical Physics [229] viXra:1408.0235 [pdf] replaced on 2014-09-01 06:52:34 ### Theoretical Background of T.T. Brown Electro-Gravity Communication System Authors: Algirdas Antano Maknickas Comments: 7 Pages. The author proposed theory of communication system working on gravity waves. Such system of devices should work if the electromagnetic field curves space-time. Theoretical results shows that the artificial change of gravity or space-time curvature should observes at the distance much more bigger than dimension of transmitter antenna. The article ends with discussion details of technical properties of working electro-gravity communication system. Category: Mathematical Physics [228] viXra:1408.0188 [pdf] replaced on 2015-01-19 06:33:07 ### Dark Matter Is Time-clock Faster Than Light In Vacuum. Authors: Dan Visser Comments: 12 Pages. In this paper formulations and calculations are exposed for a new paradigm of dark matter. Dark matter does not exists of solid particles. Dark matter exists of ‘faster time-cells’ than standard-time-based-on-light-speed. These ‘cells’ may sometimes give high-energetic particles, such as e.g. neutrinos, a velocity-gain, which can violate the light-speed in vacuum. In this perspective dark matter can be detected by the ‘combination of energy per time-volume and simultaneously a small light-flash’. Therefore the focus must be on detection of clock-energy during light-flashes !! Put a clock into the dark matter detection-configuration and the energy of the ‘time energy-density’ will change the clock-period, while it also gives a light-flash per second! The ‘dark matter time-cells’ are independent on whether time is relative or not. The assumption to describe dark matter as solid particles, such as ‘wimps’, ‘axions’, or ‘dark matter being its own anti-particle’, is therefore false. The new dark matter paradigm is based on analysis and worked out in this ‘paper’ as a part of a wider framework, called the Double Torus Theory for the Universe. This is a replacement for the Big Bang theory. The wish of this paper is to contribute to the dark matter research-project-teams, who aim to detect dark matter in the up-coming period to 2017 in the UK, USA, Italy, the Netherlands and other countries. Despite all the institutional- and press-commotion of OPERA an ICARUS in 2012 I postpone neutrinos indeed can be affected by ‘dark matter faster-time-cells’. These imply the violation of General Relativity Theory (GRT) and Quantum Theory (QT). A calculation proves that e.g. 62 nanosecond velocity-gain wouldn’t be a hazardous value, but can vary depending on the intensity of the dark matter’s circular-acceleration in vacuum. This is explained in this ‘paper’. It also means not always a violation of GRT and QT will happen. Separately and consistently an additional formulation (and calculation) is given about how the vacuum-energy-density of the QT can be eliminated from its extreme too large value compared to GRT. Category: Mathematical Physics [227] viXra:1408.0144 [pdf] replaced on 2014-09-03 11:36:17 ### The Physicalist Program Authors: Miguel A. Sanchez-Rey Comments: 20 Pages. We'll present the groundwork for the physicalist program and suggest it's implications. Category: Mathematical Physics [226] viXra:1408.0072 [pdf] replaced on 2014-08-16 15:01:48 ### A Physical Axiom System Based on the Spirit Authors: Zhang yunfan Comments: 29 Pages. This paper established a physical axiom system. By the axiom system we can derive important physical laws such as momentum conservation law, Newton's second law, Newton's law of gravity, Schrodinger equation and Maxwell's equations, simplified existing physical theories and explain some physical phenomenons those unresolved by traditional physical theories. We can also derive Schwarzschild solution of external spherically symmetric gravitational field, gravitational red shift equation, proved that if in large-scale distance, Newton's law of gravity and red shift equation must be corrected, the data by corrected formulas meet the astronomical observed results well. Category: Mathematical Physics [225] viXra:1408.0018 [pdf] replaced on 2015-04-02 08:43:55 ### Die Entschlüsselung Der Feinstrukturkonstante Authors: Bernd Ganter Comments: Paper in German language. 110 pages. Comments to bernd.ganter.fsk@gmx.de please. This paper is about dimensions and fundamental forces in the universe, and especially the derivation of the fine structure constant, the value of which has remained unexplained for almost 100 years now. The paper is the German parent document of the condensed version viXra:1405.0226 in English translation. If we stripped away all the empirical properties of things in the universe there are two possible things which would be left: The first is abstract mathematics, the second is information. Here we show that the strengths of the four fundamental forces correspond to their information density: Information can be transferred from one dimension to another depending on its density. This paper contains - on the basis of values gained by tetration (repeated exponentiation) - the exact calculation (including Feynman diagram calculation) of the value of the fine structure constant which differs from the measured 2010-CODATA-value by less than one billionth (a millionth of a millionth) and can thus be seen as the new and theoretically derived reference value. This value is 1 / 137.0359990744043. Category: Mathematical Physics [224] viXra:1407.0068 [pdf] replaced on 2015-02-25 06:59:16 ### Space-Time Sedeons and Their Application in Relativistic Quantum Mechanics and Field Theory Authors: Victor L. Mironov, Sergey V. Mironov Comments: 104 Pages. Revised version This book is a systematic exposition of the algebra of sixteen-component space-time values "sedeons" and their applications to describe quantum particles and fields. The book contains the results of our several articles published in the period 2008-2014. It includes a large number of carefully selected reference material relating to the use of different multi-component algebras in physical problems and may be useful as an introduction to the application of hypercomplex numbers in physics. Category: Mathematical Physics [223] viXra:1407.0068 [pdf] replaced on 2014-09-15 04:05:22 ### Space-Time Sedeons and Their Application in Relativistic Quantum Mechanics and Field Theory Authors: Victor L. Mironov, Sergey V. Mironov Comments: New version, 104 pages, 5 tables This book is a systematic exposition of the algebra of sixteen-component space-time values "sedeons" and their applications to describe quantum particles and fields. The book contains the results of our several articles published in the period 2008-2014. It includes a large number of carefully selected reference material relating to the use of different multi-component algebras in physical problems and may be useful as an introduction to the application of hypercomplex numbers in physics. Category: Mathematical Physics [222] viXra:1407.0008 [pdf] replaced on 2015-04-18 10:05:48 ### Image Comparisons of Black Hole vs. Neutron Dark Star by Ray Tracing Authors: DT Froedge Comments: 24 Pages. Presented APS Apr. 2015 In previous papers we have discussed the concept of a theory of gravitation with local energy conservation, and the properties of a large neutron star resulting when the energy of gravitation resides locally with the particle mass and not in the gravitational field [1][2][3]. A large neutron star’s surface radius grows closer to the gravitational radius as the mass increases, but is always slightly larger. As the mass increases there is a continuously greater mass defect for incoming particles. Since the localization of energy applies to the photon, a photon does not decrease in energy rising in a gravitational field, and can thus escape. Photon trajectories in a strong gravitational field have some peculiar features that are not immediately obvious, but can be investigated by the use of ray tracing procedures. The most notable is the fact that only a fraction of the blackbody radiation emitted from the surface escapes into space (about 0.00004% for Sag A*). The remainder enters orbit below the maximum photon orbit. Because of the low percent of escaping blackbody radiation, the heavy neutron stars considered in this paper will be referred to as a Neutron Dark Star (NDS). In contrast to the Black Hole (BH) which should be totally dark inside the photon shadow, the NDS will appear as a fuzzy low luminosity ball with a Full Width Half Maximum intensity diameter of about 3.85 Schwarzschild radii inside the shadow. This paper will investigate the difference in the appearance of a Neutron Dark Star and a Black Hole by using ray tracing techniques. The Event Horizon Telescope currently under development should be able to distinguish the difference between the theories. Category: Mathematical Physics [221] viXra:1406.0130 [pdf] replaced on 2015-02-15 08:47:42 ### Derivation of the Reflection Integral Equation of the Zeta Function by the Quaternionic Analysis Authors: K. Sugiyama Comments: 25 Pages. We derive the reflection integral equation of the zeta function by the quaternionic analysis. Many researchers have attempted proof of Riemann hypothesis, but they have not been successful. The proof of this Riemann hypothesis has been an important mathematical issue. In this paper, we attempt to derive the reflection integral equation from the quaternionic analysis as preparation proving Riemann hypothesis. We obtain a generating function of the inverse Mellin-transform. We obtain new generating function by multiplying the generating function with exponents and reversing the sign. We derive the reflection integral equation from inverse Z-transform of the generating function. Category: Mathematical Physics [220] viXra:1406.0065 [pdf] replaced on 2014-06-12 09:28:02 ### A Comment About the Solution in 2nd Order Schwarzschild Equation Authors: Valdir Monteiro dos Santos Godoi Comments: 2 Pages. We analyze the solution of Schwarzschild Equation taking mathematically the observation that the motion of bodies can be a spiral modulated by trigonometric functions, which may be something more important than simply mean a shift of perihelion. Category: Mathematical Physics [219] viXra:1405.0306 [pdf] replaced on 2014-05-28 07:52:03 ### Eternal Rotational Dark Torus Suggests Visible Big Bang in the Double Torus Universe. Authors: Dan Visser Comments: 11 Pages. I hope for attention in the vixra-blog and science-magazines. ‘Spatial dark matter’ and ‘two refined time-clocks smaller than the Planck-time’ cause a CMB-dipole and concentric circles in the CMB of the universe. This proves a Double Torus Universe. Hence the universe did not start with a Big Bang. These characteristics are derived, analyzed, explained in my articles of the Double Torus Theory (DTT) and proved by current lab-experiments and astronomical observations. Furthermore three levels of accelerations are derived, which prove several dimensional characteristics, such as the accelerated space expansion in Big Bang cosmology is due to rotation of the Double Torus, or such as dimensions that show dark matter is not a mass-particle like a ‘wimp’. However, the heart of the DTT is the use of ‘time smaller than the Planck-time’ (sub-quantum-time). This is the power for events beyond quantum-gravitation, which makes events visible for just 4.45%. The rest seems to remain dark, but eventually involves in the sub-quantum-dynamics of the universe. I also give a related derivation, which uses the ‘Gaussian mathematical expression’ for accelerations related to gravitation in the DTT, instead of using the Gaussian only for CMB-temperature-variations. Thereby I introduced a new ‘duonistic-parameter’ (b=0, b=1, b=2), which describes how entangled ‘duonistic neutrinos’ involve in three levels of acceleration. These ‘duonistic neutrinos’ represent space. The acceleration-levels relate to a Newton-constant (G) for G’ < G or G=0, or G”> G or G=1. The acceleration-levels performed are: An acceleration-level for CMB-dark flow and CMB-concentric circles per (±i±1)G, an acceleration-level for spatial dark flow on mass per ±G and an acceleration-level for the torus-rotation of the universe per ±G^2. Category: Mathematical Physics [218] viXra:1405.0251 [pdf] replaced on 2015-01-18 02:02:49 ### Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations Authors: A. A. Frempong Comments: 45 Pages. Copyright © A. A. Frempong Better news. After nearly 150 years of patience, the Navier-Stokes equations in 3-D for incompressible fluid flow have been analytically solved by two different methods. It is shown that these equations can be solved in 4-dimensions or n-dimensions. The author has proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no incompressible fluid flow as is known (see p. 23). By applying the above law, the hitherto unsolved magnetohydrodynamic equations were also routinely solved. In addition to the usual method of solving these equations, the N-S equations have also been solved by a second method in which the three equations are added to produce a single equation which is then integrated. The solutions by the two methods are identical, except for the constants involved. The Navier-Stokes equation will be linearized, solved, and the solution analyzed. This solution will be followed by the solution of the Euler equation. Following the Euler solution, the Navier-Stokes equation will be solved, essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in parabolic, periodic, and decreasingly exponential motion. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The convective acceleration terms produce square root function behavior and fractional terms containing square root functions with variables in the denominators and consequent turbulence behavior. For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and prove the existence of smooth solutions of the Navier-Stokes equations. Category: Mathematical Physics [217] viXra:1405.0251 [pdf] replaced on 2014-07-16 17:38:41 ### Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations Authors: A. A. Frempong Comments: 45 Pages. Better news. After nearly 150 years of patience, the Navier-Stokes equations in 3-D for incompressible fluid flow have been analytically solved by two different methods. It is shown that these equations can be solved in 4-dimensions or n-dimensions. The author has proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no incompressible fluid flow as is known (see p. 23). By applying the above law, the hitherto unsolved magnetohydrodynamic equations were also routinely solved. In addition to the usual method of solving these equations, the N-S equations have also been solved by a second method in which the three equations are added to produce a single equation which is then integrated. The solutions by the two methods are identical, except for the constants involved. The Navier-Stokes equation will be linearized, solved, and the solution analyzed. This solution will be followed by the solution of the Euler equation. Following the Euler solution, the Navier-Stokes equation will be solved, essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in parabolic, periodic, and decreasingly exponential motion. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The convective acceleration terms produce square root function behavior and fractional terms containing square root functions with variables in the denominators and consequent turbulence behavior. For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and prove the existence of smooth solutions of the Navier-Stokes equations. Category: Mathematical Physics [216] viXra:1405.0251 [pdf] replaced on 2014-07-04 23:53:22 ### Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations Authors: A. A. Frempong Comments: 45 Pages. Copyright © A. A. Frempong Better news. After nearly 150 years of patience, the Navier-Stokes equations in 3-D for incompressible fluid flow have been analytically solved by two different methods. It is shown that these equations can be solved in 4-dimensions or n-dimensions. The author has proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no incompressible fluid flow as is known (see p. 23). By applying the above law, the hitherto unsolved magnetohydrodynamic equations were also routinely solved. In addition to the usual method of solving these equations, the N-S equations have also been solved by a second method in which the three equations are added to produce a single equation which is then integrated. The solutions by the two methods are identical, except for the constants involved. The Navier-Stokes equation will be linearized, solved, and the solution analyzed. This solution will be followed by the solution of the Euler equation. Following the Euler solution, the Navier-Stokes equation will be solved, essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in parabolic, periodic, and decreasingly exponential motion. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The convective acceleration terms produce square root function behavior and fractional terms containing square root functions with variables in the denominators and consequent turbulence behavior. For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and prove the existence of smooth solutions of the Navier-Stokes equations. Category: Mathematical Physics [215] viXra:1405.0251 [pdf] replaced on 2014-06-24 14:31:33 ### Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations Authors: A. A. Frempong Comments: 45 Pages. Copyright © A. A. Frempong Better news. After nearly 150 years of patience, the Navier-Stokes equations in 3-D for incompressible fluid flow have been analytically solved by two different methods. It is shown that these equations can be solved in 4-dimensions or n-dimensions. The author has proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no incompressible fluid flow as is known (see p. 23). By applying the above law, the hitherto unsolved magnetohydrodynamic equations were also routinely solved. In addition to the usual method of solving these equations, the N-S equations have also been solved by a second method in which the three equations are added to produce a single equation which is then integrated. The solutions by the two methods are identical, except for the constants involved. The Navier-Stokes equation will be linearized, solved, and the solution analyzed. This solution will be followed by the solution of the Euler equation. Following the Euler solution, the Navier-Stokes equation will be solved, essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in parabolic, periodic, and decreasingly exponential motion. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The convective acceleration terms produce square root function behavior and fractional terms containing square root functions with variables in the denominators and consequent turbulence behavior. For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and prove the existence of smooth solutions of the Navier-Stokes equations. Category: Mathematical Physics [214] viXra:1405.0251 [pdf] replaced on 2014-06-22 18:12:52 ### Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations Authors: A. A. Frempong Comments: 45 Pages. Copyright © A. A. Frempong Better news. After nearly 150 years of patience, the Navier-Stokes equations in 3-D for incompressible fluid flow have been analytically solved by two different methods. It is shown that these equations can be solved in 4-dimensions or n-dimensions. The author has proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no incompressible fluid flow as is known (see p. 23). By applying the above law, the hitherto unsolved magnetohydrodynamic equations were also routinely solved. In addition to the usual method of solving these equations, the N-S equations have also been solved by a second method in which the three equations are added to produce a single equation which is then integrated. The solutions by the two methods are identical, except for the constants involved. The Navier-Stokes equation will be linearized, solved, and the solution analyzed. This solution will be followed by the solution of the Euler equation. Following the Euler solution, the Navier-Stokes equation will be solved, essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in parabolic, periodic, and decreasingly exponential motion. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The convective acceleration terms produce square root function behavior and fractional terms containing square root functions with variables in the denominators and consequent turbulence behavior. For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and prove the existence of smooth solutions of the Navier-Stokes equations. Category: Mathematical Physics [213] viXra:1405.0251 [pdf] replaced on 2014-06-20 23:01:10 ### Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations Authors: A. A. Frempong Comments: 45 Pages. Copyright © A. A. Frempong Better news. After nearly 150 years of patience, the Navier-Stokes equations in 3-D for incompressible fluid flow have been analytically solved by two different methods. It is shown that these equations can be solved in 4-dimensions or n-dimensions. The author has proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no incompressible fluid flow as is known (see p. 23). By applying the above law, the hitherto unsolved magnetohydrodynamic equations were also routinely solved. In addition to the usual method of solving these equations, the N-S equations have also been solved by a second method in which the three equations are added to produce a single equation which is then integrated. The solutions by the two methods are identical, except for the constants involved. The Navier-Stokes equation will be linearized, solved, and the solution analyzed. This solution will be followed by the solution of the Euler equation. Following the Euler solution, the Navier-Stokes equation will be solved, essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in parabolic, periodic, and decreasingly exponential motion. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The convective acceleration terms produce square root function behavior and fractional terms containing square root functions with variables in the denominators and consequent turbulence behavior. For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and prove the existence of smooth solutions of the Navier-Stokes equations. Category: Mathematical Physics [212] viXra:1405.0251 [pdf] replaced on 2014-05-16 14:15:22 ### Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations Authors: A. A. Frempong Comments: 35 Pages. Copyright © A. A. Frempong Good news. In this paper, after nearly 150 years of waiting, the Navier-Stokes equations in 3-D for incompressible fluid flow have been analytically solved. It is shown that these equations can be solved in 4-dimensions or n-dimensions. The author has proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio and also each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no incompressible fluid flow as is known (see p. 23). By applying the above law, the hitherto unsolved magnetohydrodynamic equations were also routinely solved. The preliminaries reveal how the ratio technique evolved as well as possible applications of the solution method in mathematics, science, engineering, business, economics, and investment decisions. The coverage is as follows. The Navier-Stokes equation will be linearized, solved and the solution analyzed. This solution will be followed by the solution of the Euler equation. Following the Euler solution, the Navier-Stokes equation will be solved, essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions revealed the role of each term of the Navier-Stokes equations in fluid flow. Most importantly, the gravity term is the indispensable term in fluid flow, and it is involved in the parabolic as well as the forward motion of fluids. The pressure gradient term is also involved in the parabolic motion of fluids. The viscosity terms are involved in parabolic, periodic and decreasingly exponential motion of fluids. The variable acceleration term is also involved in the periodic and decreasingly exponential motion of fluids. The convective acceleration terms produce square root functions and fractional terms containing square root functions. For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and thus prove the existence of smooth solutions of the Navier-Stokes equations. Category: Mathematical Physics [211] viXra:1405.0226 [pdf] replaced on 2015-01-18 09:01:02 ### The Derivation of the Fine Structure Constant Authors: Bernd Ganter Comments: 16 Pages. Comments to bernd.ganter.fsk@gmx.de please This paper is about dimensions and fundamental forces in the universe, and especially the derivation of the fine structure constant, the value of which has remained unexplained for almost 100 years now. The paper is the condensed version in English translation of the German parent document viXra:1408.0018. If we stripped away all the empirical properties of things in the universe there are two possible things which would be left: The first is abstract mathematics, the second is information. Here we show that the strengths of the four fundamental forces correspond to their information density: Information can be transferred from one dimension to another depending on its density. The derivation of the value of the fine structure constant 1/137 as result of a permanent information transfer between two- and three-dimensional worlds, corresponding to wave-particle-dualism, and a prediction for higher energies (1/128.5) can be found in the second version (v2) and in the German parent document. This revised (third) version contains the exact calculation - including Feynman diagram calculation - of the value of the fine structure constant which differs from the measured 2010-CODATA-value by less than one billionth (a millionth of a millionth) and can thus be seen as the new and theoretically derived reference value: 1/137.035999074404296. Special thanks for translation support to Mr. Joe Compton from Kentucky. Category: Mathematical Physics [210] viXra:1404.0290 [pdf] replaced on 2015-02-15 08:37:07 ### Construction of the Zeta Functions of the Quaternion and the Simple Groups Authors: K. Sugiyama Comments: 11 Pages. This paper constructs the zeta functions of the quaternion and the sporadic finite simple groups. Although many researchers have tried the proof of the Riemann hypothesis, they have not resulted in the success. The proof of this Riemann hypothesis has been an important issue of mathematics. In this paper, we construct zeta functions of the quaternion and sporadic finite simple groups as preparation proving the Riemann hypothesis. Category: Mathematical Physics [209] viXra:1404.0281 [pdf] replaced on 2015-02-15 08:42:37 ### Derivation of the Reflection Integral Equation of the Zeta Function by the Complex Analysis Authors: K. Sugiyama Comments: 40 Pages. This paper derives the reflection integral equation of the zeta function by the complex analysis. Many researchers have attempted proof of Riemann hypothesis, but have not been successful. The proof of this Riemann hypothesis has been an important mathematical issue. In this paper, we attempt to derive the reflection integral equation by the complex analysis as preparation proving Riemann hypothesis. We obtain a generating function of the inverse Mellin-transform. We obtain new generating function by multiplying the generating function with exponents and reversing the sign. We derive the reflection integral equation from inverse Z-transform of the generating function. We derive the summation equation, the asymptotic expansion, Faulhaber’s formula, and Nörlund–Rice integral from the reflection integral equation. Category: Mathematical Physics [208] viXra:1404.0281 [pdf] replaced on 2014-06-29 09:56:46 ### Derivation of the Contour Integral Equation of the Zeta Function by the Inverse Mellin Transform Authors: Koji Sugiyama Comments: 41 Pages. This paper derives the contour integral equation of the zeta function by the inverse Mellin transform. Many researchers have attempted proof of Riemann hypothesis, but have not been successful. The proof of this Riemann hypothesis has been an important mathematical issue. In this paper, we attempt to derive the contour integral equation from the inverse Mellin transform as preparation proving Riemann hypothesis. We obtain a generating function of the inverse Mellin-transform. We obtain new generating function by multiplying the generating function with exponents and reversing the sign. We derive the contour integral equation from inverse Z-transform of the generating function. We derive the summation equation, the asymptotic expansion, Faulhaber’s formula, and Nörlund–Rice integral from the contour integral equation. Category: Mathematical Physics [207] viXra:1403.0286 [pdf] replaced on 2014-07-02 12:52:37 ### The Arm Theory Authors: Arm Boris Nima Comments: 14 Pages. Did you ever wondered what is the Taylor formula for an arbitrary chosen basis ? The answer of this question is the Arm theory introduced in this article. Category: Mathematical Physics [206] viXra:1403.0271 [pdf] replaced on 2014-12-09 12:37:03 ### The Triangular Properties of Associated Legendre Functions Using the Vectorial Addition Theorem for Spherical Harmonics Authors: Rami Mehrem Comments: 7 Pages. Triangular properties of associated Legendre functions are derived using the Vectorial Addition Theorem of spherical harmonics Category: Mathematical Physics [205] viXra:1402.0151 [pdf] replaced on 2014-05-30 23:23:06 ### Some Observations on Schrödingers’s Affine Connection Authors: William O. Straub Comments: 7 Pages. Fixed typo in Eq. 5.5 In a series of papers written over the period 1944-1948, the great Austrian physicist Erwin Schrödinger presented his ideas on symmetric and non-symmetric affine connections and their possible application to general relativity. Several of these ideas were subsequently presented in his notable 1950 book "Space-Time Structure," in which Schrödinger outlined the case for both metric and general connections, symmetric and otherwise. In the following discussion we focus on one particular connection presented by Schrödinger in that book and its relationship with the non-metricity tensor. We also discuss how this connection overcomes a problem that Hermann Weyl experienced with the connection he proposed in his failed 1918 theory of the combined gravitational-electromagnetic field. A simple physical argument is then presented demonstrating that Schrödingers’s formalism accommodates electromagnetism in a more natural way than Weyl’s theory. Category: Mathematical Physics [204] viXra:1402.0151 [pdf] replaced on 2014-02-23 14:37:53 ### Some Observations on Schrödingers’s Affine Connection Authors: William O. Straub Comments: 7 Pages. A few minor revisions In a series of papers written over the period 1944-1948, the great Austrian physicist Erwin Schrödinger presented his ideas on symmetric and non-symmetric affine connections and their possible application to general relativity. Several of these ideas were subsequently presented in his notable 1950 book "Space-Time Structure," in which Schrödinger outlined the case for both metric and general connections, symmetric and otherwise. In the following discussion we focus on one particular connection presented by Schrödinger in that book and its relationship with the non-metricity tensor. We also discuss how this connection overcomes a problem that Hermann Weyl experienced with the connection he proposed in his failed 1918 theory of the combined gravitational-electromagnetic field. A simple physical argument is then presented demonstrating that Schrödingers’s formalism accommodates electromagnetism in a more natural way than Weyl’s theory. Category: Mathematical Physics [203] viXra:1402.0050 [pdf] replaced on 2014-02-23 14:13:30 ### The Cubic Equation and 137.036 Authors: J. S. Markovitch Comments: 3 Pages. A special case of the cubic equation, distinguished by having an unusually economical solution, is shown to relate to both the fine structure constant inverse (approximately 137.036) and the sines squared of the quark and lepton mixing angles. Category: Mathematical Physics [202] viXra:1401.0215 [pdf] replaced on 2014-04-04 09:00:16 ### Exploring Gravitational Phenomena in a Riemann-Minkowski Spacetime Authors: Carsten S.P. Spanheimer Comments: 31 Pages. After the concept of a locally scale-invariant spacetime has been introduced in the companion document, now physical experiments on mathematical entities will be performed to find out implications of that model. With regard to earlier solutions by others, an unbiased inspection of different gravitational scenarios under local scale-invariance in comparison with physical reality is undertaken. This gives five results at once: A suspected locality condition, a promising gravitational ansatz, a static solution for the gravitational potential in the subjective picture together with a possible static cosmic redshift, and a set of candidate terms for governing field equations of physical spacetime. Category: Mathematical Physics [201] viXra:1401.0162 [pdf] replaced on 2014-09-15 10:16:15 ### Associative Space Time Sedenions Authors: Victor L. Mironov, Sergey V. Mironov Comments: New version, 8 pages, 2 tables We present an alternative type of sixteen-component hypercomplex scalar-vector values "space-time sedenions", generating associative noncommutative space-time Clifford algebra. Category: Mathematical Physics [200] viXra:1401.0153 [pdf] replaced on 2014-10-05 15:13:48 ### An Explanation of the Entropic Nature of the Mass Using Classical Physics Authors: Nicolas Poupart Comments: 16 Pages. This paper presents a theory of the relativistic gravitational field by simply applying Carnot's principle to the gravitation and by reinforcing as inviolable the mass-energy equivalence law and the equivalence of the inertial mass and the heavy mass. It will be shown that this theory can explain easily the origin of dark matter and dark energy. In addition, it will also be shown that this theory is not distinguishable from general relativity at our experimental scale. Category: Mathematical Physics [199] viXra:1401.0153 [pdf] replaced on 2014-08-27 06:13:39 ### An Explanation of the Entropic Nature of the Mass Using Classical Physics Authors: Nicolas Poupart Comments: With seven (7) supplementary pages, in annex, with the full calculation of the galaxies dark matter. This paper presents a theory of the relativistic gravitational field by simply applying Carnot's principle to the gravitation and by reinforcing as inviolable the mass-energy equivalence law and the equivalence of the inertial mass and the heavy mass. It will be shown that this theory can explain easily the origin of dark matter and dark energy. In addition, it will also be shown that this theory is not distinguishable from general relativity at our experimental scale. Category: Mathematical Physics [198] viXra:1401.0153 [pdf] replaced on 2014-03-08 11:44:52 ### An Explanation of the Entropic Nature of the Mass Using Classical Physics Authors: Nicolas Poupart Comments: 8 Pages. This paper presents a theory of the relativistic gravitational field by simply applying Carnot's principle to the gravitation and by reinforcing as inviolable the mass-energy equivalence law and the equivalence of the inertial mass and the heavy mass. It will be shown that this theory can explain easily the origin of dark matter and dark energy. In addition, it will also be shown that this theory is not distinguishable from general relativity at our experimental scale. Category: Mathematical Physics [197] viXra:1401.0152 [pdf] replaced on 2014-10-05 15:11:01 ### Une Explication de la Nature Entropique de la Masse Utilisant la Physique Classique Authors: Nicolas Poupart Comments: 17 Pages. Cet article expose une théorie du champ gravitationnel relativiste en appliquant simplement le principe de Carnot à la gravitation et en considérant la loi d'équivalence masse-énergie ainsi que l'équivalence masse inertielle et masse pesante comme inviolable. Il sera démontré que cette théorie permet d'expliquer aisément l'origine de la matière noire ainsi que de l'énergie noire. De plus, il sera également démontré que cette théorie n'est pas différenciable de la relativité générale à notre échelle expérimentale. Category: Mathematical Physics [196] viXra:1401.0152 [pdf] replaced on 2014-08-27 06:18:27 ### Une Explication de la Nature Entropique de la Masse Utilisant la Physique Classique Authors: Nicolas Poupart Comments: 16 Pages. Synchronisation avec la version anglaise Cet article expose une théorie du champ gravitationnel relativiste en appliquant simplement le principe de Carnot à la gravitation et en considérant la loi d'équivalence masse-énergie ainsi que l'équivalence masse inertielle et masse pesante comme inviolable. Il sera démontré que cette théorie permet d'expliquer aisément l'origine de la matière noire ainsi que de l'énergie noire. De plus, il sera également démontré que cette théorie n'est pas différenciable de la relativité générale à notre échelle expérimentale. Category: Mathematical Physics [195] viXra:1401.0152 [pdf] replaced on 2014-07-18 08:06:29 ### Une Explication de la Nature Entropique de la Masse Utilisant la Physique Classique Authors: Nicolas Poupart Comments: Ajout de huit (8) pages d'annexes Cet article expose une théorie du champ gravitationnel relativiste en appliquant simplement le principe de Carnot à la gravitation et en considérant la loi d'équivalence masse-énergie ainsi que l'équivalence masse inertielle et masse pesante comme inviolable. Il sera démontré que cette théorie permet d'expliquer aisément l'origine de la matière noire ainsi que de l'énergie noire. De plus, il sera également démontré que cette théorie n'est pas différenciable de la relativité générale à notre échelle expérimentale. Category: Mathematical Physics [194] viXra:1401.0152 [pdf] replaced on 2014-03-08 11:47:40 ### Une Explication de la Nature Entropique de la Masse Utilisant la Physique Classique Authors: Nicolas Poupart Comments: 8 Pages. Cet article expose une théorie du champ gravitationnel relativiste en appliquant simplement le principe de Carnot à la gravitation et en considérant la loi d'équivalence masse-énergie ainsi que l'équivalence masse inertielle et masse pesante comme inviolable. Il sera démontré que cette théorie permet d'expliquer aisément l'origine de la matière noire ainsi que de l'énergie noire. De plus, il sera également démontré que cette théorie n'est pas différenciable de la relativité générale à notre échelle expérimentale. Category: Mathematical Physics [193] viXra:1401.0145 [pdf] replaced on 2014-04-28 12:50:04 ### Proof For A Rotational Double Torus Universe. Authors: Dan Visser Comments: 6 Pages. The Universe rotates. We live in a Double Torus Universe. A dark matter torus rotates in a larger time torus of refined time smaller than the Planck-time. The Planck-satellite showed a more detailed picture of the CMB related to Big Bang cosmology. However, I have put that in perspective of a new set of equations that belong to the framework of the Double Torus Theory. That shows my proof for a rotational dark matter Flow by warm and cold areas in the CMB. I also explain why the accelerated space-expansion in the Big Bang cosmology is an illusion. Category: Mathematical Physics [192] viXra:1401.0145 [pdf] replaced on 2014-01-26 07:38:30 ### Proof For A Rotational Double Torus Universe. Authors: Dan Visser Comments: 5 Pages. I hope Peter Coles University of Sussex UK takes notice, as well as the media. The Universe rotates. We live in a Double Torus Universe. A dark matter torus rotates in a larger time torus of refined time smaller than the Planck-time. The Planck-satellite showed a more detailed picture of the CMB related to Big Bang cosmology. However, I have put that in perspective of a new set of equations that belong to the framework of the Double Torus Theory. That shows my proof for a rotational dark matter Flow by warm and cold areas in the CMB. I also explain why the accelerated space-expansion in the Big Bang cosmology is an illusion. Category: Mathematical Physics [191] viXra:1401.0107 [pdf] replaced on 2014-04-13 13:43:39 ### The Features For Dark Matter And Dark Flow Found. Authors: Dan Visser Comments: 9 Pages. Fly-By- and GPS-satellites reveal an earth-dark matter-halo is affecting the orbit-velocities of satellites. After analysis by a new set of equations, which describe dark matter, dark matter-force and quantum-gravity combined in a new dark energy force-formula, the new formulations match a percentage whereof satellites feel extra gravity. Also the dark matter-density has been calculated. The analysis confirms dark matter exists as a halo around the earth. Secondly it shows what dark matter really is. It also shows what a dark flow is. The dark matter-features are presented in a Double Torus Cosmology, a new model for the universe, which replaces Big Bang cosmology and enables to understand dark matter better! Category: Mathematical Physics [190] viXra:1312.0164 [pdf] replaced on 2014-01-21 16:42:35 ### The Theory of the (E) Question; New Formalism of the EM Field Tensor and Bi-Vectors "à la E. Cartan". Authors: Thierry PERIAT Comments: 21 Pages. Previous explorations have proposed a plausible and totally new path unifying the generalized theory of relativity and the quantum theory. It yields a specific expression for the EM field tensor. The aim of that new chapter is to understand the meaning of that formalism. I insist on a possible link with the notion of bi-vector exposed by E. Cartan. That v3 comes to the conclusion that that formalism sometimes represents an infinitesimal variation of the 4D metric. Category: Mathematical Physics [189] viXra:1311.0196 [pdf] replaced on 2013-11-30 09:17:51 ### Sphere Geometry of Forces & Fundamental Particles of the Universe Authors: S.C. Gaudie Comments: 11 pages; mostly font 11; A4 paper; UK English; Freelance scientist. This answers fundamental questions from Wikipedia about Generations of Matter [**web 1] and related properties. Why are there three generations of quarks and leptons? Why are the ratios of masses of quarks and leptons as they are? Also, is the ratio of fundamental force strengths related to the size of the universe and why are the ratios as they are? This theory defines a “fundamental sub-structure" that is a tetrahedron with the further “sub-structure" of spheres. Another geometrical possibility, with the same values, is based on the spatial axes. The big picture could be the arrangement of the “fundamental spheres” along the axes of space. There seems to be a “universal template” for the properties of the universe. The ratio numbers can be thought of as "quantum numbers". The ratios for each of these “fundamental sub-structure", “quantum numbers” are 1, 3 & 6; simple integer values. The 1, 3, 6 “quantum numbers” ratios in this theory show why the relative masses & radii of quarks and the “heavy leptons” are their “known values”. The cube root of the mass was used to calculate a diameter ratio parameter for these. These ratios are also applied to other basic properties of the universe. This “fundamental sub-structure" has also been applied to the relative strengths of the fundamental forces determining the size of the universe at the time of their creation. The universe is believed to have gone through creation of forces, inflation stages & must, of necessity, have gone through “phase changes". These could be interconnected. This theory combines the above items into ONE overall theory. Unexpected conclusions of the theory is [1] that gravity (like the nuclear force holding protons and neutrons together) is just another aspect of the strong nuclear force. This would mean that gravity works without gravitinos as force carriers or gavity waves! It also ties the force of gravity to its interaction with space! [2] Mass is an ATTRACTION ONLY “CHARGE”! [No repulsive gravity = dark energy.] [3] This gives numerical values to different inflation stages. [My unpublished work:- accelerated expansion = “localised view” of start of a new inflation period! Natural evolution of the universe!] Category: Mathematical Physics [188] viXra:1311.0189 [pdf] replaced on 2013-12-15 09:13:30 ### Quantum-Gravity Can Be Recalculated By Refined Time Smaller Than The Planck-Time In A Rotational Double Torus Universe. Authors: Dan visser Comments: 5 Pages. I hope the press takes notice. The result violates GRT. Signed: Dan Visser, Almere, the Netherlands In particular calculations have been made for the detection of extraterrestrial high energy neutrinos. Additional the rest-energy of a neutrino is calculated (equivalent to its rest mass). But both calculations are not standard. The calculations are made from the perspective of a new model for the universe: The Double Torus hypothesis. The alternative calculation shows that the result matches a neutrino-incident in the ICECUBE-project in Antartica for a value of 250 TeV energy. Moreover, an extra calculation is made for the expected neutrino rest-energy by the Standard Model (equivalent for its rest-mass). This shows time 21 times smaller than the Planck-time can generate a neutrino-rest-energy of 2.2 eV. It also shows time 100 times smaller than the Planck-time can generate a neutrino-rest-energy of 0.1 eV. This delivers evidence for the existence of a sub-quantum-domain of refined time that affects dark vacuum-particles; this is dark matter described in the Double Torus-framework. That generates visible quantum-gravitational particles. Such a calculation could also be performed for an electron or a quark. But that is not (yet) performed in this paper. But one of the conclusions is that the detection of high energy neutrinos could turn out to be additional evidence for the existence of rotational Double Torus Universe. Category: Mathematical Physics [187] viXra:1311.0182 [pdf] replaced on 2014-02-23 04:16:59 ### All Fermion Masses and Charges Are Determined By Two Calculated Numbers Authors: Claude Michael Cassano Comments: 16 Pages. All the fermion masses may be determined from merely two numbers dependent on π , e , and a few rational fractions, and all the fermion charges thereafter., In this, now, dimension independent revision; the electron mass and the ratio of the muon mass to the electron mass are shown calculable from simple quadratic functions of π , e , and a few rational fractions. All the remaining masses may be determined from from these constants and their indexes determined by the mass-generalized Maxwell's equations. These calculated masses are all well within current specs as of this publication. In fact, more recent neutrino measurements and estimates have put their values into a rather tight range which the computed values in this update fall within. Category: Mathematical Physics [186] viXra:1311.0170 [pdf] replaced on 2013-11-28 14:20:49 ### The Reverse Side of Helmholtz Paradox: Flow with Zero Laplacian Generates a Constant Vortex Authors: Sergey V. Ershkov Comments: 6 Pages. Keywords: Helmholtz paradox, constant vortex, incompressible ideal flow The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time. In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids). Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is proved to be ideal (unviscid) due to zero Laplacian. Category: Mathematical Physics [185] viXra:1311.0170 [pdf] replaced on 2013-11-27 01:35:23 ### The Reverse Side of Helmholtz Paradox: Flow with Zero Laplacian Generates a Constant Vortex Authors: Sergey V. Ershkov Comments: 6 Pages. Keywords: Helmholtz paradox, constant vortex, incompressible ideal flow The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time. In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids). Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is turned to be ideal (unviscid) due to zero Laplacian. Category: Mathematical Physics [184] viXra:1311.0170 [pdf] replaced on 2013-11-26 08:50:02 ### The Reverse Side of Helmholtz Paradox: Flow with Zero Laplacian Generates a Constant Vortex Authors: Sergey V. Ershkov Comments: 6 Pages. Keywords: Helmholtz paradox, constant vortex, incompressible ideal flow The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time. In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids). Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is turned to be ideal (unviscid) due to zero Laplacian. Category: Mathematical Physics [183] viXra:1311.0164 [pdf] replaced on 2014-12-31 02:41:37 ### On Global Solution of Incompressible Navier-Stokes Equations Authors: Algirdas Antano Maknickas Comments: 9 Pages. The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 2D and 3D space for any shaped boundary was expressed in term of 2D and 3D global solution of Helmholtz equation accordantly. Category: Mathematical Physics [182] viXra:1311.0164 [pdf] replaced on 2014-02-20 09:01:31 ### On Global Solution of Incompressible Navier-Stokes Equations Authors: Algirdas Antano Maknickas Comments: 8 Pages. The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 2D and 3D space for any shaped boundary was expressed in term of 2D and 3D global solution of Helmholtz equation accordantly. Category: Mathematical Physics [181] viXra:1311.0164 [pdf] replaced on 2014-02-14 01:07:23 ### On Global Solution of Incompressible Navier-Stokes Equations Authors: Algirdas Antano Maknickas Comments: 7 Pages. The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 3D space for any shaped boundary is expressed in term of 3D global solution of 3D Helmholtz equation accordantly. Category: Mathematical Physics [180] viXra:1311.0164 [pdf] replaced on 2014-02-03 14:13:08 ### On Global Solution of Incompressible Navier-Stokes Equations Authors: Algirdas Antano Maknickas Comments: 7 Pages. The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 3D space for any shaped boundary is expressed in term of 3D global solution of 3D Helmholtz equation accordantly. Category: Mathematical Physics [179] viXra:1311.0164 [pdf] replaced on 2013-12-06 03:44:14 ### On Global Solution of Incompressible Navier-Stokes Equations Authors: Algirdas Antano Maknickas Comments: 6 Pages. The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 3D space for any shaped boundary is expressed in term of 3D global solution of 3D Helmholtz equation accordantly. Category: Mathematical Physics [178] viXra:1310.0235 [pdf] replaced on 2014-04-04 09:01:45 ### Scale-Invariant Embeddings in a Riemannian Spacetime Authors: Carsten S.P. Spanheimer Comments: 20 Pages. A framework for calculations in a semi-Riemannian space with the typical metric connection and curvature expressions is developed, with an emphasis on deriving them from an embedding function as a more fundamental object than the metric tensor. The scale-invariant and 'linearizing' logarithmic nature of an 'infinitesimal embedding' of a tangent space into its neighbourhood is observed, and a composition scheme of spacetime scenarios from 'outer' non-invariant and 'inner' scale-invariant embeddings is briefly outlined. Category: Mathematical Physics [177] viXra:1310.0235 [pdf] replaced on 2013-11-24 10:47:46 ### Scale-Invariant Embeddings in a Riemannian Spacetime Authors: Carsten S.P. Spanheimer Comments: 20 Pages. A framework for calculations in a semi-Riemannian space with the typical metric connection and curvature expressions is developed, with an emphasis on deriving them from an embedding function as a more fundamental object than the metric tensor. The scale-invariant and 'linearizing' logarithmic nature of an 'infinitesimal embedding' of a tangent space into its neighbourhood is observed, and a composition scheme of spacetime scenarios from 'outer' non-invariant and 'inner' scale-invariant embeddings is briefly outlined. Category: Mathematical Physics [176] viXra:1310.0191 [pdf] replaced on 2014-12-31 04:01:33 ### Cosmological Constant and the Black-Hole White-Hole Universe Authors: Malcolm Macleod Comments: 3 Pages. In this essay I look at a model of a simple rotating expanding black-hole universe with a contracting white-hole universe twin. Units of (Planck) micro black holes are transferred in discrete integer steps from the white-hole universe to the black-hole universe thereby giving a simple rationale for the expansion of the universe, Planck time, the arrow of time, the speed of light, dark energy, dark matter and the Stefan Boltzmann constant. Presuming that universe expansion will cease when$t_{universe} \sim 0K$gives a cosmological constant; Og = 1.0137$\;10^{123}$units of Planck time. Solving cosmological microwave background CMB for peak frequency of 160.2GHz gives a 1st level approximation for the age of the universe at 13.654 billion years. Category: Mathematical Physics [175] viXra:1310.0191 [pdf] replaced on 2014-10-31 08:40:50 ### Cosmological Constant Omega_{og} and the Black-Hole Universe White-Hole Universe Authors: Malcolm Macleod Comments: 3 Pages. In this essay I look at a model of a simple rotating expanding black-hole universe with a contracting white-hole universe twin. Units of Planck micro black holes are transferred in discrete integer steps from the white-hole universe to the black-hole universe thereby giving a simple rationale for the expansion of the universe, Planck time, the arrow of time, the speed of light, dark energy, dark matter and the Stefan Boltzmann constant. A discrete unit of temperature is suggested and this is used to solve the cosmological constant;$\Omega_{Og} = 1.0137\;10^{123}$units of Planck time. Results for a (constantly expanding) 13.575 billion year old black-hole correspond with the observed CMB universe mass density, cosmic radiation energy density, Hubble, temperature and peak frequency values. A non-flat$\omega = 1.019, \; \omega^2 = 1.038$universe topology is suggested. Category: Mathematical Physics [174] viXra:1310.0191 [pdf] replaced on 2014-05-29 21:12:11 ### Cosmological Constant and the Black-Hole White-Hole Universe Authors: Malcolm Macleod Comments: 4 Pages. In this essay I look at a simple rotating expanding black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete integer steps from the white-hole universe to the black-hole universe thereby giving a simple rationale for the expansion of the universe, (Planck) time, the arrow of time, the speed of light, dark energy, dark matter and the Stefan Boltzmann constant. A discrete unit of temperature is suggested and this is used to solve the cosmological constant$\Omega_{Og}$= 9.38 x$10^{122}$units of Planck time. Results for a (constantly expanding) 13.575 billion year old black-hole correspond with the observed CMB universe mass density, cosmic radiation energy density and cosmic microwave background temperature values. Category: Mathematical Physics [173] viXra:1310.0191 [pdf] replaced on 2014-04-17 10:16:12 ### Cosmological Constant and the Black-Hole White-Hole Universe Authors: Malcolm Macleod Comments: 4 Pages. In this essay I look at a simple rotating expanding black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete integer steps from the white-hole universe to the black-hole universe thereby giving a simple rationale for the expansion of the universe, (Planck) time, the arrow of time, the speed of light, dark energy, dark matter and the Stefan Boltzmann constant. A discrete unit of temperature is suggested and this is used to solve the cosmological constant to 0.101373253 x$10^{-124}$units of Planck time. Results for the universe mass density, the cosmic radiation energy density and the cosmic microwave background temperature correspond with observed. Category: Mathematical Physics [172] viXra:1310.0191 [pdf] replaced on 2014-04-10 07:06:38 ### Cosmological Constant and the Black-Hole White-Hole Universe Authors: Malcolm Macleod Comments: 3 Pages. In this essay I look at a simple rotating expanding black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete integer steps from the white-hole universe to the black-hole universe thereby giving a simple rationale for the expansion of the universe, (Planck) time, the arrow of time, the speed of light, dark energy, dark matter and the Stefan Boltzmann constant. A discrete unit of temperature is suggested and this is used to solve the cosmological constant to 0.101373253 x$10^{-124}$units of Planck time. Results for the universe mass density, the cosmic radiation energy density and the cosmic microwave background temperature correspond with observed. Category: Mathematical Physics [171] viXra:1310.0191 [pdf] replaced on 2014-03-18 11:01:26 ### Time, Dark Energy, Dark Matter and the Black-hole White-hole Universe Authors: Malcolm Macleod Comments: 2 Pages. In this essay I look at an expanding black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete integer steps from the white-hole to the black-hole thereby giving a simple rationale for the expansion of the universe, time, the arrow of time, the speed of light, dark energy and dark matter. Category: Mathematical Physics [170] viXra:1310.0191 [pdf] replaced on 2014-02-23 04:25:14 ### Time, Dark Energy and the Black-hole White-hole Universe Authors: Malcolm Macleod Comments: 2 Pages. In this essay I propose an expanding black-hole universe (ours) with a contracting white-hole universe twin. Units of Planck momentum are transferred discretely from the white-hole to the black-hole thereby giving a rationale for the expansion of the universe, time, the arrow of time, dark energy and dark matter. Category: Mathematical Physics [169] viXra:1310.0082 [pdf] replaced on 2013-12-05 01:12:07 ### The Complete Classification of Self-Similar Solutions of the Navier-Stokes Equations for Incompressible Flow Authors: Sergey V. Ershkov Comments: 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here. We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one. The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function). As for solenoidal (divergence-free) equation, the transition from Cartesian to curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations. Category: Mathematical Physics [168] viXra:1310.0082 [pdf] replaced on 2013-10-18 09:46:36 ### The Complete Classification of Self-Similar Solutions of the Navier-Stokes Equations for Incompressible Flow Authors: Sergey V. Ershkov Comments: 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here. We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one. The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function). As for solenoidal (divergence-free) equation, the transition from Cartesian to curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations. Category: Mathematical Physics [167] viXra:1310.0082 [pdf] replaced on 2013-10-15 12:32:05 ### The Complete Classification of Self-Similar Solutions of the Navier-Stokes Equations for Incompressible Flow Authors: Sergey V. Ershkov Comments: 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here. We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one. The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function). As for solenoidal (divergence-free) equation, the transition from Cartesian to curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations. Category: Mathematical Physics [166] viXra:1310.0082 [pdf] replaced on 2013-10-14 05:20:56 ### The Complete Classification of Self-Similar Solutions of the Navier-Stokes Equations for Incompressible Flow Authors: Sergey V. Ershkov Comments: 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here. We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one. The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function). As for solenoidal (divergence-free) equation, transition from Cartesian to the the curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations. Category: Mathematical Physics [165] viXra:1309.0087 [pdf] replaced on 2013-09-14 21:55:02 ### Understanding NP by Time Differentials in Logical Semantics Authors: Miguel A. Sanchez-Rey Comments: 10 Pages. The following article briefly lays out a plausible alternative to the P=NP problem, and defines a general physical approach to the computational physics involved. It makes a conjecture that the underlying differences between quantum systems and classical mechanics can be bridged by a newer and novel mathematical parameter. Category: Mathematical Physics [164] viXra:1309.0008 [pdf] replaced on 2014-09-03 14:10:22 ### Yang-Mills Gauge Invariant Theory for Space Curved Electromagnetic Field Authors: Algirdas Antano Maknickas Comments: 8 Pages. It was proposed new gauge invariant Lagrangian, where the gauge field interact with the charged electromagnetic fields. Gauge invariance was archived by replacing of particle mass with new one invariant of the field$F_{\mu\nu}F^{\mu\nu}$multiplied with calibration constant$\alpha_g$. It was shown that new proposed Lagrangian generates similar Dirac and electromagnetic field equations. Solution of Dirac equations for a free no massless particle answers to the 'question of the age' why free particle deal in experiments like a de Broil wave. Resulting wave functions of the new proposed Lagrangian will describe quantized list of bespinor particles of different masses. Finally, it was shown that renormalization of the new proposed Lagrangian is similar to QED in case similarity of new proposed Lagrangian to classic QED. Category: Mathematical Physics [163] viXra:1308.0140 [pdf] replaced on 2014-12-31 04:04:13 ### Unified Field Theory of (Nuclear, Atomic, Molecular, Gravitational) Orbitals as Anti-Photon 'orbitons' Authors: Malcolm Macleod Comments: 8 Pages. In this essay I propose an alternate interpretation whereby particles may be linked, not by the 4 forces, but by orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons or orbitons) that are trapped to form standing waves. For example, gravitational orbits would be the sum of these gravitational orbitals (orbitons), the moon is not orbiting the earth, rather it is being propelled by these orbital momenta. Likewise there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in mass density (buoyancy). As such, if we move the IPK 1kg reference bar to a different location (with a different g), then we will change its orbital mass. The fundamental unit of orbital energy, whether nuclear, atomic, molecular or gravitational reduces to E_{orbital} = E_{Planck}/(2 alpha). Category: Mathematical Physics [162] viXra:1308.0140 [pdf] replaced on 2014-03-28 04:07:37 ### Unified Field Theory of (Nuclear, Atomic, Molecular, Gravitational) Orbitals as Anti-Photon 'orbitons' Authors: Malcolm Macleod Comments: 8 Pages. In this essay I propose an alternate interpretation whereby particles may be linked, not by the 4 forces, but by orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons or orbitons) that are trapped to form standing waves. For example, gravitational orbits would be the sum of these gravitational orbitals (orbitons), the moon is not orbiting the earth, rather it is being propelled by these orbital momenta. Likewise there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in mass density (buoyancy). As such, if we move the IPK 1kg reference bar to a different location (with a different$g$), then we will change its orbital mass. The fundamental unit of orbital energy, whether nuclear, atomic, molecular or gravitational reduces to$E_{orbital} = E_{Planck}/(2.\alpha)$. Category: Mathematical Physics [161] viXra:1308.0140 [pdf] replaced on 2014-02-23 08:42:44 ### A Unified Field Theory of (Nuclear, Atomic, Molecular, Gravitational) Orbitals as Anti-Photons Authors: Malcolm Macleod Comments: 8 Pages. In this essay I propose an alternate interpretation whereby particles may be linked, not by the 4 forces, but by physical orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons) that form standing waves. For example, gravitational orbits would be the sum of these gravitational orbitals, the moon is not orbiting the earth, rather it is being propelled by these orbital momenta. Likewise there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in mass density (buoyancy). As such, if we move the IPK 1kg reference bar to a different location (with a different$g$), then we will change its relativistic mass. Total momentum appears to derive from the classical orbital momentum, an orbital rotational momentum and a spin momentum. The fundamental unit of orbital energy, whether nuclear, atomic, molecular or gravitational reduces to$E_{orbital} = E_{Planck}/(2.\alpha)$. Category: Mathematical Physics [160] viXra:1308.0140 [pdf] replaced on 2013-11-14 22:00:53 ### A Unified Field Theory of (Nuclear, Atomic, Molecular, Gravitational) Orbitals as Anti-Photons Authors: Malcolm Macleod Comments: 8 Pages. In this essay, I propose that particles may be linked, not by the 4 forces, but by physical orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons) that form standing waves. For example, gravitational orbits would be the sum of these gravitational orbitals, the moon is not orbiting the earth, rather it is being propelled by these orbital momenta. Likewise there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in mass density (buoyancy). As such, if we move the IPK 1kg reference bar to a different location (with a different$g$), then we will change its mass. Total momentum derives from the classical orbital momentum, an orbital rotational momentum and a spin momentum. The fundamental unit of orbital energy, whether nuclear, atomic, molecular or gravitational is Eorbital = EPlanck/(2*alpha). Category: Mathematical Physics [159] viXra:1308.0140 [pdf] replaced on 2013-10-27 16:12:01 ### A Unified Field Theory of (Nuclear, Atomic, Molecular, Gravitational) Orbitals as Anti-Photons Authors: Malcolm Macleod Comments: 7 Pages. In this essay I propose that particles may be linked, not by the 4 forces, but by physical orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons) that form standing waves, and so gravitational orbits then become the sum of these gravitational orbitals, the moon for example, does not orbit the earth, rather it is propelled by this orbital momentum. The orbital frequency is a function of the respective particle frequencies with a relativistic spin-momentum velocity correction. Consequently there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in buoyancy. As such, if we move the IPK 1kg reference bar to a different location (with a different$g$), then we will change its mass. Category: Mathematical Physics [158] viXra:1308.0140 [pdf] replaced on 2013-10-23 02:55:51 ### Unified Field Theory of Orbitals (Nuclear, Atomic, Molecular, Gravitational) as Anti-Photons Authors: Malcolm Macleod Comments: 7 Pages. In this essay I propose that particles may be linked, not by the 4 forces, but by physical orbitals; photons albeit of inverse phase (anti-photons) that form standing waves. Gravitational orbits then become the sum of gravitational orbitals, the moon for example, does not orbit the earth, rather it is propelled by this orbital momentum. The orbital frequency is a function of the respective particle frequencies with a relativistic spin-momentum velocity correction. Consequently there is no empty space within the atom, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in buoyancy. As such, if we move the IPK 1kg reference bar to a different location (with a different$g$), then we will change its mass. Category: Mathematical Physics [157] viXra:1308.0125 [pdf] replaced on 2015-03-09 06:18:00 ### Nonstandard Ultra-logic-systems Applied to the GGU-model Authors: Robert A. Herrmann Comments: 34 Pages. The methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmogony, the General Grand Unification Model (GGU-model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from certain observable entities, physical processes and mental procedures that are used to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is applied to it an ultra-logic-system is deduced. Another application of an hyper-algorithm yields a hyperfinite instruction paradigm that is hyper-deduced in the required sequential order. It is immediate that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patten and Wheeler participator universe requirement. A specific data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. This set is show to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A refinement is introduced that leads, when applied, to the individual development of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-field, all physical and physical-like systems are produced. Category: Mathematical Physics [156] viXra:1308.0125 [pdf] replaced on 2014-09-05 05:46:17 ### Nonstandard Ultra-logic-systems Applied to the GGU-model Authors: Robert A. Herrmann Comments: 34 Pages. This article develops and employs modern methods for mathematical modeling. This version uses these techniques to continue the development of useful refinements. In particular, the methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmogony, the General Grand Unification Model (GGU-model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from observable entities and processes or mental procedures that are employed to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is applied to it an ultra-logic-system is hyper-deduced. Another application of an hyper-algorithm yields an hyperfinite instruction paradigm that is hyped-deduced in the required order. It is immediate that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Pattern and Wheeler participator universe requirement. A specific physical data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. The set is shown to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A refinement is introduced that leads, when applied, to the individual development of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-fields all physical systems are produced. Category: Mathematical Physics [155] viXra:1308.0125 [pdf] replaced on 2014-04-14 07:44:18 ### Nonstandard Ultra-logic-systems Applied to the GGU-model Authors: Robert A. Herrmann Comments: 34 Pages. This article develops and employs modern methods for mathematical modeling. This version uses these techniques to continue the development of useful refinements. In particular, the methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmogony, the General Grand Unification Model (GGU-model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from observable entities and processes that are employed to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-world-like object such that when an hyper-algorithm, is applied to it and ultra-logic-system is hyper-deduced. Another application of the hyper-algorithm yields an hyperfinite instruction paradigm that is hyper-deduced in the required order. It is immediate that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patton and Wheeler participator universe requirements. A specific physical data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. The set is shown to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A refinement is introduced that leads, when applied, to the individual development of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-fields, all physical and physical-like systems are produced. Category: Mathematical Physics [154] viXra:1308.0125 [pdf] replaced on 2014-03-03 07:32:39 ### Nonstandard Ultra-logic-systems Applied to the GGU-model Authors: Robert A. Herrmann Comments: 34 Pages. This article develops and employs modern methods for mathematical modeling. This version uses these techniques to continue the development of useful refinements. In particular, the methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmogony, the General Grand Unification Model (GGU-Model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from observable entities and processes that are employed to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is applied to it an ultra-logic-system is hyper-deduced. Another application of an hyper-algorithm yields an hyperfinite instruction paradigm that is hyper-deduced in the required order. It is immediate that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patten and Wheeler participator universe requirement. A specific physical data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. This set is shown to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A refinement is introduced that leads, when applied, to the individual development of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-fields all physical and physical-like systems are produced. Category: Mathematical Physics [153] viXra:1308.0118 [pdf] replaced on 2015-02-27 11:24:55 ### 3 Constants MTP, a Mathematical Universe Hypothesis: Digital Mass M=1, Circular Time T=2pi, Analog Momentum P=omega Authors: Malcolm Macleod Comments: 7 Pages. In the “Trialogue on the number of fundamental constants”, Michael J. Duff, Lev B. Okun and Gabriele Veneziano debated the number of fundamental dimensioned constants in physics. L Okun maintained that 3 basic units were required and offered M=mass, T=time, L=length. In this essay I suggest MTP where P is the sqrt of momentum as from these 3 units we may derive and solve as simple geometrical shapes formulas for G, h, c, e, me, kB, μ0… to a precision limited only by the precision of the fine structure constant alpha. Results are consistent with CODATA 2010. I then demonstrate how we may assign M=1, T=2pi, P=Ώ, Ώ^2 = π^e/e^(e-1), and use these values to solve the same electron frequency formula fe. This is rationalized by the premise that the numerical value for fe = .4184896589…e-22 is independent of the set of MTP units used and thus may be used to verify the validity of any chosen set of MTP. Category: Mathematical Physics [152] viXra:1308.0118 [pdf] replaced on 2015-02-10 14:18:23 ### Planck Unit Universe of Mathematical Forms: Digital Mass M=1, Circular Time T=2pi, Analog Momentum Q=omega Authors: Malcolm Macleod Comments: 7 Pages. The principal physical constants are defined in terms of the units of mass, length, time, temperature and electric charge (the SI units: M=kg, L=m, T=s, K=kelvin, Ampere). There are also natural constants such as$\pi$and the fine structure constant alpha which have no units and so are independent of the system of units used. These may be considered as natural or universal constants. Here I discuss a Mathematical Universe Hypothesis whereby the 5 SI units (M, L, T, K, A) are reduced to 3 primary units M, T and Q as sqrt of momentum. From these 3 units and the fine structure constant alpha, formulas for the physical constants can be derived as geometrical shapes. The precisions of Planck mass (M), Planck time (T) and Planck momentum (Q) are low, however we may redefine these in terms of the 3 most accurate constants;$c$and mu_0 (exact values) and Rydberg (12-digits). The precision of our solutions for the constants G, h, e, k_B, m_e... are then limited only by the precision of the fine structure constant alpha, the solutions are consistent with CODATA 2010. A second set of units; M=1, T=2pi (radians), Q=Omega (Omega^2 = pi^e/e^(e-1)) is proposed. Both sets of M, T, Q can be equally used to solve the electron frequency as this is numerically independent of the system of units used. A solution for alpha as alpha = 137.035 996 3687(5) is suggested. Category: Mathematical Physics [151] viXra:1308.0118 [pdf] replaced on 2014-12-31 03:58:16 ### Planck Unit Mathematical Universe Hypothesis from the Fine Structure Constant Alpha and 2pi r, pi R^2 Where R = Omega = Sqrt{pi^e/e^(e-1)} = Sqrt of Planck Momentum Authors: Malcolm Macleod Comments: 6 Pages. The principal physical constants G, h, c, e, k_B, mu_0, m_e... are defined in terms of the dimensions of mass, length, time, temperature and electric charge (the SI units: M=kg, L=m, T=s, K=kelvin, Ampere). There are also natural constants such as pi and the fine structure constant alpha which have no dimensions and so are presumed independent of the system of units used. These may be considered as natural or universal constants. Proposed here is a further natural constant which I have denoted Omega (Omega^2 = pi^e/e^(e-1)) as the sqrt of Planck momentum. Natural Planck units including the electron frequency can be defined in terms of the area and/or circumference of a circle whose radius r = Omega, thus suggesting a geometrical Mathematical Universe. Replacing these natural units with our SI units gives solutions for the physical constants G, h, c, e, k_B, mu_0, m_e..., results are consistent with CODATA 2010. The solution for the electron as a magnetic monopole is independent of the system of units used, this suggests that at the Planck level the units (M,L,T,K,A) are not separate and distinct but overlap converging at this monopole. A solution for alpha = 137.035 996 3687(5) is suggested. Category: Mathematical Physics [150] viXra:1308.0118 [pdf] replaced on 2014-12-09 08:59:30 ### 3-D: Sqrt Planck Momentum, Planck Temperature/entropy, Magnetic-Monopole Universe as Geometry of 2pi, Fine Structure Constant Alpha, Omega = Sqrt(pi^e/e^(e-1)) Authors: Malcolm Macleod Comments: 7 Pages. The principal physical constants G, h, c, e, k_B, mu_0, m_e... are defined in terms of the dimensions of mass, length, time, temperature and electric charge (the SI units: M=kg, L=m, T=s, K=kelvin, Ampere). There are also natural constants such as pi and the fine structure constant alpha which have no dimensions and so are presumed independent of the system of units used. These may be considered as natural or universal constants. Proposed here is a further natural constant which I have denoted Omega (Omega^2 = \pi^e/e^{(e-1)). Using 3 dimensioned quantities a as Planck temperature (entropy) and b as sqrt of Planck momentum and a u_0 magnetic monopole, we can map the units (M,L,T,K,A) whereby; M = a b^5, L = a^5 b^3/u_0, T = a^6/u_0, A = a^3 b^3, K = a^4. We may then include the geometries to form the Planck equivalents; M = 1, T = 2 pi, L = 2 pi^2 Omega^2... By scaling a = 0.507\;863\;234\;501... x 10^{-7} and b = 0.844\;134\;182\;055... we may then solve G, h, c, e, k_B, mu_0, m_e... the accuracy is limited by the precisions of the Rydberg constant (12-digit) and the fine structure constant alpha. Results are consistent with CODATA 2010. A solution for alpha as alpha = 137.035\; 996\; 3687(5) is suggested. We may note that the magnetic monopole 3rd dimension u_0, from which the electron frequency formula is derived, does not scale. Regardless of the system of units used, u_0 = 1. suggesting the magnetic monopole as a fundamental unit. Category: Mathematical Physics [149] viXra:1308.0118 [pdf] replaced on 2014-11-29 07:32:33 ### 2-D (Planck Time/entropy and Sqrt of Planck Momentum) Magnetic Monopole Universe as Geometry of 2pi, Fine Structure Constant Alpha and Omega = Pi^e/e^(e-1) Authors: Malcolm Macleod Comments: 7 Pages. The principal physical constants G, h, c, e, k_B, mu_0, m_e... are defined in terms of the dimensions of mass, length, time, temperature and electric charge (the SI units: M=kg, L=m, T=s, K=kelvin, Ampere). There are also natural constants such as pi and the fine structure constant alpha which have no dimensions and so are presumed independent of the system of units used. These may be considered as natural or universal constants. Proposed here is a further natural constant which I have denoted Omega (Omega^2 = \pi^e/e^{(e-1)}). Using 2 dimensioned quantities a = entropy (Planck time) and b = sqrt of Planck momentum, we can map the units (M,L,T,K,A) to form the physical constants whereby; M = 1a b^5, L = 2pi^2 Omega^2 a^5 b^3, T = 2pi a^6, A = 64 pi^3 Omega^3 / alpha a^3 b^3, etc. By scaling a = 0.507\;863\;234\;501... x 10^{-7} and b = 0.844\;134\;182\;055... we may solve G, h, c, e, k_B, mu_0, m_e... the accuracy is limited by the precisions of the Rydberg constant (12-digit) and the fine structure constant alpha. Results are consistent with CODATA 2010. A solution for alpha as alpha = 137.035\; 996\; 3687(5) is suggested. Dimensions a and b cancel to form a magnetic monopole u_0 = a^0 b^0 from which a formula for the electron frequency is derived. As this monopole is both dimensionless and unitary (u_0 = 1) we have the basis for a Planck unit Mathematical Universe Hypothesis. Category: Mathematical Physics [148] viXra:1308.0118 [pdf] replaced on 2014-11-24 09:21:15 ### A 3-D Planck Unit Mathematical Universe: Momentum, Time and Magnetic Monopole as the Geometry of 2pi, Fine Structure Constant Alpha and Omega = Pi^e/e^(e-1) Authors: Malcolm Macleod Comments: 7 Pages. The principal physical constants G, h, c, e, k_B, mu_0, m_e... are defined in terms of the dimensions of mass, length, time, temperature and electric charge (the SI units: M=kg, L=m, T=s, K=kelvin, Ampere). There are also natural constants such as pi and the fine structure constant alpha which have no dimensions and so are presumed independent of the system of units used. These may be considered as natural or universal constants. Proposed here is a further natural constant which I have denoted Omega (Omega^2 = \pi^e/e^{(e-1)}). Using 2 dimensioned quantities a = s^{1/6} and$b = \frac{kg^{1/8}m^{1/8}}{s^{1/8}} and a magnetic monopole {u_0} = \frac{kg^{3/8}s^{11/24}}{m^{5/8}} whose dimensions cancel (u_0 = 1), we can map the units (M,L,T,K,A) to form the physical constants whereby; M = 1a b^5 u_0, L = 2pi^2 Omega^2 a^5 b^3/u_0, T = 2pi a^6, A = 64 pi^3 Omega^3 / alpha a^3 b^3 u_0^3, etc. By scaling a = 0.507\;863\;234\;501... x 10^{-7} and b = 0.844\;134\;182\;055... we may solve G, h, c, e, k_B, mu_0, m_e... the accuracy is limited by the precisions of the Rydberg constant (12-digit) and the fine structure constant alpha. Results are consistent with CODATA 2010. A solution for alpha as alpha = 137.035\; 996\; 3687(5) is suggested. An electron formula is defined in terms of this magnetic monopole u_0 which, being unitary both numerically and in dimensional analysis, suggests a Mathematical Universe.
Category: Mathematical Physics

[147] viXra:1308.0118 [pdf] replaced on 2014-11-11 11:12:08

### 2-D Planck Unit Universe: 2pi, Fine Structure Constant Alpha, Omega Pi^e/e^{(e-1)} and Q the Sqrt of Planck Momentum Sqrt{kg.m/s}

Authors: Malcolm Macleod

The principal physical constants G, h, c, e, k_B, mu_0, m_e... are defined in terms of the dimensions of mass, length, time, temperature and electric charge (the SI units: M=kg, L=m, T=s, K=kelvin, Ampere). There are also natural constants such as pi and the fine structure constant alpha which have no dimensions and so are presumed independent of the system of units used. These may be considered as natural or universal constants. Proposed here is a further natural constant which I have denoted Omega (Omega^2 = pi^e/e^{(e-1)}) as a square root of Planck momentum analogue. From 2pi, Omega^2 and alpha.Omega^3, we can construct fundamental geometries. Using 2 dimensioned quantities a^x and b^y where a = {kg^{3/8}s^{5/8}}/{m^{5/8}} and b = {kg^{1/8}m^{1/8}}/{s^{1/8}}, we can map the units (M,L,T,K,A) and assign to the above geometries to form the physical constants whereby; M = 1 a b^5, L = 2pi^2 Omega^2 a^5 b^3, T = 2pi a^6, A = 64 pi^3 Omega^3 / alpha a^3 b^3, etc. By scaling a and b we may solve G, h, c, e, k_B, mu_0, m_e... the accuracy of each solution is limited by the precisions of the Rydberg constant (12-digit) and the fine structure constant alpha. Results are consistent with CODATA 2010. A solution for alpha as alpha = 137.035 996 3687(5) is proposed. The dimensionless state (a^0, b^0) is a magnetic monopole of which the electron frequency is given as an example.
Category: Mathematical Physics

[146] viXra:1308.0118 [pdf] replaced on 2014-10-31 08:53:01

### The 2-D Planck Universe: 2pi, Fine Structure Constant Alpha, Omega = Pi^e/e^(e-1), Sqrt of Planck Time and Sqrt of Planck Momentum

Authors: Malcolm Macleod

The principal physical constants G, h, c, e, k_B, mu_0, m_e... are defined in terms of the dimensions of mass, length, time, temperature and electric charge (M,L,T,K,A). There are also natural constants such as pi and the fine structure constant alpha which have no dimensions and so are presumed independent of the system of units used. These may be considered as natural or universal constants. Proposed here is a further natural constant which I have denoted Omega. From 2pi, alpha and Omega (Omega = \pi^e/e^(e-1)), basic formulas for time, mass, length and charge are proposed in terms of 2 dimensions $a$ (sqrt of Planck time) and $b$ (sqrt of Planck momentum). These base units are then scaled to their Planck unit equivalents from which G, h, c, e, k_B, mu_0, m_e... are solved, the accuracy of each solution is limited by the (12-digit) precision of the Rydberg constant. Results are consistent with CODATA 2010. As the SI units (kg,m,k,A) can be constructed using the sqrt of Planck time and sqrt of Planck momentum, these 2 quantities could be considered as universal dimensions. By comparing the Planck electron with the SI electron, a solution for alpha as alpha = 137.035 996 368(2) is proposed.
Category: Mathematical Physics

[145] viXra:1308.0118 [pdf] replaced on 2014-04-10 07:11:53

### Planck Unit Theory: Fine Structure Constant Alpha and Sqrt of Planck Momentum

Authors: Malcolm Macleod

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A principle constraint with constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits which in turn limits the usefulness of Planck theories. By postulating the sqrt of Planck momentum $Q$ as a link between mass and charge, we can formulate the above primary constants as geometrical shapes and then define them in terms of the 4 most accurate constants $c$ (exact), permeability of vacuum $\mu_0$ (exact), Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision) giving us solutions to the Planck units whose precision is limited only by the precision of alpha. A resultant Planck unit theory emerges which suggests that particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. The dimensions of our universe then reduce to the 3 units (dimensions) of motion; Planck momentum, Planck time and velocity c.
Category: Mathematical Physics

[144] viXra:1308.0118 [pdf] replaced on 2014-03-18 11:04:27

### Planck Unit Theory: Fine Structure Constant Alpha and Sqrt of Planck Momentum

Authors: Malcolm Macleod

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A principle constraint with constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits which in turn limits the usefulness of Planck theories. By postulating the sqrt of Planck momentum $Q$ as a link between mass and charge, we can formulate the above primary constants as geometrical shapes and then define them in terms of the 4 most accurate constants $c$ (exact), permeability of vacuum $\mu_0$ (exact), Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision) giving us solutions to the Planck units whose precision is limited only by the precision of alpha. A resultant Planck unit theory emerges which suggests that particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. The dimensions of our universe then reduce to the 3 units (dimensions) of motion; Planck momentum, Planck time and velocity c.
Category: Mathematical Physics

[143] viXra:1308.0118 [pdf] replaced on 2014-02-23 04:21:40

### Planck Unit Theory: Fine Structure Constant Alpha and Sqrt of Planck Momentum

Authors: Malcolm Macleod

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A major problem in constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits. By postulating the sqrt of Planck momentum $Q$ as the link between mass and charge, a 'Planck' ampere $A_Q$ is constructed as a geometrical shape; the volume of velocity/mass. From this Planck Ampere can then be derived $\mu_0$ (permeability of vacuum) which in turn gives a formula for Planck length $l_p$ and for a magnetic monopole ($A.l_p$). From the monopole can be formed an electron which is then used to solve the Rydberg constant $R$. Consequently $G$, $h$, $e$, $m_e$... can then be solved in terms of the 4 most accurate constants $c$, $\mu_0$, Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision). Planck temperature $T_P$ and so Boltzmanns constant $k_B$ are functions of the ampere and velocity ($A.c$). The electron formula suggests a Planck unit theory whereby particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. This wave-particle duality (oscillation) suggests a MUH Mathematical Universe Hypothesis where particles and photons modulate magnetic monopoles. The dimensions of our universe then reduce to the 3 dimensions of motion; Planck momentum, Planck time and velocity c.
Category: Mathematical Physics

[142] viXra:1308.0118 [pdf] replaced on 2014-01-04 23:12:26

### Planck Unit Theory: Fine Structure Constant Alpha and Sqrt of Planck Momentum

Authors: Malcolm Macleod

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A major problem in constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits. By postulating the sqrt of Planck momentum $Q$ as the link between mass and charge, a 'Planck' ampere $A_Q$ is constructed as a geometrical shape; the volume of velocity/mass. From this Planck Ampere can then be derived $\mu_0$ (permeability of vacuum) which in turn gives a formula for Planck length $l_p$ and for a magnetic monopole ($A.l_p$). From the monopole can be formed an electron which is then used to solve the Rydberg constant $R$. Consequently $G$, $h$, $e$, $m_e$... can then be solved in terms of the 4 most accurate constants $c$, $\mu_0$, Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision). Planck temperature $T_P$ and so Boltzmanns constant $k_B$ are functions of the ampere and velocity $A.c$. The electron formula suggests a Planck unit theory whereby particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. This wave-particle duality (oscillation) suggests a MUH Mathematical Universe Hypothesis where particles and photons modulate magnetic monopoles. The dimensions of our universe then reduce to the 3 dimensions of motion; sqrt of Planck momentum, Planck time and c.
Category: Mathematical Physics

[141] viXra:1308.0118 [pdf] replaced on 2013-10-09 07:00:22

### Planck Unit Theory: Fine Structure Constant Alpha and Sqrt of Planck Momentum

Authors: Malcolm Macleod

The primary constants; G, c, h, e (or mu_0), alpha and m_e range in precision from low G (4-digits) to exact values (c, mu_0). A major problem in constructing a Planck unit theory is that the Planck units are limited to the precision of G. By postulating the sqrt of Planck momentum as a link between mass and charge, a 'Planck' ampere A_Q may be constructed as a geometrical shape; the volume of velocity/mass. From this Planck Ampere can then be derived e and mu_0 (permeability of vacuum). We may then use mu_0 to solve Planck length l_p and this gives a formula for the electron (as a magnetic monopole). G, h, e and m_e can be now be solved using the 4 most accurate constants c, mu_0, Rydberg constant R (12 digit precision) and the fine structure constant alpha alpha (10 digit precision). The electron magnetic monopole suggests a Planck unit theory whereby particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) mass Planck-event (Planck-time) point-state oscillation. This wave-particle duality (oscillation) becomes the basis for a MUH Mathematical Universe Hypothesis. The dimensions of our universe reduce to the 3 units of motion; sqrt of Planck momentum, Planck time and c.
Category: Mathematical Physics

[140] viXra:1308.0107 [pdf] replaced on 2014-06-05 23:50:12

### Critical Analysis of the Mathematical Formalism of Theoretical Physics. Iv. Trigonometry

Authors: Temur Z. Kalanov

Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
Category: Mathematical Physics

[139] viXra:1308.0091 [pdf] replaced on 2014-09-01 15:20:26

### Mathematical Time

Authors: Peter Waaben

An infinitesimal approach
Category: Mathematical Physics

[138] viXra:1308.0080 [pdf] replaced on 2013-09-24 05:12:15

### Improving the Koide Formula

Authors: Branko Zivlak
Comments: 6 Pages. 16 formulas, 2 tables

Koide formula has improved on the result 2/3 in the formula (14). The tau lepton mass is also calculated. This is third version of the article.
Category: Mathematical Physics

[137] viXra:1308.0080 [pdf] replaced on 2013-09-22 09:57:33

### Improving the Koide Formula

Authors: Branko Zivlak
Comments: 6 Pages. 16 formulas, 2 tables

Abstract. The author corrects the Koide formula to the result 2/3, employing the methods from the articles previously published at viXra.org. The tau lepton mass is also calculated. This is second version of the article.
Category: Mathematical Physics

[136] viXra:1308.0069 [pdf] replaced on 2014-04-19 05:51:03

### Abel Resummation , Regularization, Renormalization and Infinite Series

Authors: Jose Javier Garcia Moreta

 ABSTRACT: We Study the use of Abel summation applied to the evaluation of infinite series and infinite (divergent) integrals , we give several examples of how we can obtain a regularization for the case of divergent sums and integrals.  Keywords: = Abel sum formula,Abel-Plana formula, poles , infinities, renormalization, regularization, multiple integrals, Casimir effect.
Category: Mathematical Physics

[135] viXra:1306.0236 [pdf] replaced on 2014-07-10 08:46:29

### On the Real Representations of the Poincare Group

Authors: Leonardo Pedro

The formulation of quantum mechanics with a complex Hilbert space is equivalent to a formulation with a real Hilbert space and particular density matrix and observables. We study the real representations of the Poincare group, motivated by the fact that the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity. We review the map from the complex to the real irreducible representations—finite- dimensional or unitary—of a Lie group on a Hilbert space. Then we show that all the finite-dimensional real representations of the identity component of the Lorentz group are also representations of the parity, in contrast with many complex representations. We show that any localizable unitary representation of the Poincare group, compatible with Poincare covariance, verifies: 1) it is self-conjugate (regardless it is real or complex); 2) it is a direct sum of irreducible representations which are massive or massless with discrete helicity. 3) it respects causality; 4) it is an irreducible representation of the Poincare group (including parity) if and only if it is: a)real and b)massive with spin 1/2 or massless with helicity 1/2. Finally, the energy positivity problem is discussed in a many-particles context.
Category: Mathematical Physics

[134] viXra:1306.0236 [pdf] replaced on 2014-03-06 11:06:17

### On the Real Representations of the Poincare Group

Authors: Leonardo Pedro

We do a study of the real representations of the Poincare group, motivated by the fol- lowing: i) the classical electromagnetic field —from which the Poincare group was originally defined— transforms as a real representation of the Poincare group; ii) the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity, while the complex representation corresponding to the photon is not localizable. We start by reviewing the map from the complex to the real irreducible representations— finite-dimensional or unitary—of a Lie group on a Hilbert space. Then we show that all the finite-dimensional real representations of the identity compo- nent of the Lorentz group are also representations of the full Lorentz group, in contrast with many complex representations. We finally study the unitary irreducible representations of the Poincare group with dis- crete spin or helicity and show that: for each pair of complex representations with pos- itive/negative energy, there is one real representation; the localization, compatible with causality and Poincare covariance, exists for representations with discrete spin or helicity.
Category: Mathematical Physics

[133] viXra:1306.0236 [pdf] replaced on 2013-08-27 17:39:42

### On the Real Representations of the Poincare Group

Authors: Leonardo Pedro

We study the real representations of the Poincare group and its relation with the complex representations. The classical electromagnetic field — from which the Poincare group was originally defined — is a real representation of the Poincare group. We show that there is a map from the complex to the real irreducible representations of a Lie group on a Hilbert space — the map is known in the finite-dimensional representations of a real Lie algebra. We show that all the finite-dimensional real representations of the restricted Lorentz group are also representations of the full Lorentz group, in contrast with many complex representations. We study the unitary irreducible representations of the Poincare group with discrete spin and show that for each pair of complex representations with positive/negative energy, there is one real representation; we show that there are unitary transformations, defining linear and angular momenta spaces which are common for the real and complex representations.
Category: Mathematical Physics

[132] viXra:1306.0209 [pdf] replaced on 2013-07-20 13:50:22

### A 15-Page Collection of Notes on my Mathematical Articles

Authors: Andrew Nassif

This is a collection of some of my notes in mathematical physics and Quantum Field Theory. This also includes the P vs. NP computational proof, the Zeta Function Data graphed, Notes on some common topics in Mathematics and Mathematical Physics, and Computational Mathematics as well as Three Dimensional Data Graphing.
Category: Mathematical Physics

[131] viXra:1306.0026 [pdf] replaced on 2014-07-12 05:49:35

### Extended Prigogine Theorem: Method for Universal Characterization of Complex System Evolution

Authors: Sergey A. Kamenshchikov
Comments: 8 Pages. Published unaltered at Chaos and Complexity Letters, Volume 8, Issue 1, 2014, pp. 63-71. Author: ru.linkedin.com/pub/sergey-kamenshchikov/60/8b1/21a/

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, injected into system and power of energy, dissipated through internal nonlinear mechanisms. It was found out that basic phase parameter as control parameter must be delimited for two types of system - accelerator and decelerator. It was suggested to select zero state entropy on through condition of zero value for entropy production. Zero state introduces universal principle of disorder characterization. On basis of self organization S – theorem we have derived relations for entropy production behavior in the vicinity stationary state of system. Advantage of these relations in comparison to classical Prigogine theorem is versatility of their application to arbitrary nonlinear systems. It was found out that extended Prigogine theorem introduces two relations for accelerator and decelerator correspondingly, which remarks their quantitative difference. At the same time classic Prigogine theorem makes possible description of linear decelerator only. For unstable motion it corresponds to strange attractor.
Category: Mathematical Physics

[130] viXra:1306.0020 [pdf] replaced on 2015-02-19 08:34:48

### Foundations of Quantum Field Theory and It's Particulates

Authors: Miguel A. Sanchez-Rey

We propose a solution to the Mass Gap and Yang Mills problem establish by the Clay Mathematics Institute.
Category: Mathematical Physics

[129] viXra:1306.0020 [pdf] replaced on 2013-07-27 17:22:09

### Foundations of Quantum Field Theory and It's Particulates

Authors: Miguel A. Sanchez-Rey

We propose a solution to the Mass Gap and Yang Mills problem establish by the Clay Mathematics Institute.
Category: Mathematical Physics

[128] viXra:1305.0202 [pdf] replaced on 2014-08-03 19:19:59

### Initiating the Newtonian Gravitational N-Body Spherical Simplification Algorithm on the Inopin Holographic Ring Topology

Authors: Nathan O. Schmidt

We propose a preliminary algorithm which is designed to reduce aspects of the n-body problem to a 2-body problem for holographic principle compliance. The objective is to share an alternative view-point on the n-body problem to try and generate a simpler solution in the future. The algorithm operates 2D and 3D data structures to initiate the encoding of the chaotic dynamical system equipped with modified superfluid order parameter fields in both 3D and 4D versions of the Inopin holographic ring (IHR) topology. For the algorithm, we arbitrarily select one point-mass to be the origin and, from that reference frame, we subsequently engage a series of instructions to consolidate the residual (n-1)-bodies to the IHR. Through a step-by-step example, we demonstrate that the algorithm yields "IHR effective" (IHRE) net quantities that enable us to hypothetically define an IHRE potential, kinetic, and Lagrangian.
Category: Mathematical Physics

[127] viXra:1305.0201 [pdf] replaced on 2014-07-28 05:49:23

### The Majorana Spinor Representation of the Poincare Group

Authors: Leonardo Pedro
Comments: 14 Pages. Propostion 7.2 corrected

There are Poincare group representations on complex Hilbert spaces, like the Dirac spinor field, or real Hilbert spaces, like the electromagnetic field tensor. The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor field is a space-time dependent Majorana spinor, solution of the free Dirac equation. The Majorana-Fourier and Majorana-Hankel transforms of Majorana spinor fields are defined and related to the linear and angular momenta of a spin one-half representation of the Poincare group. We show that the Majorana spinor field with finite mass is an unitary irreducible projective representation of the Poincare group on a real Hilbert space. Since the Bargmann-Wigner equations are valid for all spins and are based on the free Dirac equation, these results open the possibility to study Poincare group representations with arbitrary spins on real Hilbert spaces.
Category: Mathematical Physics

[126] viXra:1305.0201 [pdf] replaced on 2013-06-20 06:07:51

### The Majorana Spinor Representation of the Poincare Group

Authors: Leonardo Pedro

The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor field is a space-time dependent Majorana spinor, solution of the free Dirac equation. We show that the Majorana spinor field with finite mass is a real orthogo- nal irreducible representation of the Poincare group. The Majorana-Fourier and Majorana-Hankel transforms of Majorana spinor fields are defined and related to the linear and angular momentums of a spin one-half representation of the Poincare group.
Category: Mathematical Physics

[125] viXra:1305.0201 [pdf] replaced on 2013-06-06 08:24:04

### The Majorana Spinor Representation of the Poincare Group

Authors: Leonardo Pedro

The Dirac spinor is an element of a 4 dimensional complex vector space, while the Majorana spinor is an element of a 4 dimensional real vector space. Unlike on the Dirac spinor, the Lorentz group projective representation on the Majorana spinor is irreducible, even if parity and time reversal are not included. The spinor fields are space- time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier and Majorana-Hankel transforms and relate them to the linear and angular momenta of a spin one-half representation of the Poincare group. We show that, even if parity and time reversal are not included, the projective representation of the Poincare group on the Majorana spinor field is orthogonal and irreducible, while on the Dirac spinor field it is (anti-)unitary and reducible.
Category: Mathematical Physics

[124] viXra:1305.0171 [pdf] replaced on 2013-07-25 15:35:48

### Zeta Regularization Method Applied to the Calculation of Divergent Integrals

Authors: Jose javier garcia Moreta

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization
Category: Mathematical Physics

[123] viXra:1305.0171 [pdf] replaced on 2013-07-01 15:36:18

### Zeta Regularization Method Applied to the Calculation of Divergent Integrals

Authors: Jose Javier Garcia Moreta

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional
Category: Mathematical Physics

[122] viXra:1305.0171 [pdf] replaced on 2013-06-27 17:07:06

### Zeta Regularization Method Applied to the Calculation of Divergent Divergent Integrals

Authors: Jose Javier garcia Moreta

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization
Category: Mathematical Physics

[121] viXra:1305.0085 [pdf] replaced on 2013-08-09 16:17:16

### A Complex and Triplex Framework for Encoding the Riemannian Dual Space-Time Topology Equipped with Order Parameter Fields

Authors: Nathan O. Schmidt

In this work, we forge a powerful, easy-to-visualize, flexible, consistent, and disciplined abstract vector framework for particle and astro physics that is compliant with the holographic principle. We demonstrate that the structural properties of the complex number and the sphere enable us to introduce and define the triplex number---an influential information structure that is similar to the 3D hyper-complex number by D. White and P. Nylander---which identifies a 3D analogue of (2D) complex space. Consequently, we engage the complex and triplex numbers as abstract vectors to systematically encode the state space of the Riemannian dual 3D and 4D space-time topologies, where space and time are dual and interconnected; we use the triplex numbers (with triplex multiplication) to extend 1D and 2D algebraic systems to 3D and 4D configurations. In doing so, we equip space-time with order parameter fields for topological deformations. Finally, to exemplify our motivation, we provide three example applications for this framework.
Category: Mathematical Physics

[120] viXra:1305.0085 [pdf] replaced on 2013-07-05 21:49:21

### A Complex and Triplex Framework for Encoding the Riemannian Dual Space-Time Topology Equipped with Order Parameter Fields

Authors: Nathan O. Schmidt

In this work, we forge a powerful, easy-to-visualize, flexible, consistent, and disciplined abstract vector framework for particle and astro physics that is compliant with the holographic principle. We demonstrate that the structural properties of the complex number and the sphere enable us to introduce and define the triplex number---an influential information structure that is similar to the 3D hyper-complex number by D. White and P. Nylander---which identifies a 3D analogue of (2D) complex space. Consequently, we engage the complex and triplex numbers as abstract vectors to systematically encode the state space of the Riemannian dual 3D and 4D space-time topologies, where space and time are dual and interconnected; we use the triplex numbers (with triplex multiplication) to extend 1D and 2D algebraic systems to 3D and 4D configurations. In doing so, we equip space-time with order parameter fields for topological deformations. Finally, to exemplify our motivation, we provide three example applications for this framework.
Category: Mathematical Physics

[119] viXra:1304.0106 [pdf] replaced on 2013-05-18 22:57:55

### The Generalizations of the First Noether Theorem.

Authors: Vyacheslav Telnin

This paper deals with the generalizations of the First Noether theorem. It takes into account not only the first derivatives of the fields by the coordinates in Lagrangian, but also the second. And this theorem is generalized on the curved spaces. And also it's generalized on asymmetric metric tensors.
Category: Mathematical Physics

[118] viXra:1304.0013 [pdf] replaced on 2013-08-26 05:01:28

### Borel Resummation and the Solution of Integral Equations

Authors: Jose Javier garcia Moreta

ABSTRACT: In this paper we study the methods of Borel resummation applied to the solution of integral equation with symmetric Kernels K(xs) and to the study of the Riesz criterion , which is important to the Riemann Hypothesis •Keywords: Integral equation, Borel resummation, divergent series
Category: Mathematical Physics

[117] viXra:1304.0013 [pdf] replaced on 2013-08-16 06:23:06

### Borel Resummation and the Solution of Integral Equations

Authors: Jose Javier garcia Moreta

ABSTRACT: In this paper we study the methods of Borel resummation applied to the solution of integral equation with symmetric Kernels K(xs) and to the study of the Riesz criterion , which is important to the Riemann Hypothesis
Category: Mathematical Physics

[116] viXra:1304.0013 [pdf] replaced on 2013-07-12 07:48:22

### Borel Resummation and the Solution of Integral Equations

Authors: Jose javier garcia Moreta

ABSTRACT: In this paper we study the methods of Borel resummation applied to the solution of integral equation with symmetric Kernels K(xs) and to the study of the Riesz criterion , which is important to the Riemann Hypothesis
Category: Mathematical Physics

[115] viXra:1304.0010 [pdf] replaced on 2014-04-28 10:03:00

### New Cosmological Hypothesis Matches Observations By New Dark Energy-Time Applied To Dark Matter For The Existence Of A Rotational Double Torus Universe.

Authors: Dan Visser

The Double Torus hypothesis stands for a new architecture for the Universe. Based on practical evidence, another dark energy drives the dynamics making the Big Bang an illusion. There has not been a Big Bang! New dark energy applies two extra time-clocks from below the Planck-time to dark matter. The implication is: The universe exists of a Double Torus of the dark energy-time enclosing and intertwining an inner dark matter torus. This might sound controversial, but a new ‘dark energy-force formula’ and related calculations, described within the Double Torus framework in several ‘papers’, enables a match with real observed phenomena, such as: 1) A smallest Newton-acceleration, a dark matter-acceleration in galaxies, 2) an anomalous deceleration of the Pioneer 1 and 2 satellites, 3) a dark flow of spatial dark matter, 4) a solution eliminating the discrepancy of vacuum-energy-density (between General Relativity and Quantum-Mechanics calculations), 5) an α-dipole that indicates a torus-shape for the universe, 6) four times shifted ‘hot- and cold spots’ in the CMB, 7) an explanation for why 4,9% matter is visible, 26,8% is dark matter and 67,3% is dark energy and 8) at last why for ½ the squared-Planck-length gravity turns into anti-gravity. All the issues for evidence are described in my former ‘papers’ (see references), whereof the last two ones are in concept and will be published soon. However, particularly this paper relates to the combination of Newton quantum-gravity-force and dark matter-force, both implemented in one (new) formula. The dark matter force could be gravitational (+) and (-) , which means an anti-gravitational property of dark matter is highlighted in this paper. In this respect the measured laboratory acceleration-limit for Newton-gravity, 5 x 10^-14 m/s^2, theoretically is set to a lower value of 2.8659 x10^-14 m/s^2. That is remarkable, because no other formula in science is at hand for that. In general the dynamics for the Double Torus hypothesis is developed by DAN Visser, Almere, the Netherlands. He is an independent cosmologist and painting-artist. His conclusion is: The universe did not start with a Big Bang, but is a rotational cyclic-curved Double Torus, which recalculates reality eternally and independent on the scale one imagines the walls of the universe
Category: Mathematical Physics

[114] viXra:1304.0010 [pdf] replaced on 2013-06-28 15:16:39

### New Cosmological Hypothesis Match Observations by New Dark Energy-Time Applied to Dark Matter for the Existence of a Double Torus Universe.

Authors: Dan Visser
Comments: 12 Pages. Version 2 on June 28 2013 (textual and calculation-corrections)

The Double Torus hypothesis stands for a new architecture for the Universe. Based on practical evidence, another dark energy drives the dynamics making the Big Bang an illusion. There has not been a Big Bang! New dark energy applies two extra time-clocks from below the Planck-time to dark matter. The implication is: The universe exists of a Double Torus of the dark energy-time enclosing and intertwining an inner dark matter torus. This might sound controversial, but a new ‘dark energy-force formula’ and related calculations, described within the Double Torus framework in several ‘papers’, enables a match with real observed phenomena, such as: 1) A smallest Newton-acceleration, a dark matter-acceleration in galaxies, 2) an anomalous deceleration of the Pioneer 1 and 2 satellites, 3) a dark flow of spatial dark matter, 4) a solution eliminating the discrepancy of vacuum-energy-density (between General Relativity and Quantum-Mechanics calculations), 5) an α-dipole that indicates a torus-shape for the universe, 6) four times shifted ‘hot- and cold spots’ in the CMB, 7) an explanation for why 4,9% matter is visible, 26,8% is dark matter and 67,3% is dark energy and 8) at last why for ½ the squared-Planck-length gravity turns into anti-gravity. All the issues for evidence are described in my former ‘papers’ (see references), whereof the last two ones are in concept and will be published soon. However, particularly this paper relates to the combination of Newton quantum-gravity-force and dark matter-force, both implemented in one (new) formula. The dark matter force could be gravitational (+) and (-) , which means an anti-gravitational property of dark matter is highlighted in this paper. In this respect the measured laboratory acceleration-limit for Newton-gravity, 5 x 10^-14 m/s^2, theoretically is set to a lower value of 2.8659 x 10^-14 m/s^2. That is remarkable, because no other formula in science is at hand for that. In general the dynamics for the Double Torus hypothesis is developed by DAN Visser, Almere, the Netherlands. He is an independent cosmologist and painting-artist. His conclusion is: The universe did not start with a Big Bang, but is a rotational cyclic-curved Double Torus, which recalculates reality eternally and independent on the scale one imagines the walls of the universe.
Category: Mathematical Physics

[113] viXra:1303.0090 [pdf] replaced on 2013-12-14 15:25:42

### Gravitational Forces Are not Conservative

Authors: Florentino Muñiz Ania

This article shows how the gravitational force is conservative only in ideal models of small size. It is shown as strictly mathematical generally is not conservative. From it you can get energy by asymmetric systems. Spanish: En este artículo se muestra como la fuerza gravitatoria sólo es conservativa en modelos ideales de pequeño tamaño. Se demuestra con rigor matemático como, en general, no es conservativa. De ella se puede obtener energía mediante sistemas asimétricos.
Category: Mathematical Physics

[112] viXra:1303.0090 [pdf] replaced on 2013-03-27 10:34:03

### Gravitational Forces Are not Conservative

Authors: Florentino Muñiz Ania
Comments: 2 Pages. Sólo hablo español.

This article shows how the gravitational force is conservative only in ideal models of small size. It is shown as strictly mathematical generally is not conservative. From it you can get energy by asymmetric systems. Spanish: En este artículo se muestra como la fuerza gravitatoria sólo es conservativa en modelos ideales de pequeño tamaño. Se demuestra con rigor matemático como, en general, no es conservativa. De ella se puede obtener energía mediante sistemas asimétricos. vixra.org@gmail.com
Category: Mathematical Physics

[111] viXra:1303.0008 [pdf] replaced on 2014-05-30 13:10:39

### On the Söllinger, Weizsäcker Relations and Bošković’s Curve of Force (English Version)

Authors: Branko Zivlak
Comments: 7 Pages. 16 formulas, 1 table

In "The Code of Nature" [1] Helmut Söllinger gives Carl Friedrich von Weizsacker's (1912-2007) relationship between the fundamental physical constants. The first section examines Söllinger's the relationship between the masses of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory.
Category: Mathematical Physics

[110] viXra:1303.0008 [pdf] replaced on 2014-05-13 03:48:30

### On the Söllinger, Weizsäcker Relations and Bošković’s Curve of Force (English Version)

Authors: Branko Zivlak
Comments: 7 Pages. 15 relations, 1 table, 1 figure

In "The Code of Nature" [1] Helmut Söllinger gives his and Carl Friedrich von Weizsacker's (1912-2007) relationships between the fundamental physical constants. The first section examines Söllinger's the relationship between the masses of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory.
Category: Mathematical Physics

[109] viXra:1302.0154 [pdf] replaced on 2014-05-30 13:13:59

### On the Söllinger, Weizsäcker Relations and Bošković’s Curve of Force

Authors: Branko Zivlak
Comments: 7 Pages. 16 formulas, 1 table

In "The Code of Nature" [1] Helmut Söllinger gives Carl Friedrich von Weizsäcker's (1912-2007) the relationship between the fundamental physical constants. The first section examines the relationship between the mass of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory. This version is written on the languages of Bošković’s father and mother.
Category: Mathematical Physics

[108] viXra:1302.0154 [pdf] replaced on 2014-05-13 14:04:20

### On the Söllinger, Weizsäcker Relations and Bošković’s Curve of Force

Authors: Branko Zivlak
Comments: 7 Pages. 15 relations, 1 table, 1 figure

In "The Code of Nature" [1] Helmut Söllinger gives his and Carl Friedrich von Weizsäcker's (1912-2007) the relationship between the fundamental physical constants. The first section examines the relationship between the mass of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory. This version is written on the languages of Bošković’s father and mother.
Category: Mathematical Physics

[107] viXra:1302.0154 [pdf] replaced on 2014-05-13 03:44:47

### On the Söllinger, Weizsäcker Relations and Bošković’s Curve of Force

Authors: Branko Zivlak
Comments: 77 Pages. language Serbian+Italian, 15 formulas, 1Table, 1 figure

In "The Code of Nature" [1] Helmut Söllinger gives his and Carl Friedrich von Weizsäcker's (1912-2007) the relationship between the fundamental physical constants. The first section examines the relationship between the mass of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory. This version is written, in the lenguages, Bošković’s father and mother.
Category: Mathematical Physics

[106] viXra:1302.0095 [pdf] replaced on 2013-07-09 00:23:49

### Fractional Lagrangian and Hamiltonian Formulations in Field Theory

Authors: Hosein Nasrolahpour

The fractional variational principle represents an important part of fractional calculus and has found many applications. There are several versions of fractional variational principles and so different kinds of fractional Euler-Lagrange equations. In this paper, we propose the fractional sine-Gordon Lagrangian density. Then using the fractional Euler-Lagrange equations we obtain fractional sine-Gordon equation.
Category: Mathematical Physics

[105] viXra:1302.0059 [pdf] replaced on 2014-12-27 16:00:06

### Exact Solution of Helmholtz Equation for the Case of Non-Paraxial Gaussian Beams

Authors: Sergey V. Ershkov
Comments: 8 Pages. Keywords: Helmholtz equation, paraxial approximation, Gaussian beam

A new type of exact solutions of the full 3 dimensional spatial Helmholtz equation for the case of non-paraxial Gaussian beams is presented here. We consider appropriate representation of the solution for Gaussian beams in a spherical coordinate system by substituting it to the full 3 dimensional spatial Helmholtz Equation. Analyzing the structure of the final equation, we obtain that governing equations for the components of our solution are represented by the proper Riccati equations of complex value, which has no analytical solution in general case. But we find one of the possible exact solution which is proved to satisfy to such an equations for Gaussian beams.
Category: Mathematical Physics

[104] viXra:1302.0059 [pdf] replaced on 2014-12-24 16:23:18

### Exact Solution of Helmholtz Equation for the Case of Non-Paraxial Gaussian Beams

Authors: Sergey V. Ershkov
Comments: 8 Pages. Keywords: Helmholtz equation, paraxial approximation, Gaussian beam

A new type of exact solutions of the full 3 dimensional spatial Helmholtz equation for the case of non-paraxial Gaussian beams is presented here. We consider appropriate representation of the solution for Gaussian beams in a spherical coordinate system by substituting it to the full 3 dimensional spatial Helmholtz Equation. Analyzing the structure of the final equation, we obtain that governing equations for the components of our solution are represented by the proper Riccati equations of complex value, which has no analytical solution in general case. But we find one of the possible exact solution which is proved to satisfy to such an equations for Gaussian beams.
Category: Mathematical Physics

[103] viXra:1302.0059 [pdf] replaced on 2014-10-28 19:10:05

### Exact Solution of Helmholtz Equation for the Case of Non-Paraxial Gaussian Beams

Authors: Sergey V. Ershkov
Comments: 7 Pages. Keywords: Helmholtz equation, paraxial approximation, Gaussian beam

A new type of exact solutions of the full 3 dimensional spatial Helmholtz equation for the case of non-paraxial Gaussian beams is presented here. We consider appropriate representation of the solution for Gaussian beams in a spherical coordinate system by substituting it to the full 3 dimensional spatial Helmholtz Equation. Analyzing the structure of the final equation, we obtain one of the possible exact solution which is proved to satisfy to such an equation for Gaussian beams. Also the proper examples of implementing of the paraxial approximation for Gaussian beam could easily be obtained for a new type of exact solution of Helmholtz equation.
Category: Mathematical Physics

[102] viXra:1301.0078 [pdf] replaced on 2013-02-08 08:52:48

### Riemann Zeros Quantum Chaos Functional Determinants and Trace Formulae

Authors: Jose Javier Garcia

We study the relation between the Guzwiller Trace for a dynamical system and the Riemann-Weil trace formula for the Riemann zeros, using the Bohr-Sommerfeld quantization condition and the fractional calculus we obtain a method to define implicitly a potential , we apply this method to define a Hamiltonian whose energies are the square of the Riemann zeros (imaginary part) , also we show that for big ‘x’ the potential is very close to an exponential function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, WKB semiclassical approximation, Gutzwiller trace formula, Bohr-Sommerfeld quantization,exponential potential.
Category: Mathematical Physics

[101] viXra:1301.0078 [pdf] replaced on 2013-01-21 13:14:38

### Riemann Zeros Quantum Chaos Functional Determinants and Trace Formulae

Authors: Jose Javier Garcia

We study the relation between the Guzwiller Trace for a dynamical system and the Riemann-Weil trace formula for the Riemann zeros, using the Bohr-Sommerfeld quantization condition and the fractional calculus we obtain a method to define implicitly a potential , we apply this method to define a Hamiltonian whose energies are the square of the Riemann zeros (imaginary part) , also we show that for big ‘x’ the potential is very close to an exponential function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, WKB semiclassical approximation, Gutzwiller trace formula, Bohr-Sommerfeld quantization,exponential potential.
Category: Mathematical Physics

[100] viXra:1301.0076 [pdf] replaced on 2014-07-12 06:05:18

### Clustering and Uncertainty in Perfect Chaos Systems

Authors: Sergey A. Kamenshchikov
Comments: 9 Pages. Journal of Chaos, Volume 2014, Article ID 292096. Author: ru.linkedin.com/pub/sergey-kamenshchikov/60/8b1/21a/

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed to find a principal consequence: a chaotic system with uniform dynamic properties tends to instable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation. Key words: clustering, anomalous transport, Fokker-Planck equation, uncertainties relation.
Category: Mathematical Physics

[99] viXra:1301.0076 [pdf] replaced on 2014-04-08 12:53:00

### Clustering and Uncertainty in Perfect Chaos Systems

Authors: Sergey A. Kamenshchikov

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed to find a principal consequence: a chaotic system with uniform dynamic properties tends to instable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation.
Category: Mathematical Physics

[98] viXra:1301.0076 [pdf] replaced on 2014-04-08 00:17:28

### Clustering and Uncertainty in Perfect Chaos Systems

Authors: Sergey A. Kamenshchikov

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed to find a principal consequence: a chaotic system with uniform dynamic properties tends to instable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation.
Category: Mathematical Physics

[97] viXra:1301.0076 [pdf] replaced on 2013-03-13 07:10:48

### Universal Principles of Perfect Chaos

Authors: Sergey Kamenshchikov
Comments: 12 Pages. Author is looking for postdoc position. kamphys@gmail.com

The purpose of this work was to introduce strict, comprehensive definition of perfect chaos, to find out its basic properties in terms of phase transitions and give connections for uncertainties, lying in base of perfect chaos concept. Concept of perfect chaos as undetermined description was introduced basing on two formalized necessary and sufficient conditions: finite phase space resolution and instability of phase space trajectories. Properties of Kolmogorov system, including phase mixing, turned out to be consequences of chaotic state but not its comprehensive and sufficient conditions.Description relativity was defined as mandatory property of perfect chaos. The same areas of phase space may show regular or chaotic properties depending on space - time description accuracy. Herewith evolution of physical system in given generalized phase space can be represented by consequence of regular states and intermediate transitions. For chaotic state with uniform diffusion it was found out that nonlinear dispersion law is mandatory property.One in its turn necessarily leads to space - time instability of probability density and appearance of probability cavities in phase space - phase space attractors where particles density grows up. Case of chaotic state with fixed boundary and diffusion was considered. It turned out that Fourier decomposition allows to derive relations between coordinate - momentum and time - energy definition uncertainties. It was shown that chaos diffusion factor is the only parameter, limiting product of corresponding uncertainties.
Category: Mathematical Physics

[96] viXra:1212.0081 [pdf] replaced on 2013-01-06 01:38:58

### Unified Integro-Differential Equation for Relaxation and Oscillation

Authors: Hosein Nasrolahpour
Comments: 3 Pages. Another short report on " Fractional Classical Mechanics" :Prespacetime Journal| November 2012 | Volume 3| Issue 13 | pp. 1247-1250

In this paper we discuss some important consequences of application of fractional operators in physics. Also we present a unified integro-differential equation for relaxation and oscillation. We focus on time fractional formalism whose derivative is in Caputo sense.
Category: Mathematical Physics

[95] viXra:1211.0143 [pdf] replaced on 2014-04-19 05:52:35

### Riemann Zeros and an Exponential Potential

Authors: Jose Javier Garcia Moreta

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue staircase includes the oscillatory and smooth part of the Number of Riemann zeros. In this paper and for simplicity we use units so 2m1  Keywords: = Riemann Hypothesis, WKB semiclassical approximation, exponential potential
Category: Mathematical Physics

[94] viXra:1211.0143 [pdf] replaced on 2014-03-14 14:23:41

### Riemann Zeros and a Exponential Potential

Authors: Jose Javier Garcia Moreta

ABSTRACT: We study a given exponential potential on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue staircase includes the oscillatory and smooth part of the Number of Riemann zeros. In this paper and for simplicity we use units so •Keywords: = Riemann Hypothesis, WKB semiclassical approximation, exponential potential.
Category: Mathematical Physics

[93] viXra:1211.0143 [pdf] replaced on 2013-01-02 14:31:57

### Riemann Zeros and an Exponential Potential

Authors: Jose Javier Garcia

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue
Category: Mathematical Physics

[92] viXra:1211.0143 [pdf] replaced on 2012-12-13 05:41:21

### Riemann Zeros and an Exponential Potential

Authors: Jose Javier Garcia

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue staircase includes the oscillatory and smooth part of the Number of Riemann zeros. In this paper and for simplicity we use units so 2m =1= h · Keywords: = Riemann
Category: Mathematical Physics

[91] viXra:1211.0143 [pdf] replaced on 2012-11-29 04:29:08

### Riemann Zeros and an Exponential Potential

Authors: Jose Javier Garcia Moreta

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue staircase includes the oscillatory and smooth part of the Number of Riemann
Category: Mathematical Physics

[90] viXra:1211.0051 [pdf] replaced on 2013-04-02 13:59:43

### A Note on Fractional Electrodynamics

Authors: Hosein Nasrolahpour

We investigate the time evolution of the fractional electromagnetic waves by using the time fractional Maxwell's equations. We show that electromagnetic plane wave has amplitude which exhibits an algebraic decay, at asymptotically long times.
Category: Mathematical Physics

[89] viXra:1210.0123 [pdf] replaced on 2012-11-19 15:12:36

### The Symmetry Groups of Light

Authors: John A. Gowan

In the mathematical terms of Evariste Galois' "Group Theory", the "Tetrahedron Model" is a description of the symmetry group of light, including its destruction by asymmetric weak force decays (producing our matter-only Cosmos), and its on-going restoration in obedience to Noether's Theorem of symmetry conservation (as in the conversion of bound to free energy in stars). The usual symmetry group identified with light is that of local phase transformations, and it is designated as either SO(2) or U(1). However, I am suggesting here that light contains a very much larger (and more interesting) symmetry group associated with its transformation into particle-antiparticle pairs (and back again into light). I don't know what the formal designation of this group might be. For an expert's explanation of the formal aspects of symmetry and group theory, See: Keith Devlin The Language of Mathematics Chap. 5 "The Mathematics of Beauty", 1998 W. H. Freeman & Co. (Holt Paperbacks); see also: Ian Stewart Why Beauty is Truth Chapt. 13 "The Five Dimensional Man", Basic Books 2007.
Category: Mathematical Physics

[88] viXra:1210.0123 [pdf] replaced on 2012-11-10 12:47:27

### The Symmetry Groups of Light

Authors: John A. Gowan

A symmetry group consists (for one example) of a collection of figures that can be transformed into one another without changing the original. The symmetry group of an equilateral triangle (say) consists of all the triangles that can be created from an original by means of rotation, translation, reflection, etc. - provided the transformed articles are indistinguishable from the original. How do we apply this notion to the case of light? In what sense is there a symmetry group associated with (consisting of) transformations of light (free electromagnetic radiation)? Beyond the simple phase transformations of the electromagnetic field, the examples of interest here are the particle-antiparticle pairs of the Dirac/Heisenberg "vacuum" of spacetime. These particle-antiparticle pairs are constantly produced from borrowed energy and instantaneously annihilate each other in an endless cycle of creation and destruction alternating between light and virtual particles, a cycle which has been ongoing throughout spacetime since its beginning in the "Big Bang". Since they are "virtual" rather than "real" particles we do not notice them even though they are everywhere around us. Essentially, we do not notice them because their symmetry is so complete. We only notice the asymmetries which surround (and comprise) us.
Category: Mathematical Physics

[87] viXra:1210.0123 [pdf] replaced on 2012-11-01 15:42:48

### The Symmetry Groups of Light

Authors: John A. Gowan

A symmetry group consists (for one example) of a collection of figures that can be transformed into one another without changing the original. The symmetry group of an equilateral triangle (say) consists of all the triangles that can be created from an original by means of rotation, translation, reflection, etc. - provided the transformed articles are indistinguishable from the original. How do we apply this notion to the case of light? In what sense is there a symmetry group associated with (consisting of) transformations of light (free electromagnetic radiation)? Beyond the simple phase transformations of the electromagnetic field, the examples of interest here are the particle-antiparticle pairs of the Dirac/Heisenberg "vacuum" of spacetime. These particle-antiparticle pairs are constantly produced from borrowed energy and instantaneously annihilate each other in an endless cycle of creation and destruction alternating between light and virtual particles, a cycle which has been ongoing throughout spacetime since its beginning in the "Big Bang". Since they are "virtual" rather than "real" particles we do not notice them even though they are everywhere around us. Essentially, we do not notice them because their symmetry is so complete. We only notice the asymmetries which surround (and comprise) us.
Category: Mathematical Physics

[86] viXra:1210.0114 [pdf] replaced on 2012-11-05 13:03:49

### The Cuantifiplane

Authors: Jose M. Hernandez

is fine
Category: Mathematical Physics

[85] viXra:1210.0114 [pdf] replaced on 2012-10-24 15:21:37

### The Cuantifiplane (1)

Authors: Jose M Hernandez

is fine
Category: Mathematical Physics

[84] viXra:1207.0089 [pdf] replaced on 2012-09-07 09:16:02

### Electrical Maxwell Demon and Szilard Engine Utilizing Johnson Noise, Measurement, Logic and Control

Authors: Laszlo B. Kish, Claes-Göran Granqvist
Comments: 17 Pages. Accepted for publication in PLOS ONE (September 6, 2012)

We introduce a purely electrical version of Maxwell’s demon which does not involve mechanically moving parts such as trapdoors, etc. It consists of a capacitor, resistors, amplifiers, logic circuitry and electronically controlled switches and uses thermal noise in resistors (Johnson noise) to pump heat. The only types of energy of importance in this demon are electrical energy and heat. We also demonstrate an entirely electrical version of Szilard’s engine, i.e., an information-controlled device that can produce work by employing thermal fluctuations. The only moving part is a piston that executes work, and the engine has purely electronic controls and it is free of the major weakness of the original Szilard engine in not requiring removal and repositioning the piston at the end of the cycle. For both devices, the energy dissipation in the memory and other binary informatics components are insignificant compared to the exponentially large energy dissipation in the analog part responsible for creating new information by measurement and decision. This result contradicts the view that the energy dissipation in the memory during erasure is the most essential dissipation process in a demon. Nevertheless the dissipation in the memory and information processing parts is sufficient to secure the Second Law of Thermodynamics.
Category: Mathematical Physics

[83] viXra:1206.0069 [pdf] replaced on 2012-09-26 14:59:59

### A Functional Determinant Expression for the Riemann XI Function

Authors: Jose Javier Garcia Moreta

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law, Quantum chaos.
Category: Mathematical Physics

[82] viXra:1206.0069 [pdf] replaced on 2012-08-26 07:01:41

### A Functional Determinant Expression for the Riemann XI-Function

Authors: Jose Javier Garcia Moreta

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law, Quantum chaos.
Category: Mathematical Physics

[81] viXra:1206.0069 [pdf] replaced on 2012-07-06 06:09:46

### A Functional Determinant Expression for the Riemann XI Function

Authors: Jose Javier Garcia Moreta

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law, Quantum chaos.
Category: Mathematical Physics

[80] viXra:1206.0069 [pdf] replaced on 2012-06-25 04:35:14

### A Functional Determinant Expression for the Riemann XI Function

Authors: Jose Javier Garcia Moreta

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law, Quantum chaos.
Category: Mathematical Physics

[79] viXra:1206.0064 [pdf] replaced on 2013-01-05 04:47:27

### Time Fractional Formalism: Classical and Quantum Phenomena

Authors: Hosein Nasrolahpour

In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can provide a deeper understanding of the physical interpretations of fractional derivative.
Category: Mathematical Physics

[78] viXra:1206.0049 [pdf] replaced on 2012-07-29 15:28:19

### A Technique for Cataloging Types of Particles and Types of Stuff

Authors: Thomas J. Buckholtz

We develop theory leading to an ability to catalog types of elementary particles. The resulting catalog provides for known interaction-mediating bosons, non-traditional interaction-carrying bosons, and fermions. Some ratios of numbers of instances of various types of particles are 1:6:24:48. Potentially, the actual ratios of densities of baryonic matter, dark matter, dark energy are 1:5:18 and do not depend on time, even though interpretations of data provide ratios that vary with the age of the universe. Potentially there is another type of stuff. Here, 5=6-1, 18=24-6, and there could be 24=48-24 units of the other type of stuff.
Category: Mathematical Physics

[77] viXra:1206.0049 [pdf] replaced on 2012-07-23 15:55:48

### A Technique for Cataloging Types of Particles and Types of Stuff

Authors: Thomas J. Buckholtz

We develop theory leading to an ability to catalog types of elementary particles. The resulting catalog provides for known interaction-mediating bosons, non-traditional interaction-carrying bosons, and fermions. Ratios of theoretical numbers of analogs of various types of particles may be consistent with observed ratios of densities for baryonic matter, dark matter, and dark energy.
Category: Mathematical Physics

[76] viXra:1204.0043 [pdf] replaced on 2012-05-20 06:08:09

### Duonistic Neutrinos Violate Relativity.

Authors: Dan Visser

Neutrinos-faster-than-light? The science-battle is not yet over! ‘Yes’, said the OPERA-team in September 22 2011. ‘No’, said the ICARUS-team in February 23 2012. But this paper carries on that it is undoubtedly correct that neutrinos can go faster-than-light. Neutrinos can only do that in neutrino-pairs: I call these pairs Duonistic Neutrinos! This paper presents the set of equations to prove that. The smallest gravity-acceleration g’ appears to be prior to the trajectory of single packaged neutrinos. OPERA and ICARUS might be right both in the end.
Category: Mathematical Physics

[75] viXra:1203.0067 [pdf] replaced on 2013-03-24 16:48:31

### In Search Of A Variant Kaluza Theory

Authors: Robert Watson
Comments: 34 Pages. ...looking better now...

Kaluza's 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is at the root of many modern attempts to develop new physical theories. Lacking non-null electromagnetic fields however the theory is incomplete. Variants of the theory are explored to find ways to introduce non-null solutions by making the fifth dimension more physical, using alternative, weaker cylinder conditions. The Lorentz force law is investigated starting with a non-Maxwellian definition of charge, this is assumed to be related to Maxwellian charge by ansatz. Order of magnitude methods are used. Kaluza theory remains inadequate to support electromagnetism in full, non-null solutions are not readily shown to be admitted. An argument is made in favour of torsion resolving this issue. Postulates are derived from the argument for a variant theory. The charge ansatz is shown to follow from the postulates. It is concluded that Kaluza's 5D space and torsion need to go together in a Kaluza-Cartan theory. Tentatively, generalized Bel super-energy is hypothesized to be a conserved quantity.
Category: Mathematical Physics

[74] viXra:1201.0117 [pdf] replaced on 2013-06-29 15:21:39

### New Dark Energy and Letter to the Nobel Committee.

Authors: Dan Visser
Comments: 10 Pages. This version-2 of June 29 2013 comprehends important notes: My formulas used in the appendix (letter to the Nobel Committee) are much more analyzed afterwards in following ‘papers’. So this moment, June 29 2013, I decided to keep this paper active.

This paper describes an interim stage in the Double Torus hypothesis’ development. I also implemented a message of “Nobel Nominations in a New World” to the Nobel Committee. These seemingly different looking subjects are importantly connected in a plead to change the way Nobel-nominations are performed in a changing world with internet and alternative archives, such as viXra. The point is here, that institutional established physics and cosmology are blocking new ideas from the public domain. Therefore an appendix has been added to this paper to summarize in a nutshell, relativity, space-expansion, accelerated space-expansion and the one time-direction in the Big Bang Cosmology, in order to explain better what new dark energy is in the Double Torus. That message is meant for the Nobel Committee. Furthermore three-why’s are answered: Why are two extra time-directions needed in a new cosmology? Why is the introduction of dark mass, squared? Why would there be a Double Torus for New Cosmology? Also the basic-formulas are summarized, referring to my papers, such as the dark energy force formula from my thought-experiment, followed by its transformed-version: the force smaller than the smallest gravity. In the end New Dark Energy is formulated as a product of new dark mass (squared) and two extra time-directions from below the Planck scale. This marks that New Dark Energy could recalculate the established dual unitary-entangled quantum-spaces faster backwards in time than time goes forward in the Big Bang Cosmology! This affects the established quantum dynamics and classical reality towards the past and future differently than Einstein’s General Relativity is prescribing. The letter to the Nobel Committee is send by me, because no other institutions is doing that for me.
Category: Mathematical Physics

[73] viXra:1112.0094 [pdf] replaced on 2012-09-07 10:45:39

### Particle Mass Ratios

Authors: DT Froedge
Comments: 15 Pages. This should be the final. Accuracies calculated in parts per billion

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, yielding specific values for some well studied particles. The additional nuclear modes postulated, are similar to the Schrodinger modes in the atom, and the mass ratios calculated for these particles have been calculated within the experimental values, with accuracies up to 2.4 parts per billion. The examined particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0.
Category: Mathematical Physics

[72] viXra:1112.0094 [pdf] replaced on 2012-08-18 08:31:46

### Particle Mass Ratios

Authors: DT Froedge
Comments: 14 Pages. Finally, very precise values.

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles have been calculated within the experimental values. Those particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0
Category: Mathematical Physics

[71] viXra:1112.0094 [pdf] replaced on 2012-08-14 21:31:58

### Particle Mass Ratios

Authors: DT Froedge
Comments: 13 Pages. This worked out

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles have been calculated within the experimental values. Those particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0
Category: Mathematical Physics

[70] viXra:1112.0094 [pdf] replaced on 2012-08-13 21:58:31

### Particle Mass Ratios

Authors: DT Froedge
Comments: 14 Pages. finally figured it out,

Based on the developments in a previous paper, this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles have been calculated within the experimental values.Those particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0.
Category: Mathematical Physics

[69] viXra:1112.0094 [pdf] replaced on 2012-07-22 13:23:18

### Particle Mass Ratios

Authors: DT Froedge
Comments: 10 Pages. Major improvement, ongoing project.

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles are very close the observed mass ratios. Integral amplitudes for the Pauli and quark matrix are shown to produce values that are far more accurate than those that could be produced by random coincidence.
Category: Mathematical Physics

[68] viXra:1112.0094 [pdf] replaced on 2012-07-07 14:28:58

### Particle Mass Ratios

Authors: DT Froedge
Comments: 13 Pages. A little progress.

Based on the developments in a previous paper, this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.
Category: Mathematical Physics

[67] viXra:1112.0094 [pdf] replaced on 2012-06-07 14:41:38

### Particle Mass Ratios

Authors: DT Froedge

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.
Category: Mathematical Physics

[66] viXra:1112.0094 [pdf] replaced on 2012-03-11 12:59:44

### Particle Mass Ratios

Authors: DT Froedge
Comments: 12 Pages. This is the 6Th and final revision (v3-11-12),

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.
Category: Mathematical Physics

[65] viXra:1111.0106 [pdf] replaced on 2013-11-10 15:33:06

### A New Force Smaller Than The Smallest Gravity

Authors: Dan Visser

In this version 3 the formulations are given for the existence of a force smaller than the smallest gravity. This is a new dark energy force, which affects neutrinos differently than is assumed according to current physics. The formulations also imply a different look on the Higgs-mass and dark matter-mass. A deeper analysis became important, because a new cosmological hypothesis is involved. The CERN-experiments on these issues are far from criticism. My set of equations mentioned in my paper “A New Dark Energy Force Theoretically Calculates Faster-than-light-neutrinos” and “Duonistic Neutrinos Violate Relativity” reveal such a criticism. However, until now my formulations withstand a hurricane, even after a Director of the OPERA-project had to resign. My set of equations theoretically proves the neutrino-faster-than-light experiments had to be investigated to the bottom.
Category: Mathematical Physics

[64] viXra:1111.0106 [pdf] replaced on 2012-05-16 14:36:33

### A New Force Smaller Than The Smallest Gravity.

Authors: Dan Visser

In this version2 the formulations are given for the existence of a force smaller than the smallest gravity. This is a new dark energy force, which affects neutrinos differently than is assumed according to current physics. The formulations also imply a different look on the Higgs-mass and dark matter-mass. A deeper analysis became important, because a new cosmological hypothesis is involved. The CERN-experiments on these issues are far from criticism. My set of equations mentioned in my paper “A New Dark Energy Force Theoretically Calculates Faster-than-light-neutrinos” and “Duonistic Neutrinos Violate Relativity”, reveal such a criticism. However, until now my formulations withstand a hurricane, even after a Director of the OPERA-project had to resign. My set of equations theoretically proves the neutrino-faster-than-light experiments had to be investigated to the bottom.
Category: Mathematical Physics

[63] viXra:1111.0091 [pdf] replaced on 2012-01-30 08:18:27

### Langlands Conjectures in TGD Framework

Authors: Matti Pitkänen

The arguments of this article support the view that in TGD Universe number theoretic and geometric Langlands conjectures could be understood very naturally. The basic notions are following.

1. Zero energy ontology (ZEO) and the related notion of causal diamond CD (CD is short hand for the cartesian product of causal diamond of M4 and of CP2). ZEO leads to the notion of partonic 2-surfaces at the light-like boundaries of CD and to the notion of string world sheet. These notions are central in the recent view about TGD. One can assign to the partonic 2-surfaces a conformal moduli space having as additional coordinates the positions of braid strand ends (punctures). By electric-magnetic duality this moduli space must correspond closely to the moduli space of string world sheets.

2. Electric-magnetic duality realized in terms of string world sheets and partonic 2-surfaces. The group G and its Langlands dual LG would correspond to the time-like and space-like braidings. Duality predicts that the moduli space of string world sheets is very closely related to that for the partonic 2-surfaces. The strong form of 4-D general coordinate invariance implying electric-magnetic duality and S-duality as well as strong form of holography indeed predicts that the collection of string world sheets is fixed once the collection of partonic 2-surfaces at light-like boundaries of CD and its sub-CDs is known.

3. The proposal is that finite measurement resolution is realized in terms of inclusions of hyperfinite factors of type II1 at quantum level and represented in terms of confining effective gauge group. This effective gauge group could be some associate of G: gauge group, Kac-Moody group or its quantum counterpart, or so called twisted quantum Yangian strongly suggested by twistor considerations. At space-time level the finite measurement resolution would be represented in terms of braids at space-time level which come in two varieties correspond to braids assignable to space-like surfaces at the two light-like boundaries of CD and with light-like 3-surfaces at which the signature of the induced metric changes and which are identified as orbits of partonic 2-surfaces connecting the future and past boundaries of CDs.

There are several steps leading from G to its twisted quantum Yangian. The first step replaces point like particles with partonic 2-surfaces: this brings in Kac-Moody character. The second step brings in finite measurement resolution meaning that Kac-Moody type algebra is replaced with its quantum version. The third step brings in zero energy ontology: one cannot treat single partonic surface or string world sheet as independent unit: always the collection of partonic 2-surfaces and corresponding string worlds sheets defines the geometric structure so that multilocality and therefore quantum Yangian algebra with multilocal generators is unavoidable.

In finite measurement resolution geometric Langlands duality and number theoretic Langlands duality are very closely related since partonic 2-surface is effectively replaced with the punctures representing the ends of braid strands and the orbit of this set under a discrete subgroup of G defines effectively a collection of "rational" 2-surfaces. The number of the "rational" surfaces in geometric Langlands conjecture replaces the number of rational points of partonic 2-surface in its number theoretic variant. The ability to compute both these numbers is very relevant for quantum TGD.

4. The natural identification of the associate of G is as quantum Yangian of Kac-Moody type group associated with Minkowskian open string model assignable to string world sheet representing a string moving in the moduli space of partonic 2-surface. The dual group corresponds to Euclidian string model with partonic 2-surface representing string orbit in the moduli space of the string world sheets. The Kac-Moody algebra assigned with simply laced G is obtained using the standard tachyonic free field representation obtained as ordered exponentials of Cartan algebra generators identified as transversal parts of M4 coordinates for the braid strands. The importance of the free field representation generalizing to the case of non-simply laced groups in the realization of finite measurement resolution in terms of Kac-Moody algebra cannot be over-emphasized.

5. Langlands duality involves besides harmonic analysis side also the number theoretic side. Galois groups (collections of them) defined by infinite primes and integers having representation as symplectic flows defining braidings. I have earlier proposed that the hierarchy of these Galois groups define what might be regarded as a non-commutative homology and cohomology. Also G has this kind of representation which explains why the representations of these two kinds of groups are so intimately related. This relationship could be seen as a generalization of the MacKay correspondence between finite subgroups of SU(2) and simply laced Lie groups.

6. Symplectic group of the light-cone boundary acting as isometries of the WCW geometry kenociteallb/compl1 allowing to represent projectively both Galois groups and symmetry groups as symplectic flows so that the non-commutative cohomology would have braided representation. This leads to braided counterparts for both Galois group and effective symmetry group.

7. The moduli space for Higgs bundle playing central role in the approach of Witten and Kapustin to geometric Landlands program is in TGD framework replaced with the conformal moduli space for partonic 2-surfaces. It is not however possible to speak about Higgs field although moduli defined the analog of Higgs vacuum expectation value. Note that in TGD Universe the most natural assumption is that all Higgs like states are "eaten" by gauge bosons so that also photon and gluons become massive. This mechanism would be very general and mean that massless representations of Poincare group organize to massive ones via the formation of bound states. It might be however possible to see the contribution of p-adic thermodynamics depending on genus as analogous to Higgs contribution since the conformal moduli are analogous to vacuum expectation of Higgs field.

Category: Mathematical Physics

[62] viXra:1111.0090 [pdf] replaced on 2012-01-30 08:22:30

### How Infinite Primes Relate to Other Views About Mathematical Infinity?

Authors: Matti Pitkänen

Infinite primes is a purely TGD inspired notion. The notion of infinity is number theoretical and infinite primes have well defined divisibility properties. One can partially order them by the real norm. p-Adic norms of infinite primes are well defined and finite. The construction of infinite primes is a hierarchical procedure structurally equivalent to a repeated second quantization of a supersymmetric arithmetic quantum field theory. At the lowest level bosons and fermions are labelled by ordinary primes. At the next level one obtains free Fock states plus states having interpretation as bound many particle states. The many particle states of a given level become the single particle states of the next level and one can repeat the construction ad infinitum. The analogy with quantum theory is intriguing and I have proposed that the quantum states in TGD Universe correspond to octonionic generalizations of infinite primes. It is interesting to compare infinite primes (and integers) to the Cantorian view about infinite ordinals and cardinals. The basic problems of Cantor's approach which relate to the axiom of choice, continuum hypothesis, and Russell's antinomy: all these problems relate to the definition of ordinals as sets. In TGD framework infinite primes, integers, and rationals are defined purely algebraically so that these problems are avoided. It is not surprising that these approaches are not equivalent. For instance, sum and product for Cantorian ordinals are not commutative unlike for infinite integers defined in terms of infinite primes.

Set theory defines the foundations of modern mathematics. Set theory relies strongly on classical physics, and the obvious question is whether one should reconsider the foundations of mathematics in light of quantum physics. Is set theory really the correct approach to axiomatization?

1. Quantum view about consciousness and cognition leads to a proposal that p-adic physics serves as a correlate for cognition. Together with the notion of infinite primes this suggests that number theory should play a key role in the axiomatics.
2. Algebraic geometry allows algebraization of the set theory and this kind of approach suggests itself strongly in physics inspired approach to the foundations of mathematics. This means powerful limitations on the notion of set.
3. Finite measurement resolution and finite resolution of cognition could have implications also for the foundations of mathematics and relate directly to the fact that all numerical approaches reduce to an approximation using rationals with a cutoff on the number of binary digits.
4. The TGD inspired vision about consciousness implies evolution by quantum jumps meaning that also evolution of mathematics so that no fixed system of axioms can ever catch all the mathematical truths for the simple reason that mathematicians themselves evolve with mathematics.
I will discuss possible impact of these observations on the foundations of physical mathematics assuming that one accepts the TGD inspired view about infinity, about the notion of number, and the restrictions on the notion of set suggested by classical TGD.

Category: Mathematical Physics

[61] viXra:1111.0089 [pdf] replaced on 2012-01-30 08:24:00

### Motives and Infinite Primes

Authors: Matti Pitkänen

In this article the goal is to find whether the general mathematical structures associated with twistor approach, superstring models and M-theory could have a generalization or a modification in TGD framework. The contents of the chapter is an outcome of a rather spontaneous process, and represents rather unexpected new insights about TGD resulting as outcome of the comparisons.

1. Infinite primes, Galois groups, algebraic geometry, and TGD

In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and cohomology groups for them. The notion of cohomology giving rise also to homology if Poincare duality holds true is central. The number of various cohomology theories has inflated and one of the basic challenges to find a sufficiently general approach allowing to interpret various cohomology theories as variations of the same motive as Grothendieck, who is the pioneer of the field responsible for many of the basic notions and visions, expressed it.

Cohomology requires a definition of integral for forms for all number fields. In p-adic context the lack of well-ordering of p-adic numbers implies difficulties both in homology and cohomology since the notion of boundary does not exist in topological sense. The notion of definite integral is problematic for the same reason. This has led to a proposal of reducing integration to Fourier analysis working for symmetric spaces but requiring algebraic extensions of p-adic numbers and an appropriate definition of the p-adic symmetric space. The definition is not unique and the interpretation is in terms of the varying measurement resolution.

The notion of infinite has gradually turned out to be more and more important for quantum TGD. Infinite primes, integers, and rationals form a hierarchy completely analogous to a hierarchy of second quantization for a super-symmetric arithmetic quantum field theory. The simplest infinite primes representing elementary particles at given level are in one-one correspondence with many-particle states of the previous level. More complex infinite primes have interpretation in terms of bound states.

1. What makes infinite primes interesting from the point of view of algebraic geometry is that infinite primes, integers and rationals at the n:th level of the hierarchy are in 1-1 correspondence with rational functions of n arguments. One can solve the roots of associated polynomials and perform a root decomposition of infinite primes at various levels of the hierarchy and assign to them Galois groups acting as automorphisms of the field extensions of polynomials defined by the roots coming as restrictions of the basic polynomial to planes xn=0, xn=xn-1=0, etc...

2. These Galois groups are suggested to define non-commutative generalization of homotopy and homology theories and non-linear boundary operation for which a geometric interpretation in terms of the restriction to lower-dimensional plane is proposed. The Galois group Gk would be analogous to the relative homology group relative to the plane xk-1=0 representing boundary and makes sense for all number fields also geometrically. One can ask whether the invariance of the complex of groups under the permutations of the orders of variables in the reduction process is necessary. Physical interpretation suggests that this is not the case and that all the groups obtained by the permutations are needed for a full description.

3. The algebraic counterpart of boundary map would map the elements of Gk identified as analog of homotopy group to the commutator group [Gk-2,Gk-2] and therefore to the unit element of the abelianized group defining cohomology group. In order to obtains something analogous to the ordinary homology and cohomology groups one must however replaces Galois groups by their group algebras with values in some field or ring. This allows to define the analogs of homotopy and homology groups as their abelianizations. Cohomotopy, and cohomology would emerge as duals of homotopy and homology in the dual of the group algebra.

4. That the algebraic representation of the boundary operation is not expected to be unique turns into blessing when on keeps the TGD as almost topological QFT vision as the guide line. One can include all boundary homomorphisms subject to the condition that the anticommutator δikδjk-1jkδik-1 maps to the group algebra of the commutator group [Gk-2,Gk-2]. By adding dual generators one obtains what looks like a generalization of anticommutative fermionic algebra and what comes in mind is the spectrum of quantum states of a SUSY algebra spanned by bosonic states realized as group algebra elements and fermionic states realized in terms of homotopy and cohomotopy and in abelianized version in terms of homology and cohomology. Galois group action allows to organize quantum states into multiplets of Galois groups acting as symmetry groups of physics. Poincare duality would map the analogs of fermionic creation operators to annihilation operators and vice versa and the counterpart of pairing of k:th and n-k:th homology groups would be inner product analogous to that given by Grassmann integration. The interpretation in terms of fermions turns however to be wrong and the more appropriate interpretation is in terms of Dolbeault cohomology applying to forms with homomorphic and antiholomorphic indices.

5. The intuitive idea that the Galois group is analogous to 1-D homotopy group which is the only non-commutative homotopy group, the structure of infinite primes analogous to the braids of braids of braids of ... structure, the fact that Galois group is a subgroup of permutation group, and the possibility to lift permutation group to a braid group suggests a representation as flows of 2-D plane with punctures giving a direct connection with topological quantum field theories for braids, knots and links. The natural assumption is that the flows are induced from transformations of the symplectic group acting on δ M2+/-× CP2 representing quantum fluctuating degrees of freedom associated with WCW ("world of classical worlds"). Discretization of WCW and cutoff in the number of modes would be due to the finite measurement resolution. The outcome would be rather far reaching: finite measurement resolution would allow to construct WCW spinor fields explicitly using the machinery of number theory and algebraic geometry.

6. A connection with operads is highly suggestive. What is nice from TGD perspective is that the non-commutative generalization homology and homotopy has direct connection to the basic structure of quantum TGD almost topological quantum theory where braids are basic objects and also to hyper-finite factors of type II1. This notion of Galois group makes sense only for the algebraic varieties for which coefficient field is algebraic extension of some number field. Braid group approach however allows to generalize the approach to completely general polynomials since the braid group make sense also when the ends points for the braid are not algebraic points (roots of the polynomial).

This construction would realize the number theoretical, algebraic geometrical, and topological content in the construction of quantum states in TGD framework in accordance with TGD as almost TQFT philosophy, TGD as infinite-D geometry, and TGD as generalized number theory visions.

This picture leads also to a proposal how p-adic integrals could be defined in TGD framework.

1. The calculation of twistorial amplitudes reduces to multi-dimensional residue calculus. Motivic integration gives excellent hopes for the p-adic existence of this calculus and braid representation would give space-time representation for the residue integrals in terms of the braid points representing poles of the integrand: this would conform with quantum classical correspondence. The power of 2π appearing in multiple residue integral is problematic unless it disappears from scattering amplitudes. Otherwise one must allow an extension of p-adic numbers to a ring containing powers of 2π.

2. Weak form of electric-magnetic duality and the general solution ansatz for preferred extremals reduce the Kähler action defining the Kähler function for WCW to the integral of Chern-Simons 3-form. Hence the reduction to cohomology takes places at space-time level and since p-adic cohomology exists there are excellent hopes about the existence of p-adic variant of Kähler action. The existence of the exponent of Kähler gives additional powerful constraints on the value of the Kähler fuction in the intersection of real and p-adic worlds consisting of algebraic partonic 2-surfaces and allows to guess the general form of the Kähler action in p-adic context.

3. One also should define p-adic integration for vacuum functional at the level of WCW. p-Adic thermodynamics serves as a guideline leading to the condition that in p-adic sector exponent of Kähler action is of form (m/n)r, where m/n is divisible by a positive power of p-adic prime p. This implies that one has sum over contributions coming as powers of p and the challenge is to calculate the integral for K= constant surfaces using the integration measure defined by an infinite power of Kähler form of WCW reducing the integral to cohomology which should make sense also p-adically. The p-adicization of the WCW integrals has been discussed already earlier using an approach based on harmonic analysis in symmetric spaces and these two approaches should be equivalent. One could also consider a more general quantization of Kähler action as sum K=K1+K2 where K1=rlog(m/n) and K2=n, with n divisible by p since exp(n) exists in this case and one has exp(K)= (m/n)r × exp(n). Also transcendental extensions of p-adic numbers involving n+p-2 powers of e1/n can be considered.

4. If the Galois group algebras indeed define a representation for WCW spinor fields in finite measurement resolution, also WCW integration would reduce to summations over the Galois groups involved so that integrals would be well-defined in all number fields.

3. Floer homology, Gromov-Witten invariants, and TGD

Floer homology defines a generalization of Morse theory allowing to deduce symplectic homology groups by studying Morse theory in loop space of the symplectic manifold. Since the symplectic transformations of the boundary of δ M4+/-× CP2 define isometry group of WCW, it is very natural to expect that Kähler action defines a generalization of the Floer homology allowing to understand the symplectic aspects of quantum TGD. The hierarchy of Planck constants implied by the one-to-many correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates leads naturally to singular coverings of the imbedding space and the resulting symplectic Morse theory could characterize the homology of these coverings.

One ends up to a more precise definition of vacuum functional: Kähler action reduces Chern-Simons terms (imaginary in Minkowskian regions and real in Euclidian regions) so that it has both phase and real exponent which makes the functional integral well-defined. Both the phase factor and its conjugate must be allowed and the resulting degeneracy of ground state could allow to understand qualitatively the delicacies of CP breaking and its sensitivity to the parameters of the system. The critical points with respect to zero modes correspond to those for Kähler function. The critical points with respect to complex coordinates associated with quantum fluctuating degrees of freedom are not allowed by the positive definiteness of Kähler metric of WCW. One can say that Kähler and Morse functions define the real and imaginary parts of the exponent of vacuum functional.

The generalization of Floer homology inspires several new insights. In particular, space-time surface as hyper-quaternionic surface could define the 4-D counterpart for pseudo-holomorphic 2-surfaces in Floer homology. Holomorphic partonic 2-surfaces could in turn correspond to the extrema of Kähler function with respect to zero modes and holomorphy would be accompanied by super-symmetry.

Gromov-Witten invariants appear in Floer homology and topological string theories and this inspires the attempt to build an overall view about their role in TGD. Generalization of topological string theories of type A and B to TGD framework is proposed. The TGD counterpart of the mirror symmetry would be the equivalence of formulations of TGD in H=M4× CP2 and in CP3× CP3 with space-time surfaces replaced with 6-D sphere bundles.

4. K-theory, branes, and TGD

K-theory and its generalizations play a fundamental role in super-string models and M-theory since they allow a topological classification of branes. After representing some physical objections against the notion of brane more technical problems of this approach are discussed briefly and it is proposed how TGD allows to overcome these problems. A more precise formulation of the weak form of electric-magnetic duality emerges: the original formulation was not quite correct for space-time regions with Euclidian signature of the induced metric. The question about possible TGD counterparts of R-R and NS-NS fields and S, T, and U dualities is discussed.

5. p-Adic space-time sheets as correlates for Boolean cognition

p-Adic physics is interpreted as physical correlate for cognition. The so called Stone spaces are in one-one correspondence with Boolean algebras and have typically 2-adic topologies. A generalization to p-adic case with the interpretation of p pinary digits as physically representable Boolean statements of a Boolean algebra with 2n>p>pn-1 statements is encouraged by p-adic length scale hypothesis. Stone spaces are synonymous with profinite spaces about which both finite and infinite Galois groups represent basic examples. This provides a strong support for the connection between Boolean cognition and p-adic space-time physics. The Stone space character of Galois groups suggests also a deep connection between number theory and cognition and some arguments providing support for this vision are discussed.

Category: Mathematical Physics

[60] viXra:1111.0088 [pdf] replaced on 2012-01-30 08:34:19

### Could One Generalize Braid Invariant Defined by Vacuum Expecation of Wilson Loop to and Invariant of Braid Cobordisms and of 2-Knots?

Authors: Matti Pitkänen

Witten was awarded by Fields medal from a construction recipe of Jones polynomial based on topological QFT assigned with braids and based on Chern-Simons action. Recently Witten has been working with an attempt to understand in terms of quantum theory the so called Khovanov polynomial associated with a much more abstract link invariant whose interpretation and real understanding remains still open.

The attempts to understand Witten's thoughts lead to a series of questions unavoidably culminating to the frustrating "Why I do not have the brain of Witten making perhaps possible to answer these questions?". This one must just accept. In this article I summarize some thoughts inspired by the associations of the talk of Witten with quantum TGD and with the model of DNA as topological quantum computer. In my own childish manner I dare believe that these associations are interesting and dare also hope that some more brainy individual might take them seriously.

An idea inspired by TGD approach which also main streamer might find interesting is that the Jones invariant defined as vacuum expectation for a Wilson loop in 2+1-D space-time generalizes to a vacuum expectation for a collection of Wilson loops in 2+2-D space-time and could define an invariant for 2-D knots and for cobordisms of braids analogous to Jones polynomial. As a matter fact, it turns out that a generalization of gauge field known as gerbe is needed and that in TGD framework classical color gauge fields defined the gauge potentials of this field. Also topological string theory in 4-D space-time could define this kind of invariants. Of course, it might well be that this kind of ideas have been already discussed in literature.

Category: Mathematical Physics

[59] viXra:1111.0086 [pdf] replaced on 2012-01-30 08:45:30

### Yangian Symmetry, Twistors, and TGD

Authors: Matti Pitkänen

There have been impressive steps in the understanding of N=4 maximally sypersymmetric YM theory possessing 4-D super-conformal symmetry. This theory is related by AdS/CFT duality to certain string theory in AdS5× S5 background. Second stringy representation was discovered by Witten and is based on 6-D Calabi-Yau manifold defined by twistors. The unifying proposal is that so called Yangian symmetry is behind the mathematical miracles involved.

In the following I will discuss briefly the notion of Yangian symmetry and suggest its generalization in TGD framework by replacing conformal algebra with appropriate super-conformal algebras. Also a possible realization of twistor approach and the construction of scattering amplitudes in terms of Yangian invariants defined by Grassmannian integrals is considered in TGD framework and based on the idea that in zero energy ontology one can represent massive states as bound states of massless particles. There is also a proposal for a physical interpretation of the Cartan algebra of Yangian algebra allowing to understand at the fundamental level how the mass spectrum of n-particle bound states could be understood in terms of the n-local charges of the Yangian algebra.

Twistors were originally introduced by Penrose to characterize the solutions of Maxwell's equations. Kähler action is Maxwell action for the induced Kähler form of CP2. The preferred extremals allow a very concrete interpretation in terms of modes of massless non-linear field. Both conformally compactified Minkowski space identifiable as so called causal diamond and CP2 allow a description in terms of twistors. These observations inspire the proposal that a generalization of Witten's twistor string theory relying on the identification of twistor string world sheets with certain holomorphic surfaces assigned with Feynman diagrams could allow a formulation of quantum TGD in terms of 3-dimensional holomorphic surfaces of CP3× CP3 mapped to 6-surfaces dual CP3× CP3, which are sphere bundles so that they are projected in a natural manner to 4-D space-time surfaces. Very general physical and mathematical arguments lead to a highly unique proposal for the holomorphic differential equations defining the complex 3-surfaces conjectured to correspond to the preferred extremals of Kähler action.

Category: Mathematical Physics

[58] viXra:1111.0085 [pdf] replaced on 2012-03-16 03:44:46

### A Possible Explanation for Shnoll Effect

Authors: Matti Pitkänen

Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.

These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.

The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II1 (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λi) for a positive integer valued variable n characterized by rational-valued parameters λi is obtained by replacing n and the integers characterizing λi with so called quantum integers depending on the quantum phase qm=exp(i2π/m). Quantum integer nq must be defined as the product of quantum counterparts pq of the primes p appearing in the prime decomposition of n. One has pq= sin(2π p/m)/sin(2π/m) for p≠ P and pq=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.

The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers Pn to P-n and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ Pn)=∑ I(Pn). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n+n-, n+q>0 with fixed n-q<0, are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct.

The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ kpΔ R/R and Δ m/m≈ kmΔ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.

Category: Mathematical Physics

[57] viXra:1111.0085 [pdf] replaced on 2012-01-30 08:52:00

### A Possible Explanation for Shnoll Effect

Authors: Matti Pitkänen

Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.

These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.

The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II1 (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λi) for a positive integer valued variable n characterized by rational-valued parameters λi is obtained by replacing n and the integers characterizing λi with so called quantum integers depending on the quantum phase qm=exp(i2π/m). Quantum integer nq must be defined as the product of quantum counterparts pq of the primes p appearing in the prime decomposition of n. One has pq= sin(2π p/m)/sin(2π/m) for p≠ P and pq=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.

The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers Pn to P-n and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ Pn)=∑ I(Pn). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n+n-, n+q>0 with fixed n-q<0, are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct.

The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ kpΔ R/R and Δ m/m≈ kmΔ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.

Category: Mathematical Physics

[56] viXra:1111.0026 [pdf] replaced on 2014-12-31 04:06:33

### Spherical Electron from 'quark' Magnetic Monopole Sigma = 2 Pi^2/3 Alpha^2 e C

Authors: Malcolm Macleod

In this essay I propose a geometrical formula for a dimensionless magnetic monopole sigma constructed from Planck time, elementary charge, -c and alpha, the fine structure constant. A formula for the electron may be constructed from these monopoles, this formula suggests that the charge distribution of the electron is perfectly symmetrical. As this monopole comprises a 1/3rd part of electron charge, it is analogous to the quark. If all charges therefore emanate from this monopole, even if charges have opposite polarity, their magnitudes must be equivalent, the differences between the proton and electron for example being geometrical rather than physical. Furthermore, these formulas suggest a Planck universe, wave-particle duality becoming a wave-state to Planck-state oscillation.
Category: Mathematical Physics

[55] viXra:1111.0026 [pdf] replaced on 2014-04-10 07:09:16

### Spherical Electron from 'quark' Magnetic Monopole

Authors: Malcolm Macleod

Proposed is a geometrical formula for a dimensionless magnetic monopole constructed from Planck time, elementary charge, -c and alpha, the fine structure constant. A formula for the electron may be constructed from these monopoles, this formula suggests that the charge distribution of the electron is perfectly symmetrical. As this monopole comprises a 1/3rd part of electron charge, it is analogous to the quark which in turn suggests that the basis for all charge is this monopole, consequently, although charges may have opposite polarity, their magnitudes must be equivalent, the differences between the proton and electron for example being geometrical rather than physical. A temperature particle labeled the 'kelvon' is proposed. Furthermore, these formulas suggest a Mathematical Universe constructed from Planck units, wave-particle duality becoming a wave-state to Planck point-state oscillation.
Category: Mathematical Physics

[54] viXra:1110.0030 [pdf] replaced on 2012-05-16 03:31:46

### A New Dark Energy Force Theoretically Calculates Faster-than-light-neutrinos.

Authors: Dan Visser

Version2 is written after my paper “Duonistic Neutrinos Violate Relativity”. A theoretical calculation with a new dark energy force formula discloses the correctness of the experimental faster-than-light-neutrinos in the CERN-San Grasso experiment. The formulation in this paper theoretically confirms that Einstein’s Relativity could be violated. This introduces the obligation to accept a new cosmological model, called the Double Torus hypothesis . The theoretical calculation in this paper is based on a new momentum of dark energy force. This paper theoretically calculates 62.8 nanosecond for the experimental detected early-arrival of muon-neutrinos related to how light-in-vacuum would have arrived. This is a marvelous close match compared to the ((60.7 ± 6.9 (stat.) ± 7.4 (sys.)) nanosecond found during the ‘neutrino-flight path’ from CERN to San Grasso in the OPERA-project. However, this version-2 paper also makes clear neutrinos can only go faster-than-light in neutrino-pairs: I call these pairs Duonistic Neutrinos! Just as in the paper “Duonistic Neutrinos Violate Relativity”. This paper presents the set of equations to prove that.
Category: Mathematical Physics

[53] viXra:1108.0005 [pdf] replaced on 2012-04-20 10:27:21

### Black Hole vs. Variable Rest Mass Neutron Star

Authors: DT Froedge
Comments: 13 Pages. Clarifying some points of previous version

In a previous paper we have discussed the conjecture of a variable particle rest mass as a function of gravitational potential [1]. This paper discuses the implications, in regard to a large neutron star, and contrast the difference between the predicted phenomena, and Black Hole theory as put fourth by standard GR. As most know, Einstein was not convinced of the existence of Black Holes, but modern solutions of the GR field equations appear to agree with the experimental evidence. There are some problems however, as are well known, the explanations for the diffuse, and the persistent source gamma ray emissions from the galactic center, do not have an adequate explanation, and the energy engines driving Quasars and AGNs are not sufficiently explained. This paper will explore the differences between VRM neutron stars, and Black Holes, for the purpose of identifying detectable, and measurable phenomena. The validity of this theory will be established on the finding of massive neutron stars or massive pulsars. >3 suns.
Category: Mathematical Physics

[52] viXra:1106.0018 [pdf] replaced on 2015-04-08 12:26:22

### Exact Solution of 2D Plane-Parallel Flow for Glacier Dynamics

Authors: Sergey V. Ershkov
Comments: 8 Pages. Keywords: Glacier dynamics, basal slip, glacial ice

A new exact solution of Glacier dynamics is presented here in terms of viscous-plastic theory of 2-dimensional movements within (x, y)-plane. Most of researchers used to investigate preferably 2D solution of Glacier dynamics in (x, z)-plane: -by using the continuity equation, they obtain (x, z)-profile of Glacier in dependence on initial conditions of ice flow. We proved that (x, y)-component of stress-tensor is a harmonic function, it let us execute the conditions of Liouville's theorem which allow to obtain the exact expression for the components of velocity of Glacier ice flux in (x, y)-directions.
Category: Mathematical Physics

[51] viXra:1106.0018 [pdf] replaced on 2015-03-11 14:27:43

### Exact Solution of 2D Plane-Parallel Flow for Glacier Dynamics

Authors: Sergey V. Ershkov
Comments: 7 Pages. Keywords: Glacier dynamics, basal slip, glacial ice

A new exact solution of Glacier dynamics is presented here in terms of viscous-plastic theory of 2-dimensional movements within (x, y)-plane. Most of researchers used to investigate preferably 2D solution of Glacier dynamics in (x, z)-plane: -by using the continuity equation, they obtain (x, z)-profile of Glacier in dependence on initial conditions of ice flow. We proved that (x, y)-component of stress-tensor is a harmonic function, it let us execute the conditions of Liouville's theorem which allow to obtain the exact expression for the components of velocity of Glacier ice flux in (x, y)-directions.
Category: Mathematical Physics

[50] viXra:1106.0018 [pdf] replaced on 2015-03-11 04:08:06

### Exact Solution of 2D Plane-Parallel Flow for Glacier Dynamics

Authors: Sergey V. Ershkov
Comments: 6 Pages. Keywords: Glacier dynamics, basal slip, glacial ice

A new exact solution of Glacier dynamics is presented here in terms of viscous-plastic theory of 2-dimensional movements within (x, y)-plane. Most of researchers used to investigate preferably 2D solution of Glacier dynamics in (x, z)-plane: -by using the continuity equation, they obtain (x, z)-profile of Glacier in dependence on initial conditions of ice flow. We proved that (x, y)-component of stress-tensor is a harmonic function, it let us execute the conditions of Liouville's theorem which allow to obtain the exact expression for the components of velocity of Glacier ice flux in (x, y)-directions.
Category: Mathematical Physics

[49] viXra:1106.0018 [pdf] replaced on 2015-01-09 09:46:50

### Exact Solution of Viscous-Plastic Flow Equations for Glacier Dynamics in 2-Dimensional Case

Authors: Sergey V. Ershkov
Comments: 7 Pages. Keywords: Glacier dynamics, basal slip, glacial ice, Riccati ODE

A new exact solution of Glacier dynamics is presented here in terms of viscous-plastic theory of movements for 2-dimensional profile (x, y), where x(t) = y(t). Such a 2-D solution of Glacier dynamics could be associated with Riccati’s type in general case. Due to a very special character of Riccati’s type ordinary differential equation, it’s general solution is proved to have a proper gap for the components of a solution. It means a possibility of sudden gradient catastrophe at definite meaning of time-parameter (for 2-D flat profile of Glacier, (x, y)-components of ice velocity moving). So, Glacier might be moving suddenly with acceleration periodically: (x, y)-components of ice velocity achieve hundred meters /per day from few meters (per day).
Category: Mathematical Physics

[48] viXra:1106.0018 [pdf] replaced on 23 Jun 2011

### Exact Solution of Viscous-Plastic Flow Equations for Glacier Dynamics in 2-Dimensional Case.

Authors: Sergey V. Ershkov

Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D solution of Ice dynamics could be classified as Riccati's type. Due to a very special character of Riccati's type equation, it's general solution is proved to have a proper gap of components of such a solution.
Category: Mathematical Physics

[47] viXra:1106.0018 [pdf] replaced on 20 Jun 2011

### Exact Solution of Viscous-Plastic Flow Equations for Glacier Dynamics in 2-Dimensional Case.

Authors: Sergey V. Ershkov

Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D solution of Ice dynamics could be classified as Riccati's type. Due to a very special character of Riccati's type equation, it's general solution is proved to have a proper gap of components of such a solution.
Category: Mathematical Physics

[46] viXra:1105.0022 [pdf] replaced on 2013-05-13 17:01:06

### Hard Theoretical Evidence for the Dark Energy Force Formula in a Double Torus Universe.

Authors: Dan Visser

This paper shows how my ‘dark energy force formula’ emerges five more space- and two more time-dimensions in nature. The ‘formula’ is earlier described in vixra-papers, announcing the universe is a Double Torus of dark energy and dark matter. The ‘formula’ represents a completely different force than the cosmological constant of Einstein, which is used to explain the accelerated expansion in Big Bang cosmology. With this in mind, two independent experimental investigations have given additional proof for my ‘dark energy force formula’, as follows: 1) The ratio of five extra space-dimensions and two extra time dimensions represent the up- and down electron-spin, behaving in a ‘chessboard-structure’ and associated with grapheme-experiments. 2) A computer-simulation shows a Double Torus, artificially emerging from two colliding black-holes. These results match with my hypothesis that the universe indeed is a Double Torus of dark energy and dark matter, because my (new) ’dark energy force formula‘ matches these two investigations. This (new) force could therefore have a link to topological insulators to guide light without scattering in quantum-computers.
Category: Mathematical Physics

[45] viXra:1104.0085 [pdf] replaced on 2014-01-07 10:17:53

### Dark Matter Formula For Fundamental Calculation Of Satellite Flybys In Hyperbolic Orbits.

Authors: Dan Visser
Comments: 7 Pages. Version-3 removed mistakes in interpretation.

In version-1 for the first time an announcement was made in this paper to have found fundamental evidence for the flyby-anomalies of six satellites earlier investigated by John Anderson and co-workers of the Jet Propulsion Laboratory (JPL) in Pasadena USA. The central part of this theoretical evidence exists of a ‘dark matter flow’ being the cause of a velocity-change for satellites during their ‘flyby’ along the earth. A formula is given to calculate the velocity-change caused by the dark matter flow. The origin of the evidence is related to a ‘dark energy force formula‘, which is a new force in a new proposed cosmological model describing dark energy and dark matter in a double torus geometry. Version-2 replaces version-1, because I read about new investigation of GPS satellites, which predict dark matter surrounding the earth-equator. In version-2 I cleared an expression without an effect on the original end-result of version-1 and I extended it with the calculation of the energy satellites are feeling from dark matter around the earth-equator. Version-3 makes much better clear that satellites can be used to calculate the dark energy density flow around the earth-equator from the perspective of a new cosmological model: The Double Torus Universe.
Category: Mathematical Physics

[44] viXra:1104.0085 [pdf] replaced on 2014-01-06 16:48:19

### Dark Matter Formula For Fundamental Calculation Of Satellite Flybys In Hyperbolic Orbits.

Authors: Dan Visser

In version-1 for the first time an announcement was made in this paper to have found fundamental evidence for the flyby-anomalies of six satellites earlier investigated by John Anderson and co-workers of the Jet Propulsion Laboratory (JPL) in Pasadena USA. The central part of this theoretical evidence exists of a ‘dark matter flow’ being the cause of a velocity-change for satellites during their ‘flyby’ along the earth. A formula is given to calculate the velocity-change caused by the dark matter flow. The origin of the evidence is related to a ‘dark energy force formula‘, which is a new force in a new proposed cosmological model describing dark energy and dark matter in a double torus geometry. Version-2 replaces version-1, because I read about new investigation of GPS satellites, which predict dark matter surrounding the earth-equator. In version-2 I cleared an expression without an effect on the original end-result of version-1 and I extended it with the calculation of the energy satellites are feeling from dark matter around the earth-equator.
Category: Mathematical Physics

[43] viXra:1103.0115 [pdf] replaced on 2012-04-11 06:16:58

### A Note on the Action at a Distance

Authors: José Francisco García Juliá

We consider that the action at a distance is carried out by virtual carriers of the force, which are created and annihilated in the vacuum by the field in a time less than that of the Heisenberg's uncertainty.
Category: Mathematical Physics

[42] viXra:1103.0115 [pdf] replaced on 2012-02-14 08:13:39

### A Note on the Action at a Distance

Authors: José Francisco García Juliá

We consider that the action at a distance is carried out by virtual carriers of the force, which are created and annihilated in the vacuum by the field in a time less than that of the Heisenberg's uncertainty.
Category: Mathematical Physics

[41] viXra:1103.0115 [pdf] replaced on 2012-01-26 10:29:23

### A Note on the Action at a Distance

Authors: José Francisco García Juliá

We consider that the action at a distance is carried out by virtual carriers of the force, which are created and annihilated in the vacuum by the field in a time less than that of the Heisenberg's uncertainty.
Category: Mathematical Physics

[40] viXra:1103.0012 [pdf] replaced on 2013-06-26 16:43:29

### Double Torus Cosmology Reveals Cosmic Microwave Background To Measure Dark Energy.

Authors: Dan Visser
Comments: 7 Pages. version 2 removes a ommission the notation of the formula, however renewed analysis implies no change in calculated results

This paper announces dark energy to be measured as a cosmic microwave background frame in the Double Torus hypothesis. This Double Torus (CMB)-frame is related to a specific quantum-state of dark energy and dark matter. In addition this paper also refers to a planned dark energy interferometer-project, which is expected to be operational in 2014. Both aspects can be combined in order to get a better expectation and interpretation of the detection of dark energy. This paper has motivated me to calculate a specific value for the Double Torus dark energy. The calculated value is about 4 x 10^-114 [X.s] in 6.4 x 10^-48 [m^2]. A new kind of spin-quantum-state [X.s] is introduced as a property of dark energy in the Double Torus. Probably this paper might be of interest to the dark energy interferometer-project. It surely is of importance for the discrepancy that exists in vacuum energy density.
Category: Mathematical Physics

[39] viXra:1102.0032 [pdf] replaced on 3 Oct 2011

### Quintessence-Momentum as Link Between Mass and Charge

Authors: Malcolm Macleod
Comments: 3 pages. v1 in Russian, v4 in English

The natural constants, G; h; e, μ0 and me are presented as geometrical shapes in terms of Planck momentum, α (Sommerfeld fine structure constant) and c. A square root solution of Planck momentum denoted Quintessence-momentum Q links the mass and charge constants. The electron formula describes a dimensionless magnetic monopole. The Rydberg constant R1, the most accurate of the natural constants, is used for crossreference, the solutions are consistent with CODATA 2010 precision.
Category: Mathematical Physics

[38] viXra:1102.0032 [pdf] replaced on 18 May 2011

### Quintessence-Momentum as Link Between Mass and Charge

Authors: Malcolm Macleod
Comments: 3 pages. v1 in Russian, v3 in English

A mathematical description of the natural constants, G, h, e, μ0 me R, is presented in terms of momentum Q, alpha (Sommerfeld fine structure constant) and c. This momentum is referred to as Quintessence-momentum and is the square root of Planck momentum. The formulas describe geometrical forms, the units are consistent with corresponding SI units and the numerical values, including the Rydberg constant and the vacuum permeability, are consistent with CODATA 2006.
Category: Mathematical Physics

[37] viXra:1102.0032 [pdf] replaced on 20 Feb 2011

### Quintessence-Momentum as Link Between Mass and Charge

Authors: Malcolm Macleod
Comments: 3 pages. v1 in Russian, v2 in English

This paper suggests a 'quantity of momentum', a square root of Planck momentum, here referred to as Quintessence-momentum, as a natural unit that is common to both mass and charge. In terms of this Quintessence momentum Q, alpha (Sommerfeld fine structure constant) and c; geometrical formulas for the natural physical constants and the electron mass are proposed. Results are consistent with CODATA 2006.
Category: Mathematical Physics

[36] viXra:1102.0027 [pdf] replaced on 2012-09-06 04:35:29

### Scale Dimension as the Fifth Dimension of Spacetime

Authors: Sergey G. Fedosin
Comments: 5 Pages. Turkish Journal of Physics, 2012, Vol. 36, No 3, P. 461 – 464.

The scale dimension discovered in the theory of infinite nesting of matter is studied from the perspective of physical implementation of well-studied four-and n-dimensional geometric objects. Adding the scale dimension to Minkowski four-dimensional space means the necessity to use the five-dimensional spacetime.
Category: Mathematical Physics

[35] viXra:1102.0027 [pdf] replaced on 18 Feb 2011

### Scale Dimension as the Fifth Dimension of Spacetime

Authors: Sergey G. Fedosin
Comments: 4 pages. v1 in Russian, v2 in English

The scale dimension which is discovered in the theory of infinite nesting of matter is studied from the perspective of the physical implementation of well-studied four-and n-dimensional geometric objects. Adding of the scale dimension to Minkowski space means the need to use the five-dimensional spacetime.
Category: Mathematical Physics

[34] viXra:1101.0037 [pdf] replaced on 12 Jan 2011

### Fine Structure Constant α ~ 1/137.036 and Blackbody Radiation Constant αR ~ 1/157.555

Authors: Ke Xiao

The fine structure constant α = e2/hc ~ 1/137.036 and the blackbody radiation constant αR = e2(aR/k4B)1/3 ~ 1/157.555 are linked by prime numbers. The blackbody radiation constant is a new method to measure the fine structure constant. It also links the fine structure constant to the Boltzmann constant.
Category: Mathematical Physics

[33] viXra:1012.0052 [pdf] replaced on 17 Jan 2011

### 32 Point Groups of Three Dimensional Crystal Cells Described by 5 Bits

Authors: Giuliano Bettini
Comments: 9 pages, v3 in Italian, v2 in English, corrections to the tables, and a new table added.

There are 32 possible combinations of symmetry operations that define the external symmetry of crystals. These 32 possible combinations result in the 32 crystal classes. But for a radar engineer it is inevitable to associate "32" to "5 bits". I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with a (tentative) physical meaning of each bit. Each bit means a physical property.
Category: Mathematical Physics

[32] viXra:1012.0052 [pdf] replaced on 1 Jan 2011

### 32 Point Groups of Three Dimensional Crystal Cells Described by 5 Bits

Authors: Giuliano Bettini
Comments: 9 pages, v1 in Italian, v2 in English, corrections to the tables, and a new table added.

There are 32 possible combinations of symmetry operations that define the external symmetry of crystals. These 32 possible combinations result in the 32 crystal classes. But for a radar engineer it is inevitable to associate "32" to "5 bits". I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with a (tentative) physical meaning of each bit. Each bit means a physical property.
Category: Mathematical Physics

[31] viXra:1012.0031 [pdf] replaced on 16 Dec 2010

### Further on Non-Cartesian Systems

Authors: Elemér E Rosinger

A class of non-Cartesian physical systems, [7], are those whose composite state spaces are given by significantly extended tensor products. A more detailed presentation of the way such extended tensor products are constructed is offered, based on a step by step comparison with the construction of usual tensor products. This presentation clarifies the extent to which the extended tensor products are indeed more general than the usual ones.
Category: Mathematical Physics

[30] viXra:1010.0014 [pdf] replaced on 1 Jun 2011

### Deeper Properties Through Dark and Visible-Matter in a New Cosmological Twin-Tori Model (TTM).

Authors: Dan Visser

A new cosmological model, named the Twin-Tori Model (TTM)[1], postulates a dark energy force Fde , which empowers the dynamic of a lower order universe, well known as the big bang. In this paper I introduce the 1st derivative F'de of this dark energy force to reveal deeper properties of the TTM, such as: why quantummechanics exists in the big bang, why dark matter and visible matter are equally responsible for gravity in galaxies for 1/4 of the density of dark matter at a specific length, why the big bang universe is recalculated by subquantumlevel-information below the Plancklength, and why the impression of space-expansion is due to the higher order cosmological model TTM.
Category: Mathematical Physics

[29] viXra:1010.0013 [pdf] replaced on 2013-11-25 09:05:44

### Thought-Experiment Provides a Formula for (New) Dark Energy Force (Version-3).

Authors: Dan Visser
Comments: 11 Pages. Version-3 is only textual modified and not mathematically altered. It services a better understanding of the beginning of the Double Torus framework.

A (new) ‘dark energy force-formula’ was introduced on April 10 2004 by Dan Visser, Almere, the Netherlands on his website (reference 1a). The (new) formula was picked up by a PhD-mathematician and -Physics, Christopher Forbes (UK), in the summer of 2009, leading to email-contact among them, and resulting in a publication of a general mathematical expression, whereof Dan’s (new) ‘dark energy force-formula’ indeed resulted from the general expressing (reference 2). Additional an amount of (new) dark energy resulted too. Afterwards Dan published his derivation of the (new) force in the Vixra-archive on October 7 2010 (in retrospective). He called his mathematical exercises a ‘thought-experiment’. That had as result the (new) ‘dark energy force-formula’. In the versions following (version-2 and -3) only textual changes were made for servicing a better understanding of the thought-experiment, of course without altering the original mathematical content. Further development was focussed on working–out the (new) dynamics in the Double Torus hypothesis. This is a hypothesis that claims the Big Bang cosmology can no longer be maintained as the model for the universe. The main issue in ‘Dan’s-thought-experiment’ is a scaling-away-principle’,which is characterized by ‘scaling-away’ two black holes from each other (small and large), as well as ‘melting them together’ and making them ‘temperature connected’. Then an observer would receive the same evaporation-radiation from both black holes at the same time. These three exercises (scaling-away, melting-together and temperature-connection) had the aim to keep entropy conserved in the universe. However, ‘scaling-away’ causes a ‘change of dark information’ at the surface of one or the other black hole. Such a change had to correspond to a ‘new force’. That was further exercised, analyzed, synthesized, combined and translated as a mathematical thought-experiment. The result: Dan’s (new) ‘dark energy force-formula’.
Category: Mathematical Physics

[28] viXra:1010.0013 [pdf] replaced on 2013-01-02 15:57:11

### Thought-Experiment Provides a Formula for (New) Dark Energy Force.

Authors: Dan Visser

A (new) ‘dark energy force-formula’ was introduced on April 10 2004 on Dan Visser’s website. His (new) formula was picked up by a PhD-mathematician and - Physics, Christopher Forbes (UK) in the summer of 2009, leading to email-contact among them, and resulting in a publication of a general mathematical expression, whereof Dan Visser’s (new) ‘dark energy force-formula’ came out as a solution. The derivation of this (new) force was then published in the Vixra-archive on October 7 2010 (in retrospective). The ‘thought-experiment’ is described as a mathematical exercise, which in the end is expressed as Dan Visser's (new) ‘dark energy force-formula’. Since then only textual changes were made for the benefit of a better explanation of the hypothesis, without altering the original mathematical content. The main issue in the ‘thought-experiment’ is a ‘non-relativistic scaling principle’, characterized as ‘scaling-away’ two black holes from each other (small and large), as well as ‘melting them together’. Both ‘movements’ presents a ‘change of dark information’. This was further analyzed, synthesized, combined and translated mathematically by Dan Visser, into a force of ‘extra time’ hitting an observer’s eye. The result is the (new) ‘dark energy force’, a ‘non-relativistic force’.
Category: Mathematical Physics

[27] viXra:1009.0047 [pdf] replaced on 2013-05-03 15:35:33

### Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series and Divergent Integrals

Authors: Jose Javier Garcia Moreta

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization •Keywords: = Riemann Zeta function, Functional determinant, Zeta regularization, divergent series .
Category: Mathematical Physics

[26] viXra:1009.0007 [pdf] replaced on 2012-03-21 15:41:57

### A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations

Authors: DT Froedge

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are, and single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by then by defining an action field based on the endpoint action of the particles in the system, develop a solution which properly illustrates internal dynamics as well as particle interactions. The complete function has both real, and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle masses are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent parts of the Systemfunction. A clear relation between the classical and quantum properties of particles is made, increasing the scope of QM.
Category: Mathematical Physics

[25] viXra:1009.0007 [pdf] replaced on 2012-03-11 13:10:52

### A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations

Authors: DT Froedge
Comments: 39 Pages. For presentation April 12 APS Atlanta Verson V012612 (ongoing)

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are approximations, and single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by then by defining an action field based on the endpoint action of the particles in the system, develop a solution which properly illustrates internal dynamics as well as particle interactions. The complete function has both real, and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle masses are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent parts of the Systemfunction. A clear relation between the classical and quantum properties of particles is made, increasing the scope of QM.
Category: Mathematical Physics

[24] viXra:1009.0007 [pdf] replaced on 2011-12-21 11:44:45

### A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations

Authors: DT Froedge

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by modifying the methods of Path Integrals, develop a solution which describes the internal dynamics as well as particle interactions of quantum particles. The complete function has both real and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent components. A clear distinction between the classical and quantum properties of particles is made, increasing the scope of QM.
Category: Mathematical Physics

[23] viXra:1009.0007 [pdf] replaced on 2 Jul 2011

### A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations

Authors: D.T. Froedge

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an interacting atomic system, eigenvalues represent particle energies in an interacting system of particles. An equation and a solution is proposed that treats all of the particles in the universe as a single system. The proposed solution is a descriptor of a symmetric, light speed expanding group of interacting particles having familiar constituents.
Category: Mathematical Physics

[22] viXra:1009.0007 [pdf] replaced on 5 Mar 2011

### A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations

Authors: D.T. Froedge
Comments: 17 pages 38 equations 98kb

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an interacting atomic system, eigenvalues represent particle energies in an interacting system of particles. An equation is proposed that has vector solutions defined in Dirac, or Clifford algebra, that treats all of the particles in the universe as a single system. The proposed solution is a descriptor of a symmetric, light speed expanding group of interacting particles having real, as well as the familiar QM constituents.
Category: Mathematical Physics

[21] viXra:1007.0005 [pdf] replaced on 2012-11-22 05:57:29

### A Hamiltonian Whose Energies Are the Zeros of the Riemann XI Function

Authors: Jose Javier Garcia Moreta

· ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in one dimension 2 2 d V (x) dx - + for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros 2 n n E =g Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to simplify notation. · Keywords: = Riemann Hypothesis, Functional determinant,
Category: Mathematical Physics

[20] viXra:1007.0005 [pdf] replaced on 2012-03-26 15:13:42

### A Hamiltonian Operator Whose Energies Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garicia Moreta

· ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in one dimension 2 2 d V (x) dx - + for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros 2 n n E =g Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to simplify notation. · Keywords: = Riemann Hypothesis, Functional determinant,
Category: Mathematical Physics

[19] viXra:1007.0005 [pdf] replaced on 2012-10-06 04:12:18

### A Hamiltonian Whose Energies Are the Zeros of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta

• ABSTRACT: We give an spectral interpretation of the non-trivial zeros of the Riemann Xi-function. The main idea of the paper is to find a Hamiltonian (Hermitian) operator in the form with an even potential whose energies are precisely , the zeros of the Riemann Xi-function . In order to obtain this Hamiltonian we use the WKB method and the Bohr-sommerfeld quantization condition for the energies. We also prove the fact that the Riemann Xi-function is proportional to the Functional determinant in the sense of a zeta-regularized determinant In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law.
Category: Mathematical Physics

[18] viXra:1007.0005 [pdf] replaced on 2012-03-26 15:02:21

### A Hamiltonian Operator Whose Energies Are the Roots of the Riemann XI-Function 1 2

Authors: Jose Javier Garcia Moreta

ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in one dimension 2 2 d V (x) dx - + for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros 2 n n E =g Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to simplify notation. · Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula , Quantum chaos.
Category: Mathematical Physics

[17] viXra:1007.0005 [pdf] replaced on 2012-01-25 05:58:47

### A Hamiltonian Operator Whose Energies Are the Roots of the Riemann XI-Function

Authors: Jose Javier garcia

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is .In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as or (square) in the same case we will refer to the potential inside this Hamiltonian either as or to simplify notation. Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula , Quantum chaos.
Category: Mathematical Physics

[16] viXra:1007.0005 [pdf] replaced on 2011-12-14 13:56:54

### A Hamiltonian Operator Whose Roots Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta
Comments: 23 Pages. there is an ERROR, whenever it says 'Whose zeros' should we put 'Whose Energies' (A Hamiltonian has no zeros)H

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is .In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as or (square) in the same case we will refer to the potential inside this Hamiltonian either as or to simplify notation.
Category: Mathematical Physics

[15] viXra:1007.0005 [pdf] replaced on 2011-12-04 07:54:17

### A Hamiltonian Operator Whose Zeros Are the Roots of the Riemann XI-Function

Authors: Jose Javier Garcia Moreta

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is
Category: Mathematical Physics

[14] viXra:1006.0042 [pdf] replaced on 2012-01-30 21:36:44

### The Geometry of CP2 and its Relationship to Standard Model

Authors: Matti Pitkänen

This appendix contains basic facts about CP2 as a symmetric space and Kähler manifold. The coding of the standard model symmetries to the geometry of CP2, the physical interpretation of the induced spinor connection in terms of electro-weak gauge potentials, and basic facts about induced gauge fields are discussed
Category: Mathematical Physics

[13] viXra:1006.0041 [pdf] replaced on 2012-01-30 21:40:48

### Could the Dynamics of Kähler Action Predict the Hierarchy of Planck Constants?

Authors: Matti Pitkänen

The original justification for the hierarchy of Planck constants came from the indications that Planck constant could have large values in both astrophysical systems involving dark matter and also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also factor spaces of CD and CP2 emerged from consistency conditions. It however seems that TGD actually predicts this hierarchy of covering spaces. The extreme non-linearity of the field equations defined by Kähler action means that the correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates is 1-to-many. This leads naturally to the introduction of the covering space of CD x CP2, where CD denotes causal diamond defined as intersection of future and past directed light-cones.
Category: Mathematical Physics

[12] viXra:1006.0040 [pdf] replaced on 2012-01-30 21:49:56

### Weak Form of Electric-Magnetic Duality and Its Implications

Authors: Matti Pitkänen

The notion of electric magnetic duality emerged already two decades ago in the attempts to formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable step of progress took place in the understanding of this notion. This concept leads to the identification of the physical particles as string like objects defined by magnetic charged wormhole throats connected by magnetic ux tubes. The second end of the string contains particle having electroweak isospin neutralizing that of elementary fermion and the size scale of the string is electro-weak scale would be in question. Hence the screening of electro-weak force takes place via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic duality leads also to a detailed understanding of how TGD reduces to almost topological quantum field theory. A surprising outcome is the necessity to replace CP2 Kähler form in Kähler action with its sum with S2 Kähler form.
Category: Mathematical Physics

[11] viXra:1006.0039 [pdf] replaced on 2012-01-30 21:53:06

### How to Define Generalized Feynman Diagrams?

Authors: Matti Pitkänen

Generalized Feynman diagrams have become the central notion of quantum TGD and one might even say that space-time surfaces can be identified as generalized Feynman diagrams. The challenge is to assign a precise mathematical content for this notion, show their mathematical existence, and develop a machinery for calculating them. Zero energy ontology has led to a dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially from the basic identifications as does also unitarity and non-trivial coupling constant evolution. There are however several formidable looking challenges left.

1. One should perform the functional integral over WCW degrees of freedom for fixed values of on mass shell momenta appearing in the internal lines. After this one must perform integral or summation over loop momenta.
2. One must define the functional integral also in the p-adic context. p-Adic Fourier analysis relying on algebraic continuation raises hopes in this respect. p-Adicity suggests strongly that the loop momenta are discretized and ZEO predicts this kind of discretization naturally.
In this article a proposal giving excellent hopes for achieving these challenges is discussed.
Category: Mathematical Physics

[10] viXra:1006.0038 [pdf] replaced on 2012-01-30 21:55:27

### Physics as Generalized Number Theory: Infinite Primes

Authors: Matti Pitkänen

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.

1. The fusion of real physic and various p-adic physics to a single coherent whole by generalizing the number concept by fusing real numbers and various p-adic number fields along common rationals. Extensions of p-adic number fields can be introduced by gluing them along common algebraic numbers to reals. Algebraic continuation of the physics from rationals and their their extensions to various number fields (generalization of completion process for rationals) is the key idea, and the challenge is to understand whether how one could achieve this dream. A profound implication is that purely local p-adic physics would code for the p-adic fractality of long length length scale real physics and vice versa, and one could understand the origins of p-adic length scale hypothesis.
2. Second part of the vision involves hyper counterparts of the classical number fields defined as subspaces of their complexifications with Minkowskian signature of metric. Allowed space-time surfaces would correspond to what might be called hyper-quaternionic sub-manifolds of a hyper-octonionic space and mappable to M4× CP2 in natural manner. One could assign to each point of space-time surface a hyper-quaternionic 4-plane which is the plane defined by the modified gamma matrices but not tangent plane in general. Hence the basic variational principle of TGD would have deep number theoretic content.
3. The third part of the vision involves infinite primes identifiable in terms of an infinite hierarchy of second quantized arithmetic quantum fields theories on one hand, and as having representations as space-time surfaces analogous to zero loci of polynomials on the other hand. Single space-time point would have an infinitely complex structure since real unity can be represented as a ratio of infinite numbers in infinitely many manners each having its own number theoretic anatomy. Single space-time point would be in principle able to represent in its structure the quantum state of the entire universe. This number theoretic variant of Brahman=Atman identity would make Universe an algebraic hologram.

Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes.

Besides this holy trinity I will discuss loosely related topics. Included are possible applications of category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.

Category: Mathematical Physics

[9] viXra:1006.0038 [pdf] replaced on 3 Nov 2010

### Physics as Generalized Number Theory: Infinite Primes

Authors: Matti Pitkänen

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.

1. The fusion of real physic and various p-adic physics to a single coherent whole by generalizing the number concept by fusing real numbers and various p-adic number fields along common rationals. Extensions of p-adic number fields can be introduced by gluing them along common algebraic numbers to reals. Algebraic continuation of the physics from rationals and their their extensions to various number fields (generalization of completion process for rationals) is the key idea, and the challenge is to understand whether how one could achieve this dream. A profound implication is that purely local p-adic physics would code for the p-adic fractality of long length length scale real physics and vice versa, and one could understand the origins of p-adic length scale hypothesis.
2. Second part of the vision involves hyper counterparts of the classical number fields defined as subspaces of their complexifications with Minkowskian signature of metric. Allowed space-time surfaces would correspond to what might be called hyper-quaternionic sub-manifolds of a hyper-octonionic space and mappable to M4× CP2 in natural manner. One could assign to each point of space-time surface a hyper-quaternionic 4-plane which is the plane defined by the modified gamma matrices but not tangent plane in general. Hence the basic variational principle of TGD would have deep number theoretic content.
3. The third part of the vision involves infinite primes identifiable in terms of an infinite hierarchy of second quantized arithmetic quantum fields theories on one hand, and as having representations as space-time surfaces analogous to zero loci of polynomials on the other hand. Single space-time point would have an infinitely complex structure since real unity can be represented as a ratio of infinite numbers in infinitely many manners each having its own number theoretic anatomy. Single space-time point would be in principle able to represent in its structure the quantum state of the entire universe. This number theoretic variant of Brahman=Atman identity would make Universe an algebraic hologram.

Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes.

Besides this holy trinity I will discuss loosely related topics. Included are possible applications of category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.

Category: Mathematical Physics

[8] viXra:1006.0037 [pdf] replaced on 2012-01-30 21:56:36

### Physics as Generalized Number Theory: Classical Number Fields

Authors: Matti Pitkänen

Physics as a generalized number theory program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields discussed in this article, and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article the connection between standard model symmetries and classical number fields is discussed. The basis vision is that the geometry of the infinite-dimensional WCW ("world of classical worlds") is unique from its mere existence. This leads to its identification as union of symmetric spaces whose Kähler geometries are fixed by generalized conformal symmetries. This fixes space-time dimension and the decomposition M4 x S and the idea is that the symmetries of the Kähler manifold S make it somehow unique. The motivating observations are that the dimensions of classical number fields are the dimensions of partonic 2-surfaces, space-time surfaces, and imbedding space and M8 can be identified as hyper-octonions- a sub-space of complexified octonions obtained by adding a commuting imaginary unit. This stimulates some questions. Could one understand S = CP2 number theoretically in the sense that M8 and H = M4 x CP2 be in some deep sense equivalent ("number theoretical compactification" or M8 - H duality)? Could associativity define the fundamental dynamical principle so that space-time surfaces could be regarded as associative or co-associative (defined properly) sub-manifolds of M8 or equivalently of H. One can indeed define the associativite (co-associative) 4-surfaces using octonionic representation of gamma matrices of 8-D spaces as surfaces for which the modified gamma matrices span an associate (co-associative) sub-space at each point of space-time surface. Also M8 - H duality holds true if one assumes that this associative sub-space at each point contains preferred plane of M8 identifiable as a preferred commutative or co-commutative plane (this condition generalizes to an integral distribution of commutative planes in M8). These planes are parametrized by CP2 and this leads to M8 - H duality. WCW itself can be identified as the space of 4-D local sub-algebras of the local Clifford algebra of M8 or H which are associative or co-associative. An open conjecture is that this characterization of the space-time surfaces is equivalent with the preferred extremal property of Kähler action with preferred extremal identified as a critical extremal allowing infinite-dimensional algebra of vanishing second variations.
Category: Mathematical Physics

[7] viXra:1006.0036 [pdf] replaced on 2012-01-30 21:58:07

### Physics as Generalized Number Theory: P-Adic Physics and Number Theoretic Universality

Authors: Matti Pitkänen

Category: Mathematical Physics

[6] viXra:1006.0035 [pdf] replaced on 2012-01-30 22:01:55

### Construction of Configuration Space Spinor Structure

Authors: Matti Pitkänen

There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first approach relies on a direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach discussed in this article relies on the construction of spinor structure based on the hypothesis that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for the second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of spinor structure. This implies a geometrization of fermionic statistics. The basic philosophy is that at fundamental level the construction of WCW geometry reduces to the second quantization of the induced spinor fields using Dirac action. This assumption is parallel with the bosonic emergence stating that all gauge bosons are pairs of fermion and antifermion at opposite throats of wormhole contact. Vacuum function is identified as Dirac determinant and the conjecture is that it reduces to the exponent of Kähler function. In order to achieve internal consistency induced gamma matrices appearing in Dirac operator must be replaced by the modified gamma matrices defined uniquely by Kähler action and one must also assume that extremals of Kähler action are in question so that the classical space-time dynamics reduces to a consistency condition. This implies also super-symmetries and the fermionic oscillator algebra at partonic 2-surfaces has intepretation as N = 1 generalization of space-time supersymmetry algebra different however from standard SUSY algebra in that Majorana spinors are not needed. This algebra serves as a building brick of various super-conformal algebras involved. The requirement that there exist deformations giving rise to conserved Noether charges requires that the preferred extremals are critical in the sense that the second variation of the Kähler action vanishes for these deformations. Thus Bohr orbit property could correspond to criticality or at least involve it. Quantum classical correspondence demands that quantum numbers are coded to the properties of the preferred extremals given by the Dirac determinant and this requires a linear coupling to the conserved quantum charges in Cartan algebra. Effective 2-dimensionality allows a measurement interaction term only in 3-D Chern-Simons Dirac action assignable to the wormhole throats and the ends of the space-time surfaces at the boundaries of CD. This allows also to have physical propagators reducing to Dirac propagator not possible without the measurement interaction term. An essential point is that the measurement interaction corresponds formally to a gauge transformation for the induced Kähler gauge potential. If one accepts the weak form of electric-magnetic duality Kähler function reduces to a generalized Chern-Simons term and the effect of measurement interaction term to Kähler function reduces effectively to the same gauge transformation. The basic vision is that WCW gamma matrices are expressible as super-symplectic charges at the boundaries of CD. The basic building brick of WCW is the product of infinite-D symmetric spaces assignable to the ends of the propagator line of the generalized Feynman diagram. WCW Kähler metric has in this case "kinetic" parts associated with the ends and "interaction" part between the ends. General expressions for the super-counterparts of WCW ux Hamiltoniansand for the matrix elements of WCW metric in terms of their anticommutators are proposed on basis of this picture.
Category: Mathematical Physics

[5] viXra:1006.0034 [pdf] replaced on 2012-01-30 22:03:21

### Construction of Configuration Space Geometry from Symmetry Principles

Authors: Matti Pitkänen

There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first one relies on a direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach relies on the construction of spinor structure assuming that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for the second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of spinor structure. In this article the construction of Kähler form and metric based on symmetries is discussed. The basic vision is that WCW can be regarded as the space of generalized Feynman diagrams with lines thickned to light-like 3-surfaces and vertices identified as partonic 2-surfaces. In zero energy ontology the strong form of General Coordinate Invariance (GCI) implies effective 2-dimensionality and the basic objects are pairs partonic 2-surfaces X2 at opposite light-like boundaries of causal diamonds (CDs). The hypothesis is that WCW can be regarded as a union of infinite-dimensional symmetric spaces G/H labeled by zero modes having an interpretation as classical, non-quantum uctuating variables. A crucial role is played by the metric 2-dimensionality of the light-cone boundary δM+4 + and of light-like 3-surfaces implying a generalization of conformal invariance. The group G acting as isometries of WCW is tentatively identified as the symplectic group of δM+4 x CP2 localized with respect to X2. H is identified as Kac-Moody type group associated with isometries of H = M+4 x CP2 acting on light-like 3-surfaces and thus on X2. An explicit construction for the Hamiltonians of WCW isometry algebra as so called ux Hamiltonians is proposed and also the elements of Kähler form can be constructed in terms of these. Explicit expressions for WCW ux Hamiltonians as functionals of complex coordinates of the Cartesisian product of the infinite-dimensional symmetric spaces having as points the partonic 2-surfaces defining the ends of the the light 3-surface (line of generalized Feynman diagram) are proposed.
Category: Mathematical Physics

[4] viXra:1006.0033 [pdf] replaced on 2012-01-30 22:05:03

### Identification of the Configuration Space Kähler Function

Authors: Matti Pitkänen

There are two basic approaches to quantum TGD. The first approach, which is discussed in this article, is a generalization of Einstein's geometrization program of physics to an infinitedimensional context. Second approach is based on the identification of physics as a generalized number theory. The first approach relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of classical worlds" (WCW) identified as the space of 3-surfaces in in certain 8-dimensional space. There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first approach relies on direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach relies on the construction of spinor structure based on the hypothesis that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of WCW spinor structure. In this article the proposal for Kähler function based on the requirement of 4-dimensional General Coordinate Invariance implying that its definition must assign to a given 3-surface a unique space-time surface. Quantum classical correspondence requires that this surface is a preferred extremal of some some general coordinate invariant action, and so called Kähler action is a unique candidate in this respect. The preferred extremal has intepretation as an analog of Bohr orbit so that classical physics becomes and exact part of WCW geometry and therefore also quantum physics. The basic challenge is the explicit identification of WCW Kähler function K. Two assumptions lead to the identification of K as a sum of Chern-Simons type terms associated with the ends of causal diamond and with the light-like wormhole throats at which the signature of the induced metric changes. The first assumption is the weak form of electric magnetic duality. Second assumption is that the Kähler current for preferred extremals satisfies the condition jK ^ djK = 0 implying that the ow parameter of the ow lines of jK defines a global space-time coordinate. This would mean that the vision about reduction to almost topological QFT would be realized. Second challenge is the understanding of the space-time correlates of quantum criticality. Electric-magnetic duality helps considerably here. The realization that the hierarchy of Planck constant realized in terms of coverings of the imbedding space follows from basic quantum TGD leads to a further understanding. The extreme non-linearity of canonical momentum densities as functions of time derivatives of the imbedding space coordinates implies that the correspondence between these two variables is not 1-1 so that it is natural to introduce coverings of CD x CP2. This leads also to a precise geometric characterization of the criticality of the preferred extremals.
Category: Mathematical Physics

[3] viXra:1006.0032 [pdf] replaced on 2012-01-30 22:06:21

### Physics as Infinite-dimensional Geometry and Generalized Number Theory: Basic Visions

Authors: Matti Pitkänen

There are two basic approaches to the construction of quantum TGD. The first approach relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of classical worlds" identified as the space of 3-surfaces in in certain 8-dimensional space. Essentially a generalization of the Einstein's geometrization of physics program is in question. The second vision is the identification of physics as a generalized number theory. This program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields (in particular, identifying associativity condition as the basic dynamical principle), and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article brief summaries of physics as infinite-dimensional geometry and generalized number theory are given to be followed by more detailed articles.
Category: Mathematical Physics

[2] viXra:1001.0042 [pdf] replaced on 2012-03-11 09:16:42

### Zeta Regularization Applied to the Problem of Riemann Hypothesis and the Calculation of Divergent Integrals

Authors: Jose Javier Garcia Moreta