Mathematical Physics

1602 Submissions

[8] viXra:1602.0254 [pdf] submitted on 2016-02-20 10:55:25

Note on a Possible Solution of Navier-Stokes Equations

Authors: Abdelmajid Ben Hadj Salem
Comments: 16 Pages. In French.

The papier presents an essay of the resolution of Navier-Stokes equations under the hypothesis (A) of the open problem cited by Clay Institute (C.L. Fefferman, 2006).
Category: Mathematical Physics

[7] viXra:1602.0167 [pdf] replaced on 2016-05-28 11:19:59

The Lorentz Force Law And Kaluza Theories

Authors: Robert Watson
Comments: 39 Pages. Some important corrections made in v2 using dimensional analysis

Kaluza's 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is inspiration for many modern attempts to develop new physical theories. The original theory has problems which may well be overcome, and thus Kaluza theory should be looked at again: it is a natural, if not necessary, geometric unification of gravity and electromagnetism. Here a general demonstration that the Lorentz force law can be derived from a range of Kaluza theories is presented. This is investigated via non-Maxwellian kinetic definitions of charge that are divergence-free and relate Maxwellian charge to 5D components of momentum. The possible role of torsion is considered as an extension. It is shown, however, that symmetric torsion components are likely not admissible in any prospective theory. As a result Kaluza's original theory is rehabilitated and a call for deeper analysis made.
Category: Mathematical Physics

[6] viXra:1602.0122 [pdf] replaced on 2016-07-19 15:17:16

A Short Note on Time Inversion Symmetry And Reversibility

Authors: Hans Detlef Hüttenbach
Comments: 4 Pages.

A simple mathematical proof reveals that time-inversion symmetry and reversibility are different concepts, which also resolves the Loschmidt paradox.
Category: Mathematical Physics

[5] viXra:1602.0114 [pdf] replaced on 2016-10-04 04:52:04

Double Conformal Space-Time Algebra

Authors: Robert B. Easter
Comments: 184 Pages.

This paper introduces the G(4,8) Double Conformal Space-Time Algebra (DCSTA). G(4,8) DCSTA is a straightforward extension of the G(2,8) Double Conformal Space Algebra (DCSA), which is a different form of the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA). G(4,8) DCSTA extends G(2,8) DCSA with spacetime boost operations and differential operators for differentiation with respect to the pseudospatial time w=ct direction and time t. The spacetime boost operation can implement anisotropic dilation (directed non-uniform scaling) of quadric surface entities. DCSTA is a high-dimensional 12D embedding of the G(1,3) Space-Time Algebra (STA) and is a doubling of the G(2,4) Conformal Space-Time Algebra (CSTA). The 2-vector quadric surface entities of the DCSA subalgebra appear in DCSTA as quadric surfaces at zero velocity that can be boosted into moving surfaces with constant velocities that display the length contraction effect of special relativity. DCSTA inherits doubled forms of all CSTA entities and versors. The doubled CSTA entities (standard DCSTA entities) include points, hypercones, hyperplanes, hyperpseudospheres, and other entities formed as their intersections, such as planes, lines, spatial spheres and circles, and spacetime hyperboloids (pseudospheres) and hyperbolas (pseudocircles). The doubled CSTA versors (DCSTA versors) include rotor, hyperbolic rotor (boost), translator, dilator, and their compositions such as the translated-rotor, translated-boost, and translated-dilator. The DCSTA versors provide a complete set of spacetime transformation operators on all DCSTA entities. DCSTA inherits the DCSA 2-vector spatial entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) and gains Darboux pseudocyclides formed in spacetime with the pseudospatial time dimension. All DCSTA entities can be reflected in, and intersected with, the standard DCSTA entities. To demonstrate G(4,8) DCSTA as concrete mathematics with possible applications, this paper includes sample code and example calculations using the symbolic computer algebra system SymPy.
Category: Mathematical Physics

[4] viXra:1602.0095 [pdf] submitted on 2016-02-08 12:08:17

Hypotetical Quantum of Temperature

Authors: Branko Zivlak
Comments: 4 Pages. 12 formulas

After examining the relationships in the universe, is determined a hypothetical quantum temperature and then obtained temperature of cosmic microwave background radiation (CMB). It is rejected an explanation of that temperature as a result of the relic radiation from the Big Bang.
Category: Mathematical Physics

[3] viXra:1602.0049 [pdf] submitted on 2016-02-04 10:02:29

Mathematics in Physics

Authors: Jean Claude Dutailly
Comments: 380 Pages. New on QM, RG, gravitation

This book proposes a review and, on some important points, a new interpretation of the main concepts of Theoretical Physics. Rather than offering an interpretation based on exotic physical assumptions (additional dimension, new particle, cosmological phenomenon,…) or a brand new abstract mathematical formalism, it proceeds to a systematic review of the main concepts of Physics, as Physicists have always understood them : space, time, material body, force fields, momentum, energy… and propose the right mathematical tools to deal with them, chosen among well known mathematical theories. After a short introduction about the place of Mathematics in Physics, a new interpretation of the main axioms of Quantum Mechanics is proposed. It is proven that these axioms come actually from the way mathematical models are expressed, and this leads to theorems which validate most of the usual computations and provide safe and clear conditions for their use, as it is shown in the rest of the book. Relativity is introduced through the construct of the Geometry of General Relativity, based on 5 propositions and the use of tetrads and fiber bundles, which provide tools to deal with practical problems, such as deformable solids. A review of the concept of momenta leads to the introduction of spinors in the framework of Clifford algebras. It gives a clear understanding of spin and antiparticles. The force fields are introduced through connections, in the, now well known, framework of gauge theories, which is here extended to the gravitational field. It shows that this field has actually a rotational and a transversal component, which are masked under the usual treatment by the metric and the Levy-Civita connection. A thorough attention is given to the topic of the propagation of fields with interesting results, notably to explore gravitation. The general theory of lagrangians in the application of the Principle of Least Action is reviewed, and two general models, incorporating all particles and fields are explored, and used for the introduction of the concepts of currents and energy-momentum tensor. Precise guidelines are given to find operational solutions of the equations of the gravitational field in the most general case. The last chapter shows that bosons can be understood as discontinuities in the fields. In this 4th version of this book, changes have been made : - in Relativist Geometry : the ideas are the same, but the chapter has been rewritten, notably to introduce the causal structure and explain the link with the practical measures of time and space; - in Spinors : the relation with momenta has been introduced explicitly - in Force fields : the section dedicated to the propagation of fields is new, and is an important addition. - in Continuous Models : the section about currents and energy-momentum tensor are new. - in Discontinuous Processes : the section about bosons has been rewritten and the model improved.
Category: Mathematical Physics

[2] viXra:1602.0048 [pdf] submitted on 2016-02-04 10:11:31

Physical Law from Experimental Data

Authors: Domenico Oricchio
Comments: 11 Pages.

I open a dusty old drawer, and I found this article, rejected by every journal, with a complete, total loss of time; a thing that I'll never make; and I change only the bibliography, that is to initially conceived . The old idea sounds interesting, and here, on vixra, there is not rejection. I don't remember the whole theory, and the whole programs, but it can be useful to others; so I share it with you. It seem that without the complication of the least common divisor, the calculation is more simple, and elegant.
Category: Mathematical Physics

[1] viXra:1602.0010 [pdf] replaced on 2016-02-05 04:29:56

The Theory of Idealiscience

Authors: Zhang Yunfan
Comments: 36 Pages.

The theory of idealiscience is an accurate theoretical model, by the model we can deduce most important laws of Physics, explain a lot of physical mysteries, even a lot of basic and important philosophical questions. we can also get the theoretical values of a lot of physical constants, even some of the constants can not be deduced by traditional physical theories, such as neutron mass and magnetic moment,Avogadro constant and so on.
Category: Mathematical Physics