Mathematical Physics

1707 Submissions

[14] viXra:1707.0301 [pdf] submitted on 2017-07-23 12:42:25

Theoretical Physics

Authors: Jean C.Dutailly
Comments: 405 Pages.

This book proposes a review and, on important points, a new formulation 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 proposes the right mathematical objects to deal with them, chosen among well grounded mathematical theories. Proceeding this way, the reader will have a comprehensive, consistent and rigorous understanding of the main topics of the Physics of the XXI° century, together with many tools to do practical computations. After a short introduction about the meaning of Theories 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, from 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 motion leads to associate a frame to all material bodies, whatever their scale, and to the representation of motion in Clifford Algebras. Momenta, translational and rotational, are then represented by spinors, which provide a clear explanation for the spin and the existence of anti-particles. The force fields are introduced through connections, in the 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 new and important results. 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 solutions for the equations representing a system in the most general case. The topic of the last chapter is discontinuous processes. The phenomenon of collision is studied, and we show that bosons can be understood as discontinuities in the fields.
Category: Mathematical Physics

[13] viXra:1707.0296 [pdf] submitted on 2017-07-22 15:52:25

Fractal Arts: a 2D-Mfdfa Approach

Authors: Sayan Nag
Comments: 6 Pages.

“Art attracts us only by what it reveals of our most secret self.”- Alfred North Whitehead The basic building blocks upon which the natural world is built are Fractals. Recognizing these patterns in Nature is essential-because of these patterns Nature is so aesthetically pleasing. We try to find these patterns everywhere instinctively. In our work we look forward to find the fractality in Abstract art-the paintings of the renowned artist Jackson Pollock using a novel approach of 2D-Multifractal Detrended Fluctuation Analysis in his paintings.
Category: Mathematical Physics

[12] viXra:1707.0284 [pdf] submitted on 2017-07-21 09:18:46

Deepening Questions about Electron Deep Orbits of the Hydrogen Atom

Authors: Jean-Luc Paillet, Andrew Meulenberg
Comments: 12 Pages. Submitted to 12th Intern. Workshop on Anomalies in Hydrogen Loaded Metal.

In previous works, we analyzed and countered arguments against the deep orbits, as discussed in published solutions. Moreover, we revealed the essential role of Special Relativity as source of electron deep orbits (EDOs). We also showed, from a well-known analytic method of solution of the Dirac equation, that the obtained EDOs have a positive energy. When including the magnetic interactions near the nucleus, we observed a breakthrough in how to satisfy the Heisenberg Uncertainty Relation (HUR) for electrons confined near the nucleus, in a radial zone of only a few fm. Here we chose a different method, by directly facing the HUR for such confined electrons, from which we deduce the coefficient γ of these highly relativistic electrons. Then we show the effective Coulomb potential due to a relativistic correction, can maintain the electrons in containment. Next we resume and deepen our study of the effects of EM interactions near the nucleus. We first obtain computation results: though approximate, we can effectively expect high-energy resonances near the nucleus. These results should be confirmed by using QFT-based methods.
Category: Mathematical Physics

[11] viXra:1707.0266 [pdf] replaced on 2017-09-12 11:36:00

An Ideal MHD as a System of Coupled Quaternionic Riccati Equations for MHD Power Generator, and Outline for Finding Their Solutions

Authors: Victor Christianto, Florentin Smarandache
Comments: 6 Pages. This paper has been submitted to a conference administered for IEEE (BCWSP 2017)

In recent years, there are several proposals of using MHD theory for clean power generators on top of coal plant. But the theory involved appears too complicated, so in this paper we will use a simpler approach using ideal MHD equations which then they can be reduced to a system of coupled quaternionic Riccati equations. Further numerical and experimental investigations are advisable.
Category: Mathematical Physics

[10] viXra:1707.0216 [pdf] submitted on 2017-07-15 19:08:22

The Role of Dialectical Forces in Quantum Physics and General Relativity

Authors: Tracy Klein
Comments: 9 Pages.

The following manuscript establishes the role of dialectical forces in our physical universe. The dialectical relationship links opposing theories of quantum mechanics and bridges the gap between quantum physics and general relativity.
Category: Mathematical Physics

[9] viXra:1707.0195 [pdf] submitted on 2017-07-14 03:38:22

Mathematical Origins of Comparative Nonequivalence in Physics

Authors: Paris Samuel Miles-Brenden
Comments: 10 Pages. The laws of physics in their abstraction are blind to the world.

The laws of physics in their abstraction are blind to the world.
Category: Mathematical Physics

[8] viXra:1707.0193 [pdf] submitted on 2017-07-13 13:33:10

Veblen's Identities, Maxwell's Equations and Weyl's Unified Field Theory

Authors: William O. Straub
Comments: 3 Pages.

An intriguing connection between some work of Oswald Veblen with that of Hermann Weyl is presented.
Category: Mathematical Physics

[7] viXra:1707.0144 [pdf] submitted on 2017-07-11 03:13:02

The Ultimate Nature of Reality Part 1

Authors: John Peel
Comments: 35 Pages. Part 1 of two files regarding information fields

The role of geometry in particle physics
Category: Mathematical Physics

[6] viXra:1707.0129 [pdf] submitted on 2017-07-09 21:31:05

The Ultimate Nature of Reality

Authors: John Peel
Comments: 72 Pages. Perhaps important

This paper hopes to clarify the notion of Information Fields and the role of geometry in particle physics.
Category: Mathematical Physics

[5] viXra:1707.0128 [pdf] submitted on 2017-07-09 22:59:57

Gravitational Forces Revisited

Authors: Jack Bidnik
Comments: 13 Pages.

Abstract: This paper explains my derivation of a number of equations to describe gravitational forces from the relativistic relative momentum of Albert Einstein's Special Relativity. One of these equations parallels Issac Newton's Gravitational Equation by replacing the Gravitational Constant, G, with a velocity dependent expression. The resulting equation is applied to the orbital parameters of the planets and a number of their moons, with very close results. The forces derived have applications in other areas of physics, including electromagnetic force, and have some surprising properties hitherto unknown in physics. I derive these results with no external forces assumed to be present, so that the only mechanical force here must be gravity.
Category: Mathematical Physics

[4] viXra:1707.0109 [pdf] replaced on 2017-10-24 08:37:37

General Exact Tetrahedron Argument for the Fundamental Laws of Continuum Mechanics

Authors: Ehsan Azadi
Comments: 28 pages

In this article, we give a general exact mathematical framework that all the fundamental relations and conservation equations of continuum mechanics can be derived based on it. We consider a general integral equation contains the parameters that act on the volume and the surface of the integral's domain. The idea is to determine how many local relations can be derived from this general integral equation and what these local relations are. After obtaining the general Cauchy lemma, we derive two other local relations by a new general exact tetrahedron argument. So, there are three local relations that can be derived from the general integral equation. Then we show that all the fundamental laws of continuum mechanics, including the conservation of mass, linear momentum, angular momentum, energy, and the entropy law, can be considered in this general framework. Applying the general three local relations to the integral form of the fundamental laws of continuum mechanics in this new framework leads to exact derivation of the mass flow, continuity equation, Cauchy lemma for traction vectors, existence of stress tensor, general equation of motion, symmetry of stress tensor, existence of heat flux vector, differential energy equation, and differential form of the Clausius-Duhem inequality for entropy law. The general exact tetrahedron argument is an exact proof that removes all the challenges on derivation of the fundamental relations of continuum mechanics. In this proof, there is no approximate or limited process and all the parameters are exact point-based functions. Also, it gives a new understanding and a deep insight into the origins and the physics and mathematics of the fundamental relations and conservation equations of continuum mechanics. This general mathematical framework can be used in many branches of continuum physics and the other sciences.
Category: Mathematical Physics

[3] viXra:1707.0106 [pdf] replaced on 2017-10-22 06:26:44

Cauchy Tetrahedron Argument and the Proofs of the Existence of Stress Tensor, a Comprehensive Review, Challenges, and Improvements

Authors: Ehsan Azadi
Comments: 34 pages

In 1822, Cauchy presented the idea of traction vector that contains both the normal and tangential components of the internal surface forces per unit area and gave the tetrahedron argument to prove the existence of stress tensor. These great achievements form the main part of the foundation of continuum mechanics. For about two centuries, some versions of tetrahedron argument and a few other proofs of the existence of stress tensor are presented in every text on continuum mechanics, fluid mechanics, and the relevant subjects. In this article, we show the birth, importance, and location of these Cauchy's achievements, then by presenting the formal tetrahedron argument in detail, for the first time, we extract some fundamental challenges. These conceptual challenges are related to the result of applying the conservation of linear momentum to any mass element, the order of magnitude of the surface and volume terms, the definition of traction vectors on the surfaces that pass through the same point, the approximate processes in the derivation of stress tensor, and some others. In a comprehensive review, we present the different tetrahedron arguments and the proofs of the existence of stress tensor, discuss the challenges in each one, and classify them in two general approaches. In the first approach that is followed in most texts, the traction vectors do not exactly define on the surfaces that pass through the same point, so most of the challenges hold. But in the second approach, the traction vectors are defined on the surfaces that pass exactly through the same point, therefore some of the relevant challenges are removed. We also study the improved works of Hamel and Backus, and indicate that the original work of Backus removes most of the challenges. This article shows that the foundation of continuum mechanics is not a finished subject and there are still some fundamental challenges.
Category: Mathematical Physics

[2] viXra:1707.0056 [pdf] replaced on 2017-10-23 06:28:26

Exact Tetrahedron Argument for the Existence of Stress Tensor and General Equation of Motion

Authors: Ehsan Azadi
Comments: 20 pages

The birth of modern continuum mechanics is the Cauchy's idea for traction vectors and his achievements of the existence of stress tensor and derivation of the general equation of motion. He gave a proof of the existence of stress tensor that is called Cauchy tetrahedron argument. But there are some challenges on the different versions of tetrahedron argument and the proofs of the existence of stress tensor. We give a new proof of the existence of stress tensor and derivation of the general equation of motion. The exact tetrahedron argument gives us, for the first time, a clear and deep insight into the origins and the nature of these fundamental concepts and equations of continuum mechanics. This new approach leads to the exact definition and derivation of these fundamental parameters and relations of continuum mechanics. By the exact tetrahedron argument we derived the relation for the existence of stress tensor and the general equation of motion, simultaneously. In this new proof, there is no limited, average, or approximate process and all of the effective parameters are exact values. Also in this proof, we show that all the challenges on the previous tetrahedron arguments and the proofs of the existence of stress tensor are removed.
Category: Mathematical Physics

[1] viXra:1707.0022 [pdf] replaced on 2017-07-03 00:54:24

A Computer Algebra Solution of Ermakov Equation Corresponding to Diffusion Interpretation of Wave Mechanics

Authors: Victor Christianto, Florentin Smarandache
Comments: 8 Pages. This paper has not been submitted to a journal. Your comments are welcome

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details.
Category: Mathematical Physics