Mathematical Physics

1802 Submissions

[20] viXra:1802.0441 [pdf] submitted on 2018-02-28 12:07:01

Einstein/newton Duality: an Ontological-Phase Topological Field Theory

Authors: Richard L Amoroso
Comments: 17 Pages. Preprint, to appear in IOP (2018) conference proceedings, PIRT, Moscow 2017

Newton claimed instantaneous G-influence; Einstein insisted no influence propagated faster than c . Quantum Mechanics (QM) the so-called basement of reality, posits a Quantum Gravity, for which no a priori science exists. We propose a paradigm shift with duality between a semi-quantum Standard Model (SM) limit and Large-Scale Additional Dimensionality (LSXD) in a modified M-Theoretic Unified Field (UF) brane arena as the regime of integration described by an Ontological-Phase Topological Field Theory (OPTFT) requiring fundamental changes in the concept of dimensionality and matter. OPTFT is developed to formally describe 3rd regime Unified Field Mechanics (UFM) (classical- Quantum-UFM) to relate Newton-Einstein duality by added degrees of freedom in a semiquantum limit enabling topological Dirac-Majorana doublet fusion supervening the uncertainty principle.
Category: Mathematical Physics

[19] viXra:1802.0438 [pdf] submitted on 2018-02-28 14:07:14

Spinors, Twistors, Quaternions and Complex Space

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 18 Pages. https://doi.org/10.1142/9789814324250_0011

Utilizing the spinor approach, electromagnetic and gravitational metrics are mapable to the twistor algebra, which corresponds to the complexified Minkowski space. Quaternion transformations relate to spin and rotation corresponding to the twistor analysis.
Category: Mathematical Physics

[18] viXra:1802.0436 [pdf] submitted on 2018-02-28 16:02:08

Relativistic Dirac Quantum Theory in Complex Minkowski Space and Tachyonic Signaling

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 24 Pages. https://doi.org/10.1142/9789814324250_0012

In this paper we develop complex solutions to the Dirac equation and discuss various implications and applications.
Category: Mathematical Physics

[17] viXra:1802.0424 [pdf] submitted on 2018-02-28 10:01:12

The Complex Form of Relativistic Maxwell's Equations

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 17 Pages. https://doi.org/10.1142/9789814324250_0007

We outline the relativistic formalism which gives a more comprehensive explanation of the complexification scheme. Such issues as considering the Higgs Boson as a soliton depends on Lorentz invariance and relativistic causality constraints. We relate the complexification of Maxwell's equations to models of nonlocal micro and macro phenomena. In this chapter we relate the electromagnetic fields, F and A , the potentials to the gravitational field, G . We examine, for example, the manner in which advanced potentials may explain the remote connectedness which is indicated by the Clauser test of Bell's theorem. Similar arguments apply to Young's double slit experiment. The collective coherent phenomena of superconductivity is also explainable by considering the relativistic field theoretic approach in which wave equations are solved in the complex Minkowski space.
Category: Mathematical Physics

[16] viXra:1802.0423 [pdf] submitted on 2018-02-28 10:40:02

Real and Complex Amended Maxwell’s Equations for Non-Abelian Gauge Groups

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 8 Pages. https://doi.org/10.1142/9789814324250_0008

In this work we analyze, calculate and extend modification of Maxwell’s equations in a complex Minkowski metric, M4 in a C2 complexified 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. Weyl identified the U1 gauge group for the standard Maxwell’s equations in its nonrelativistic form in M4 space. We expand the form of the elegant electromagnetic equations and express them in C4 space for the nonrelativistic formalism and for the relativistic formalism of the equations. The advanced and retarded formalisms are also examined. In the case where Maxwell’s equations are solved in C4 space, or the complex 8-space, we can extend the theory to considerations of other gauge groups such as SL(2,c), SUn for n > 2 and SU2 expanding the approach beyond U1 gauge conditions.
Category: Mathematical Physics

[15] viXra:1802.0422 [pdf] submitted on 2018-02-28 11:05:16

Sub and Superluminal Transformations of the Complex Vector Potential

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 10 Pages. https://doi.org/10.1142/9789814324250_0009

We consider in this chapter the transformations of an oscillatory form of A mu in a complex 12D Minkowski space. The form of the transformation of A mu or (A , Phi) depends on whether such a transformation is a superluminal Lorentz transformation (SLT) or a subluminal Lorentz transformation.
Category: Mathematical Physics

[14] viXra:1802.0419 [pdf] submitted on 2018-02-28 11:55:59

The Schrödinger Equation in Complex Minkowski Space

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 17 Pages. https://doi.org/10.1142/9789814324250_0010

We develop a formalism for the Schrödinger equation in an eight dimensional (8D) 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 and anticipatory quantum theory. Certainly, the most desirable consequence of scientific discovery is the ability to refine our concepts of reality.
Category: Mathematical Physics

[13] viXra:1802.0416 [pdf] submitted on 2018-02-27 15:16:59

Structure, Properties and Implications of Complex Minkowski Spaces

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 26 Pages. https://doi.org/10.1142/9789814324250_0002

We consider the properties and implications of three n > 4 multidimensional geometries. These are Descartes geometry [1], the properties and implications of which are enumerated in [2-6]. Both macroscopic and microscopic implications of these geometries are presented. We also develop several forms of complex Minkowski space in terms of a generalized metric containing terms derived from real and imaginary coordinates. The metric of the space is real and therefore physical [7-17]. This geometry is found to be one-to-one with Kaluza-Klein geometry [18-20] in which there has been much recent interest in developing M-Theory, in particular in the apparent relationship between the gravitational and electromagnetic fields often called Quantum Gravity. We have discussed the properties and implications of complex geometries in a number of works. The basic structure of the geometries is based on the construction of complexified dimensions, consisting of orthogonal real and imaginary parts. We examine the implication of a complex 8-space geometry in which we introduce imaginary components for each real spatial dimension, X = (x,y,z) and temporal dimension, t.
Category: Mathematical Physics

[12] viXra:1802.0412 [pdf] submitted on 2018-02-27 17:30:47

The Complexification of Maxwell's Equations

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 27 Pages. https://doi.org/10.1142/9789814324250_0005

In this work we demonstrate that complex electric and magnetic fields are consistent with a geometry consisting of complex spacetime. We thus demonstrate that complex spacetime coordinates are not inconsistent with electromagnetic phenomena and may point to a direction for its unification with gravitational phenomena, in the weak Weyl field limit. The particular case we examine in detail is for an electron in a field where we derive Coulomb's equation. We examine this unification using the Weyl geometry in the linear approximation of the gravitational field.
Category: Mathematical Physics

[11] viXra:1802.0411 [pdf] submitted on 2018-02-27 17:57:51

Vector and Scalar Potentials, Advanced and Retarded Waves and Nonlocal Phenomena

Authors: Richard L Amoroso, Elizabeth A Rauscher
Comments: 8 Pages. https://doi.org/10.1142/9789814324250_0006

The issue of whether Bell's theorem and other remote connectedness phenomena, such as Young's double slit experiment, demands superluminal or space-like signals or prior generated luminal signals is an area of hot debate. This also relates to the existence of advanced vs. retarded potentials and annihilation creation operators which are of interest in this regard. Using the complex model of we will examine the issue of the nonlocality of Bell's theorem as quantum mechanical ‘transactions’ providing a microscopic communication path between detectors across space-like intervals, which violate the EPR locality postulate [1]. See Chap. 4. This picture appears consistent with the remote connectedness properties of complex Minkowski space. Also, there are implications for macroscopic communications channels; another area of debate. Detailed discussions of Bell's theorem are given in [2].
Category: Mathematical Physics

[10] viXra:1802.0355 [pdf] replaced on 2018-02-25 07:26:12

A Refinement to Nonstandard Ultea-Logic-Systems Applied to the Ggu-Model

Authors: Robert A. Herrmann
Comments: 32 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 (GGUmodel), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from certain observable entities, which are physical processes and mental procedures that we use 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 in the required sequential order. It is shown that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patten and Wheeler participator universe requirements. In this version, the participator process portion of the GGU-model is significantly altered from the original process presented and a correction is made to an equation and its applications. A specific data-set is generalized and the set of all ultrapropertons 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 process is introduced that leads, when applied, to the individual developmental 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. In this refinement, the page 11 statement, in the original version of this paper on quantum theory, is completely modified and the previous statement is now essentially incorrect.
Category: Mathematical Physics

[9] viXra:1802.0310 [pdf] submitted on 2018-02-21 18:46:48

Structural Optimization by Using the Stiffness Homogenization

Authors: Yongsop Ri, Namhyok Ri, Jonggwang Pak, Iljin Kim, Zhihua Chen –Department of Mechanics Enineering, Kim Il Sung University, Pyongyang, DPR of Korea - School of Civil Engineering, Tianjin University, Tianjin 300072, PR of Chi
Comments: 21 Pages.

The topology optimization using the homogenization method is to find optimal layout of microstructures which satisfies design demand in the neighborhood of an arbitrary point in a given design domain. The homogenization approach is to compute proper mechanical properties of those microstructures in terms of integral averaging by accepting the periodicity assumption and characteristic function. In this paper, we described a stiffness homogenization theory that is able to avoid the complication of the homogenization approach and reduce the computation cost by considering the topology optimization process in consistence with the finite element analysis. The method can be applied more flexibly to individual or simultaneous optimization of the topology, shape, size and material layout. We discussed a stiffness homogenization during meshing the space structure with different kinds of elements in detail. An optimal criterion for the minimum weight design problem, as one of typical optimization design problems, was derived and the computational algorithm was presented. Numerical results of an example were compared with previous methods, which show the validation of the method.
Category: Mathematical Physics

[8] viXra:1802.0239 [pdf] submitted on 2018-02-18 13:58:51

Angular Moments (Spins) of Wave Vortices (Loks). Refinements.

Authors: Alexander I.Dubinyansky, Pavel Churlyaev.
Comments: 6 Pages. dubinyansky@mail.ru http://universe100.narod.ru/ http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html (English)

Development of the mathematical model of the elastic universe. The spins of the loks (0,0), (1,0) and (1,1) are calculated. Assumptions are made regarding other loks. Further conclusions were drawn on the identification of elementary particles in a set of loks.
Category: Mathematical Physics

[7] viXra:1802.0231 [pdf] submitted on 2018-02-19 00:43:55

Electrostatics, Gravity, and Galactic Force

Authors: Jack Bidnik
Comments: 6 Pages.

Electrostatics, Gravity, and Galactic Force © US 2015 by Jack Bidnik This paper is a continuation of my paper entitled Gravitational Forces Revisited (GFR), http://vixra.org/abs/1707.0128 and may be considered as Chapter 2 of the concepts developed in that paper. Two corollaries of the derivation of Gs in GFR are elaborated here to show that the formula can be extended to include both the smallest and the largest masses and spaces. The same formula can give both the electrostatic force of the Hydrogen atom and also the force which counteracts the centrifugal force of large galaxies. I believe this development nullifies the most basic motive for postulating dark matter, which is that the gravitational force at such high speeds could not hold the galaxy together. Examples are given for galaxies of various size. The paper starts with continuing analysis of the mathematical conclusion in GFR that the derived force Ft is equivalent to the centripetal force of the orbit vo2/r. This analysis is perhaps superfluous since there is no other acceleration present radially than the one derived for Ft , but I present various looks at the math to dispel any nagging doubts. Another set of doubts to be dispelled involves the idea of frames of motion. It suffices to point out that when one uses the reduced mass, it is the equivalent of the motion of either mass in the frame of the other, since it is the equivalent of one mass being stationary.
Category: Mathematical Physics

[6] viXra:1802.0207 [pdf] submitted on 2018-02-16 06:19:14

The Energy of Wave Vortices (Loks).

Authors: Alexander I. Dubinyansky, Pavel Churlyaev.
Comments: 7 Pages. dubinyansky@mail.ru http://universe100.narod.ru/ http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html (English)

Development of the mathematical model of the elastic universe. The energy of the loks (0,0), (1,0) and (1,1) are calculated. Assumptions are made regarding other loks. The first conclusions on the identification of elementary particles in a set of loks are made.
Category: Mathematical Physics

[5] viXra:1802.0183 [pdf] submitted on 2018-02-15 07:40:11

Electromagnetic-Power-based Modal Classification, Modal Expansion, and Modal Decomposition for Perfect Electric Conductors

Authors: Renzun Lian
Comments: 5 Pages.

Traditionally, all working modes of a perfect electric conductor are classified into resonant modes, inductive modes, and capacitive modes, and the resonant modes are further classified into internal resonant modes and external resonant modes. In this paper, the resonant modes are alternatively classified into intrinsically resonant modes and non-intrinsically resonant modes, and the intrinsically resonant modes are further classified into non-radiative intrinsically resonant modes and radiative intrinsically resonant modes. Based on the modal expansion corresponding to this new modal classification, an alternative modal decomposition method is proposed. In addition, it is also proved that: all intrinsically resonant modes and all non-radiative intrinsically resonant modes constitute linear spaces respectively, but all resonant modes and all radiative intrinsically resonant modes cannot constitute spaces respectively.
Category: Mathematical Physics

[4] viXra:1802.0114 [pdf] submitted on 2018-02-11 01:51:57

CompContr, LF, and Incalculability

Authors: Miguel A. Sanchez-Rey
Comments: 2 Pages.

A no-brainer.
Category: Mathematical Physics

[3] viXra:1802.0109 [pdf] replaced on 2018-02-27 11:00:13

The KdV Equations over Manifolds

Authors: Antoine Balan
Comments: 3 pages, written in french

The KdV equations are defined over manifolds. The system is integrable and we show that it is reduced to usual KdV equations.
Category: Mathematical Physics

[2] viXra:1802.0055 [pdf] submitted on 2018-02-05 20:46:50

Formulation of Maxwell Field Equations from a General System of Linear First Order Partial Differential Equations

Authors: Vu B Ho
Comments: 9 Pages.

In this work we show that, as in the case of Dirac equation, it is possible to formulate Maxwell field equations of electromagnetism from a general system of linear first order partial differential equations. A prominent feature that emerges from formulating Dirac and Maxwell field equations from a general system of linear first order partial differential equations is that the field equations must be formed in such a way that the functions that represent the system also obey a wave equation. This type of mathematical duality may be related to the wave-particle duality in quantum physics.
Category: Mathematical Physics

[1] viXra:1802.0016 [pdf] submitted on 2018-02-02 23:39:32

Big Bounce and a Chanced Tuning .

Authors: Durgadas Datta.
Comments: 7 Pages. A paper for CERN .

The meaning of fine tuning and emergent gravitation.
Category: Mathematical Physics