A local-ether wave equation unifying quantum mechanics, electromagnetics, and gravitation

An important milestone in quantum physics has been reachedby the publication of the Relativistic Quantum MechanicalDirac Equation in 1928. However, the Dirac equationrepresents a 1-Dimensional quantum mechanical equationwhich is unable to describe the 4-Dimensional PhysicalReality.In this article the 4-Dimensional Relativistic QuantumMechanical Dirac Equation expressed in the vectorprobability functions  and the complex conjugated vectorprobability function  *will be published. To realize this, theclassical boundaries of physics has to be changed. It isnecessary to go back in time 300 years ago. More than 200years ago before the Dirac Equation had been published.A Return to the Inception of Physics. The time of IsaacNewton who published in 1687 in the “PhilosophiaeNaturalis Principia Mathematica” a Universal FundamentalPrinciple in Physics which was in Harmony with Science andReligion. The Universal Path, the Leitmotiv, the UniversalConcept in Physics. Newton found the concept of “UniversalEquilibrium” which he formulated in his famous thirdequation Action = - Reaction. This article presents a New Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity.The physical concept of quantum mechanical probability waves has been created during the famous 1927 5th Solvay Conference. During that period there were several circumstances which came together and made it possible to create an unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrödinger published his famous material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrödinger’s wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell this was impossible. According to Maxwell’s equations Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason these material waves in Schrödinger’s wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrödinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function.In the New Theory it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined Electromagnetic waves could not be considered to be the material waves expressed in Schrödinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge and magnetic spin at discrete values.

Maxwell unified the disparate concepts of electric and magnetic fields with one theory (electromagnetism) and Einstein then unified the disparate theories of electromagnetism and mechanics with one kinematics (Minkowski space of special relativity). In this talk, we will briefly explain how the disparate kinematics of quantum mechanics (finite-dimensional Hilbert space) and special relativity can be unified with one principle (relativity principle). This result follows from the axiomatic reconstruction of quantum mechanics via information-theoretic principles, which has successfully recast quantum mechanics as a principle theory a la Einstein, i.e., the formalism of the theory follows from an empirically discovered fact, just like special relativity. According to the quantum reconstruction program, the empirically discovered fact whence the Hilbert space formalism of quantum mechanics is Information Invariance & Continuity. Of course, the empirically discovered fact whence the Lorentz transformations of special relativity is the light postulate, i.e., everyone measures the same value for the speed of light c, regardless of their relative motions. Obviously, the light postulate can be justified by the relativity principle—the laws of physics are the same in all inertial reference frames—because c is a constant of Nature per Maxwell’s electromagnetism. [We label this “NPRF + c” for short, where NPRF stands for “no preferred reference frame.”] As we will show, Information Invariance & Continuity can also be justified by the relativity principle by first spatializing the quantum reconstruction program’s operational notion of measurement. In that case, Information Invariance & Continuity entails the empirically discovered fact that everyone measures the same value for Planck’s constant h, regardless of their relative spatial orientations or locations (Planck postulate). Since Poincar’e transformations relate inertial reference frames via spatial rotations and translations as well as boosts, and h is a constant of Nature per Planck’s radiation law, the relativity principle justifies the Planck postulate (NPRF + h) just like it justifies the light postulate (NPRF + c). Thus, the kinematics of quantum mechanics and special relativity are unified in that both follow most fundamentally from the relativity principle in the adynamical global constraints NPRF + h and NPRF + c. This approach provides a principle solution to the mystery of quantum entanglement that does not violate locality, statistical independence, intersubjective agreement, or the uniqueness of experimental outcomes and it does not alter quantum mechanics as a principle theory. An ontology consistent with this unification is introduced and we deflate both the ‘big’ and ‘small’measurement problems.

Galileo Galilei was the first scientist to hypothesize a universal principle of relativity, but he neither proposed, nor limited his principle to, the so-called “Galilean transformation.” The danger in calling the classical transformation “Galilean” is that students begin to believe that Galilei's principle of relativity is somehow limited to the classical transformation and classical mechanics, thus neglecting its universality. Because Galilei's 1632 statement [Dialogue Concerning the Two Chief World Systems—Ptolemaic and Copernican, 2nd ed., translated by S. Drake (University of California Press, Berkeley, 1967), pp. 186–188] of the principle is remarkably similar to Poincaré's well accepted statement [Proceedings of the Congress of Arts and Science, Universal Exposition, St. Louis, 1904, edited by H. J. Rogers (Houghton Mifflin and Company, Boston, 1904), Vol. 1, pp. 604–622], Galilei should be given greater recognition for it. However, the so-called Galilean transformation might be better named the “Euclidean space-time transformation” since it is shown here that universal Euclidean space actually requires time to be universal, that is, t′ = t. It is not usually realized that the Euclidean transformation assumes lightspeed to be infinite. Pedagogical thought should be given to combining the Galilean principle of relativity, the Euclidean transformation and Newton's mechanics as “Ordinary Relativity” to distinguish it from “Special Relativity.” This would have pedagogical and conceptual value as a model and precursor to special relativity. Finally, it is suggested that the current use of “relativistic” is incorrect when applied exclusively to special relativity, for it implies that classical mechanics is non-relativistic.

The conference brought together people working in mathematical general relativity, a field which lies at the interface of analysis, differential geometry and physics. There was a mix of established workers in the subject with participants at the start of their careers and researchers from neighbouring fields. The Einstein equations are at the heart of general relativity theory. They form a system of evolution equations and their solutions are conveniently parametrized by initial data. These initial data are required to satisfy constraint equations and these were the topic of several lectures at the conference. The talks of Corvino and Pollack were concerned with recent progress in methods for constructing solutions of the constraints. An important concept for solutions of the constraints is that of mass, including quasilocal mass. This was a central theme of the talks of Degeratu, Huisken and Shi. Huisken introduced a striking new approach to the definition of mass based on isoperimetric inequalities. Dain presented a variational characterization of the extreme Reissner–Nordström solution, thus relating the study of the constraint equations to the theory of black holes. The talk of Wohlfarth was rather outside the main area of the conference. He described a new concept of geometry motivated by string theory which may come to enrich the circle of ideas within mathematical relativity. Many of the talks at the conference were on evolution equations related to general relativity. Dafermos and Finster presented results related to the dynamical stability of black holes. Dafermos described new results on the rate of decay of solutions of the wave equation on the Schwarzschild spacetime while Finster explained applications of methods of functional analysis to the wave equation on the Kerr spacetime. Struwe's talk concerned uniqueness for supercritical nonlinear wave equations which from the point of view of the Einstein equations are an important example to compare with. The Maxwell equations are another important comparison system and Bauer showed how they can be used to understand more about radiation formulae. Velázquez gave an introduction to singularity formation in the Keller–Segel model, a parabolic system coming from mathematical biology. This is a possible source of insight for obtaining a rigorous understanding of critical collapse in general relativity. The talks of Andréasson, Choptuik and Lindblom dealt with various aspects of the application of numerical techniques to the study of the Einstein evolution equations. Choptuik showed impressive new simulations of coalescing black holes due to Pretorius which could hardly have been imagined just a year ago. Cosmology is at present a very active area of research in general relativity. This is in part due to the challenge of understanding the observed accelerated expansion of our universe. Mathematics is beginning to make its mark in this subject and this was reflected by talks of Heinzle, Rendall and Tod. Mathematical relativity is a meeting point for many ideas and the abstracts which follow give some idea of the variety of the subject. In fact the spectrum of topics discussed by the participants at the conference was much wider than those for which talks could be scheduled. By limiting the number of presentations it was possible to leave plenty of time for people to exchange insights. The lively interactions observed make us hopeful that this conference has given a boost to the development of the subject in the next few years.

Ontology is integral to the two most fundamental scientific theories of the twentieth century: quantum theory and the special and general theories of relativity. Issues that drove the development of quantum theory include the reality of quanta, the simultaneous wave- and particle-like nature of matter and energy, determinism, probability and randomness, Schrodinger’s wave equation, and Heisenberg’s uncertainty principle. So did the reality of the predictions about space, time, matter, energy, and the universe itself that were deduced from the special and general theories of relativity. Dirac’s prediction of antimatter based solely on the mathematics of his theory of the electron and Pauli’s prediction of the neutrino based on his belief in quantum mechanics are cases in point. Ontological interpretations of the uncertainty principle, of quantum vacuum energy fields, and of Schrodinger’s probability waves in the form of multiple universe theories further illustrate this point.

De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ <mml:math display="inline"> <mml:msqrt> <mml:mn>2</mml:mn> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">V</mml:mi> </mml:msqrt> </mml:math> = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.

Traditionally, certain physical theories have been thought to have relativity principles associated with them. Associated with Newtonian mechanics is the principle of Galilean relativity, associated with special relativity is the special or restricted principle of relativity, associated with general relativity is the general principle of relativity, etc. Such relativity principles are often expressed in terms of groups of transformations. The principle of Galilean relativity is expressed by the ‘invariance’ of Newtonian mechanics under the Galilean group, that of special relativity by the ‘invariance’ of special relativity under the Lorentz group, and that of general relativity by the ‘invariance’ (or ‘covariance’) of general relativity under the group of all 1–1 transformations with non-vanishing Jacobian. Unfortunately, just what these various groups are groups of, and exactly how they are associated with given physical theories, has been far from clear. Similarly, the nature and role of the various relativity principles has been correspondingly unclear.

Maxwell's equations and the Lorentz force law are developed by applying the transformations of special relativity to Gauss's law on the flux of the electric field, ∫E · dS = 4πqenclosed, provided that electromagnetic signals are propagated with the speed of light, and that the electric force on a test charge is velocity-independent and does not depend on time derivatives of the source position of order higher than the acceleration.

The time dependent Schrodinger equation is frequently ‘derived’ by postulating the energy E → iℏ(∂/∂t) and momentum p⃗ → (ℏ/i)∇⃗ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely ‘a particle is what a particle detector detects.’ This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation.

Propagation and radiation of electromagnetic waves in a lossless, reciprocal, chiral medium is studied in this thesis. Such a medium is described electromagnetically by the constitutive relations D = eE + iγB and H = iγE + (1/µ)B. The constants e, µ, γ are real and have values that are fixed by the size, shape, and the spatial distribution of the elements that collectively compose the medium. The plane wave propagation in an unbounded chiral medium is considered. The propagation constants are obtained and the polarization properties of electromagnetic waves in such a medium are discussed in detail. The problem of reflection from, and transmission through a semi-infinite chiral medium is solved by obtaining the Fresnel equations. The conditions for the total internal reflection of the incident wave from the interface, and the existance of the Brewster angle are obtained. The effects of the chirality on the polarization and intensity of the reflected wave from the chiral half-space are discussed and illustrated by employing the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence. The radiation emitted by an oscillating dipole in an unbounded, lossless, chiral medium is calculated. From the constitutive relations and from the time-harmonic Maxwell equations ∇ x E = iωB and ∇ x H = J - iωD, it is seen that the wave equation for such a medium is given by ∇ x ∇ x E - ω2µeE - 2ωµγ∇ x E = iωµJ where the source term J is the current density of the oscillating dipole and where E is the electric vector of the radiated field. The desired solution of this wave equation is found by the dyadic Green's function method, that is, by first constructing the dyadic Green's function Γ and then evaluating the expression E = iωµ∫Γ(r,r')•J(r')dV'. The dyadic Green's function Γ and the components of the radiated electric field E are obtained in closed form. The components of the radiated B, D, and H fields can be derived from knowledge of E by using the Maxwell equation B = (1/iω)∇ x E and the constitutive relations. The wave impedance of the medium and the radiation resistance of the dipole are also obtained. The effects of the chiral medium on the polarization and intensity of the dipole radiation are discussed.

Analysis of the electromagnetic (EM) waves emitted from partial discharge (PD) is useful from the viewpoint of non- contact diagnosis for power equipment. It's important to model the generation and propagation of the EM waves emitted from PD for understanding the physical mechanism. Maxwell's equations for the EM waves are replaced by a set of finite difference equations such as the finite-difference time-domain (FDTD) method. The FDTD suffers from phase error caused by its numerical dispersion. We numerically analyzes the EM waves emitted from PD in time-frequency using the constrained interpolation profile (CIP) method, which is higher accuracy than the FDTD, and the in-place fast Haar wavelet transform (IP-FHWT). Numerical results show that the proposed method based on the CIP and the IP-FHWT is useful for analyzing the relationship between the consecutive PD pulses and the EM waves.

The subject of this study is the special theory of relativity (SRT) by A. Einstein, the debate about which has been going on for more than a hundred years. The aim of the study is to evaluate SRT from the side of whether everything that is discussed in this theory and thus in the new, relativistic physics is possible in nature itself. At the same time, the author pays special attention to three issues: the principle of relativity, the necessary condition for the objectivity of the content of scientific theories and the Einstein style of scientific thinking, which predetermined the ideological component of SRT and all relativistic physics. But such issues as relativistic reductions of lengths and durations, the relativity of simultaneity and a single space-time do not remain without attention. The study revealed the fallacy of a long-standing and widespread opinion about the relativity of properties. The necessary condition for the objectivity of scientific theories is revealed. The natural form of expression of quantities is revealed and the non-relative nature of all natural quantities is shown. The hidden form of relativity inherent in the SRT postulate about the constancy of the speed of light in all inertial reference frames and extended in SRT to the magnitude of all lengths and durations considered in it is revealed. It is shown that such relativity is based on the dependence of the quantities on the choice of their reflection systems. It is shown that such dependence is impossible in nature itself. It is concluded that the SRT is erroneous. At the same time, the factors that served as favorable ground for the emergence and spread of this erroneous theory are listed.

Einstein assumed the “principle of relativity” when constructing the special theory of relativity (STR). He claimed that all inertial frames are equivalent, and that it is impossible to discriminate between inertial frames. However, among the coordinate systems regarded by Einstein as inertial frames, there are some in which light propagates isotropically, and some in which light propagates anisotropically. A method has been found which discriminates between these. This paper discusses the “triplet thought experiment” in which accelerated motion is eliminated from the famous twin paradox thought experiment of the STR. Here the inertial frames regarded as equivalent by the STR are identified as “classically stationary frames SCl” and “classically moving frames (S'Cl) ” First, an observer M in frame performs the triplet thought experiment, and it is confirmed that the delay in time which elapses in the moving frame agrees with the predictions of the STR. Next, an observer in rocket A (S'Cl) performs the triplet thought experiment, and observes the same time delay. Before starting movement at constant velocity, rocket A experiences accelerated motion. The coordinate system of rocket A cannot be regarded physically as a stationary frame. Even so, observer A observes the delay predicted by the STR. If it can be accepted that frames SCl are included in inertial frames, then the problem of the twin paradox will no longer be a paradox.

The canonical approach to quantizing quantum gravity is understood to suffer from pathological non-renomalizability. Nevertheless in the context of effective field theory, a viable perturbative approach to calculating elementary processes is possible. Some non-perturbative approaches, most notably loop quantum gravity and combinatorial quantum gravity imply the existence of a minimal length. To circumvent the seeming contradiction between the existence of a minimum length and the principle of special relativity, Double Special Relativity introduces modified dispersion relationships that reconcile the conflict. In this work, we combine these dispersion relationships with an effective field theory approach to compute the first post Newtonian correction to the bending of light by a massive object. The calculation offers the prospect of a directly measurable effect that rests upon both the existence of a quantized gravitational field and a minimal length. Experimental verification would provide evidence of the existence of a quantum theory of gravity, and the fundamental quantization of spacetime with a bound on the minimal distance.

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional “short-range gravity” are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.