A Unified Theory of Classical and Quantum Light

2018

It is shown that relativistic wave equations for free, massless fields display quantum-classical complementarity.

Journal of Physics A: Mathematical and General, 1997

A review of old inconsistencies of Classical Electrodynamics (CED) and of some new ideas that solve them is presented. Problems with causality violating solutions of the wave equation and of the electron equation of motion, and problems with the non-integrable singularity of its self-field energy tensor are well known. The correct interpretation of the two (advanced and retarded) Lienard-Wiechert solutions are in terms of creation and annihilation of particles in classical physics. They are both retarded solutions. Previous work on the short distance limit of CED of a spinless point electron are based on a faulty assumption which causes the well known inconsistencies of the theory: a diverging self-energy (the non-integrable singularity of its self-field energy tensor) and a causalityviolating third order equation of motion (the Lorentz-Dirac equation). The correct assumption fixes these problems without any change in the Maxwell's equations and let exposed, in the zero-distance limit, the discrete nature of light: the flux of energy from a point charge is discrete in time. CED cannot have a true equation of motion but only an effective one, as a consequence of the intrinsic meaning of the Faraday-Maxwell concept of field that does not correspond to the classical description of photon exchange, but only to the smearing of its effects in the space around the charge. This, in varied degrees, is transferred to QED and to other field theories that are based on the same concept of fields as space-smeared interactions.

The Zitterbewegung model of an electron offers a classical interpretation for interference and diffraction of electrons. The idea is very intuitive because it incorporates John Wheeler's idea of mass without mass: we have an indivisible naked charge that has no properties but its charge and its size (the classical electron radius) and it is easy to understand that the electromagnetic oscillation that keeps this tiny circular current going -like a perpetual current ring in some superconducting material -cannot be separated from it. In contrast, we keep wondering: what keeps a photon together? Hence, the real challenge for any realist interpretation of quantum mechanics is to explain the quantization of light: what are these photons?

2011

A new quantum representation of the electro-magneti c field is introduced based on a bilinear expansion of the field in terms of quark creation and annihilati on operators. This representation has definite adva ntages, leading automatically to the transversal nature of photons and eliminating the need for artificial gau e fixing. However, this representation seems unable to produce the correct expectation value of the ene rgy of a photon. To cure this situation a new continuous q antum number is introduced, which entails new positional information of a classical nature. In st andard applications of quantum field theory these d egrees of freedom are hidden as they only lead to trivial phase factors. However, in many-body situations and when the state vectors are superpositions of moment um s ates, the phase factors can no longer be ignor ed and provide positional information about the partic les. Hence, in situations typical of classical syst ems the “hidden” degrees of freedom emerg...

Abstract In an enlarged Einstein-Maxwell theory, infinitesimal gauge transformations produce equations for a scalar field. These lead to wave mechanics.

2011

The proposed paper presents the unobserved inadequacies in de Broglie's given concepts of wave-particle duality and matter waves in the year 1923. The commonly admitted quantum energy or frequency expression hν=γmc 2 is shown to be inappropriate for matter waves and is acceptable only for photons, where the symbols have their usual meanings. The superluminal phase velocity expression c 2 /υ, for matter waves, is investigated in detail and is also reported to be inadequate in the proposed paper. The rectifications in the inadequate concepts of de Broglie's theory and refinements in the analogy implementation between light waves and matter waves are presented, which provides the modified frequency and phase velocity expression for matter waves. Mathematical proofs for the proposed modified frequency and phase velocity expression are also presented. In accordance with the proposed concepts, a wave-particle duality picture is presented which elucidates the questions coupled with the wave-particle duality concepts, existing in the literature. Consequently, particle type nature is shown to be a characteristic of waves only, independent from the presence of matter. The modifications introduced in the frequency expression for matter waves leads to variation in the wave function expression for a freely moving particle and its energy operators, with appropriate justifications provided in the paper. A new relation between the Kinetic energy and Momentum of the moving body is also proposed and is subsequently applied to introduce novel General and Relativistic Quantum Mechanical Wave Equations. Applications of these equations in bound state quantum mechanical systems, presented in the paper, provide the information regarding particle's general and relativistic behavior in such systems. Moreover, the proposed wave equations can also be transformed into Schrödinger's and Dirac's equations. The interrelation of Schrödinger's, Dirac's and proposed equations with the universal wave equation is also presented.

Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.

2008

In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic’s relativistic equations are obtained in the presence of electromagnetic fields for both the density function and the probability amplitude. It is shown that, within the present theory’s scope, Dirac’s second order equation should be considered the fundamental one in spite of the first order equation. A relativistic expression is obtained for the statistical potential. Axioms are again altered and made compatible with the general theory of relativity. These postulates, together with the idea of the statistical potential, allow us to obtain a general relativistic quantum theory for ensembles composed of single particle systems. 1

2018

In the last article, an approach was developed to form an analogy of the wave function and derive analogies for both the mathematical forms of the Dirac and Klein-Gordon equations. The analogies obtained were the transformations from the classical real model forms to the forms in complex space. The analogous of the Klein-Gordon equation was derived from the analogous Dirac equation as in the case of quantum mechanics. In the present work, the forms of Dirac and Klein-Gordon equations were derived as a direct transformation from the classical model. It was found that the Dirac equation form may be related to a complex velocity equation. The Dirac's Hamiltonian and coefficients correspond to each other in these analogies. The Klein-Gordon equation form may be related to the complex acceleration equation. The complex acceleration equation can explain the generation of the flat spacetime. Although this approach is classical, it may show a possibility of unifying relativistic quantum mechanics and special relativity in a single model and throw light on the undetectable aether.

Mathematics, 2021

A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin-zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and spacelike intervals, are treated equally, which makes the new theory fully symmetric and consistent with the special theory of relativity. The theory correctly reproduces the classical action of a relativistic particle in the path integral formalism, and allows for the introduction of a new quantity called vector-mass, whose physical implications for nonlocality, the uncertainty principle, and quantum vacuum are described and discussed.