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On the Hyper-Symmetric Maxwell Equations and Its Applications

Zhi Yong Cheng

Published Aug 1, 2014• 0 citations
OpenAlex

Abstract

In this paper, we propose a new space-time structure that is the three-dimensional time structure by comparison to the three-dimensional space. These two space-time structures are completely symmetrical. We improve the Maxwell equations in the new space-time structure by adding a new set of equations. The new set of equations has the space-time symmetrical structure by comparison to the old one. We can also obtain another type of wave equation by solving the hyper-symmetric Maxwell equations. The new wave equation contains both time and space coordinates. The general solution of this new wave equation can be divided into two parts. One part corresponds to the free particles, which means the localized electromagnetic wave or virtual photon. The amplitude of the localized electromagnetic wave will decrease exponentially when the distance from the mass center increasing. Another part of the general solution corresponds to the bound state of the particles. The equation of the localized electromagnetic wave in bound state is consistent with the Schrodinger’s equation. So we can draw the conclusion that the Schrodinger’s equation is just a special case of the localized electromagnetic wave equation. We can get the new interpretation of the wave function in quantum mechanics based on these analyses. The new interpretation shows that the essence of the wave function in quantum theory is the localized electromagnetic wave or virtual photon. So we can solve the problem of the collapse of the wave function based on the new interpretation. In order to proof the correctness of the localized electromagnetic wave or virtual photon, we apply it to solve the problem of Helium atom’s ground state energy. The theoretic calculation results are very satisfactory. Our calculation shows that the theoretic value of Helium atom’s ground state energy is -2.9033864868188(69)a.u., which is very close to the experiment results.

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In this paper, we propose a new space-time structure that is the three-dimensional time structure by comparison to the three-dimensional space. These two space-time structures are completely symmetrical. We improve the Maxwell equations in the new space-time structure by adding a new set of equations. The new set of equations has the space-time symmetrical structure by comparison to the old one. We can also obtain another type of wave equation by solving the hyper-symmetric Maxwell equations. The new wave equation contains both time and space coordinates. The general solution of this new wave equation can be divided into two parts. One part corresponds to the free particles, which means the localized electromagnetic wave or virtual photon. The amplitude of the localized electromagnetic wave will decrease exponentially when the distance from the mass center increasing. Another part of the general solution corresponds to the bound state of the particles. The equation of the localized electromagnetic wave in bound state is consistent with the Schrodinger’s equation. So we can draw the conclusion that the Schrodinger’s equation is just a special case of the localized electromagnetic wave equation. We can get the new interpretation of the wave function in quantum mechanics based on these analyses. The new interpretation shows that the essence of the wave function in quantum theory is the localized electromagnetic wave or virtual photon. So we can solve the problem of the collapse of the wave function based on the new interpretation. In order to proof the correctness of the localized electromagnetic wave or virtual photon, we apply it to solve the problem of Helium atom’s ground state energy. The theoretic calculation results are very satisfactory. Our calculation shows that the theoretic value of Helium atom’s ground state energy is -2.9033864868188(69)a.u., which is very close to the experiment results.
The Schr?dinger differential equation is what we usually solve for the microscopic particles in non-relativistic quantum mechanics. Niels Bohr suggested the power two of the (usually) complex answer shows the probability of the particle’s existence at a point of space. Also, the time dependence of Schrodinger wave equation is one whereas for light in electromagnetism is two. In this paper, we show a solution for both problems. We derive a Wave Equation for the energy of every system. This electromagnetic wave equation is shown to convert to those classical (i.e. the Schrodinger) and special relativistic (i.e. Klein-Gordon) quantum mechanical equations. Also, accordingly there definitely is a physical meaning to answer to this wave equation. And therefore, switching the probabilistic interpretation of quantum mechanics to a deterministic one as (Albert) Einstein demanded.
Until the introduction of Special Relativity by Hendrik Antoon Lorentz, Herman Minkovski and Albert Einstein in 1905 and General Relativity by Albert Einstein in 1916, Physics has been 3-Dimensional. After this period, Physics became in generally 4-Dimensional with the time as the fourth dimension. For that reason it is remarkable that till now quantum physics has been described by 3-dimensional equations like the Schrodinger wave equation and the relativistic Dirac equation. In this article the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation expressed in the vector probability functions and the complex conjugated vector probability function will be published. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time 300 years ago. More than 200 years ago before the Dirac Equation had been published. A Return to the Inception of Physics. The time of Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics which was in Harmony with Science and Religion. The Universal Path, the Leitmotiv, the Universal Concept in Physics. Newton found the concept of “Universal Equilibrium” which he formulated in his famous third equation 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 Schrodinger 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 Schrodinger’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 Schrodinger’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 Schrodinger’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 Schrodinger'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. Key words : General Relativity; Quantum Physics; Dirac Equation; Gravitational-Electromagnetic Interaction; Black Holes; Gravitational-Electromagnetic Confinement; Electromagnetism; Quantum Optics
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.
The present work is concerned with de Broglie's quantum theory of light. It is assumed that the photon is described by a Hermitian wave function with 16 components. Using this wave function it is shown that the 32 of de Broglie's equations are reduced to one set of 16 equations in the form: [equation] where the [alpha]'[rho] are Dirac matrices and [psi] is a matrix with 16 components. The electromagnetic quantities associated with the photon are described by means of the Dirac matrices operating on [psi] in a specified way. It is shown also that these electromagnetic quantities satisfy Maxwell's equations as a result of the equation the interaction between an electron and a photon is developed and the matrix elements for the radiation transitions are calculated. It is further shown that the above wave equation can be considered as the superposition of two similar wave equations, one for the positive energy photons and the other for the negative energy photons. To each of these states there corresponds electromagnetic quantities defined by the above method. It is the superposition of these fields which gives rise to the reality of the electromagnetic field, found in experience. The wave mechanics of the positive energy photon is discussed and the method of second quantization is applied to its wave function, from which we deduce the commutation relations for the complex fields.
In this paper, the quantum dynamics was obtained in the framework of the general theory of relativity, where a quantum particle is described by a distribution of matter, with amplitude functions of the matter density, in the two conjugate spaces of the spatial coordinates and of the momentum, called wave functions. For a free particle, these wave functions are conjugate wave packets in the coordinate and momentum spaces, with time-dependent phases proportional to the relativistic Lagrangian, as the wave velocities in the coordinate space are equal to the distribution velocity described by the wave packet in this space. From the wave velocities of the particle wave functions, Lorentz’s force and the Maxwell equations were obtained. From the wave/group equation in the momentum space describing the Lorentz force, the expressions of the electric and magnetic fields as functions of the electric potential conjugated to time and of the vector potential conjugated to the coordinates in the particle-field Lagrangian were obtained. With these expressions, the electric and magnetic fields that satisfy the Faraday-Maxwell law of electromagnetic induction and the two Gauss-Maxwell laws of these fields were obtained. The Ampère-Maxwell law is obtained only by taking into account the physical consistency of the matter-field interaction of the equality of the propagation field velocity with the maximum relativistic velocity c. For a quantum particle in the electromagnetic field, dynamic equations in the coordinate and momentum spaces and the particle and antiparticle wave functions were obtained. It was shown that the electromagnetic potentials as functions of the coordinates describing the matter distribution of the quantum particle do not alter this distribution – under the action of an electromagnetic a quantum particle moves as a whole. The scattering or tunneling rate in an electromagnetic field, for the two possible cases, with the spin conservation, or inversion, were obtained. This description of a quantum particle as a distribution of matter with a density amplitude/wavefunction of the form of a wave packet, with the time-dependent phase proportional to the relativistic Lagrangian as a function of the metric tensor including also the gravitational field, enables the application of this theory in quantum gravity and quantum field theory in agreement with general relativity.