This article proposes an interpretation of quantum physics based on the theory of solitons. According to this interpretation, the elementary particle (in particular, the electron) is a soliton solution of the system of nonlinear equations, while the linear equations of quantum mechanics for the wave functions represent the boundary conditions for soliton solutions. The nonlinear equations for the quantum electron are hypothesized to be the usual Maxwell equations in which the charge and current densities are expressed through quadratic combinations of the electromagnetic field strength. The complex wave function describing the motion of the electron in this case is the usual electromagnetic wave, where the real part is the electric field strength, and the imaginary part is the magnetic field strength. Soliton equations, Maxwell equations and quantum equations are easily written using 3+1 Pauli matrices, which indicates that the 3+1 system of coordinates of space and time is a natural realization of the particle-wave soliton world. The proposed interpretation allows combining both the Copenhagen interpretation and Bohm's theory of "hidden" variables.
This article proposes an interpretation of quantum physics based on the theory of solitons. According to this interpretation, the elementary particle (in particular, the electron) is a soliton solution of the system of nonlinear equations, while the linear equations of quantum mechanics for the wave functions represent the boundary conditions for soliton solutions. The nonlinear equations for the quantum electron are hypothesized to be the usual Maxwell equations in which the charge and current densities are expressed through quadratic combinations of the electromagnetic field strength. The complex wave function describing the motion of the electron in this case is the usual electromagnetic wave, where the real part is the electric field strength, and the imaginary part is the magnetic field strength. Soliton equations, Maxwell equations and quantum equations are easily written using 3+1 Pauli matrices, which indicates that the 3+1 system of coordinates of space and time is a natural realization of the particle-wave soliton world. The proposed interpretation allows combining both the Copenhagen interpretation and Bohm's theory of "hidden" variables.
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.
Essentially, we solve the particle-field equations obtained in the matter distribution quantum mechanics. In the framework of this theory, a particle is described by a density amplitude function, we call wave function, as a packet of waves with the time dependent phases proportional to the relativistic Lagrangian. The mass quantization of such a particle, as a distribution of matter, is obtained from the equality of the spatial integral of the density with the mass as a characteristic of the relativistic dynamics of this matter. The particle dynamics, as a motion of a mass spatial distribution, is obtained from the equality of the wave propagation velocities with the distribution coordinate velocities. This description is a physical one, compared to the Schrödinger-Heisenberg description leading to unphysical results as a null velocity for the kinetic energy as a constant of motion, or Zitterbewegung. The description of a particle interaction with an electromagnetic field by additional Lagrangian terms, with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and an electric potential conjugated to time, leads to the Lorentz force, and the Maxwell equations. In the two conjugated spaces, of the coordinates and of the momentum, the dynamics of a quantum particle is described by propagation operators, depending on the coordinate-momentum product, applied to time dependent wave functions satisfying matter-field equations. Unlike the standard Schrödinger or Schrödinger-Dirac equations, depending only on the Hamiltonian operator, instead of the Hamiltonian these equations contain the Lagrangian, which, besides the Hamiltonian, include additional terms with an explicit dependence on velocity, as it is expected in a relativistic theory. We obtain the wave function of a particle-antiparticle system interacting with an electromagnetic field, as a wave packet of spinors propagating in space with finite dimensions, given by the finite definition domain of the density function, in the space of the matter-field momentum, as a constant of motion. We show that an electrically charged quantum particle, rotating in a central electric field, generates a vector potential with a magnetic field perpendicular to the rotational plane and an electric field in this plane. By a quantum transition, a photon is emitted in the particle rotational plane, with the magnetic field perpendicular to this plane, and the electric field contained in this plane. In this framework, the vector potential rotation is correlated to a particle momentum rotation, for the canonical matter-field momentum as a constant of motion, without any electromagnetic field radiated outside.
Through studying we investigate the sense of the wave function of the mass and charge the density distributions of the quantum system. According to the protective calculation, a charged quantum system has effective distribution of mass and charging density in space, proportional to the square of the absolute value of its wave function. In a practical interpretation a wave function of the quantum system can be taken as a definition of either a physical field or the ergodic motion of a particle. The main distinction among the ergodic movement of a sphere and a cell lies in the concurrent property a sphere occurs simultaneously in space, while the agosic movement of a cell is spatially separated in time. If the wave function is a physical force, then the mass and charging density are simultaneously distributed in space to the charged quantum system and thus to the gravitational and electrostatic self-interactions of its wave function. This not only contradicts the superposition principle of quantum mechanics but also contradicts the findings of the experiments. Therefore, wave function is not a definition of a physical area, but rather a transient phase of a material.Each moment has a single localized particle with mass and charge, so the wave function is not auto-introduced. Therefore, it has been argued that the classical ergodic model may not correspond to quantum mechanics for determining constant motion of the particles. Based on the negative result, we say the wave function is a random and unsatisfactory explanation of the particles' quantum motion in nature.In this view, the square of the absolute value of the wave function not only gives the particles' potential in certain locations but also the potential where the cell is. The proposed Latest wave-function description offers a natural practical other than orthodox interpretation, and also suggests that the Broglie-Bohm theory and the interpretation of many worlds are incorrect, and the theories of dynamic collapse They are heading in the right direction by accepting collapse of wave function.
In the first part of this work (http://www.arxiv.org/abs/quant-ph/0509044), it was shown that the Klein-Gordon-Maxwell electrodynamics in the unitary gauge allows natural elimination of the particle wave function and describes independent evolution of the electromagnetic field. Therefore, the electromagnetic field can be regarded as the guiding field in the Bohm interpretation of quantum mechanics. An extension of those results to the Dirac-Maxwell electrodynamics was less general, but represented at least an interesting toy model of quantum theory. Another model based on the Dirac-Maxwell electrodynamics is considered in this work. The model also typically allows elimination of the wave function and describes independent evolution of the electromagnetic field.
A well-known mystery in quantum mechanics is wave–particle duality: Is an electron a point mass or a physical wave? What is the physical meaning of its wave function? About a hundred years ago, there was a famous debate between Bohr and Einstein on this topic. Their question is still open today. This paper reviews a new theoretical framework to address this problem. Here, it is hypothesized that both photons and electrons are quantized excitation waves of the vacuum, the physical properties of which can be modeled based on the Maxwell theory. Using the method of Helmholtz decomposition, one can show that the wave function of the particle is associated with an electric vector potential called “ Z”, which plays the role of basic field for the excitation wave. Using this framework, the quantum wave equations can be derived based on a quantization of the Maxwell theory. This work suggests that, the quantum wave function truly represents a physical wave; the wave packet looks like a “particle” only in the macroscopic view. Because the vacuum excitation obeys the principle of all-or-none, the probability of detecting this “particle” is related to the wave function as suggested in the Copenhagen interpretation.
An important milestone in quantum physics was reached by the publication of the Relativistic Quantum Mechanical Dirac Equation in 1928. However, the Dirac equation represents a 1-Dimensional quantum mechanical equation which is unable to describe the 4-Dimensional Physical Reality. 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 discussed. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time more than 200 years ago before the Dirac Equation had been published. Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics was in Harmony with Science and Religion. Newton found the concept of “Universal Equilibrium” which he mentioned 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 originated during the famous 5th Solvay Conference in 1927. During that period there were several circumstances that came together and made it possible to create a 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 well-known 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.