In the de Broglie-Bohm formulation of quantum theory, the quantum force exactly cancels the Coulomb attractive force in atomic \emph{s}-states. In this paper it is contended, based on energy conservation, that the force on a charge in a time-advanced electromagnetic field is of opposite sign to the Lorentz force due to the retarded field, and that such an advanced classical electromagnetic force accounts for part of Bohm's quantum force. If Coulomb attraction is negated, then some other mechanism must bind electrons to the nuclei of atoms. It is proposed magnetic interactions between relativistically-moving charges may account for atomic binding without assumption of a Coulomb potential. If charged spin-half particles always move luminally, as the Dirac theory implies, and so moving give rise to the intrinsic magnetic moment, then magnetic spin-spin interactions stronger than currently recognized are to be expected. Part of the magnetic interaction between equal-mass Dirac particles has been previously shown to be radial and inverse-square, of equal strength to Coulomb interaction, and sinusoidally modulated by interparticle separation with a spatial period equal the de Broglie wavelength. The Coulomb-like spin-spin interaction is further elaborated to show explicit correspondence with the de Broglie matter wave and Schrodinger wavefunction. It is proposed spin-spin interactions as expected according to this line of reasoning can properly account for the formation of atoms, if the electromagnetic interaction in atoms is classical and time symmetric, and if quarks and leptons are composed of more-fundamental spin-half particles.
In the de Broglie-Bohm formulation of quantum theory, the quantum force exactly cancels the Coulomb attractive force in atomic \emph{s}-states. In this paper it is contended, based on energy conservation, that the force on a charge in a time-advanced electromagnetic field is of opposite sign to the Lorentz force due to the retarded field, and that such an advanced classical electromagnetic force accounts for part of Bohm's quantum force. If Coulomb attraction is negated, then some other mechanism must bind electrons to the nuclei of atoms. It is proposed magnetic interactions between relativistically-moving charges may account for atomic binding without assumption of a Coulomb potential. If charged spin-half particles always move luminally, as the Dirac theory implies, and so moving give rise to the intrinsic magnetic moment, then magnetic spin-spin interactions stronger than currently recognized are to be expected. Part of the magnetic interaction between equal-mass Dirac particles has been previously shown to be radial and inverse-square, of equal strength to Coulomb interaction, and sinusoidally modulated by interparticle separation with a spatial period equal the de Broglie wavelength. The Coulomb-like spin-spin interaction is further elaborated to show explicit correspondence with the de Broglie matter wave and Schrodinger wavefunction. It is proposed spin-spin interactions as expected according to this line of reasoning can properly account for the formation of atoms, if the electromagnetic interaction in atoms is classical and time symmetric, and if quarks and leptons are composed of more-fundamental spin-half particles.
In the de Broglie - Bohm formulation of quantum mechanics, the electron is stationary in the ground state of the hydrogen atom, because the quantum force exactly cancels the Coulomb attraction of the electron to the proton. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the {\em Zitterbewegung} interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that non-relativistic relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.
It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schrödinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schrödinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schrodinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schrödinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schrödinger wavefunction.
Bohr ignored the electromagnetic interaction of moving charges in atoms and only considered Coulomb forces, thus encountering half frequency difficulties. This article considers the Lorentz force to make the classical Bohr model consistent with modern quantum theory, uses de Broglie's standing wave principle instead of Bohr's quantization assumption, derives the energy level formula for hydrogen atoms, and explains the radiation mechanism of hydrogen atomic spectra. The hydrogen atom in a spectral tube emits a photon wave train during one free path, and the wavelength of the photon is the eigen wavelength of its wave train. The head wavelength of the wave train is four thirds of its eigen wavelength, and the tail wavelength of the wave train is two-thirds of its eigen wavelength.
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.
Quantum mechanics differential equations are based on the de Broglie postulate. This paper presents the repercussions on quantum mechanics differential equations when the de Broglie wavelength is replaced by a relation between the radius and the relativistic energy of a particle. This relation results from a theoretical work about the interaction of charged particles, where the particles are modelled as focal points of rays of fundamental particles with longitudinal and transversal angular momentum. Interaction of subatomic particles is described as the interaction of the angular momenta of their fundamental particles. The relationship between the solution of the differential equation for a radial Coulomb field and the Correspondence Principle is presented. All four known forces are the result of electromagnetic interactions, so that only QED is required to describe them. The potential well of an atomic nucleus is shown with the regions that are responsible for the four type of interactions defined in quantum mechanics. Also the compatibility of the gravitation model derived in the theoretical work with quantum mechanics is shown, model where gravitation is the result of the reintegration of migrated electrons and positrons to their nuclei.
Abstract We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie–Bohm theory: its reliance on the quantum probability formula to justify the particle-guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author’s previous work, these problems are examined within an analytical framework by requiring that the wave–particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy, and momentum) with their Schrödinger counterparts. In conjunction with the condition of time-reversal covariance, this implies the de Broglie–Bohm law for the particle where the quantum potential mediates the wave–particle interaction (we also show how the time-reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite’s mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie–Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie’s objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled ‘double solution’ programme. A revised set of postulates for the de Broglie–Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system.