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Internal structures of electrons and photons: The concept of extended particles revisited

Werner A. Hofer

Published Jan 1, 1998• 8 citations
OpenAlex

Abstract

The theoretical foundations of quantum mechanics and de Broglie–Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal structures of extended particles comply with a wave equation. Including external potentials yields the Schrödinger equation in this context, is arbitrary due to internal energy components. The statistical interpretation of wave functions in quantum theory as well as Heisenberg’s uncertainty relations are shown to be an expression of this, fundamental arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. Electrostatic interactions justify the initial assumption of electron–wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. The theory finally points out some fundamental difficulties for a fully covariant formulation of quantum electrodynamics, which seem to be related to the existing infinity problems in this field.

Related papers

Internal structures of electrons and photons and some consequences in relativistic physics

Werner A. Hofer

The theoretical foundations of quantum mechanics and de Broglie-Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal structures of particles comply with a wave-equation. Including external potentials yields the Schrodinger equation, which, in this context, is arbitrary due to internal energy components. The uncertainty relations are an expression of this, fundamental, arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. Electrostatic interactions justify the initial assumption of electron-wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. Aspect's experimental proof of non-locality is rejected, because these measurements imply a violation of the uncertainty relations. The paper finally points out some fundamental difficulties for a fully covariant formulation of quantum electrodynamics, which seem to be related to the existing infinity problems in this field.

arXiv:quant-ph/9707024•Jul 10, 1997•0 citations

Beyond Uncertainty: the internal structure of electrons and photons

Werner A. Hofer

The wave-structure of moving electrons is analyzed on a fundamental level by employing a modified de Broglie relation. Formalizing the wave-function $ψ$ in real notation yields internal energy components due to mass oscillations. The wave-features can then be referred to physical waves of discrete frequency $ν$ and the classical dispersion relation $λν= u $, complying with the classical wave equation. Including external potentials yields the Schrödinger equation, which, in this context, is arbitrary due to the internal energy components. It can be established that the uncertainty relations are an expression of this, fundamental, arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. The wave equations of intrinsic particle properties are Lorentz invariant considering total energy of particles, although transformations into a moving reference frame lead to an increase of intrinsic potentials. Interactions of photons and electrons are treated extensively, the results achieved are equivalent to the results in quantum theory. Electrostatic interactions provide, a posteriori, a justification for the initial assumption of electron-wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. The concept finally allows the conclusion that a significant correlation for a pair of spin particles in EPR--like measurements is likely to violate the uncertainty relations.

arXiv:quant-ph/9611009•Nov 7, 1996•6 citations

A realist view of the electron: recent advances and unsolved problems

Werner A. Hofer

In view of experimentally obtainable resolutions, equal to the Compton wavelength of an electron, the conventional interpretation of quantum mechanics no longer seems to provide a sufficiently subtle tool. Based on the intrinsic properties of extended particles we propose a new theory, which allows to describe fundamental processes with unlimited precision at the microlevel. It is shown how this framework combines classical electrodynamics and quantum mechanics in a single and consistent picture. An analysis of single measurement problems reveals that the theory is suitable to remove some of the most striking paradoxes in quantum mechanics, which are found to originate from obscuring statistical effects with physical reasoning. A possible origin of the infinity problems in relativistic quantum fields is found by analyzing electron accelerations due to photon absorption processes. The current state of the theory and existing problems are discussed briefly.

arXiv:quant-ph/9910036•Oct 8, 1999•3 citations

Uniting the wave and the particle in quantum mechanics

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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.

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We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the laboratory reference frame : an external wavefunction and an internal one. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The external wave spreads out in space over time. Mathematically, the Schrödinger equation converges to the Hamilton-Jacobi statistical equations when the Planck constant tends towards zero and the Newton trajectories are therefore approximations of the dBB trajectories. The internal wave function corresponds to the interpretation proposed by Edwin Schrödinger for whom the particle is extended. Then, the internal wave remains confined in space. Its converges, when h -> 0, to a Dirac distribution. Furthermore, we show that non-stationary solutions can exist such that the 3N-dimensional configuration space of the internal wave function can be rewritten as the product of N individual 3-dimensional internal wave functions.

arXiv:2305.19286•May 29, 2023•0 citations

Hamiltonian theory of wave and particle in quantum mechanics I. Liouville's theorem and the interpretation of the de Broglie-Bohm theory

Peter Holland

This paper and a following one develop a Hamiltonian formulation of the de Broglie-Bohm (deBB) interpretation of quantum mechanics. Drawing upon a unified Hamiltonian treatment of a classical particle and its associated ensemble, it is shown how the interaction of a particle and a spin-0 quantum wave can be consistently expressed in a canonical framework. A formulation is found in which the particle is acted upon by a force determined by the quantum potential but the particle does not react on the Schrodinger field. This requires the introduction of an additional field which the particle does act upon, and allows the deBB theory to be expressed in Hamiltonian terms. An ensemble theory for the wave-particle system based on Liouville's equation is developed, and it is shown that for a pure quantum state the particle obeys its own Liouville equation. The general particle phase space distribution that is compatible with ‖ψ‖ 2 is derived. A special case of this corresponds to the relation p = ∂S/∂q (and thus the guidance law of the deBB theory) but more general distributions, and hence non-deBB motions, are possible. This relation is interpreted as a constraint on the phase space of the composite system. Using the theory of Hamiltonian constraints it is shown that the first-order guidance law and Hamilton's second-order particle equations are dynamically equivalent.

Il Nuovo Cimento B•Sep 1, 2001•12 citations
The theoretical foundations of quantum mechanics and de Broglie–Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal structures of extended particles comply with a wave equation. Including external potentials yields the Schrödinger equation in this context, is arbitrary due to internal energy components. The statistical interpretation of wave functions in quantum theory as well as Heisenberg’s uncertainty relations are shown to be an expression of this, fundamental arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. Electrostatic interactions justify the initial assumption of electron–wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. The theory finally points out some fundamental difficulties for a fully covariant formulation of quantum electrodynamics, which seem to be related to the existing infinity problems in this field.
The theoretical foundations of quantum mechanics and de Broglie-Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal structures of particles comply with a wave-equation. Including external potentials yields the Schrodinger equation, which, in this context, is arbitrary due to internal energy components. The uncertainty relations are an expression of this, fundamental, arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. Electrostatic interactions justify the initial assumption of electron-wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. Aspect's experimental proof of non-locality is rejected, because these measurements imply a violation of the uncertainty relations. The paper finally points out some fundamental difficulties for a fully covariant formulation of quantum electrodynamics, which seem to be related to the existing infinity problems in this field.
The wave-structure of moving electrons is analyzed on a fundamental level by employing a modified de Broglie relation. Formalizing the wave-function ψψψ in real notation yields internal energy components due to mass oscillations. The wave-features can then be referred to physical waves of discrete frequency ννν and the classical dispersion relation $λν= u $, complying with the classical wave equation. Including external potentials yields the Schrödinger equation, which, in this context, is arbitrary due to the internal energy components. It can be established that the uncertainty relations are an expression of this, fundamental, arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. The wave equations of intrinsic particle properties are Lorentz invariant considering total energy of particles, although transformations into a moving reference frame lead to an increase of intrinsic potentials. Interactions of photons and electrons are treated extensively, the results achieved are equivalent to the results in quantum theory. Electrostatic interactions provide, a posteriori, a justification for the initial assumption of electron-wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. The concept finally allows the conclusion that a significant correlation for a pair of spin particles in EPR--like measurements is likely to violate the uncertainty relations.
In view of experimentally obtainable resolutions, equal to the Compton wavelength of an electron, the conventional interpretation of quantum mechanics no longer seems to provide a sufficiently subtle tool. Based on the intrinsic properties of extended particles we propose a new theory, which allows to describe fundamental processes with unlimited precision at the microlevel. It is shown how this framework combines classical electrodynamics and quantum mechanics in a single and consistent picture. An analysis of single measurement problems reveals that the theory is suitable to remove some of the most striking paradoxes in quantum mechanics, which are found to originate from obscuring statistical effects with physical reasoning. A possible origin of the infinity problems in relativistic quantum fields is found by analyzing electron accelerations due to photon absorption processes. The current state of the theory and existing problems are discussed briefly.
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.
We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the laboratory reference frame : an external wavefunction and an internal one. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The external wave spreads out in space over time. Mathematically, the Schrödinger equation converges to the Hamilton-Jacobi statistical equations when the Planck constant tends towards zero and the Newton trajectories are therefore approximations of the dBB trajectories. The internal wave function corresponds to the interpretation proposed by Edwin Schrödinger for whom the particle is extended. Then, the internal wave remains confined in space. Its converges, when h -> 0, to a Dirac distribution. Furthermore, we show that non-stationary solutions can exist such that the 3N-dimensional configuration space of the internal wave function can be rewritten as the product of N individual 3-dimensional internal wave functions.
This paper and a following one develop a Hamiltonian formulation of the de Broglie-Bohm (deBB) interpretation of quantum mechanics. Drawing upon a unified Hamiltonian treatment of a classical particle and its associated ensemble, it is shown how the interaction of a particle and a spin-0 quantum wave can be consistently expressed in a canonical framework. A formulation is found in which the particle is acted upon by a force determined by the quantum potential but the particle does not react on the Schrodinger field. This requires the introduction of an additional field which the particle does act upon, and allows the deBB theory to be expressed in Hamiltonian terms. An ensemble theory for the wave-particle system based on Liouville's equation is developed, and it is shown that for a pure quantum state the particle obeys its own Liouville equation. The general particle phase space distribution that is compatible with ‖ψ‖ 2 is derived. A special case of this corresponds to the relation p = ∂S/∂q (and thus the guidance law of the deBB theory) but more general distributions, and hence non-deBB motions, are possible. This relation is interpreted as a constraint on the phase space of the composite system. Using the theory of Hamiltonian constraints it is shown that the first-order guidance law and Hamilton's second-order particle equations are dynamically equivalent.