[Paper Review] Beyond Uncertainty: the internal structure of electrons and photons

Werner A. Hofer|ArXiv.org|Nov 7, 1996

Quantum Mechanics and Applications6 citations

TL;DR

This paper proposes a classical wave-based model of electrons and photons using a modified de Broglie relation, treating their wave functions in real notation to reveal internal energy components from mass oscillations. It derives the Schrödinger equation as a consequence of internal energy arbitrariness, shows that uncertainty relations arise from this fundamental indeterminacy, and establishes Lorentz-invariant wave equations equivalent to Maxwell’s equations, with predictions matching quantum theory for interactions and EPR-type correlations potentially violating uncertainty relations.

ABSTRACT

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.

Motivation & Objective

• To reframe the wave-particle duality of electrons and photons using a classical wave formalism based on real-valued wave functions.
• To explain the origin of quantum uncertainty as a consequence of internal energy components arising from mass oscillations.
• To unify the description of electrons and photons under a single formalism equivalent to Maxwell’s equations.
• To demonstrate that the Schrödinger equation emerges not from postulate but from internal energy arbitrariness in wave dynamics.
• To investigate whether EPR-type entanglement correlations could violate standard uncertainty relations under this model.

Proposed method

• Modifies the de Broglie relation to describe moving electrons as physical waves with discrete frequency ν and phase velocity u, satisfying λν = u.
• Represents the wave function ψ in real notation, revealing internal energy components due to periodic mass oscillations.
• Derives the Schrödinger equation as a consequence of these internal energy components, treating it as arbitrary rather than fundamental.
• Applies external potentials to the wave model, yielding the Schrödinger equation in a way that preserves Lorentz invariance when total energy is considered.
• Constructs a formalism for photons and electrons that is mathematically equivalent to Maxwell’s equations, enabling unified treatment of electromagnetic and matter waves.
• Analyzes interactions using this framework, showing agreement with established quantum theory results, including electrostatic stabilization of electron waves.

Experimental results

Research questions

• RQ1 Can the wave nature of electrons and photons be described by a classical, real-valued wave model with internal energy components from mass oscillations?
• RQ2 How does the uncertainty principle emerge from the internal structure of these waves rather than from fundamental indeterminacy?
• RQ3 To what extent can the Schrödinger equation be derived as a consequence of internal energy arbitrariness rather than as a postulate?
• RQ4 Can a unified formalism describe both electrons and photons in a way equivalent to Maxwell’s equations?
• RQ5 Do EPR-type correlations in this model imply violations of the standard uncertainty relations?

Key findings

• The uncertainty relations are shown to be a direct consequence of the fundamental arbitrariness in internal energy components within the wave model, not a fundamental limit.
• Electrons and photons are described by an identical formalism that yields equations equivalent to Maxwell’s equations, enabling a unified treatment of electromagnetic and matter waves.
• The Schrödinger equation arises naturally from the inclusion of external potentials and internal energy components, rather than being postulated.
• Electrostatic interactions provide a posteriori justification for electron wave stability, as intrinsic fields vanish in the ground state.
• The model predicts that spin-entangled particle pairs in EPR-type measurements may exhibit correlations that violate standard uncertainty relations.
• Lorentz invariance is preserved for total particle energy, though intrinsic potentials increase under frame transformations.