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Applied Physics Research

A Dynamical Origin of Wave-Particle Duality From Stochastic Mass-Energy Interconversion

Rudolph Elliot Willis

Published Apr 8, 2026• 0 citations
Publisher

Abstract

Wave-particle duality remains one of the most striking and conceptually unresolved features of quantum mechanics. Here I present a dynamical mechanism for wave-particle duality based on spontaneous stochastic mass-energy interconversion at subatomic scales. By promoting particle mass to a fluctuating quantity consistent with Einstein’s mass-energy equivalence, I derive a Schrödinger equation with an additional stochastic kinetic-phase term. Applied to the canonical double-slit experiment, the framework shows that quantum interference arises from coherent, path-dependent phase accumulation driven by mass-energy fluctuations, while particle-like localization emerges naturally at detection. The formalism yields closed-form expressions for interference visibility, predicts a momentum- and mass-dependent decoherence rate, admits a path-integral interpretation, and enables direct experimental bounds using neutron, electron, and atom interferometry. The results provide a physically grounded account of wave-particle duality without modifying the axioms of quantum mechanics.

DOI
10.5539/apr.v18n1p67

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Wave-particle duality remains one of the most striking and conceptually unresolved features of quantum mechanics. Here I present a dynamical mechanism for wave-particle duality based on spontaneous stochastic mass-energy interconversion at subatomic scales. By promoting particle mass to a fluctuating quantity consistent with Einstein’s mass-energy equivalence, I derive a Schrödinger equation with an additional stochastic kinetic-phase term. Applied to the canonical double-slit experiment, the framework shows that quantum interference arises from coherent, path-dependent phase accumulation driven by mass-energy fluctuations, while particle-like localization emerges naturally at detection. The formalism yields closed-form expressions for interference visibility, predicts a momentum- and mass-dependent decoherence rate, admits a path-integral interpretation, and enables direct experimental bounds using neutron, electron, and atom interferometry. The results provide a physically grounded account of wave-particle duality without modifying the axioms of quantum mechanics.
Abstract Quantum interference is often seen as a manifestation of intrinsic wave–particle duality, invoking self-interference and wavefunction superposition. We propose an alternative causal framework where interference arises from interactions between a classical electron and a quantized electromagnetic field. Electrons follow definite, localized trajectories and yield discrete detection events. The wave-like interference pattern emerges statistically from stochastic, nonlocal momentum transfers mediated by quantized field modes. Simulations of double-slit experiments show that dot-like fringes arise without wavefunction collapse or intrinsic wave behavior. Doubling the electron mass narrows fringe spacing in line with de Broglie scaling, suggesting the effective wavelength results dynamically from field coupling, not as an inherent particle trait. This interpretation preserves classical realism while reproducing quantum interference as an emergent, ensemble-level phenomenon. It provides a deterministic account grounded in structured field interactions. In this view, wave–particle duality of electrons reflects the wave nature of photons—the massless U(1) gauge bosons mediating the field—rather than being a fundamental property of matter.
Quantum interference is traditionally interpreted as evidence of intrinsic wave–particle duality, invoking self-interference and wavefunction superposition. Here, we propose an alternative causal framework in which interference arises from interactions between a classical electron and a quantized electromagnetic field. In this picture, electrons follow definite, localized trajectories and produce discrete detection events, while the observed interference pattern emerges statistically from stochastic, nonlocal momentum transfers mediated by quantized field modes. Numerical simulations of the double-slit experiment show that dot-like interference fringes arise without invoking wavefunction collapse or intrinsic matter waves. Doubling the electron mass narrows the fringe spacing in agreement with de Broglie scaling, indicating that the effective wavelength emerges dynamically from particle–field coupling rather than representing an inherent property of the particle. The formulation is based on a rigorously defined Hamiltonian and derived equations describing electromagnetic coupling between particles and the slit environment. Although neutral particles such as neutrons or atoms carry no net charge monopoles, they possess electric or magnetic dipole and higher multipole moments that enable electromagnetic interactions with the slit apparatus, allowing discrete momentum transfer through the quantized field. Our simulations show that interference fringes arise from intermittent singleparticle detection events caused by stochastic momentum impulses from quantized electromagnetic modes. These results suggest a reinterpretation of wave–particle duality: the apparent wave-like behavior of matter may arise from interaction with the inherently wave-like quantized electromagnetic field—whose quanta are photons, the massless U(1)-gauge bosons—rather than from an intrinsic wave nature of the particles themselves. Our analysis is rigorous and is not speculative, because the proposed Hamiltonian for this system is physical. Within this nonlocal hidden-variable framework, the dot-like interference pattern observed in the double-slit experiment emerges from individual electrons traversing one slit at a time while receiving discrete momentum impulses from stochastic, spatially extended quantized electromagnetic fields.
This work extends the previous one-dimensional formulation of the double-slit problem to a two-dimensional framework within the Schrödinger equation, providing a more realistic representation of the physical configuration. The wavefunction is constructed through a spectral decomposition in terms of eigenstates, with a Gaussian distribution of initial energies. The temporal evolution of the system is explicitly analyzed, showing how interference patterns develop as a function of propagation time. In particular, the passage of electrons at different times is simulated, highlighting the progressive formation of fringes. A stochastic reconstruction of detection events is then introduced for the case of neutron beams, using physically realistic parameters, reproducing the emergence of the interference pattern from discrete particle-like impacts. The results show that both interference and particle-like behavior arise directly from the intrinsic mathematical structure of quantum mechanics, with no need for additional interpretative assumptions.
Wave-particle duality is widely regarded as one of the conceptual pillars of modern quantum theory, providing the framework through which the behavior of microscopic matter can be consistently interpreted. According to this principle, microscopic entities such as electrons, photons, atoms and even complex molecules exhibit both wave-like and particle-like properties depending on the experimental configuration used to observe them. This duality is quantitatively formalized through the De Broglie relation, which associates a wavelength with any particle possessing momentum. The present work provides a comprehensive theoretical analysis of the physical and mathematical foundations of wave-particle duality, focusing particularly on the De Broglie wavelength and the kinetic energy of the electron in both non-relativistic and relativistic regimes. The connection between the De Broglie hypothesis and Schrödinger’s equation is discussed in detail, highlighting the role of the kinetic energy operator and the interpretation of matter waves in terms of quantum wave packets. Experimental evidence supporting the wave nature of matter, including electron diffraction experiments and interferometry techniques, is also reviewed. Beyond their conceptual importance, these principles underpin several modern technologies, including electron microscopy, nanoscale semiconductor devices and quantum metrology. The analysis demonstrates that the De Broglie relation provides a unifying framework connecting momentum, wavelength and kinetic energy, thereby forming a fundamental bridge between classical mechanics, quantum theory and modern technological applications.
This paper revisits the wave equation originally suggested by Einstein and examines the possibility that it constitutes a complete description of particle motion without requiring a fundamental probabilistic interpretation. It proposes that intrinsic physical fluctuations of particles can account for phenomena typically attributed to quantization and superposition. The double-slit experiment is reinterpreted from this perspective, suggesting that interference patterns may arise naturally from particle fluctuations interacting with boundary conditions. This work offers a conceptual reevaluation of wave–particle duality and discusses whether quantization should be regarded as a necessary fundamental principle or as a posteriori interpretation.
Electron wave–particle duality has remained one of the long-standing conceptual problems in quantum physics. While conventional interpretations successfully describe experimental outcomes, they do not provide a clear physical cause for the transition between wave-like and particle-like behavior. This work presents a causal explanation of electron duality based on the SAN Delta-E Principle, which identifies energy imbalance as the root of physical action. In this framework, the electron is interpreted as a condensed energy packet with finite rest mass, whereas the photon represents pure energy without rest mass. Wave behavior emerges when the electron propagates under undisturbed Delta-E conditions, while particle behavior arises when interaction introduces additional energy, creating a Delta-E disturbance that forces localization. Wave function collapse is therefore explained as a physical energy-density interaction effect, rather than an observer-dependent or purely probabilistic phenomenon. By distinguishing energy condensation states and interaction-driven Delta-E imbalance, this work provides a unified, non-mystical interpretation of electron duality and offers a clear physical origin for behaviors observed in double-slit and related quantum experiments.