Standard quantum theory provides a probabilistic framework for elementary particles, and it is widely held that the underlying physical mechanisms are inherently non-classical. Here, we present a classical electrodynamic analogue model where particles are treated as tightly bound composites of oscillating charge distributions, establishing a classical analogy to pilot-wave-like dynamics. These internal oscillations transform the particle into a Hertzian dipole that emits high-frequency electromagnetic waves, which are reflected by the environmental boundaries back onto the source. We derive the resulting ponderomotive fields symbolically, providing a closed-form analytical expression for the self-force and its deterministic effect on the particle’s trajectory. By means of Monte Carlo simulations, we demonstrate that the interaction of individual particles with their own reflected wave fields in atomic configurations emulates interference and diffraction patterns reminiscent of double-slit experiments. This hybrid analytical-numerical framework recovers a trajectory-based behavior that shares qualitative features with de Broglie’s double-solution theory. While not a replacement for standard quantum mechanics, our findings explore the potential of high-frequency classical electrodynamics to emulate phenomena such as wave-particle duality and statistical uncertainty through purely deterministic matter-field interactions.
Standard quantum theory provides a probabilistic framework for elementary particles, and it is widely held that the underlying physical mechanisms are inherently non-classical. Here, we present a classical electrodynamic analogue model where particles are treated as tightly bound composites of oscillating charge distributions, establishing a classical analogy to pilot-wave-like dynamics. These internal oscillations transform the particle into a Hertzian dipole that emits high-frequency electromagnetic waves, which are reflected by the environmental boundaries back onto the source. We derive the resulting ponderomotive fields symbolically, providing a closed-form analytical expression for the self-force and its deterministic effect on the particle’s trajectory. By means of Monte Carlo simulations, we demonstrate that the interaction of individual particles with their own reflected wave fields in atomic configurations emulates interference and diffraction patterns reminiscent of double-slit experiments. This hybrid analytical-numerical framework recovers a trajectory-based behavior that shares qualitative features with de Broglie’s double-solution theory. While not a replacement for standard quantum mechanics, our findings explore the potential of high-frequency classical electrodynamics to emulate phenomena such as wave-particle duality and statistical uncertainty through purely deterministic matter-field interactions.
The deterministic origin of quantum mechanics remains one of the most enduring challenges in modern physics. While standard quantum theory provides a probabilistic framework for elementary particles, its underlying physical mechanism is often considered non-classical. Here we show that central features of quantum phenomena can emerge from a classical electrodynamic model where particles are treated as tightly bound composites of oscillating charge distributions. These internal oscillations transform the particle into a Hertzian dipole that emits high-frequency, coherent, classical electromagnetic waves. We demonstrate that these waves, when reflected by surrounding matter, generate ponderomotive fields that act back on the particle’s trajectory. Our simulations of electron trajectories in atomic configurations reproduce the interference and diffraction patterns characteristic of double-slit experiments, realizing a pilot-wave-like dynamics reminiscent of de Broglie’s double-solution theory. These findings suggest that wave-particle duality, the measurement problem, and the uncertainty principle may not be irreducible quantum axioms, but rather emergent properties of deterministic, classical interactions between matter and high-frequency electromagnetic fields.
This article investigates the consequences of assuming that elementary particles, such as electrons, are internally composed of two very large charge distributions that almost completely neutralize each other externally and can be displaced relative to one another over a distance on the order of the Planck length. Owing to this internal structure, elementary particles would be excited into oscillation during acceleration in a particle accelerator and would therefore emit very weak but extremely high-frequency, coherent, classical electromagnetic waves. In the immediate vicinity of atoms, these waves would be reflected and subsequently act back on the electron in the form of classical forces. This feedback is analyzed in detail. Starting from the electromagnetic field of a Hertzian dipole, a formalism is derived that enables the calculation of the ponderomotive field exerted on the electron by its environment. The physical implications of this mechanism are then studied using numerical simulations. The obtained results are consistent with those of real diffraction and interference experiments with electrons. These findings suggest that, contrary to the prevailing view, key aspects of quantum mechanics-such as wave-particle duality, the measurement problem, and the uncertainty principle-may be explicable within a classical framework.
A Hertzian dipole is a small antenna that emits radio waves. In this article, the interaction of a Hertzian dipole with the field reflected from the environment is analyzed. The study shows that a single Hertzian dipole can behave like a quantum object: in particular, it can interfere with itself at a double slit, owing to a ponderomotive force. Therefore, it cannot reach every location behind a double slit with the same probability, and the probability distribution for the location of an impact on a screen behind the double slit may show a clear interference pattern. This effect disappears if one of the slits is closed, or if the system of the Hertzian dipole, double slit and standing wave is disturbed by external influences. Both particle interference and the collapse of the wave function are considered to be effects that cannot be explained by classical physics. However, Hertzian dipoles can be tangible objects moving on classical trajectories, and their location and velocity can be measured simultaneously at any time. Thus, the Hertzian dipole provides an example of how central features of quantum mechanics can be explained by means of classical physics.
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.
A Hertzian dipole is a mathematical model of a small antenna that emits radio waves. In this article, the interaction of a Hertzian dipole with the field reflected from the environment is analyzed. The study shows that a single Hertzian dipole can behave like a quantum object: in particular, it can interfere with itself at a double slit, owing to a ponderomotive force. Therefore, it cannot reach every location behind a double slit with the same probability, and the probability distribution for the location of an impact on a screen behind the double slit may show a clear interference pattern. This effect disappears if one of the slits is closed, or if the system of the Hertzian dipole, double slit and standing wave is disturbed by external influences. Both particle interference and the collapse of the wave function are considered to be effects that cannot be explained by classical physics. However, Hertzian dipoles can be tangible objects moving on classical trajectories, and their location and velocity can be measured simultaneously at any time. Thus, the Hertzian dipole provides a macroscopic example of how central features of quantum mechanics can be explained in a deterministic manner. This new finding is important for several scientific disciplines, especially chemistry, materials science, electrical engineering, computer science, physics and philosophy.
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.