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A classical model of a particle passing double slits

Peifeng Wang

Published May 5, 2019• 0 citations
Publisher

Abstract

A classical model is presented that, due to electric field, when a particle is passing double slits, a self induced force can arise so that the particle is impacted by both slits simultaneously to form concentration varying patterns. While this model may not precisely account for the interference fringes, it raises a question on the origin of the diffraction patterns and imposes restrictions on wave-particle duality.

DOI
10.22541/au.155703064.43562845

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A classical model is presented that, due to electric field, when a particle is passing double slits, a self induced force can arise so that the particle is impacted by both slits simultaneously to form concentration varying patterns. While this model may not precisely account for the interference fringes, it raises a question on the origin of the diffraction patterns and imposes restrictions on wave-particle duality.
The mainstream quantum mechanics uses “probability wave superposition and single-electron self-interference” to explain electron single-slit and double-slit diffraction. This theory deviates from the essential nature of real particle interactions and has fundamental logical flaws. The electron is a negatively charged real particle with a definite physical size and high-frequency transverse oscillation; a single real particle has no physical basis for self-interference. Abandoning the abstract probability wave hypothesis, this paper establishes a complete real-interaction model including electrostatic repulsion deflection, surface electron exchange, collision scattering, microscopic refraction, and barrier diffraction, based on the three-dimensional random transverse oscillation and charge repulsion of electrons. The model uniformly explains the real formation mechanism of electron single-slit diffraction and double-slit interference fringes. This paper proves that in single-electron sequential emission, each electron passes through only one slit; all bright and dark fringes are the statistical result of multiple microscopic interactions between electrons and slit walls or the central barrier. The disappearance of fringes under observation is caused by external disturbance to the inherent oscillation and wall-interaction equilibrium, not by wave function collapse. This paper further clarifies that whether an electron can pass through a slit is determined by its transverse oscillation amplitude, not by wavelength. Amplitude directly corresponds to slit width and is the core controlling variable of diffraction. Meanwhile, if no slit is placed, electrons flying directly to the screen produce no diffraction or interference fringes, proving that electrons themselves have no self-interference ability. Fringes are generated by slit structures, not by intrinsic wave interference of electrons. This study corrects the century-long misunderstanding of electron diffraction and establishes a new microscopic diffraction mechanism consistent with classical real-particle physics.
Numerical simulations of the double slit experiment with electrons, done by Al Rabeh, are repeated and improved. As well, the simulations go from moved Coulomb charges. These tests are extended with a proof of convergence for small time steps. Al Rabeh’s idea is fully confirmed: The pattern on the target comes from diffraction of charged particles, though it does not distinguish from interference pattern. In context with other results like that from Afshar, the wave-particle duality is disproved. The issue of photons is raised.
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.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
We present a hypothetical approach to the formation of double-slit interference fringes and their disappearance upon measurement within the unified field theory (UFT) previously proposed by the author, without assuming particle–wave duality. In the UFT, the force is given by F = −H ×M2/Mp, where H is the unified energy function. Between a photon and a slit wall, Hnon-self ̸= 0 and a finite non-equilibrium force arises. The deflection angle of the photon is θ = (y + z)MDc2 (r 2 − (y 2 + z 2)) FPl , where M = m − qme/e is the effective mass of the slit wall, y is the projected radius of the slit, z is the photon radius, D is a dimensionless coupling constant, and FPl is the Planck force. First, we estimate the value of D required for interference fringes to form under realistic slit parameters, obtaining D ≳ 1024. Second, we describe the mechanism by which the radial dispersion from the two slits overlaps to produce regions of high and low photon density, i.e., bright and dark fringes. Finally, we show that when a detector is placed at the slit, a new non-equilibrium force arises between the photon and the detector, disturbing the differential force from the left and right walls, so that the radial dispersion is disrupted and the interference pattern disappears. This is a deterministic picture that explains interference and measurement without invoking wave-function collapse or the complementarity principle. This paper presents a hypothesis and specifies experimental tests.