This study defines a neutron as a string with intrinsic vibrational states and numerically clarifies the mechanism by which classical mechanical laws of motion transition into quantum mechanical matter-wave states based on the Ehrenfest Theorem. By deriving the resonance phenomenon—where spatial energy gradients and temporal vibrational terms (cosωt) synchronize within a 3D potential distribution—into a final force equation (Equation 8), this research reinterprets the wave-like characteristics of particles in double-slit experiments as deterministic physical states driven by constructive interference, thereby completing the numerical connectivity between quantum and classical mechanics.
This study defines a neutron as a string with intrinsic vibrational states and numerically clarifies the mechanism by which classical mechanical laws of motion transition into quantum mechanical matter-wave states based on the Ehrenfest Theorem. By deriving the resonance phenomenon—where spatial energy gradients and temporal vibrational terms (cosωt) synchronize within a 3D potential distribution—into a final force equation (Equation 8), this research reinterprets the wave-like characteristics of particles in double-slit experiments as deterministic physical states driven by constructive interference, thereby completing the numerical connectivity between quantum and classical mechanics.
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.
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.
## AbstractA deterministic interpretation of the double-slit experiment is proposed, in which the electron is treated as a localized particle at all times. The observed interference pattern is attributed to a real physical energy wave in the electromagnetic field, generated by the electron's accelerated motion through the field. This energy wave reaches the slit barrier, where the slit geometry creates coherent waves that merge to form a constructive interference wave. This wave redistributes energy in the field, creating an Electron-EMF coupled pathway that guides the particle to the detector. The apparent randomness of individual impacts arises from incomplete knowledge of the initial conditions, not from intrinsic indeterminism. The measurement effect is modelled as a disturbance of the coherent energy waves, either preventing the formation of the coupled pathway or destroying it after formation. The model is extended to the quantum eraser experiment, where the restoration of coherence via a polarizer naturally explains the reappearance of interference. A further extension to the delayed-choice quantum eraser is proposed, introducing the Entangled Constructive Interference Wave (ECIW) as a physical mechanism for entanglement within the model. The mechanism is shown to apply across geometries beyond the double slit. Predictions include a correlation between landing position and flight time, offering a testable distinction from standard quantum mechanical interpretations. A preliminary, illustrative mathematical framework is provided, situating the model within the pilot-wave tradition. **Keywords: ** Double-slit experiment, pilot wave, electromagnetic field, quantum interpretation, determinism, hidden variables, measurement problem, energy wave, coupled pathway, quantum eraser, delayed-choice quantum eraser, entanglement.
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.
Abstract The double-slit experiment is a classic experiment that presents the clearest manifestation of wave-particle duality, one of the fundamental principles of quantum mechanics. The double-slit experiment still remains the phenomenon that demonstrates wave-particle duality at the most fundamental level. This phenomenon quantitatively and conceptually demonstrates that microscopic objects can behave like both waves and particles at the same time. This article provides an in-depth analysis of the physical nature of dualism, the mechanism of formation of the interference pattern, and the impact of the act of observation on the dynamics of quantum systems. The need for a new perspective on this topic is due to the fact that the current uncertainty in the interpretation of quantum reality has not yet been completely eliminated, and the boundaries between classical and quantum behavior in microscopic objects are still being explored. The results presented here restructure the deep mechanisms of the interference picture, more clearly frame the relationship between observation and wavefunction collapse, and provide a quantum. Since the article attempts to provide a complete answer to the mechanism of the formation of wave-particle duality, extensive space is given to sections such as historical development, theoretical models, modern research, etc. New approaches to this phenomenon have been developed using modern research and string theory. As a result, a new mathematical expression has been proposed that explains the reasons for the initial emergence of wave-particle duality, and is also important for string theory. The article explains the measurement problem with a more effective physical structure and ontological model.
Abstract In this work, the double-slit experiment is analyzed within the framework of Medium Theory SMT, where space-time is described as a nonlinear physical medium Φ. Instead of treating interference as a purely probabilistic quantum phenomenon, SMT interprets the observed pattern as the result of coherent phase dynamics and elastic deformations of the underlying medium. It is shown that propagating δΦ-perturbations naturally produce interference structures through phase coherence and nonlinear medium response, while localized particle-like configurations correspond to stable topological excitations of Φ. The emergence of the standard interference law follows directly from the medium dynamics without invoking wavefunction collapse or intrinsic randomness. The SMT description provides a unified physical mechanism for wave–particle duality, coherence loss, and pattern formation in the double-slit experiment, linking quantum behavior to deterministic field dynamics of the physical medium.