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.
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.
This paper reexamines the concept of phase in the description of light and electromagnetic waves, focusing on its physical meaning and role in theoretical formulations. Although phase is commonly treated as a physically meaningful quantity, particularly in explaining interference phenomena such as the double-slit experiment, this work argues that phase should instead be understood as a mathematical variable introduced for convenience in solving and expressing wave equations, rather than as a physical entity. Electromagnetic waves are fully described by the wave equation, and phase naturally appears as part of its mathematical solution. This paper clarifies that phase velocity can exceed the speed of light without violating causality, precisely because phase does not correspond to the propagation of energy or information. Misinterpreting phase as a physical motion leads to conceptual confusion about the nature of light. Furthermore, the paper explores an intuitive perspective in which light is regarded as a continuous information structure, and examines how this intuition aligns with formal mathematical descriptions. It is shown that interference and related wave phenomena can be explained without assigning physical reality to phase itself, relying solely on the properties of the wave equation. By separating mathematical description from physical ontology, this work aims to refine the conceptual understanding of light and to highlight how terminology and formalism influence our interpretation of physical phenomena.
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 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 The theoretical results of quantum mechanics (QM) have been verified by experiments, but the probabilistic Copenhagen interpretation is still controversial, and many counterintuitive phenomena are still difficult to understand. To trace the origin of probability in QM, we construct the amplitudes of a space-time position in a multiparticle quantum objective system and find that the probability in QM originates from the particle number distribution rate in a unit volume near position r at time t in the multiparticle quantum objective system. Based on the origin of probability, the quantization conditions of action and the principle of least action for an elementary particle (referred to as particle) , we find that when a particle moves in space-time, it periodically and alternately exhibit particle and wave state. We have derived the formula for the fringe positions in the double-slit experiment with particles, a new certainty relation and the uncertainty relation, obtain the localized and nonlocalized spatiotemporal range of the particle, the apparent trajectory of the particle motion. Based on this, through rigorous mathematical derivation and analysis, we propose new physical interpretations of the quantum superposition state, wave-particle duality, the double-slit experiment, the Heisenberg uncertainty principle, and the quantum tunnelling effect, and these interpretations are physically logical and not counterintuitive.
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.
Huygens' principle successfully describes the propagation of spherical transverse waves, but its image of secondary wavelet superposition has never explained the physical mechanism of directed rays. This paper argues that this historical omission is the root cause of why quantum mechanical interpretation has long been trapped in the dilemmas of "wave-particle duality" and "measurement collapse." We complete the missing half of Huygens' principle by proposing that the matter wave excited by a point particle source is, in its intrinsic form, not a diffuse spherical transverse wave, but a directed longitudinal ray vibrating along the particle's direction of motion. In this model, a single particle always moves along a definite trajectory, passes through one slit of a double-slit apparatus, and does not interfere with itself. The interference pattern on the screen is the statistical result of rays converging on the screen after collision-deflection events at the slit walls. Double-slit interference, single-slit diffraction, and delayed-choice experiments are all brought into a unified collision-deflection statistical description.