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Photonics

Quantum Origin of Circular Aperture Diffraction: A Velocity-Perpendicular Force Mechanism for Wave–Particle Interaction

C Liu

Published Jul 2, 2026• 0 citations
Publisher

Abstract

Starting from the circular aperture diffraction experiment, this paper decomposes the intrinsic interactions underlying wave–particle duality and proposes a specific interaction force: the velocity-perpendicular interaction force. We derive the characterization formula of this force and show that it can induce the phenomenon of circular aperture diffraction of light, with the theoretical results being highly consistent with those calculated by the Huygens–Fresnel principle. The direction of this force is perpendicular to the relative velocity, originating from the coupling effect between the wave nature of light and the particle nature of the circular aperture structure, and it satisfies a modified inverse square law of distance related to the relative velocity. When photons pass through different positions of the circular aperture, the symmetry effect generates a net interaction time. The product of the main component of this force, the net interaction time, and the radius of the circular aperture constitutes a modulation quantity (a ratio of the Planck’s constant), which exerts an on–off modulation effect on the interaction force, thereby inducing the emergence of annular diffraction fringes. This study provides a novel physical interpretation for the circular aperture diffraction of light from the perspective of interaction forces and clarifies the possible existence form of wave–matter interaction forces. This force formula is expected to effectively describe the behavior of microscopic particles, just like the Schrödinger equation, while providing a brand-new perspective on interactions. It holds great application prospects in fields such as single-photon manipulation and quantum precision measurement.

DOI
10.3390/photonics13070643

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Starting from the circular aperture diffraction experiment, this paper decomposes the intrinsic interactions underlying wave–particle duality and proposes a specific interaction force: the velocity-perpendicular interaction force. We derive the characterization formula of this force and show that it can induce the phenomenon of circular aperture diffraction of light, with the theoretical results being highly consistent with those calculated by the Huygens–Fresnel principle. The direction of this force is perpendicular to the relative velocity, originating from the coupling effect between the wave nature of light and the particle nature of the circular aperture structure, and it satisfies a modified inverse square law of distance related to the relative velocity. When photons pass through different positions of the circular aperture, the symmetry effect generates a net interaction time. The product of the main component of this force, the net interaction time, and the radius of the circular aperture constitutes a modulation quantity (a ratio of the Planck’s constant), which exerts an on–off modulation effect on the interaction force, thereby inducing the emergence of annular diffraction fringes. This study provides a novel physical interpretation for the circular aperture diffraction of light from the perspective of interaction forces and clarifies the possible existence form of wave–matter interaction forces. This force formula is expected to effectively describe the behavior of microscopic particles, just like the Schrödinger equation, while providing a brand-new perspective on interactions. It holds great application prospects in fields such as single-photon manipulation and quantum precision measurement.
ABSTRACT In this study, we propose a formula to characterize the mechanical properties of microscopic particles from the particle‐wave interaction perspective, defining the corresponding interaction as a velocity‐perpendicular interaction force. Traditional single‐slit diffraction is mainly explained by wave theory and the Huygens–Fresnel principle. However, the single‐photon momentum recoil in diffraction suggests that it is feasible to decouple the particle and wave natures of both photons and the slit, thereby exploring the interaction force between them in depth. We find that photons at different positions inside the slit experience velocity‐perpendicular interaction force, leading to net interaction time differences related to their distances to the slit edges. Based on wave‐particle duality, the modulation quantity formed by the interaction force, net interaction time, slit scale, and Planck constant exerts an on‐off modulation effect. Within this model, photons form clear diffraction fringes, which are rigorously verified to be fully consistent with the Huygens–Fresnel principle. This work provides a dynamical reinterpretation of single‐slit diffraction and establishes a mechanical framework for quantitatively describing quantum phenomena involving particle‐wave interaction.
Since the establishment of modern optics, the physical nature of light has been debated for centuries, which finally led to the mainstream theory of waveparticle duality. This theory holds that photons intrinsically possess both particle and wave properties, and it is adopted to interpret diverse optical phenomena including rectilinear propagation, polarization, interference and diffraction, forming the fundamental framework of modern quantum optics. Nevertheless, the theory of waveparticle duality contains inherent logical defects. Its essential flaw lies in confusing two completely distinct physical concepts: the intrinsic properties of a substance itself and the morphological features of its motion trajectory. Conventional theories mistake the apparent waveshaped trajectory produced by particle motion for the intrinsic wave property of microparticles, resulting in persistent conceptual ambiguity, missing physical mechanisms and logical inconsistencies within microoptics. This paper constructs an optical underlying model from a purely particle perspective to clarify the real mechanism behind waveparticle phenomena of light. A photon is an indivisible, nonspreading, nontrailing pointlike physical particle with no intrinsic wave property. While propagating, a photon travels along a fixed straightline direction and undergoes inherent transverse oscillation within the plane perpendicular to its propagation direction. At the moment of its generation, a photon uniquely fixes its transverse oscillation angle, amplitude and frequency within the 360degree plane perpendicular to its travelling direction. Once determined, these parameters remain constant throughout propagation without random shifts or arbitrary changes. Superposition of the photon’s longitudinal rectilinear motion and fixedangle transverse oscillation generates a standard sinusoidal trajectory. Consequently, all wavelike features observed in optics are geometric apparent effects originating from particle motion trajectories, rather than material properties intrinsic to photons. Based on this model, this paper reinterprets the core physical mechanism behind doubleslit interference. Contrary to the traditional explanation of photon selfinterference or wavefield superposition, interference fringes arise from microscopic mechanical interactions between transverselyoscillating photons and slit walls when photons pass through the slits. Such interactions regularly deflect photon flight angles. After being deflected and filtered by slits, large numbers of photons form uneven statistical distributions on the receiving plane and produce macroscopically observable lightanddark fringes. This paper also defines the threshold for photonphoton interactions. Ordinaryenergy photons such as visiblelight, infrared and ultraviolet photons do not interact, collide or exchange energy with one another in free space. Only gammaraylevel highenergy photons may collide, undergo energy annihilation, and convert into material particles such as electronpositron pairs. Relying entirely on classical mechanical superposition principles and discarding the contradictory hypothesis of waveparticle duality, the proposed purelyparticle model provides selfconsistent explanations for core classical optical phenomena and achieves analytical revision for the underlying logic of optical waveparticle phenomena.
To address the theoretical gap in traditional de Broglie wave theory that fails to clarify the physical excitation mechanism of matter waves, this paper proposes the de Broglie Wave-Virtual Photon Exchange Synchronization Law and reveals the intrinsic physical origin of de Broglie matter waves from the perspective of virtual photon exchange. Based on well-recognized physical formulas including the de Broglie energy-frequency relation, the relativistic energy-momentum relation, and the core equations of quantum electrodynamics (QED), this paper carries out rigorous quantitative derivation and obtains the de Broglie Wave-Virtual Photon Exchange Synchronization Formula , which describes the relation between virtual photon exchange and the evolution of de Broglie waves. Physical analysis of the formula shows that the de Broglie matter wave is not an intrinsic and spontaneous property of particles, but a dynamic wave effect directly excited by momentum exchange between virtual photons and particles in electromagnetic interaction. The frequency, wavelength, and wave properties of the de Broglie wave are uniquely determined by the intensity and frequency of virtual photon exchange, and the two sets of physical quantities maintain strict synchronization during physical evolution. In addition, this paper clarifies the velocity-dependent modulation effect of virtual photon exchange on de Broglie waves: the modulation effect is weak at low velocities, becomes significant at high velocities, and the key wave parameters (frequency, momentum correlation) of de Broglie waves and virtual photons achieve quantitative unification as the particle velocity approaches the speed of light. This theory establishes a rigorous, quantitative, and unified relation between the virtual photon exchange mechanism and the origin of de Broglie waves, improves the physical interpretation of matter wave origin, and provides a new theoretical perspective for the study of wave-particle duality and electromagnetic interaction of microscopic particles.
The wavelet envisioned by Huygen's in diffraction phenomenon is re-interpreted as being polarized after passing through slit/hole which removed the electric field component from the Electromagnetic Radiation (EM-R), the remained wave consist of the Circular Magnetic Field (CMF), this CMF lost the speed of light and the electric field, hence it's a short distance travel field, originated from the CMF produced by accelerated electrons, integrated with the Electric Field (EF) during the Flip-Flop (F-F) mechanism producing EM-R; hence the passing of light through a single hole/slit resulted in a CMF which reproduced as rings on the monitor screen in single wave diffraction, while the interference of two such CMF in double slits experiment, produced constructive or destructive interference forming patches on the monitor screen; and the perceived electron diffraction is an enter of two CMF from a single electron into a slit then emerged to produce constructive or destructive interference, in addition to the electron which entered and emerged from the slit with the stronger CMF, the paper finally derived the origin of Planck 'constant (h) for the second time; the logical interpretation of double slits diffraction will restore the common sense in the physical world, distorted by the pilot wave.
Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.