This study reconstructs the causal structure of the double-slit experiment bydistinguishing two particle families: light-family particles (photons) andmatter-family particles (electrons). Their internal time structures differ,with photons exhibiting Δτ = 0 due to directional excitation, while electronsexhibit Δτ ≠ 0 due to three-dimensional orbital emission. Time Density Mechanics (TDM) is introduced as a causal extension of quantummechanics. TDM preserves geometric and observational causal factors—such astrajectory orientation, occlusion, observer direction, viewpoint geometry, andfocal geometry Δf—that standard quantum mechanics does not include in itsstate representation ψ(x,t). This framework provides causal explanations for interference fringes, spinmeasurements, and quantum entanglement. In particular, entanglement correlationsare interpreted as viewpoint-geometry alignment rather than nonlocal action. TDM does not contradict quantum mechanics; instead, it complements it byrestoring causal structures that quantum mechanics abstracts away. This workoffers a unified causal model for optical and matter-wave interference.
This study reconstructs the causal structure of the double-slit experiment bydistinguishing two particle families: light-family particles (photons) andmatter-family particles (electrons). Their internal time structures differ,with photons exhibiting Δτ = 0 due to directional excitation, while electronsexhibit Δτ ≠ 0 due to three-dimensional orbital emission. Time Density Mechanics (TDM) is introduced as a causal extension of quantummechanics. TDM preserves geometric and observational causal factors—such astrajectory orientation, occlusion, observer direction, viewpoint geometry, andfocal geometry Δf—that standard quantum mechanics does not include in itsstate representation ψ(x,t). This framework provides causal explanations for interference fringes, spinmeasurements, and quantum entanglement. In particular, entanglement correlationsare interpreted as viewpoint-geometry alignment rather than nonlocal action. TDM does not contradict quantum mechanics; instead, it complements it byrestoring causal structures that quantum mechanics abstracts away. This workoffers a unified causal model for optical and matter-wave interference.
Building upon the unified 4D geometry of the Causal Smoothing Framework, this paper resolves three foundational paradoxes of quantum mechanics: wave-particle duality in the double-slit experiment, the measurement problem (wave function collapse), and the origin of particle-antiparticle asymmetry. By defining particles as time-like topological knots (ds² < 0) and quantum fields as the deterministic causal smoothing of vacuum momentum fluxes along the null boundary (ds² = 0), this framework discards probabilistic observer-driven collapse. The double-slit experiment is analyzed under two distinct boundary conditions (continuous emission and single-particle emission), demonstrating that quantum statistics are simply the macroscopic interference of vacuum geometry guiding discrete knots through a chaotic ER=EPR substrate. Furthermore, the framework provides a strict geometric proof for why fermions require distinct antiparticles while gauge bosons act as their own antiparticles, rooted entirely in the chiral phase of the localized metric shear.
This paper develops a phase-first reconstruction of quantum interference within standard quantum mechanics and wave optics. Its central idea is that interference patterns become conceptually clearer when the complex phase is treated as the organizing structure and probability or intensity density is treated as the visible statistical expression of that structure. The guiding principle is: the phase structures the pattern; the density renders it visible. The paper shows how this principle applies to single-slit diffraction, double-slit interference, Airy patterns, Fourier optics, Fresnel propagation, probability current, the Madelung representation, which-way marking, reduced coherence, and quantum eraser experiments. In each case, the observed density pattern is interpreted as the visible result of coherent phase relations among amplitudes. The reconstruction is strictly conservative. It does not modify quantum mechanics, the Born rule, unitary dynamics, or standard wave optics. It introduces no new postulates and makes no new empirical prediction. Its purpose is conceptual and pedagogical: to clarify the architecture of quantum interference by placing relative phase at the center of the analysis. This work is Part I of the series The Geometry of Phase. It establishes the phase-geometric foundation for later parts of the series, where the same perspective is extended to de Broglie matter waves, proper-time phase, relativistic action, and possible curvature-coupled phase extensions.
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.
The double-slit interference experiment serves as a fundamental experiment in quantum mechanics. Core theories including wave-particle duality, quantum superposition and measurement collapse are established on the basis of this phenomenon. The mainstream Copenhagen interpretation and Bohmian pilot-wave theory rely heavily on mathematical statistical fitting to interpret experimental outcomes, yet they fail to reveal the real physical evolution mechanism of photons at the microscale. Moreover, they inherently suffer from symmetry breaking, causal discontinuity and logical inconsistency. The symmetry-breaking analogy widely adopted in academic circles contains dimensional mismatch and conceptual substitution, representing a cognitive bias that places mathematical tools above physical mechanisms. Based on the symmetry principle of classical physics and the rule of continuous causal evolution, this paper systematically identifies the core defects of mainstream quantum interpretations and points out the paradigm limitation of quantum mechanics that prioritizes mathematical fitting over physical ontology. A spatial particle resonance propagation model is proposed. This model explains that photons are essentially the resonance manifestation of space particles. When resonance passes through double slits, the resonance body splits symmetrically, and then recombines after passing through the slits to form interference. Measurement will break the symmetry of resonance, resulting in the disappearance of interference fringes. This model maintains continuous causality and geometric symmetry, and provides a new physical mechanism explanation for quantum uncertainty and measurement effects in double-slit experiments.
This work presents a unified, interpretive account of quantum interference and delayed-choice experiments that applies equally to photons and massive particles. Rather than invoking spacetime trajectories, wave–particle duality, retrocausality, or collapse postulates, the paper locates quantum interference in the coherent evolution of internal, pre-geometric degrees of freedom defined over classical spacetime. Within this framework, “which-path” questions are not merely unanswered but fundamentally ill-posed: interference arises from global coherence of an internal field subject to experimental boundary conditions, while spacetime itself remains single-valued and classical at laboratory scales. The approach reproduces all standard quantum-mechanical predictions without modification and is explicitly interpretive rather than predictive. A central result is a unified explanation of why interference occurs across disparate physical systems—photons, electrons, atoms, and molecules—while decoherence manifests through system-dependent physical mechanisms. Photons and massive particles differ in how internal coherence is lost (e.g., electromagnetic absorption versus collisional and thermal interactions), but not in the underlying principle. Delayed-choice experiments are reinterpreted without paradox: changes to the apparatus modify boundary conditions for the internal field rather than retroactively altering particle histories. By removing spacetime paths from the fundamental ontology, the framework offers a consistent, path-free account of interference, decoherence, and localized detection that preserves the empirical success of quantum mechanics while clarifying its conceptual foundations.
This paper presents a URPD-based geometric reconstruction of the double-slit interference experiment. In this formulation, the electron does not behave as a wave or a particle; instead, the interference pattern emerges from geodesic overlap relations within the relational frame manifold CPN−1\mathbb{CP}^{N-1}CPN−1. The relative phase between the two paths arises from the Kähler geometry of the Fubini–Study metric, and the disappearance of interference under which-path measurement follows from displacement-constrained frame collapse. No wave–particle duality, hidden variables, or ad hoc collapse mechanisms are required. The double-slit paradox thus becomes a direct consequence of informational-geometric structure, fully consistent with the Born rule and relativistic causality.