We propose a mathematical model for the double-slit experiment based on the block-alternating infinite products A(K,d) and B(K,d). The two products play strictly separated roles: B(K,d) encodes the background Minkowski spacetime (the stage), invariant under observation, while A(K,d) encodes the propagating matter wave (the actor), whose coherence parameter d acts as a phase switch. The coherence parameter d=1 corresponds to alternating phase (AC structure, full interference), while d=1/2 and d=infinity are algebraically identical and correspond to constant phase (DC structure, no interference). Observation---defined as physical interaction with a detector that makes path information available---transitions the observed path from d=1 to d=1/2. Unobserved paths remain at d=1 and continue to interfere. At the screen (K=1/2, the null boundary), A(1/2,d)=1 for all d, equalising the amplitudes. The interference pattern is then determined by d alone, yielding |psi|^2 = 4cos^2(pi*Delta/2) (unobserved) or |psi|^2 = 2 (observed). Combined with the envelope W[B] proportional to sinc^2(beta) arising from the Minkowski structure of B, the standard formula I proportional to sinc^2(beta)*cos^2(pi*Delta/2) is recovered as a mathematical consequence. The measurement problem is resolved algebraically: decoherence is not a collapse of the wave envelope but a transition of the phase parameter d within the A structure. The spacetime stage B is unaffected by the act of measurement.
We propose a mathematical model for the double-slit experiment based on the block-alternating infinite products A(K,d) and B(K,d). The two products play strictly separated roles: B(K,d) encodes the background Minkowski spacetime (the stage), invariant under observation, while A(K,d) encodes the propagating matter wave (the actor), whose coherence parameter d acts as a phase switch. The coherence parameter d=1 corresponds to alternating phase (AC structure, full interference), while d=1/2 and d=infinity are algebraically identical and correspond to constant phase (DC structure, no interference). Observation---defined as physical interaction with a detector that makes path information available---transitions the observed path from d=1 to d=1/2. Unobserved paths remain at d=1 and continue to interfere. At the screen (K=1/2, the null boundary), A(1/2,d)=1 for all d, equalising the amplitudes. The interference pattern is then determined by d alone, yielding |psi|^2 = 4cos^2(pi*Delta/2) (unobserved) or |psi|^2 = 2 (observed). Combined with the envelope W[B] proportional to sinc^2(beta) arising from the Minkowski structure of B, the standard formula I proportional to sinc^2(beta)cos^2(piDelta/2) is recovered as a mathematical consequence. The measurement problem is resolved algebraically: decoherence is not a collapse of the wave envelope but a transition of the phase parameter d within the A structure. The spacetime stage B is unaffected by the act of measurement.
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 manuscript presents a deterministic boundary-phase model of the double-slit experiment. In this framework, particles follow continuous, definite trajectories while interference arises from structured curvature induced by slit boundary microstructure. The wavefunction is treated as a mathematical representation of a real boundary-generated field rather than a physical matter wave.The model preserves established interference results while introducing a falsifiable experimental prediction: coherent fringe displacement scaling with engineered slit roughness. For a baseline electron configuration (100 eV beam energy, 1 m screen distance, 1 µm slit separation), a measurable 2 µm fringe shift requires a relative phase offset of approximately 0.10 radians, corresponding to the coupling condition β_eff(δ/r) ≈ 0.10.A quantitative δ-sweep prediction is provided along with explicit experimental control requirements necessary to distinguish coherent boundary-phase displacement from conventional scattering or electrostatic effects. If the predicted scaling is observed under controlled conditions, the double-slit paradox can be resolved deterministically without invoking intrinsic randomness or wavefunction collapse.This work is presented as a falsifiable experimental proposal in quantum foundations and electron interferometry.
This paper develops a fully empirical, physics-grounded reinterpretation of the double-slit experiment using the same flux-ledger framework established in Modules A–D of the Zero Infinity Research Program. By expressing quantum interference in terms of probability current density, boundary flux, and environmental decoherence, the work shows that the double-slit phenomenon requires no mysteries, hidden forces, or nonlocal metaphysics. Instead, the interference pattern emerges naturally from: Conservation of probability current, Phase-coherent flux across an open boundary, and Loss of coherence encoded as a measurable entropy-flux term Ψ∞. The analysis re-derives the standard results—interference fringes, collapse under measurement, and decoherence scaling—from first principles while embedding them within the broader conservation trilogy: Φ∞ (boundary energy flux) Ψ∞ (entropy/memory flux) Π∞ (momentum flux) This connects quantum optics to the same flux-driven framework used to model black hole mergers, spacecraft recoil, comet polarization curves, and organic spectral coherence in earlier modules. The paper also integrates cross-disciplinary results from decoherence theory, Bohmian mechanics, optical coherence tomography, and open quantum systems, showing how each maps cleanly onto a boundary-flux formalism. The result is a physically rigorous, mathematically transparent, and conceptually unifying explanation of the double-slit experiment—one that preserves standard quantum mechanics while clarifying how and where interference information is stored, exported, and erased. This work extends the Zero Infinity Program into quantum foundations, offering a synthesis of classical wave mechanics, quantum probability current, thermodynamic export, and information flow across system boundaries.
The double-slit experiment combines three observational facts: interference fringes in the coherent regime, position-resolved detections, and continuous fringe suppression under which-path resolution. Standard quantum mechanics accommodates all three through postulates without deriving them from deeper structure. This paper shows that the standard far-field interference law and the coherence-to-which-path transition follow as structural corollaries of results established in Quantum Mechanics as the Boundary Algebra of a Non-Invertible Projection (doi:10.5281/zenodo.19535588) and its companion (doi:10.5281/zenodo.19571321). Two results suffice for the algebraic derivation: the Born rule as the canonical quadratic measure on Im(Π), and the kernel spinor as the Hilbert quadrature of the boundary field. A third result — measurement irreversibility as a kinematic consequence of the projection geometry — belongs to the physical interpretation of measurement and temporal ordering within the same framework. The paper derives the Fraunhofer intensity law I(x) ∝ |Ψ₁ + Ψ₂|² and the detector-overlap formula with fringe visibility V = |γ|, within the standard Fraunhofer approximation and without additional postulates. It does not claim a first-principles derivation of the full boundary propagator or of single-event arrival statistics. A companion numerical simulation implements all three coherence regimes. A self-contained appendix summarises the three imported results in compact form.
The double-slit experiment is commonly interpreted as evidence that a single electron must be described by a spatially extended wavefunction whose path amplitudes interfere. Here, we present an alternative geometric formulation within the Bivector Standard Model, in which the observed far-field interference pattern is reproduced while the phase is attributed to an internal bivector clock carried by the electron. In this approach, each electron remains localized and produces a single detection event, while the familiar fringe pattern emerges statistically from the accumulation of many impacts. Interference arises from the comparison of clock phases associated with geometrically distinct paths, rather than from the superposition of spatial waves. The resulting probability distribution recovers the standard two-slit interference factor, the single-slit diffraction envelope, and the usual fringe-spacing relation in the Fraunhofer regime. The de Broglie wavelength emerges as the spatial manifestation of this transported phase. This formulation provides a geometric account of the origin of phase in single-electron interference, consistent with standard results while offering a distinct physical interpretation.
Abstract Since it was born before its physical achievements, light waves, which have almost no physical properties, are an abstract mathematical concept rather than an objective description. Confused by a set of dark and light streaks and a sketchy schematic that had little to do with the actual result, the double-slit test was misjudged as being caused by interfering light waves, so this plausible principle implied disastrous flaws. For example, (1) Just after passing through the double-slit device, the pattern is generated by light early or before interference. By changing the distance between the device and the screen, the pattern is only scaled synchronously without being reconstructed by interference, and imagined light-wave interference does not occur. (2) Interfering light waves can be subdivided into multiple parts and proliferate greatly. (3) A headless wave of light left outside the screen after the head disappears can still induce much interference. (4) There is no interference effect caused by reflected light waves. (5) The effect of polarization direction on interference is neglected, and the interference condition is incomplete. (6) In the mathematical model, not only are the spots with the highest brightness in the position where dark stripes should appear most, but the principle of generating multiple regular dark stripes cannot be found. (7) Since the quantum property must be carried out in the process of interference, if all conditions are not met at the same time, interference will not be triggered, and therefore, the principle of interference will be rejected. (8) Since light comes only from the radiation of the electron transition, it is impossible to generate a light source in a slit that may be a vacuum. (9) In the causality test, to verify the effect of collapse, the photon that has collapsed into a particle should be tested again with a double slit test. (10) Whether the phenomenon of "observed tampering results" obtained by observation has been tampered with. (11) When the phase is shifted π or the signal is reversed, waves become negative waves capable of annihilating themselves, which is typical of antimatter. In this case, matter and antimatter are conjoined. (12) If the general law of waves is followed, not only the targeted light wave passes through the slit. (13) The original version of the double-slit test cannot be reproduced, and the test results are different from those presented by contemporary technology. (14) Waves must obey Fourier's principle, but light waves, quantum waves and matter waves do not. (15) The modulation effect that waves must produce is not present in optical fiber communication. (16) If the light from different slits must interfere with each other, a mask full of slits will cause the lithographer to fail. (17) Since the size is much smaller than the wavelength, the photon is only a sampling of the light wave, but the corresponding physical properties are not presented. (18) The fact that the two stars orbiting each other do not change color only proves that the phenomenon of redshift is impossible but does not support the inference that the speed of light is constant. (19) The Michelson-Morley test process is not open and transparent enough, and pinhole diffraction and mechanical processing using broken lines instead of curves cannot be ruled out. (20) Kepler's law can block Hubble's law and its derivatives, dark matter and dark energy. In conclusion, Newton's particle model was wrong, but neither was the light wave theory.