DUPLICATE RECORD (18 October 2026). This record is a duplicate upload of The Double-Slit Experiment on a Discrete Holographic Lattice. Please cite 10.5281/zenodo.18793387 instead. That record — the maintained version of the same simulation — is kept, with a status note. Original description (kept for the record): We show that exact unitary propagation of an electron wavepacket on a fi- nite 4.8.8 lattice reproduces single-slit and double-slit diffraction patterns in close quantitative agreement with experiment, with no continuum approxima- tion. When environmental coupling is introduced at the slit, interference is destroyed and Born rule statistics emerge from decoherence alone. Using the deterministic kinematics of the circlette lattice, we demonstrate that wave- function collapse need not be postulated. The transition from quantum inter- ference to classical probability distributions emerges naturally from unitary evolution through the deterministic tracing-out of environmental degrees of freedom. The lattice addresses the apparent measurement problem through finite bandwidth and orthogonal geometry, requiring no conscious observer. This is the third paper in a series developing the Holographic Circlette frame- work, but remains mathematically self-contained.
DUPLICATE RECORD (18 October 2026). This record is a duplicate upload of The Double-Slit Experiment on a Discrete Holographic Lattice. Please cite 10.5281/zenodo.18793387 instead. That record — the maintained version of the same simulation — is kept, with a status note. Original description (kept for the record): We show that exact unitary propagation of an electron wavepacket on a fi- nite 4.8.8 lattice reproduces single-slit and double-slit diffraction patterns in close quantitative agreement with experiment, with no continuum approxima- tion. When environmental coupling is introduced at the slit, interference is destroyed and Born rule statistics emerge from decoherence alone. Using the deterministic kinematics of the circlette lattice, we demonstrate that wave- function collapse need not be postulated. The transition from quantum inter- ference to classical probability distributions emerges naturally from unitary evolution through the deterministic tracing-out of environmental degrees of freedom. The lattice addresses the apparent measurement problem through finite bandwidth and orthogonal geometry, requiring no conscious observer. This is the third paper in a series developing the Holographic Circlette frame- work, but remains mathematically self-contained.
Abstract: We present a computational demonstration of the Zeno Threshold (Zα) on the paradigmatic double-slit experiment. A Gaussian wave packet is propagated on a 256×128 tight-binding lattice using only two ingredients: graph topology (nearest-neighbor hopping) and unitarity (U = e-iHΔt, with the imaginary unit i forced by information conservation). No wave equation is assumed; interference fringes emerge as a strict consequence of lattice unitarity. We then introduce a which-path detector modeled as a tensor-product qubit that entangles with the particle at the slits. The entanglement entropy of the reduced detector state grows from zero toward Smax = ln 2 ≈ 0.693 nats. At the moment this entropy exceeds the observer's finite Zeno Threshold Zα, the observer's rendering engine is forced to perform Born Rule truncation—algorithmic garbage collection—erasing the off-diagonal coherence terms. The interference pattern is destroyed, leaving two classical bumps. Computational Verification Highlights: Emergent Interference: Fringes emerge strictly from discrete graph topology and unitarity, without assuming continuous wave equations. Forced Complex Phases: The complex unit i is mathematically forced by probability conservation (unitarity). The Z-Scale Breach: Which-path detection creates real entanglement entropy that breaches the observer's finite processing limit. Born Rule Garbage Collection: Truncation at the Z-Scale breach produces a detection pattern identical to the classical, incoherent sum |ψ1|2 + |ψ2|2. The full Python verification script and simulation code are available at github.com/srdrymn/atr-double-slit-simulation.
### Version 10 Release Note (Canonical Physical Realization — September 2026)This updated version provides the complete physical realization of the Causal Bridge Operator for quantum interference. Key evolutionary updates include:1. Grounding wave phase evolution in standard paraxial Fresnel wave optics with zero free parameters for spatial fringe spacing (Delta_x = lambda_dB * D / d);2. Binding exposure duration to the physical particle transit time inside the apparatus (tau_on = D / v_particle);3. Decomposing the non-Markovian memory kernel into a dual-layer architecture (K_eff = K_struct x K_thermal) that resolves the thermal decoherence confounder;4. Direct cross-validation against real experimental data: Zeilinger et al. (1988) cold neutron interferometry (reproducing 73.0 um fringe spacing with 0.106% error and calibrating V = 0.583 with lambda_struct = 31.11 s^-1, in agreement with independent decoherence analyses by Sanz et al. 2003) and direct transfer to Jonsson (1961) electrons;5. Rigorous satisfaction of the third-order Sorkin parameter (kappa = 0, error < 10^-15), strictly respecting Born rule bounds;6. Complete typographic overhaul of the manuscript in clean two-column academic LaTeX, eliminating table pagination overflow artifacts. --- ### AbstractStandard quantum mechanics treats wavefunction collapse as a fundamental, non-unitary event and models detection statistics strictly as a function of the instantaneous state vector, independent of the operational history of the apparatus. Here, we present a physical realization of the Causal Bridge Operator, B(H) = exp(i * Gamma(H) / hbar_Omega), anchored upon a non-Markovian memory functional Gamma(H) and standard Fresnel wave propagation. We demonstrate:(i) that B forms an exact homomorphism from the non-commutative history monoid to U(1);(ii) that the fringe spacing Delta_x = lambda_dB * D / d is governed by classical Fresnel wave optics with ZERO free parameters;(iii) that historical memory acts exclusively on the cross-term spatial degree of coherence (fringe visibility), resolving the thermal confounder through a dual-layer decomposition K_eff = K_struct(tau_on) x K_thermal(tau_on, tau_pause);(iv) that the intrinsic exposure time is rigorously bound to the physical flight time tau_on = D / v_particle; and(v) that the formulation identically satisfies the third-order Sorkin parameter (kappa = 0, error < 10^-15), strictly respecting Born's rule bounds. When cross-validated against the landmark cold neutron double-slit experiment of Zeilinger et al. (1988) (lambda_dB = 18.45 A, D = 5.0 m), the model reproduces the published 73.0 um fringe spacing with 0.106% error and calibrates the measured visibility (V = 0.583) with a structural decay rate of lambda_struct = 31.11 s^-1, in close agreement with independent decoherence analyses in quantum optics (~19.7 s^-1; Sanz et al. 2003). Direct transfer to electron diffraction (Jonsson 1961) predicts high-contrast fringes (K_eff ~ 1.0) without parametric readjustment due to the ~10^7x shorter transit time. Finally, observer collapse is shown to emerge naturally from path accessibility truncation (W_j -> 0) without requiring any metaphysical observer protagonism. ### KeywordsProject Omega, Double-Slit Interference, Causal Bridge Operator, Non-Markovian Dynamics, Fresnel Diffraction, Degree of Spatial Coherence, U(1) Homomorphism, Sorkin Parameter, Zeilinger Experiment, Quantum Foundations.
Description: The double-slit experiment—often called "the only mystery" of quantum mechanics—finds a straightforward resolution in the Lattice Field Medium (LFM) framework. When individual particles pass through two slits and produce an interference pattern, standard quantum mechanics invokes wave function collapse and the measurement problem. In LFM, there is no mystery: the "particle" IS a wave packet in the substrate, and waves naturally diffract and interfere. Using full GOV-01 + GOV-02 coupled dynamics, we demonstrate: A single E pulse propagates toward a χ barrier with two slits The pulse diffracts through both slits simultaneously Interference fringes appear on the detection screen Blocking one slit destroys the interference pattern The same equations that produce gravity (χ wells), dark matter (χ memory), atoms (bound E states), and molecules (overlapping χ wells) also produce wave-particle duality—which is simply wave dynamics. No collapse, no observer effect, no mystery.
Over the past several decades, single photon-based path interference in double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self-interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics.
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 “measurement problem” and the subsequent postulate of instantaneous wave-function collapse remain persistent pedagogical challenges in quantum mechanics. This paper proposes that the apparent paradox of measurement arises from an incomplete idealization of the measuring apparatus as a passive observer, rather than a physical, interacting system. By discarding the unitary state vector formalism during the act of measurement and modeling the detector explicitly as an active noise manifold using the Lindblad master equation, we demonstrate that the suppression of quantum interference is a deterministic, calculable mechanical degradation of phase coherence. Through a numerical simulation of the double-slit experiment, we show that scaling the detector’s stochastic noise rate γD smoothly reproduces the pure unitary interference regime, the weak-measurement partial decoherence regime, and the emergence of classical probability distributions, offering a concrete pedagogical alternative to non-unitary projection postulates.