Quantum interference is conventionally formulated using complex amplitudes associated with quantum alternatives or through Feynman’s path integral over possible trajectories. This article investigates a different ontology, the Single-History Record Framework (SHRF), in which a physical system has one realized history together with a record space of phase-carrying contributions associated with that history. Observable amplitudes are obtained through History-Record Summation (HRS). SHRF deliberately retains established quantum ingredients wherever possible, including complex-amplitude addition, the Born probability rule, propagation phases, and marker-state overlaps. These mathematical devices are used as predictive rules and do not imply that multiple physical histories, paths, or marker outcomes coexist.A preliminary model is developed in which rapidly varying regions of record space largely cancel while coherent record bands provide the dominant detector amplitude. For double-slit geometry, two aperture-selected bands give A(x)≈H_A (x)+H_B (x).With the established propagation phases H_A=Ce^(ikL_A ),H_B=Ce^(ikL_B ),SHRF recovers the textbook far-field fringe spacing Δx=λD/d.The same formal structure is applied to single-slit diffraction, multiple slits, which-path marking, partial distinguishability, and quantum-eraser subensembles. In particular, marker records modify the interference term through the standard overlap factor ⟨M_A∣M_B⟩,without requiring a physical superposition of marker records. The present model assumes rather than derives its phase law, record-space measure, and Born rule. It is therefore a recovery-oriented consistency construction and ontological reinterpretation, not an independent replacement for standard quantum mechanics.
Quantum interference is conventionally formulated using complex amplitudes associated with quantum alternatives or through Feynman’s path integral over possible trajectories. This article investigates a different ontology, the Single-History Record Framework (SHRF), in which a physical system has one realized history together with a record space of phase-carrying contributions associated with that history. Observable amplitudes are obtained through History-Record Summation (HRS). SHRF deliberately retains established quantum ingredients wherever possible, including complex-amplitude addition, the Born probability rule, propagation phases, and marker-state overlaps. These mathematical devices are used as predictive rules and do not imply that multiple physical histories, paths, or marker outcomes coexist.A preliminary model is developed in which rapidly varying regions of record space largely cancel while coherent record bands provide the dominant detector amplitude. For double-slit geometry, two aperture-selected bands give A(x)≈H_A (x)+H_B (x).With the established propagation phases H_A=Ce^(ikL_A ),H_B=Ce^(ikL_B ),SHRF recovers the textbook far-field fringe spacing Δx=λD/d.The same formal structure is applied to single-slit diffraction, multiple slits, which-path marking, partial distinguishability, and quantum-eraser subensembles. In particular, marker records modify the interference term through the standard overlap factor ⟨M_A∣M_B⟩,without requiring a physical superposition of marker records. The present model assumes rather than derives its phase law, record-space measure, and Born rule. It is therefore a recovery-oriented consistency construction and ontological reinterpretation, not an independent replacement for standard quantum mechanics.
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.
Can two-path quantum-interference phenomenology be understood as a property of a local time-rate field before an individual result is fixed? We investigate this question in a matter-free effective dynamical branch of the Enchan framework. A real local time-rate field, initialized with field and velocity data, propagates through two apertures and produces a non-additive, oscillatory screen-energy-flux pattern without primitive particles, a primitive wavefunction, Born weights, or a collapse operation. Its normalized cross term is 0.533636, 0.529264, and 0.526779 on three successively refined grids. A linear-response control retains the effect, identifying a broader coherent-field mechanism. We then evolve a coupled field/path-tag model in which the passing field writes opposite tag orientations near the two slits. Across a frozen five-strength sweep, the independently measured route-tag overlap and unresolved interference decrease together; their Pearson correlations are 0.996786 and 0.998675 on two numerical levels. The screen is computed from the evolved fields without multiplying a reference fringe by a tag-overlap factor. The additional tag channel and slit-local antisymmetric coupling are explicit minimal model assumptions, not a unique derivation from the canonical scalar ontology. The physical comparisons are route removal, path tagging with both routes open, and localized screen recording. A half-amplitude control reduces flux to 24.64% while retaining the normalized cross term. A third calculation reuses the exact Q0 field and defines a nonnegative screen event measure from the accumulated positive forward energy flux, J_+(y) = integral max(F_E,x, 0) dt. One localized screen coordinate is drawn per independent preparation from the normalized J+ distribution. In a fixed 600-event realization, the binned hit histogram has Pearson correlation 0.9553 and total-variation distance 0.0949 relative to the binned event measure. This finite-sample agreement is a consistency check of the explicit forward-flux readout, not an independent validation and not a derivation of the Born rule. Interference, path-tagging, and one-hit event realization are therefore supported at their separately stated model levels, while microscopic detector selection and experimental confirmation of the proposed ontology are outside the scope of this study. The release includes the manuscript PDF, a standalone reproducibility ZIP with manuscript sources, frozen numerical solvers and inputs, lightweight results and figures, an English reproduction manual, LICENSE, and SHA-256 checksums. The manuscript is dated 18 September 2026. No private repository, external dataset, or GPU is required. Enchan Research & Verification License v1.0. Copyright (c) 2026 Mitsuhiro Kobayashi. All rights reserved.
If Richard Feynman's path integral formulation had been proposed not merely as a computational tool for probability amplitudes, but as a fundamental physical ontology—namely, that "all histories collectively constitute reality"—the foundational paradigm of physics would have undergone a profound transformation. Traditional physics treats a single trajectory of a system in spacetime as the primary object and path integration as a summation technique over possible paths. This paper systematically develops an alternative framework: Physics of History Space, where the ensemble of all possible histories serves as the irreduceable primary object of physical description. Within this paradigm, physical reality is defined by the topology, measure, and algebraic structures over the space of histories, rather than being restricted to a single actualized trajectory. We establish the mathematical formulation of history space and re-examine the measurement problem in quantum mechanics, the problem of initial conditions in cosmology, and the philosophy of time. We demonstrate that classical single-trajectory spacetime emerges merely as a low-dimensional projection of history space under decoherence and stationary phase limits.
This paper presents a foundational thought experiment and proposes a radical ontological framework for interpreting quantum mechanics and the nature of time. It moves beyond conventional interpretations by testing them against a novel scenario: a hypothetical "time machine" (device 𝒲) capable of passively reading the past state of a quantum system without interacting with it. The central testbed is the classic double-slit experiment. In Stage 1, performed at time T_0, the experiment is run without any path detection, yielding the standard interference pattern. In Stage 2, at a later time T_0 + ΔT, the device 𝒲 is used to retroactively "read" the precise state of the system at the moment the electron passed the slit plane. The pivotal question is: What information about the electron's path will 𝒲 find? The analysis demonstrates that established interpretations face significant paradoxes: The Copenhagen Interpretation risks falling into retrocausality, as the mere potential for future path-information readout could retroactively collapse the interference pattern. The Many-Worlds Interpretation leads to internal inconsistency, as the deterministic, single-path history observed within a given branch by 𝒲 contradicts the interference pattern observed in that same branch's past. The de Broglie-Bohm (dBB) Interpretation, while positing a hidden trajectory, struggles with the mechanism of how 𝒲 could read this information without interacting with the guiding pilot wave, which is essential for the interference effect. As a resolution, the paper proposes a new ontological model based on a geometric, discrete conception of reality. The core tenets are: Fundamental Entities: Reality is a dynamic network of "p-gluons," postulated as geometric quanta of spacetime. Discrete Frames: Observable reality is not continuous but consists of a sequential generation of discrete, global "frames" (K_i). Each frame is a complete geometric snapshot of the entire p-gluon network's configuration. The Axiom of Record Economy (AOZ): This is the central formal postulate. At each generative step, at most one frame from the space of locally possible states (ℋ_poss) is physically realized. A frame is generated if and only if it satisfies a condition of global consistency with the entire history, as determined by a fundamental "algorithm of reality" (𝒜). Crucially, states in ℋ_poss that are not selected for generation attain no ontological status whatsoever; they are abstract possibilities, not unrecorded facts. Emergent Time: Observable time is not a fundamental background parameter but an emergent measure of the rate (Ḳ) at which these global frames are generated. Within this Frame-Recording Ontology, the time-machine paradox finds an elegant and decisive solution: In the double-slit experiment without a detector, the only configuration consistent (via algorithm 𝒜) with the future observation of an interference pattern is a global superposed state. This state, describable as an extended pattern of geometric correlations in the p-gluon network encompassing both slits, is the one and only frame generated (K_T0). Deterministic "path" frames (electron at S_1 or S_2) are not generated; they remain unrealized abstractions. Therefore, when device 𝒲 reads the past, it accesses the sole ontological record: frame K_T0. It finds no geometric data corresponding to a classical path because such data was never physically recorded. The answer is not "the information is hidden" (epistemology), but "the corresponding fact was never generated" (ontology). The paper elaborates on the non-anthropomorphic, non-teleological nature of algorithm 𝒜, framing it as a constraining structure akin to a variational principle rather than a conscious selector. It discusses the model's implications for the measurement problem (reinterpreted as the generation of a "classical" frame), nonlocality, and its philosophical shift from epistemic to ontological indeterminacy. Methodology: The work is developed using the author's "Pencil Case Philosophy" or "Sonar Modeling" approach. This methodology begins by constructing minimal axiomatic building blocks (p-gluons, AOZ, 𝒜), activates the system, and rigorously traces its logical consequences without prior commitment to reproducing existing theoretical frameworks.
Paper 74 — No Quantum Superposition This paper argues, by reductio ad absurdum, that the physical realisation of superposition — simultaneous multi-location existence — is incompatible with seven independent and well-established physical principles: (1) the observational fact that no infinite physical quantity has ever been measured; (2) conservation of energy; (3) the mass-energy equivalence E = mc²; (4) the Bekenstein entropy bound; (5) the second law of thermodynamics; (6) the Heisenberg uncertainty principle; and (7) causality. The foundational identification is that information, energy, and mass stand in proportional existential relation (Bekenstein bound: I ∝ M; Landauer principle: ΔE ∝ ΔI; mass-energy equivalence: E = mc²). Complete superposition requires infinite information processing, and therefore infinite energy and infinite mass — quantities universally absent from the observational record of physics. Finite N-state superposition is excluded by a complementary argument: maintaining N states simultaneously requires N times the information-processing load of a single undetermined state, violating the principle that nature selects minimum-load configurations. The positive alternative proposed is the undetermined state: during matter-wave propagation, the matter wave is real and physically present, but matter has not yet appeared at any location. This is not a hidden-variable state but an ontological absence of localisation prior to the formation of a constructive interference maximum. Paper 75 — The Double-Slit Experiment Reinterpreted This paper applies the undetermined-state ontology to the paradigmatic demonstration of quantum mechanics. The de Broglie matter wave — a real physical wave — passes through both slits, while the particle remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The disappearance of the interference pattern upon which-path measurement is explained without wavefunction collapse: the measurement interaction physically disrupts the matter wave's coherent two-slit propagation. Three experimentally testable predictions distinguish this framework: (1) weak-measurement trajectory reconstruction should reveal single-path trajectories 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; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. The Schrödinger equation and Born's rule are retained without modification. Paper 76 — Discriminating Experiments for the Constructive-Interference Account of Gravity This paper derives the specific numerical values predicted by Paper 29 — n(r) from the Schwarzschild metric, Δφ = k₀∫[n₁(r)−n₂(r)]dr from the medium-structure integral, and Δx_max = f(∇n, geometry, λ₀) from the interference structure — and assesses whether current experimental technology can measure the gap between Paper 29's predictions and standard QM's predictions. Three formal conditions for a discriminating experiment are established: structural absence of the variable from standard QM, signal exceeding current resolution, and impossibility of alternative explanation. Two experimental classes satisfy all three conditions with existing apparatus: COW path-geometry (predicted δ(Δφ) ~ 10⁻³ rad vs. resolution ~10⁻⁴ rad, path shape structurally absent from the standard COW formula) and slit-material density (predicted Δx_max ~ tens of nm vs. resolution 1–5 nm, material density structurally absent from Δy ≈ λL/a). Cumulative agreement across both systems constitutes genuine inductive support for the proposed mechanism. Paper 77 — From Electrons to Fullerenes This paper addresses three questions that Paper 76 does not: (1) why the slit-material density experiment has never been performed in the hundred years since matter-wave interferometry began — the answer being that standard QM contains no density variable in the slit formula, so experimenters had no reason to vary it, with the Copenhagen prohibition on mechanism questions as the deeper structural reason; (2) why confirmation in exactly two systems — electrons and fullerenes C₆₀ — is sufficient to establish the theoretical outline across six orders of magnitude in mass, because these systems are maximally independent in particle type, mass, apparatus, energy scale, and decoherence environment; (3) what confirmation across this mass range would establish for physics: the first experimentally supported identification of the physical mechanism of gravity, the first experimentally verifiable quantum-gravity connection at accessible energy scales, a physical grounding of Born's rule, and a mechanistic account of the measurement problem. A complete three-layer control protocol for excluding the slit-width confound is specified. Paper 78 — A Three-Dimensional Experimental Matrix This paper extends the experimental programme by introducing slit thickness as a third independent variable alongside matter-wave species and slit-material density. The wave-mechanical account predicts that phase shift scales linearly with slit thickness d: Δφ(ρ,d) = (2π/λ)·[n(ρ)−1]·d — a prediction structurally absent from standard QM, which assigns no physical role to slit thickness. The resulting 5×5×3 matrix of 75 independent measurements has a random coincidence probability of approximately 1/1,728,000, rendering chance agreement with theoretical prediction physically impossible. Three-layer control protocols for fabrication, TEM cross-section verification, and linearity testing are specified for the thickness dimension. Together, the five papers constitute a complete programme: ontological foundation (P74), phenomenological reinterpretation (P75), formal discriminating analysis (P76), strategic and historical argument (P77), and three-dimensional experimental design (P78).
A Set-Based Alternative to the Hilbert-Space Formalism: Two-Slit Interference in the CEGS Framework This work presents a deterministic reformulation of the two-slit experiment within the Calculus of Element Generated Sets (CEGS), a set-based framework for modeling physical systems without assuming Hilbert space as a fundamental structure. Instead of representing quantum states as vectors in a complex Hilbert space, physical states are described as structured sets of phase-generating elements subject to intrinsic constraint operations prior to aggregation. Within this framework, observable quantities arise only after a coherent aggregation map acts on constrained generative sets. The standard interference pattern of the two-slit experiment is recovered exactly at the level of observable predictions, preserving empirical equivalence with conventional quantum mechanics. A central conceptual shift is that complex amplitudes are not treated as fundamental entities. Instead, they emerge as effective compressed representations of underlying distributed phase structures under observer-dependent projection. In this view, Hilbert space is interpreted as an emergent effective description rather than a primary ontological structure. The formulation provides a deterministic and structural alternative perspective on quantum interference, contributing to ongoing discussions in quantum foundations, interpretation of quantum mechanics, and set-based or non-vectorial reformulations of physical theory. The analysis is restricted to the two-slit experiment as a minimal test case, while maintaining consistency with standard quantum predictions.