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.
We explore a dynamical two-time model in which each particle carries (1) a classical relativistictime coordinate t and (2) a rapidly oscillating internal “quantum time” τ . We show that whenan ensemble of such particles propagates through a pair of phase-selective apertures, the resultingdistribution on a detector screen forms interference patterns with perfect fringe contrast, full left-right symmetry, stable fringe spacing, and narrow peaks, even though no wave equation, no complexamplitudes, and no Hilbert space are invoked anywhere in the simulation. We find that the model robustly reproduces an entire suite of wave phenomena: coherent wavefrontpropagation, standing-wave modes above the slits, Fraunhofer-like interference bands, and rotation-dependent fringe tilts. The interference pattern is invariant under slit width, consistent with theinterpretation that the slits act as phase filters rather than spatial apertures. Finally, we describe falsifiable experimental predictions, including modified decay-rate signaturesfor relativistic radioactive ions whose internal quantum-time oscillations should modulate undertime dilation
A Calculable Model in One, Two, and Three Spatial Dimensions This preprint develops a first calculable basis for the treatment of records and feedback in probabilistic presentism. It introduces the V3 reconstruction through an explicit quantum model, retaining potentialities through the joint quantum state while removing an additional scalar degree of actualization. Model and contribution A propagating excitation couples locally to a two-state memory. The resulting record remains readable over a declared finite interval. A fixed reflector returns the excitation, and interventions on the memory affect its later field evolution. A sufficient storage bound follows from occupation of the interaction region. The same scalar lattice law is implemented in one, two and three spatial dimensions. Reproducibility The accompanying archive contains the simulation programs, 24 reference runs, 12 step/domain comparisons, four calculated figures, independent solver checks, storage-bound counter-tests, spatial-snapshot audits and instructions. The reference batch was reproduced from an extracted package in the recorded environment. A CPU is sufficient; no GPU dependency is required. Scope Quantum dynamics, Born probabilities and the terminal reading instrument are adopted. The results establish properties of the declared finite model. Physical outcome selection, emergent duration relations, gravity, continuum Maxwell electrodynamics and experimental discrimination of the ontology remain open. This is a partial calculable formulation of the presentist programme. Related publications and provenance Main V2: French original, 10 January 2026, 10.5281/zenodo.18207811; English translation 2.0-en, 9 September 2026, 10.5281/zenodo.22675807. Wave-particle duality: French original, 28 January 2026, 10.5281/zenodo.18404150; English translation 1.0-en, 9 September 2026, 10.5281/zenodo.22677490. Feedback loops: French original, 4 September 2026, 10.5281/zenodo.22307131; English translation 1.0-en, 9 September 2026, 10.5281/zenodo.22678920. Files and licenses The PDF contains the illustrated article. The ZIP contains the manuscript source, PDF, programs, figures, data, audits, instructions and license notices. Text, figures and data are licensed under CC BY 4.0; software source is licensed under MIT. These licenses apply to the respective components described in LICENSES.md. Author: Alexandre Leroy. Affiliation: LA RESIDENCE Développement. Independent research in theoretical physics and the philosophy of time. Contact: a.leroy.research@gmail.com.
We reconstruct nonrelativistic quantum mechanics from exactly three physical axioms: microscopic ontic definiteness and finite localization, physical reality of the spacetime-vacuum substrate, and persistent causal source–response coupling. The single-run physical state is a finite topological core, its actual causal history, the substrate state, its sector, and the associated historical disturbance. A wave function is not identified with that ontic tuple. It is a ray in a Hilbert representation of admissible preparations and response amplitudes; a density operator is a statistical or reduced representation; and a record is a stable macroscopic event. The logical construction is acyclic. Finite-energy sector spaces and their continuous symmetry representations lead, under explicit representation conditions, to a complex Hilbert direct sum. A closed semibounded quadratic form defines the Hamiltonian and its self-adjoint realization. The standard Schrödinger action, unitary propagation, probability current, spectral observables, uncertainty relations, composite-system tensor products, spin representations, exchange sectors, instruments, and completely positive open dynamics then follow on their declared domains. Gleason-type reasoning fixes the Born form only after additivity, noncontextuality, continuity, and preparation–detector calibration are stated. Those operational conditions are not hidden physical axioms. The distribution of unresolved ontic initial data that realizes quantum equilibrium remains a realization certificate, not a theorem of topology alone. The Heisenberg representation is derived as a controlled transport of observables after Hilbert space and the self-adjoint generator have been constructed. Strongly continuous time translation, two-parameter nonautonomous propagation, common-domain Heisenberg equations, spectral matrix mechanics, regular Weyl relations, open-system adjoints, and instrument effects are connected by one certificate. Schrödinger and Heisenberg predictions are proved equivalent for one-time and finite instrument records, while finite-core, historical, truncation, domain, and detector errors remain separately bounded. Three frozen matrix benchmarks verify low-energy oscillator truncation and its state-weighted CCR defect, second-order unitary convergence for a driven doublet, Schrödinger–Heisenberg equality for a sequential instrument, finite auxiliary-history truncation, and quadratic leakage scaling for a conditional Dirac–Pauli interface. Independent reproduction, including the extended-precision audit, is closed for the frozen packet; physical coefficient calibration remains open. The next interface connects an owner-resolved Dirac–Pauli Hamiltonian to spin records through a Ward-compatible vertex, a causal passive history kernel, an independently audited doublet projection, SPAM-aware forward probabilities, nuisance-profiled identifiability, and a noncompensatory coefficient-to-record error theorem. The DPHC identifiability coordinate is executed on a frozen synthetic response family. A single-scale design is rank deficient, whereas an eighteen-setting frequency–gradient–order–time design has full profiled rank, controlled conditioning, near-nominal finite-sample coverage, and a calibrated held-out statistic. A robust twenty-setting design raises the worst registered information eigenvalue by
20.12%. A ten-parameter nonlinear audit exhibits an exact radiative–detector equivalence curve. An independent dark record breaks that symmetry and restores full local rank. Continuous-set robustness, validated global exclusion, and independent implementation are executed, while physical response identification and empirical calibration remain open. Measurement is treated as a dynamics of system, apparatus, environment, and actual history. Unitary premeasurement and decoherence select robust record sectors but do not by themselves select one record. The three-axiom ontology supplies one actual branch history, while a measurable response map from the complete initial state and instrument to the final record supplies the missing dynamical content. Bell correlations require contextual and nonfactorizable ontic response while parameter independence and operational no-signalling are retained; no controllable superluminal channel is introduced. Historical response produces causal non-Markov Hamiltonians and memory-kernel master equations. Their normalization, positivity, complete positivity, and energy ledger are derived from a unitary enlarged realization whenever such a dilation exists. Finite-core form factors and causal memory yield explicit departures from point-core Markov quantum mechanics. Standard quantum mechanics is recovered as the unresolved-core, sector-fixed, quantum-equilibrium, short-memory limit. Quantum field theory is retained as a successful local, spectral, and asymptotic calculus, but field operators, Fock vectors, and vacuum functionals remain effective representations until a noncircular map from finite carriers and their complete causal histories has been certified. The manuscript proves a sequence of previously open analytic, mathematical, measurement, topological, statistical, and computational obligations on explicitly declared domains. These include non-Markov diffusion, graph-norm stability, distorted-wave and pole variation, finite passive-memory realization, Fisher-information identifiability, detector pushforwards, unique-record basins, Born-representation bounds, measurement independence, topology–Dirac charge conjugation, Stern–Gerlach records, action-scale matching, rank-two spin projection, Finkelstein–Rubinstein topology, Clifford reconstruction, and parent-to-record realization maps. Eighteen groups of numerical obligations are executed on frozen reference models. They cover spectral and scattering calculations, oscillator and two-level dynamics, Schrödinger–Heisenberg equivalence, finite-history truncation, Dirac–Pauli and Foldy–Wouthuysen reduction, gauge covariance, interference, Bell and GHZ correlations, open-system memory, Stern–Gerlach records, identifiability, global searches, topological invariants, path products, semiclassical limits, partial-wave optical closure, the relativistic/QFT interface, and conservative-parent two-level dynamics. Every environment explicitly typed as a computational obligation now has an executed frozen-model certificate; empirical identification and separately typed experimental inputs remain open. The present manuscript differs so substantially from the earlier version in scope, logical architecture, proofs, and executable certificates that it is issued as a new upload rather than as a minor revision. Because the subject is both foundational and technically consequential, readers professionally engaged in quantum foundations, mathematical physics, quantum measurement, or related fields are encouraged to consult both versions: the earlier version preserves the developmental route, whereas the present version gives the substantially expanded and reorganized reconstruction. ## Keywords Axiomatic quantum mechanics; finite particle histories; retarded Green functions; Schrödinger equation; Dirac equation; Born rule; topological spin; quantum measurement; non-Markovian dynamics; classical limit.
Although position and time have different mathematical roles in quantum mechanics, with one being an operator and the other being a parameter, there is a space-time duality in quantum phenomena: a lot of quantum phenomena that were first observed in the spatial domain were later observed in the temporal domain as well. In this context, we propose a modified version of the double-double-slit experiment using entangled atom pairs to observe a non-local interference in the arrival time distribution, which is analogous to the non-local interference observed in the arrival position distribution. However, computing the arrival time distribution in quantum mechanics is a challenging open problem, and so to overcome this problem we employ a Bohmian treatment. Based on this approach, we numerically demonstrate that there is a complementary relationship between the one-particle and two-particle interference visibilities in the arrival time distribution, which is analogous to the complementary relationship observed in the position distribution. These results can be used to test the Bohmian arrival time distribution in a strict manner, i.e., where the semiclassical approximation breaks down. Moreover, our approach to investigating this experiment can be applied to a wide range of phenomena, and it seems that the predicted non-local temporal interference and associated complementary relationship are universal behaviors of entangled quantum systems that may manifest in various phenomena.
Although position and time have different mathematical roles in quantum mechanics, with one being an operator and the other being a parameter, there is a space-time duality in quantum phenomena-a lot of quantum phenomena that were first observed in the spatial domain were later observed in the temporal domain as well. In this context, we propose a modified version of the double-double-slit experiment using entangled atom pairs to observe a non-local interference in the arrival time distribution, which is analogous to the non-local interference observed in the arrival position distribution. However, computing the arrival time distribution in quantum mechanics is a challenging open problem, and so to overcome this problem we employ a Bohmian treatment. Based on this approach, we numerically demonstrate that there is a complementary relationship between the one-particle and two-particle interference visibilities in the arrival time distribution, which is analogous to the complementary relationship observed in the position distribution. These results can be used to test the Bohmian arrival time distribution in a strict manner, i.e., where the semiclassical approximation breaks down. Moreover, our approach to investigating this experiment can be applied to a wide range of phenomena, and it seems that the predicted non-local temporal interference and associated complementary relationship are universal behaviors of entangled quantum systems that may manifest in various phenomena.