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Phase-Flow Coherence (PFC v7)

Momose, Tetsuya

Published Dec 3, 2025• 3 citations
Publisher

Abstract

Notice (Updated Framework):This paper presents a constructive formulation of Phase-Flow Coherence (PFC).A newer paper, PFC v4, reformulates the same results in an eliminative (no-go) framework, showing that Born-rule weighting and Schrödinger-type dynamics are internally inevitable under finite resolution and non-privileged representation. Readers interested in the final, assumption-minimal formulation are strongly encouraged to consult:Phase-Flow Coherence (PFC) v4 — DOI: [v4 DOI]10.5281/zenodo.18322699 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ A deterministic phase-fiber formulation of quantum mechanics based on Fisher reduction.This v2.5 version strengthens the previous PFC v2 by:(i) a rigorous derivation of the quantum potential from Fisher information,(ii) explicit handling of the β non-coherence term under θ-periodicity,(iii) entropic coarse-graining for measurement,(iv) an experimentally testable bound on interferometric visibility.All probabilistic features emerge from finite angular resolution on S¹.The theory is self-contained and falsifiable.

DOI
10.5281/zenodo.17797652

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Archival record. This paper predates the current MOF–SRT–FDC–PFC framework and is retained for historical and priority purposes. Its subject matter has been revised, absorbed, or superseded by the current framework papers. ------------------------------------------------------------------------------------------------------------------------------------ This short theoretical note formulates a bridge between Relative Determination, the Minimal Ontological Foundation (MOF), Finite Distinguishability Closure (FDC), and Phase-Flow Coherence (PFC). The central claim is that probability need not be introduced as primitive global randomness. Instead, when a globally non-random structural realization is read through a finite internal ledger, multiple globally distinct realizations may be mapped to a single internal ledger state. If a later readout partitions this unresolved bundle into possible outcomes, the internal ledger is forced to represent the partition by normalized relative weights. The note first defines a ledger-relative probability representation using a finite ledger map from a structural closure domain to internal ledger states. It then shows that the domain is not a hidden-variable catalogue or an absolute classical value ledger, but a structural closure domain compatible with the relative-determination viewpoint. The second part specializes the abstract ledger-compatible measure to the PFC phase-bundle setting. Under phase invariance, orthogonal-sector additivity, non-negativity, and finite ledger closure, a functional-equation argument shows that the minimal admissible phase-bundle measure is proportional to the squared complex amplitude. This yields the Born-type weight as a specialization of ledger-relative probability. The paper does not claim that all physical probabilities are derived, nor that randomness is fundamental at the global level. Its purpose is to record a structural bridge: finite internal distinguishability forces probability representation, and PFC supplies the phase-measure specialization leading to Born-type weights.

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Notice (Updated Framework):This paper presents a constructive formulation of Phase-Flow Coherence (PFC).A newer paper, PFC v4, reformulates the same results in an eliminative (no-go) framework, showing that Born-rule weighting and Schrödinger-type dynamics are internally inevitable under finite resolution and non-privileged representation. Readers interested in the final, assumption-minimal formulation are strongly encouraged to consult:Phase-Flow Coherence (PFC) v4 — DOI: [v4 DOI]10.5281/zenodo.18322699 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ A deterministic phase-fiber formulation of quantum mechanics based on Fisher reduction.This v2.5 version strengthens the previous PFC v2 by:(i) a rigorous derivation of the quantum potential from Fisher information,(ii) explicit handling of the β non-coherence term under θ-periodicity,(iii) entropic coarse-graining for measurement,(iv) an experimentally testable bound on interferometric visibility.All probabilistic features emerge from finite angular resolution on S¹.The theory is self-contained and falsifiable.
(Note: Please refer to Version 3 (v3) of The Dynamics of Discrete Fact: A Phase-Transition Theory of Wavefunction Collapse for the updated and expanded presentation of the framework). _______________________ This is Version 2 of The Dynamics of Discrete Fact, presenting an expanded and clarified construction of wavefunction collapse as a genuine physical phenomenon: a nonequilibrium phase transition in a macroscopic measurement apparatus. As before, collapse is modeled as a critical instability in an emergent order parameter governed by time-dependent Ginzburg–Landau dynamics. Discrete outcomes arise through spontaneous symmetry breaking in the apparatus–environment system, while Born weights are preserved via probability-conserving basin flow in the associated Fokker–Planck description—without modifying the Schrödinger equation or introducing new constants. Relative to v1, v2 (i) makes the single-run (outcome-conditional) collapse dynamics explicit rather than implicit, (ii) strengthens the Born-rule preservation argument by tying basin structure more directly to apparatus symmetry, and (iii) tightens the experimental discussion by specifying the regimes in which critical signatures are and are not expected. The framework retains concrete signatures—critical slowing near threshold, hysteresis under parameter cycling, metastability, and outcome-correlated transient detector spikes—and positions collapse alongside emergent macroscopic instabilities such as superconductivity and ferromagnetism.
This paper presents a structural derivation of quantum dynamics and probability from a minimal set of pre-physical assumptions: non-privileged phase space, finite resolution, and measure-preserving global dynamics. Rather than postulating quantum axioms, the framework shows how internal probabilistic interpretation (Born rule) and Schrödinger-type dynamics emerge as necessary consequences of finite-resolution internal projections applied to a globally deterministic phase-flow structure. The paper emphasizes a strict separation between global density and internal probability, and includes a structural log clarifying where assumptions are introduced and where they are explicitly excluded. This is Version 1. Subsequent versions may refine appendix structure, notation, and cross-referencing without altering the core theoretical results. Note (2026):A refined and structurally clarified successor to this work is now available as“Phase-Flow Coherence v3: Inevitability of Quantum Dynamics from Finite Resolution and Non-Privileged Phase Space”.The present paper should be regarded as a detailed intermediate derivation, while PFC v3 presents the finalized inevitability result within the MOF framework.
This record provides an index and dependency declaration for a one-way trilogy of works: (1) Minimal Ontological Foundation (MOF v3)(2) Phase–Flow Coherence (PFC v4)(3) Alpha Locking (v6) The trilogy establishes a finite-resolution rigidity chain, proceeding strictly in one direction. MOF v3 fixes the minimal ontological conditions for world-formation, from which irreversible internal update order (time), internal projection (measurement), and structural probability follow as necessary consequences. PFC v4 fixes the unique internally coherent representation of dynamics and probability under those conditions, eliminating all alternatives except Schrödinger-type bookkeeping with Born-rule weighting. Alpha Locking v6 completes the chain by showing that finite-resolution update structures cannot terminate arbitrarily. A unique minimal admissible depth is forced under purely discrete accept/reject predicates, leaving the fine-structure constant as a structural residue. No result depends on downstream assumptions.No fitting, tuning, or optimization is introduced at any stage. This overview introduces no new claims and contains no additional results.It serves solely to fix reading order, dependency, and scope.
Archival record. This paper predates the current MOF–SRT–FDC–PFC framework and is retained for historical and priority purposes. Its subject matter has been revised, absorbed, or superseded by the current framework papers. ------------------------------------------------------------------------------------------------------------------------------------ This short theoretical note formulates a bridge between Relative Determination, the Minimal Ontological Foundation (MOF), Finite Distinguishability Closure (FDC), and Phase-Flow Coherence (PFC). The central claim is that probability need not be introduced as primitive global randomness. Instead, when a globally non-random structural realization is read through a finite internal ledger, multiple globally distinct realizations may be mapped to a single internal ledger state. If a later readout partitions this unresolved bundle into possible outcomes, the internal ledger is forced to represent the partition by normalized relative weights. The note first defines a ledger-relative probability representation using a finite ledger map from a structural closure domain to internal ledger states. It then shows that the domain is not a hidden-variable catalogue or an absolute classical value ledger, but a structural closure domain compatible with the relative-determination viewpoint. The second part specializes the abstract ledger-compatible measure to the PFC phase-bundle setting. Under phase invariance, orthogonal-sector additivity, non-negativity, and finite ledger closure, a functional-equation argument shows that the minimal admissible phase-bundle measure is proportional to the squared complex amplitude. This yields the Born-type weight as a specialization of ledger-relative probability. The paper does not claim that all physical probabilities are derived, nor that randomness is fundamental at the global level. Its purpose is to record a structural bridge: finite internal distinguishability forces probability representation, and PFC supplies the phase-measure specialization leading to Born-type weights.