Phase-Flow Coherence v2 Article Swipe
Phase-Flow Coherence (PFC) v2 provides a deterministic and geometric reformulation of non-relativistic quantum mechanics. The theory replaces the complex wavefunction with a pair of real fields defined on a compact internal phase fiber S¹ over configuration space: an amplitude distribution w(x,θ,t) and a phase potential φ(x,θ,t). Their dynamics follow a measure-preserving Liouville flow derived from a real variational principle. The action includes two rigidity terms that penalize spatial gradients and phase-fiber gradients of w. After averaging over the fiber, the spatial rigidity term reduces to the standard Fisher functional for the observable density ρ(x,t). We prove the Fisher Reduction Theorem: the averaged Fisher quantity equals the Fisher information of ρ plus a non-negative defect measuring fiber incoherence. In the phase-coherent sector the defect vanishes, and the effective action generates the familiar quantum potential as a purely geometric consequence. By introducing ψ(x,t) = sqrt(ρ) times exp(i·φ̄ / sqrt(kappa)), where φ̄ is the fiber-averaged phase, the continuity and Hamilton–Jacobi equations are equivalent to the Schrödinger equation with an effective Planck constant sqrt(kappa). The PFC framework therefore derives the complex wavefunction and the Schrödinger dynamics as emergent descriptors of an underlying deterministic field theory. No stochastic collapse, branching universes, or ad hoc probability postulates are required. Probabilistic outcomes arise operationally from finite phase resolution. Any real measurement device can only resolve the internal phase within a non-zero interval, which enforces coarse-graining on the fiber. Born’s rule then appears as a projection of the deterministic density ρ(x,t) onto phase-unresolved observables. The apparent irreversibility of measurement originates from information loss in this projection, not from fundamental randomness. Gravity, spacetime curvature, and the possible relation between phase resolution and the fine-structure constant are outside the scope of this version. The theory presented here is mathematically self-consistent, entirely deterministic, and compatible with standard quantum predictions in the coherent sector. It provides a concrete bridge between Fisher geometry, Liouville dynamics, and emergent complex quantum mechanics.
Related Topics
Concepts
Coherence (philosophical gambling strategy)
Mathematics
Statistical physics
Observable
Quantum
Infinitesimal
Probability density function
Fisher information
Probabilistic logic
Probability distribution
Rigidity (electromagnetism)
Action (physics)
Wave function
Quantum mechanics
Stochastic process
Quantum entanglement
Joint probability distribution
Physics
Projection (relational algebra)
Mathematical analysis
Scaling
Measure (data warehouse)
Classical mechanics
Planck
Amplitude
Hidden variable theory
Quantum system
Phase space
Probability theory
Photon
Statistical model
Geometric phase
Quantum field theory
Field (mathematics)
Phase (matter)
Probability amplitude
Flow (mathematics)
Random variable
Probability measure
Statistical mechanics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.5281/zenodo.17746916
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7107944573
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W7107944573Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17746916Digital Object Identifier
- Title
-
Phase-Flow Coherence v2Work title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-28Full publication date if available
- Authors
-
Momose, TetsuyaList of authors in order
- Landing page
-
https://doi.org/10.5281/zenodo.17746916Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://doi.org/10.5281/zenodo.17746916Direct OA link when available
- Concepts
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Coherence (philosophical gambling strategy), Mathematics, Statistical physics, Observable, Quantum, Infinitesimal, Probability density function, Fisher information, Probabilistic logic, Probability distribution, Rigidity (electromagnetism), Action (physics), Wave function, Quantum mechanics, Stochastic process, Quantum entanglement, Joint probability distribution, Physics, Projection (relational algebra), Mathematical analysis, Scaling, Measure (data warehouse), Classical mechanics, Planck, Amplitude, Hidden variable theory, Quantum system, Phase space, Probability theory, Photon, Statistical model, Geometric phase, Quantum field theory, Field (mathematics), Phase (matter), Probability amplitude, Flow (mathematics), Random variable, Probability measure, Statistical mechanicsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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| abstract_inverted_index.that | 65 |
| abstract_inverted_index.then | 233 |
| abstract_inverted_index.this | 256, 281 |
| abstract_inverted_index.with | 20, 164, 294 |
| abstract_inverted_index.φ̄ | 148 |
| abstract_inverted_index.(PFC) | 2 |
| abstract_inverted_index.After | 74 |
| abstract_inverted_index.Their | 46 |
| abstract_inverted_index.arise | 205 |
| abstract_inverted_index.fiber | 32, 115 |
| abstract_inverted_index.field | 189 |
| abstract_inverted_index.phase | 31, 43, 209, 220, 270 |
| abstract_inverted_index.prove | 95 |
| abstract_inverted_index.scope | 279 |
| abstract_inverted_index.terms | 64 |
| abstract_inverted_index.times | 143 |
| abstract_inverted_index.where | 147 |
| abstract_inverted_index.which | 225 |
| abstract_inverted_index.Fisher | 87, 97, 102, 106, 308 |
| abstract_inverted_index.Planck | 167 |
| abstract_inverted_index.action | 60, 127 |
| abstract_inverted_index.bridge | 306 |
| abstract_inverted_index.defect | 113, 122 |
| abstract_inverted_index.device | 214 |
| abstract_inverted_index.equals | 104 |
| abstract_inverted_index.fiber, | 78 |
| abstract_inverted_index.fiber. | 230 |
| abstract_inverted_index.fields | 25 |
| abstract_inverted_index.finite | 208 |
| abstract_inverted_index.follow | 48 |
| abstract_inverted_index.phase, | 152 |
| abstract_inverted_index.purely | 135 |
| abstract_inverted_index.sector | 120 |
| abstract_inverted_index.space: | 36 |
| abstract_inverted_index.theory | 15, 284 |
| abstract_inverted_index.within | 221 |
| abstract_inverted_index.appears | 234 |
| abstract_inverted_index.between | 269, 307 |
| abstract_inverted_index.compact | 29 |
| abstract_inverted_index.complex | 18, 176, 314 |
| abstract_inverted_index.defined | 26 |
| abstract_inverted_index.density | 92, 241 |
| abstract_inverted_index.derived | 53 |
| abstract_inverted_index.derives | 174 |
| abstract_inverted_index.outside | 277 |
| abstract_inverted_index.quantum | 12, 131, 296, 315 |
| abstract_inverted_index.reduces | 83 |
| abstract_inverted_index.resolve | 217 |
| abstract_inverted_index.sector. | 301 |
| abstract_inverted_index.spatial | 67, 80 |
| abstract_inverted_index.theory. | 190 |
| abstract_inverted_index.ρ(x,t) | 242 |
| abstract_inverted_index.ψ(x,t) | 140 |
| abstract_inverted_index.Born’s | 231 |
| abstract_inverted_index.Gravity, | 262 |
| abstract_inverted_index.Theorem: | 99 |
| abstract_inverted_index.apparent | 247 |
| abstract_inverted_index.averaged | 101 |
| abstract_inverted_index.coherent | 300 |
| abstract_inverted_index.concrete | 305 |
| abstract_inverted_index.constant | 168, 275 |
| abstract_inverted_index.dynamics | 47, 181 |
| abstract_inverted_index.emergent | 183, 313 |
| abstract_inverted_index.enforces | 226 |
| abstract_inverted_index.entirely | 290 |
| abstract_inverted_index.equation | 163 |
| abstract_inverted_index.familiar | 130 |
| abstract_inverted_index.includes | 61 |
| abstract_inverted_index.internal | 30, 219 |
| abstract_inverted_index.non-zero | 223 |
| abstract_inverted_index.outcomes | 204 |
| abstract_inverted_index.penalize | 66 |
| abstract_inverted_index.possible | 267 |
| abstract_inverted_index.provides | 4, 303 |
| abstract_inverted_index.quantity | 103 |
| abstract_inverted_index.relation | 268 |
| abstract_inverted_index.replaces | 16 |
| abstract_inverted_index.rigidity | 63, 81 |
| abstract_inverted_index.sqrt(ρ) | 142 |
| abstract_inverted_index.standard | 86, 295 |
| abstract_inverted_index.version. | 282 |
| abstract_inverted_index.ρ(x,t). | 93 |
| abstract_inverted_index.Coherence | 1 |
| abstract_inverted_index.Liouville | 51, 310 |
| abstract_inverted_index.Reduction | 98 |
| abstract_inverted_index.amplitude | 38 |
| abstract_inverted_index.averaging | 75 |
| abstract_inverted_index.branching | 194 |
| abstract_inverted_index.collapse, | 193 |
| abstract_inverted_index.dynamics, | 311 |
| abstract_inverted_index.effective | 126, 166 |
| abstract_inverted_index.equations | 157 |
| abstract_inverted_index.framework | 172 |
| abstract_inverted_index.generates | 128 |
| abstract_inverted_index.geometric | 8, 136 |
| abstract_inverted_index.geometry, | 309 |
| abstract_inverted_index.gradients | 68, 71 |
| abstract_inverted_index.interval, | 224 |
| abstract_inverted_index.measuring | 114 |
| abstract_inverted_index.potential | 44, 132 |
| abstract_inverted_index.presented | 285 |
| abstract_inverted_index.required. | 202 |
| abstract_inverted_index.spacetime | 263 |
| abstract_inverted_index.therefore | 173 |
| abstract_inverted_index.vanishes, | 123 |
| abstract_inverted_index.w(x,θ,t) | 40 |
| abstract_inverted_index.Phase-Flow | 0 |
| abstract_inverted_index.compatible | 293 |
| abstract_inverted_index.continuity | 154 |
| abstract_inverted_index.curvature, | 264 |
| abstract_inverted_index.equivalent | 159 |
| abstract_inverted_index.functional | 88 |
| abstract_inverted_index.mechanics. | 13, 316 |
| abstract_inverted_index.observable | 91 |
| abstract_inverted_index.originates | 251 |
| abstract_inverted_index.postulates | 200 |
| abstract_inverted_index.principle. | 58 |
| abstract_inverted_index.projection | 237 |
| abstract_inverted_index.resolution | 271 |
| abstract_inverted_index.stochastic | 192 |
| abstract_inverted_index.underlying | 187 |
| abstract_inverted_index.universes, | 195 |
| abstract_inverted_index.descriptors | 184 |
| abstract_inverted_index.exp(i·φ̄ | 144 |
| abstract_inverted_index.fundamental | 260 |
| abstract_inverted_index.information | 107, 253 |
| abstract_inverted_index.introducing | 139 |
| abstract_inverted_index.measurement | 213, 250 |
| abstract_inverted_index.phase-fiber | 70 |
| abstract_inverted_index.predictions | 297 |
| abstract_inverted_index.probability | 199 |
| abstract_inverted_index.projection, | 257 |
| abstract_inverted_index.randomness. | 261 |
| abstract_inverted_index.resolution. | 210 |
| abstract_inverted_index.variational | 57 |
| abstract_inverted_index.φ(x,θ,t). | 45 |
| abstract_inverted_index.Schrödinger | 162, 180 |
| abstract_inverted_index.consequence. | 137 |
| abstract_inverted_index.distribution | 39 |
| abstract_inverted_index.incoherence. | 116 |
| abstract_inverted_index.non-negative | 112 |
| abstract_inverted_index.observables. | 245 |
| abstract_inverted_index.sqrt(kappa). | 169 |
| abstract_inverted_index.wavefunction | 19, 177 |
| abstract_inverted_index.Probabilistic | 203 |
| abstract_inverted_index.configuration | 35 |
| abstract_inverted_index.deterministic | 6, 188, 240 |
| abstract_inverted_index.operationally | 206 |
| abstract_inverted_index.reformulation | 9 |
| abstract_inverted_index.sqrt(kappa)), | 146 |
| abstract_inverted_index.deterministic, | 291 |
| abstract_inverted_index.fiber-averaged | 151 |
| abstract_inverted_index.fine-structure | 274 |
| abstract_inverted_index.mathematically | 288 |
| abstract_inverted_index.phase-coherent | 119 |
| abstract_inverted_index.coarse-graining | 227 |
| abstract_inverted_index.irreversibility | 248 |
| abstract_inverted_index.non-relativistic | 11 |
| abstract_inverted_index.phase-unresolved | 244 |
| abstract_inverted_index.self-consistent, | 289 |
| abstract_inverted_index.Hamilton–Jacobi | 156 |
| abstract_inverted_index.measure-preserving | 50 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |