Geometric Reaction: From Quantum Hydrodynamics to a Cross-Domain Generative Principle

Geometric Reaction (First Law). Geometry is the operative container; any realized (above-threshold) difference within it induces a reaction R that unfolds as tempo T (time as rhythm of change) and residue M (persistent form, including matter). The recursive cycle geometry → reaction → new geometry appears across physics, biology, engineering, and narrative. From an action functional in density ρ and phase S, the framework yields a continuity equation and a Hamilton–Jacobi equation with a geometric information term Q[ρ,g]; under standard regularity (ρ > 0, phase single-valued up to 2πℏ) these recover the Schrödinger equation as an equivalent representation. Probabilities enter via the ensemble identification ρ = |ψ|² (not by derivation). The stance preserves causality and non-signalling and is compatible with PBR and Bell constraints. Randomness and infinity are treated as signals of incomplete mapping, not foundations. Universality is presented as a hypothesis, open to empirical and theoretical falsification via the stated counterexamples. Preprint; not peer-reviewed. Feedback and review are welcome.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-08-27
DOI
https://doi.org/10.5281/zenodo.17049147
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Geometric Reaction: From Quantum Hydrodynamics to a Cross-Domain Generative Principle

Zenodo (CERN European Organization for Nuclear Research)
Geochemistry and Geologic Mapping
article

Geometric Reaction: From Quantum Hydrodynamics to a Cross-Domain Generative Principle

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Abstract

Geometric Reaction (First Law). Geometry is the operative container; any realized (above-threshold) difference within it induces a reaction R that unfolds as tempo T (time as rhythm of change) and residue M (persistent form, including matter). The recursive cycle geometry → reaction → new geometry appears across physics, biology, engineering, and narrative. From an action functional in density ρ and phase S, the framework yields a continuity equation and a Hamilton–Jacobi equation with a geometric information term Q[ρ,g]; under standard regularity (ρ > 0, phase single-valued up to 2πℏ) these recover the Schrödinger equation as an equivalent representation. Probabilities enter via the ensemble identification ρ = |ψ|² (not by derivation). The stance preserves causality and non-signalling and is compatible with PBR and Bell constraints. Randomness and infinity are treated as signals of incomplete mapping, not foundations. Universality is presented as a hypothesis, open to empirical and theoretical falsification via the stated counterexamples. Preprint; not peer-reviewed. Feedback and review are welcome.

Zenodo (CERN European Organization for Nuclear Research)
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Geochemistry and Geologic Mapping
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