Geometric Reaction: A Hydrodynamic Restatement of Quantum Mechanics and a Generative Conjecture

This work introduces the postulate of Geometric Reaction (G → R = T + M) within the Law of Generative Order: geometry is treated as absolute, and difference within geometry must react, producing time and matter. Starting from an action for density ρ and phase S, variation yields the continuity equation and a Hamilton–Jacobi equation with a quantum potential Q[ρ, g]; together they are mathematically equivalent to the Schrödinger equation and recover standard benchmarks, including the hydrogen 1s state and Gaussian wave-packet spreading. Thus the framework provides a hydrodynamic restatement of quantum mechanics that does not postulate probability. Beyond this recovery, we conjecture that Geometric Reaction functions as a generative rule across scales. The framework is compatible with loophole-free Bell tests and PBR: determinism is contextual and global, correlations are nonlocal yet non-signalling, and ensemble statistics follow the Born rule as epistemic summaries of unresolved geometry. Back-reaction (G → R → G′) offers a possible link to spacetime dynamics, and we sketch an experimental handle via curvature-coupled modifications of Q. These conjectures remain provisional and open to test. Disclaimer. Preprint; not peer reviewed. Equations and derivations are presented in good faith and may contain errors. Feedback and critical review are welcome.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-08-27
DOI
https://doi.org/10.5281/zenodo.16994765
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Geometric Reaction: A Hydrodynamic Restatement of Quantum Mechanics and a Generative Conjecture

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

Geometric Reaction: A Hydrodynamic Restatement of Quantum Mechanics and a Generative Conjecture

article en

Abstract

This work introduces the postulate of Geometric Reaction (G → R = T + M) within the Law of Generative Order: geometry is treated as absolute, and difference within geometry must react, producing time and matter. Starting from an action for density ρ and phase S, variation yields the continuity equation and a Hamilton–Jacobi equation with a quantum potential Q[ρ, g]; together they are mathematically equivalent to the Schrödinger equation and recover standard benchmarks, including the hydrogen 1s state and Gaussian wave-packet spreading. Thus the framework provides a hydrodynamic restatement of quantum mechanics that does not postulate probability. Beyond this recovery, we conjecture that Geometric Reaction functions as a generative rule across scales. The framework is compatible with loophole-free Bell tests and PBR: determinism is contextual and global, correlations are nonlocal yet non-signalling, and ensemble statistics follow the Born rule as epistemic summaries of unresolved geometry. Back-reaction (G → R → G′) offers a possible link to spacetime dynamics, and we sketch an experimental handle via curvature-coupled modifications of Q. These conjectures remain provisional and open to test. Disclaimer. Preprint; not peer reviewed. Equations and derivations are presented in good faith and may contain errors. Feedback and critical review are welcome.

Zenodo (CERN European Organization for Nuclear Research)
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