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Unified Coherence Geometry: A Common Action for Physical Fields

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Internal ID: CGI-RSR-000011
Document Type: Research Paper
Status: Public
Domains: Physics, Foundations
Research Topics: Actions, fields

Abstract


This work introduces Coherence Geometry (CG), a unified geometric framework in which the governing equations of physics arise as domain-specific projections of a single variational principle. Every physical system is represented by a continuous coherence field

Φ(x,t)=A(x,t)[eiθ1(x,t),eiθ2(x,t),…,eiθN(x,t)]T,\Phi(x,t) = A(x,t)\,[\,e^{i\theta_1(x,t)},\,e^{i\theta_2(x,t)},\,\ldots,\,e^{i\theta_N(x,t)}\,]^{\!\mathrm{T}},

where the internal phases {θk} are mutually orthogonal components of the multi-phase algebra \(M\), and \(A\) encodes local coherence amplitude. The Unified Coherence Action (UCA) governs the evolution of this field, and its constrained forms reproduce the major laws of physics: Newtonian and gravitational dynamics from low-curvature motion, Maxwell’s equations from dual-phase alignment, the Schroedinger and Dirac systems from stationary curvature flow, thermodynamic and hydrodynamic transport from coarse-grained curvature averaging, and the Einstein field equations from global phase preservation in spacetime. Across these regimes, quantities such as energy, momentum, temperature, and curvature emerge as geometric measures of coherence transport rather than independent constructs. Quantization follows from topological closure of phase channels, entropy from the fragmentation of alignment basins, and relativistic invariance from the coherence limit of phase propagation. Cross-domain analysis reveals that conserved quantities arise from Noether-like symmetries of the coherence action, establishing a continuous equivalence between field, flux, and curvature. The result is a unified description in which classical mechanics, quantum theory, thermodynamics, and relativity are not separate frameworks but complementary projections of a single geometric principle:  that coherence—the capacity of a field to maintain alignment under curvature— is the fundamental invariant of nature.

Available Document

DOI: 10.5281/zenodo.20119489

Citation:
Petersen, B. L., Johnson, R. K., & Bruno, A. E. (2026). Unified Coherence Geometry: A Common Action for Physical Fields. Zenodo. https://doi.org/10.5281/zenodo.20119489

Source Code and Supporting Materials

None

Summary and Notes

This paper is listed in the Foundation Papers section because it serves as a source document for CDR-01.

Related Work

CGI-RSR-000012: The Unified Coherence Functional: A Closed GenerativeBasis for Mathematics

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