Amplitude–Phase Geometry of Vacuum Resonances: Mass, Charge, Electromagnetic and Gravitational Coupling from Detuned Phase Structure
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2026
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| _version_ | 1866902337125089280 |
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| author | DELATORRE, JOHN |
| author_facet | DELATORRE, JOHN |
| contents | <p>This paper presents a proof of concept for a unified geometric description of mass, charge,<br>and the fundamental interactions within the Primeon Framework. The goal is to establishfeasibility — that a single amplitude-phase field ℘( ) = ( ) Θ( ) on a prime-logarithm internal<br>coordinate can coherently generate the qualitative structure of particle physics and gravity —<br>rather than to make quantitative predictions. Free parameters are identified and their physical<br>interpretation is given; their derivation from first principles is left for subsequent work.<br>From a variational principle we derive a conserved phase current and construct an effective<br>2D metric [1, 2] whose scalar curvature is computed explicitly. Physical mass is defined as the<br>curvature functional phys = ∫ | | , with a free scale parameter. We introduce a phaselocking potential = 0( ) − Λ 2 cos(4Θ) with Λ > 0 and prove that quarter-turn locking is dynamically stable [3], so that exact locking yields neutral states as a theorem on stable fixed points — the strongest single result of the paper.<br>Nonzero charge arises only from detuned, parity-asymmetric phase configurations, appears at second order in the detuning field, and is evaluated in closed form. The detuning parameter is recast as a collective coordinate [4] measuring phase-core displacement; charge origin is identified with the question of whether an effective potential eff( ) has minima at ≠ 0. The framework is extended to spacetime via a joint action and collective-coordinate reduction, coupling the internal current to an Abelian gauge field [5] and deriving Maxwell-like field equations, charge conservation, and the Lorentz force law. Gravitational coupling is included<br>through a point-particle stress–energy tensor sourcing the Einstein equations [6].<br>A separate analysis establishes the 2D Einstein-Hilbert obstruction (the Gauss-Bonnet boundaryterm collapse [7]) and shows that a JT-like dilaton extension [1, 2, 8] = ∫[ ⋅ − ( )] admits the sech profile as a vacuum solution when ( ) = 4 25 2 0 5 − 2 23 3. The exact curvature mass is derived as phys = (8 2 2 0(√2−1))/3 .<br>All assumptions and free parameters are stated explicitly. The paper is intended as a foundation for quantitative development in subsequent work.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19561013 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Amplitude–Phase Geometry of Vacuum Resonances: Mass, Charge, Electromagnetic and Gravitational Coupling from Detuned Phase Structure DELATORRE, JOHN General Relativity Theoretical Physics Primeon Framework Quantum Physics Cosmology metric Christoffel Symbols Ricci Scalar Charge Soliton Chirality, Parity Electromagnetic Coupling Phase Current Gauge Field Action Charge Conservation Lorentz Force Gauge Symmetry <p>This paper presents a proof of concept for a unified geometric description of mass, charge,<br>and the fundamental interactions within the Primeon Framework. The goal is to establishfeasibility — that a single amplitude-phase field ℘( ) = ( ) Θ( ) on a prime-logarithm internal<br>coordinate can coherently generate the qualitative structure of particle physics and gravity —<br>rather than to make quantitative predictions. Free parameters are identified and their physical<br>interpretation is given; their derivation from first principles is left for subsequent work.<br>From a variational principle we derive a conserved phase current and construct an effective<br>2D metric [1, 2] whose scalar curvature is computed explicitly. Physical mass is defined as the<br>curvature functional phys = ∫ | | , with a free scale parameter. We introduce a phaselocking potential = 0( ) − Λ 2 cos(4Θ) with Λ > 0 and prove that quarter-turn locking is dynamically stable [3], so that exact locking yields neutral states as a theorem on stable fixed points — the strongest single result of the paper.<br>Nonzero charge arises only from detuned, parity-asymmetric phase configurations, appears at second order in the detuning field, and is evaluated in closed form. The detuning parameter is recast as a collective coordinate [4] measuring phase-core displacement; charge origin is identified with the question of whether an effective potential eff( ) has minima at ≠ 0. The framework is extended to spacetime via a joint action and collective-coordinate reduction, coupling the internal current to an Abelian gauge field [5] and deriving Maxwell-like field equations, charge conservation, and the Lorentz force law. Gravitational coupling is included<br>through a point-particle stress–energy tensor sourcing the Einstein equations [6].<br>A separate analysis establishes the 2D Einstein-Hilbert obstruction (the Gauss-Bonnet boundaryterm collapse [7]) and shows that a JT-like dilaton extension [1, 2, 8] = ∫[ ⋅ − ( )] admits the sech profile as a vacuum solution when ( ) = 4 25 2 0 5 − 2 23 3. The exact curvature mass is derived as phys = (8 2 2 0(√2−1))/3 .<br>All assumptions and free parameters are stated explicitly. The paper is intended as a foundation for quantitative development in subsequent work.</p> |
| title | Amplitude–Phase Geometry of Vacuum Resonances: Mass, Charge, Electromagnetic and Gravitational Coupling from Detuned Phase Structure |
| topic | General Relativity Theoretical Physics Primeon Framework Quantum Physics Cosmology metric Christoffel Symbols Ricci Scalar Charge Soliton Chirality, Parity Electromagnetic Coupling Phase Current Gauge Field Action Charge Conservation Lorentz Force Gauge Symmetry |
| url | https://doi.org/10.5281/zenodo.19561013 |