A Time-Role Audit of Foundational Physics: Clock-Language Mapping Across Quantum, Classical, and Gravitational Equations (v2)
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2026
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| author | Monk |
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| contents | <h2 class="MsoNormal"><strong>Abstract</strong></h2> <p class="MsoNormal">This paper presents a systematic algebraic audit of how the variable functions across foundational equations in physics — classical, quantum, relativistic, and gravitational. Building on a previously published five-role time taxonomy, we apply explicit time-role labeling to the Dirac equation, Schrödinger equation, hydrogen atom energy, de Broglie relations, Newtonian mechanics, and the Schwarzschild metric. In every case, the same three structural roles emerge: background evolution time , internal oscillation period , and propagation travel time .</p> <p class="MsoNormal">The audit produces a sector map showing which time roles govern which physical domains. Energy and mass scales are carried solely by . Momentum and propagation are carried solely by . Evolution and ordering are governed by . Newtonian mechanics is the mixed sector in which all three roles appear simultaneously. The Schrödinger equation is identified as the bridge equation that explicitly equates evolution with a combination of and .</p> <p class="MsoNormal">From the Dirac plane wave structure, a natural phase form falls out:</p> <p class="MsoNormal"><br><br></p> <p class="MsoNormal">Using only the time-labeled transition amplitude integral, we show that energy transfer between two systems is maximized precisely when their internal oscillation rates are matched — a resonance condition expressed entirely in clock language without invoking quantum postulates directly.</p> <p class="MsoNormal">No new predictions are claimed. No new physics is introduced. The sole result is a consistent, parsimonious re-expression of known physics in a reduced language, with two free parameters ( and ) governing the audited sector. All open walls are stated explicitly.</p> <p class="MsoNormal">This work is a structural audit and reparameterization of existing physical equations. It does not introduce new dynamical laws or modify any empirical predictions. Its purpose is to expose consistent role separation within existing mathematics.<br><br><strong>Notation hygiene note.</strong> In this version, is a role category, not always a single identical quantity. The de Broglie propagation time is written , while the Lorentz propagation clock is written , related by . Radial coordinate light-crossing time in the Schwarzschild section is separately labeled . These distinctions introduce no new free parameter; they only prevent conflating related propagation clocks across different sectors. In phase expressions, the intended normalized plane-wave form is , up to sign convention.<br><br>Citation Updates on v4- we want to be clear we're not claiming anything here but algebraic <br><br></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20032858 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Time-Role Audit of Foundational Physics: Clock-Language Mapping Across Quantum, Classical, and Gravitational Equations (v2) Monk time taxonomy, foundational physics, underdetermination, Lorentz structure, Dirac equation, Schrödinger equation, Schwarzschild metric, phase alignment, clock framework, mathematical physics <h2 class="MsoNormal"><strong>Abstract</strong></h2> <p class="MsoNormal">This paper presents a systematic algebraic audit of how the variable functions across foundational equations in physics — classical, quantum, relativistic, and gravitational. Building on a previously published five-role time taxonomy, we apply explicit time-role labeling to the Dirac equation, Schrödinger equation, hydrogen atom energy, de Broglie relations, Newtonian mechanics, and the Schwarzschild metric. In every case, the same three structural roles emerge: background evolution time , internal oscillation period , and propagation travel time .</p> <p class="MsoNormal">The audit produces a sector map showing which time roles govern which physical domains. Energy and mass scales are carried solely by . Momentum and propagation are carried solely by . Evolution and ordering are governed by . Newtonian mechanics is the mixed sector in which all three roles appear simultaneously. The Schrödinger equation is identified as the bridge equation that explicitly equates evolution with a combination of and .</p> <p class="MsoNormal">From the Dirac plane wave structure, a natural phase form falls out:</p> <p class="MsoNormal"><br><br></p> <p class="MsoNormal">Using only the time-labeled transition amplitude integral, we show that energy transfer between two systems is maximized precisely when their internal oscillation rates are matched — a resonance condition expressed entirely in clock language without invoking quantum postulates directly.</p> <p class="MsoNormal">No new predictions are claimed. No new physics is introduced. The sole result is a consistent, parsimonious re-expression of known physics in a reduced language, with two free parameters ( and ) governing the audited sector. All open walls are stated explicitly.</p> <p class="MsoNormal">This work is a structural audit and reparameterization of existing physical equations. It does not introduce new dynamical laws or modify any empirical predictions. Its purpose is to expose consistent role separation within existing mathematics.<br><br><strong>Notation hygiene note.</strong> In this version, is a role category, not always a single identical quantity. The de Broglie propagation time is written , while the Lorentz propagation clock is written , related by . Radial coordinate light-crossing time in the Schwarzschild section is separately labeled . These distinctions introduce no new free parameter; they only prevent conflating related propagation clocks across different sectors. In phase expressions, the intended normalized plane-wave form is , up to sign convention.<br><br>Citation Updates on v4- we want to be clear we're not claiming anything here but algebraic <br><br></p> |
| title | A Time-Role Audit of Foundational Physics: Clock-Language Mapping Across Quantum, Classical, and Gravitational Equations (v2) |
| topic | time taxonomy, foundational physics, underdetermination, Lorentz structure, Dirac equation, Schrödinger equation, Schwarzschild metric, phase alignment, clock framework, mathematical physics |
| url | https://doi.org/10.5281/zenodo.20032858 |