| _version_ | 1866901905927569408 |
|---|---|
| author | Jonatan P. Camargo |
| author_facet | Jonatan P. Camargo |
| contents | <p>We present a variational formulation in which the phase is identified as the operational manifestation of the accumulated action, establishing a structural unification between different physical regimes. It is shown that the fundamental phase of any admissible system is given by \[ \phi = \frac{S}{\hbar}, \] from which it follows that the frequency — and, therefore, the operational content of time — emerges directly from the rate of action accumulation, \[ \omega = \frac{\dot S}{\hbar}. \]</p> <p>The analysis of the relative phase evolution between independent systems leads to the demonstration that interferential coherence is, in general, episodic, being characterized by a discrete set of instants of compatibility.</p> <p>This results in a precise formulation of the physical interaction as \[ E_{\mathrm{int}} = E_{\mathrm{esp}} \cap E_\phi, \] in which the occurrence of observable events is filtered by phase compatibility.</p> <p>It is further shown that massive and massless regimes correspond to different parameterizations of the same phase structure, eliminating the need for distinct ontologies for these cases. The introduction of linear classical operators, such as macroscopic electromagnetic systems, allows us to demonstrate that such operators act exclusively on the observed phase, \[ \phi_{\mathrm{obs}} = \phi_{\mathrm{fund}} + \phi_C, \] shifting the synchronization instants without altering the underlying variational dynamics.</p> <p>As a result, a rigorous distinction is established between the structural level and the observational level: the action governs the fundamental dynamics, while the observed phase corresponds to its operational projection under reading transformations. Finally, the possibility of an extended variational framework in which the experimental apparatus is incorporated into a global functional \(S_{\mathrm{tot}}\) is discussed, leaving this construction as a program for future work.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19394702 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | From Action to Observation: Structural Separation between Fundamental Phase and Classical Phase in Relativistic Dynamics Jonatan P. Camargo <p>We present a variational formulation in which the phase is identified as the operational manifestation of the accumulated action, establishing a structural unification between different physical regimes. It is shown that the fundamental phase of any admissible system is given by \[ \phi = \frac{S}{\hbar}, \] from which it follows that the frequency — and, therefore, the operational content of time — emerges directly from the rate of action accumulation, \[ \omega = \frac{\dot S}{\hbar}. \]</p> <p>The analysis of the relative phase evolution between independent systems leads to the demonstration that interferential coherence is, in general, episodic, being characterized by a discrete set of instants of compatibility.</p> <p>This results in a precise formulation of the physical interaction as \[ E_{\mathrm{int}} = E_{\mathrm{esp}} \cap E_\phi, \] in which the occurrence of observable events is filtered by phase compatibility.</p> <p>It is further shown that massive and massless regimes correspond to different parameterizations of the same phase structure, eliminating the need for distinct ontologies for these cases. The introduction of linear classical operators, such as macroscopic electromagnetic systems, allows us to demonstrate that such operators act exclusively on the observed phase, \[ \phi_{\mathrm{obs}} = \phi_{\mathrm{fund}} + \phi_C, \] shifting the synchronization instants without altering the underlying variational dynamics.</p> <p>As a result, a rigorous distinction is established between the structural level and the observational level: the action governs the fundamental dynamics, while the observed phase corresponds to its operational projection under reading transformations. Finally, the possibility of an extended variational framework in which the experimental apparatus is incorporated into a global functional \(S_{\mathrm{tot}}\) is discussed, leaving this construction as a program for future work.</p> |
| title | From Action to Observation: Structural Separation between Fundamental Phase and Classical Phase in Relativistic Dynamics |
| url | https://doi.org/10.5281/zenodo.19394702 |