| _version_ | 1866901482315448320 |
|---|---|
| author | Morrow, Robert T ChatGPY(OpenAI) |
| author_facet | Morrow, Robert T ChatGPY(OpenAI) |
| contents | <p>Closure Theory provides a geometric framework in which mass, quantisation, and coupling arise from the requirement that curvature must close. In this work, we clarify the<br>relationship between intrinsic structure, dynamical representation, and physical observation<br>by identifying two distinct mappings within the theory.<br>The transformation between the intrinsic (T-domain) and dynamical (t-domain) descriptions is shown to preserve the full physical content of the system, corresponding to a change<br>of variables in which closure is encoded implicitly through invariant relations. In contrast,<br>the projection from the dynamical domain to observables is information-reducing, suppressing internal phase structure and yielding measurable quantities.<br>Within this framework, the dynamical variables admit an internal phase structure consistent with the invariant relations of relativistic physics. Energy and momentum are thereby<br>interpreted as components of an underlying phase-structured circulation, constrained by closure and recurrence. States conventionally described as being at rest correspond to closed<br>internal circulation, while motion reflects a redistribution of this structure under transformation.<br>This distinction provides a unified interpretation of invariant quantities as phase-averaged<br>manifestations of an underlying dynamical process, without the introduction of independent<br>hidden variables. Residual asymmetries in the phase structure give rise to higher-order<br>effects, providing a common geometric origin for both coupling constants and mass corrections.<br>The framework preserves standard observable relations while situating them within a<br>deeper geometric structure, establishing a foundation for further investigation of closure,<br>recurrence, and phase in physical systems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19851190 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Closure Theory: Intrinsic Domain, Dynamic Domain and Observable Projection Morrow, Robert T ChatGPY(OpenAI) <p>Closure Theory provides a geometric framework in which mass, quantisation, and coupling arise from the requirement that curvature must close. In this work, we clarify the<br>relationship between intrinsic structure, dynamical representation, and physical observation<br>by identifying two distinct mappings within the theory.<br>The transformation between the intrinsic (T-domain) and dynamical (t-domain) descriptions is shown to preserve the full physical content of the system, corresponding to a change<br>of variables in which closure is encoded implicitly through invariant relations. In contrast,<br>the projection from the dynamical domain to observables is information-reducing, suppressing internal phase structure and yielding measurable quantities.<br>Within this framework, the dynamical variables admit an internal phase structure consistent with the invariant relations of relativistic physics. Energy and momentum are thereby<br>interpreted as components of an underlying phase-structured circulation, constrained by closure and recurrence. States conventionally described as being at rest correspond to closed<br>internal circulation, while motion reflects a redistribution of this structure under transformation.<br>This distinction provides a unified interpretation of invariant quantities as phase-averaged<br>manifestations of an underlying dynamical process, without the introduction of independent<br>hidden variables. Residual asymmetries in the phase structure give rise to higher-order<br>effects, providing a common geometric origin for both coupling constants and mass corrections.<br>The framework preserves standard observable relations while situating them within a<br>deeper geometric structure, establishing a foundation for further investigation of closure,<br>recurrence, and phase in physical systems.</p> |
| title | Closure Theory: Intrinsic Domain, Dynamic Domain and Observable Projection |
| url | https://doi.org/10.5281/zenodo.19851190 |