Mass and Complexity from Coupling Constraint Geometry
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| Natura: | Recurso digital |
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2025
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| _version_ | 1866901892480630784 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p>This work advances the Relational Thermodynamic Layered Index (RTLI) framework by reframing its core structures as <em>logically unavoidable consequences of coupling</em>, rather than postulated features. Any system with more than one degree of freedom must exchange information and energy; the central question is not whether coupling occurs, but which coupling regimes preserve coherence without collapse.</p> <p>We show that under-coupling leads to fragmentation, over-coupling leads to runaway synchronization, and only a narrow stability corridor permits bounded, reversible interaction. Within this corridor, quadratic coupling cost emerges as the unique stable form compatible with feedback and reversibility. Constant relative coupling cost then enforces exponential accumulation, selecting <span>e</span> as the natural base.</p> <p>The RTLI corridor geometry follows necessarily: approximate orthogonality between relational layers, toroidal configuration space as the minimal topology supporting bidirectional closure, and discrete coherence levels generated by phase-transition (rectangle) completions. Mass is interpreted as stored synchronization lag arising from asymmetric coupling, not as an intrinsic substance.</p> <p>Within this constraint framework, the electron mass emerges from corridor geometry as</p> <p><span>m_e c^2 = E_{\text{corridor}} \, e^{4\pi^2/e},</span></p> <p>with agreement at the sub-percent level using a single empirically anchored energy scale. Parallel <span>e</span>-based scaling appears in biological complexity metrics and adaptive information systems, suggesting a shared structural origin.</p> <p>The results do not replace Standard Model or biological dynamics, but provide a unifying constraint-level explanation for why stable systems across domains organize around the same thresholds. The framework yields clear falsification criteria and reframes mass, time, and complexity as consequences of unavoidable coupling geometry.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17946628 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Mass and Complexity from Coupling Constraint Geometry De Jesus, Elias Relational Physics Coupling Necessity Coherence Thresholds Quadratic Coupling Cost Exponential Scaling Relational Mass Synchronization Lag Toroidal Phase Space Depth Principle Electron Mass Geometry Information–Energy Coupling Phase Transitions Constraint-Driven Physics AI Stability and Grokking Cross-Domain Scaling Laws <p>This work advances the Relational Thermodynamic Layered Index (RTLI) framework by reframing its core structures as <em>logically unavoidable consequences of coupling</em>, rather than postulated features. Any system with more than one degree of freedom must exchange information and energy; the central question is not whether coupling occurs, but which coupling regimes preserve coherence without collapse.</p> <p>We show that under-coupling leads to fragmentation, over-coupling leads to runaway synchronization, and only a narrow stability corridor permits bounded, reversible interaction. Within this corridor, quadratic coupling cost emerges as the unique stable form compatible with feedback and reversibility. Constant relative coupling cost then enforces exponential accumulation, selecting <span>e</span> as the natural base.</p> <p>The RTLI corridor geometry follows necessarily: approximate orthogonality between relational layers, toroidal configuration space as the minimal topology supporting bidirectional closure, and discrete coherence levels generated by phase-transition (rectangle) completions. Mass is interpreted as stored synchronization lag arising from asymmetric coupling, not as an intrinsic substance.</p> <p>Within this constraint framework, the electron mass emerges from corridor geometry as</p> <p><span>m_e c^2 = E_{\text{corridor}} \, e^{4\pi^2/e},</span></p> <p>with agreement at the sub-percent level using a single empirically anchored energy scale. Parallel <span>e</span>-based scaling appears in biological complexity metrics and adaptive information systems, suggesting a shared structural origin.</p> <p>The results do not replace Standard Model or biological dynamics, but provide a unifying constraint-level explanation for why stable systems across domains organize around the same thresholds. The framework yields clear falsification criteria and reframes mass, time, and complexity as consequences of unavoidable coupling geometry.</p> |
| title | Mass and Complexity from Coupling Constraint Geometry |
| topic | Relational Physics Coupling Necessity Coherence Thresholds Quadratic Coupling Cost Exponential Scaling Relational Mass Synchronization Lag Toroidal Phase Space Depth Principle Electron Mass Geometry Information–Energy Coupling Phase Transitions Constraint-Driven Physics AI Stability and Grokking Cross-Domain Scaling Laws |
| url | https://doi.org/10.5281/zenodo.17946628 |