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| Natura: | Recurso digital |
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Zenodo
2026
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| Accesso online: | https://doi.org/10.5281/zenodo.19600822 |
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Sommario:
- <p>We present a rigorously Lorentz-covariant, parameter-free geometric framework in which a universal small effective coupling in the 2\%-5\% range emerges dynamically from the topological closure of helical particle worldlines in Minkowski spacetime. The value $\eta \sim 0.03$ should not be interpreted as a fundamental constant, but as a dynamically selected value within a stability window defined by geometric and topological constraints. The theory is built from three minimal, physically motivated axioms: the invariant speed of light, a covariant decomposition of timelike worldlines into longitudinal drift and transverse helical degrees of freedom, and a global topological closure constraint on the $S^2$ directional manifold of transverse motion.</p> <p>We derive the core quantization condition for the dimensionless coupling parameter $\eta = v_\parallel/c$ via variational minimization of a fully covariant worldline action, yielding:<br>\[<br>\eta = \frac{2\pi}{N} + \delta\eta_{\text{topo}},<br>\]<br>where $N \in \mathbb{Z}^+$ is the integer winding number of the helical trajectory on the 2-sphere, and $\delta\eta_{\text{topo}}$ is the curvature-induced topological residual derived rigorously from the geodesic deviation equation of general relativity. Using Lyapunov stability analysis of transverse perturbations, we demonstrate that the winding number is dynamically stabilized in the range $N \in [125, 314]$ by a sign change in the Lyapunov exponent, naturally yielding the universal coupling range $\eta \in [0.02, 0.05]$ with no free parameters or manual tuning.</p> <p>We analyze the full geometric phase structure of the theory, identify the critical point where the Lyapunov exponent crosses zero, and derive quantitative predictions for the shift in $\eta$ under different gravitational potentials, providing a direct, measurable link between our framework and general relativity. We propose four concrete, experimentally feasible tests of the theory using existing facilities, with detailed systematic error budgets. All results are consistent with established special relativity and general relativity in the appropriate limits, and we present strict falsifiability criteria aligned with the standards of Physical Review D.</p>