Authors: Xavier Aupí
This article forms the second part of the study entitled textit{The Fundamental Cycle: A Harmonic Reinterpretation of Relativity and Its Cosmological Implications}. Whereas the first part focused on macroscopic systems, the present work applies the same universal framework at the microscopic level. We begin by emphasizing the wave-like nature of relativity. Subsequently, we provide a geometric derivation of the de Broglie and Planck-Einstein relations. This derivation leads to a representation of particles as sets of rotating elements in spacetime. Next, we derive the uncertainty principle within the relativistic framework, contingent upon the following experimentally testable conjecture: there exist specific momentum values for which a particle becomes unobservable.We then introduce discrete time, which refines the earlier conception of particles as sets of continuously rotating elements into a model of discrete rotation. In this model, the elements undergo a collective cyclic exchange along the vertices of a regular polygon---or, more generally, a regular star polygon---in synchrony with the tick of proper time. This structure provides the foundation for defining spin as an intrinsic property emerging from the cyclic symmetry of the particle’s internal dynamics within discrete spacetime.Once spin is established, we derive the fundamental relation ( hf_o = m_o c^2 ). Finally, a quantum-level expression for gravity is obtained.
Comments: 45 Pages.
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[v1] 2025-07-14 17:36:48
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