Relational Time Flow from Particles’ Internal Cyclic Times: Why Elementary Cycles Theory Works

Elementary particles exhibit intrinsic phase recurrences, \rev{implicit in the undulatory description}, so each can serve as a ``virtually perfect'' reference relativistic clock. From this perspective, Rovelli's ``timeless'' viewpoint is best read not as denying time, but as denying the fundamentality of any preferred external time coordinate: time persists as internal cyclic variables carried by particles, covariantly modulated by energy exchange and relativistic transformations. \rev{Then,} macroscopic flow arises from records and thermodynamic coarse-graining. This Letter shows that cyclic internal times of elementary systems are fully compatible with the ordinary non-compact relativistic time flow observed in nature. In particular, it identifies the fundamental ``internal'' variables underlying physical relativistic time with the particles' intrinsic cyclic times and their relational covariant modulations. Supported by theoretical and phenomenological results established in previous works, intrinsic temporal periodicity constitutes the fundamental principle of Elementary Cycles Theory and acts as exact quantization condition.