Temporal Mechanics
Author: Edwin Pease
Version: April 2026
DOI: 10.5281/zenodo.19897815
Abstract: By identifying Schrödinger phase, proper time, and internal holonomy as related aspects of a single temporal structure, Temporal Mechanics proposes a common geometric origin for the distinct notions of time appearing in quantum theory and relativity. In this framework, clocks unwind a hidden periodic structure whose abelian holonomy is shared by quantum phase and proper time. The internal sector is modeled as a compact three-torus \mathcal M_\tau\cong\mathbb T^3 equipped with a U(3) bundle whose determinant line is identified, by a chosen phase lock, with the auxiliary U(1) line of a \mathrm{Spin}^c(1,3) structure on an emergent Lorentzian spacetime \mathcal M_4. The traceless sector carries nonabelian geometric structures allowing Higgs-like and flavor degrees of freedom which are interpreted as modes of the internal connection. The induced internal Dirac spectrum provides geometric mass scales. This reinterpretation of proper time, gauge structure, and mass as related manifestations of a common temporal geometry removes the tension between quantum mechanics and relativity.