By identifying Schrödinger’s 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 ℳ τ ≅ 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 Spin c ( 1 , 3 ) structure on an emergent Lorentzian spacetime ℳ 4 . The traceless sector carries non-Abelian geometric structures allowing Higgs and flavor degrees of freedom, which are interpreted as modes of the internal connection, while the induced internal Dirac spectrum provides rest masses. This framework proposes a geometric mechanism by which quantum phase, proper time, internal gauge holonomy, and spectral masses may be realized as different projections of a single phase-locked temporal bundle that is compatible with the Standard Model.
KeywordsSchr?dinger PhaseProper TimeHolonomy
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