Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed

The Temporal Equivalence Principle (TEP) proposes a covariant reformulation of relativity in which proper time is a dynamical field and the speed of light is an emergent, strictly local invariant rather than a global constant. The framework employs two metrics on a single spacetime manifold—a gravitational metric and a causal (matter) metric—related by a conformal–disformal map. This preserves local Lorentz invariance while predicting synchronization holonomy, a path-dependent timing offset absent in general relativity. The preprint develops the full action, field equations, conservation laws, Parametrized Post-Newtonian (PPN) mapping, and screening mechanisms, and outlines multiple falsifiable tests using optical clock networks, portable and interplanetary time transfer, and multi-messenger observations.

Preliminary analysis of 62.7 million GNSS atomic clock measurements identifies distance-structured correlations (λ = 3,330–4,549 km) within the predicted range and apparent coupling to Earth's orbital motion and planetary gravitational influences. These findings require independent validation and peer review. See the companion experimental analysis: DOI: 10.5281/zenodo.17127229.

Website: https://matthewsmawfield.github.io/TEP/