The Mount Wilson Paradigm: Restoring the Eternal Universe via the Temporal Equivalence Principle

Abstract

Cosmological redshift is standardly interpreted as a geometric signature of spatial expansion. This interpretation requires a fundamental assumption that is defined herein as the Isochrony Axiom: the premise that, after gravitational and kinematic effects derived from the spacetime metric have been included, the calibration of every matter clock is fully exhausted by that single metric, so that no independently dynamical field may rescale matter proper time across cosmological epochs. Standard single-metric cosmology closed the temporal sector before the redshift was interpreted. In this paper, it is demonstrated that when matter-clock calibration is permitted an independent dynamical scalar degree of freedom (phi), the measured cosmological redshift (z) can be rigorously derived from the ratio of matter-clock calibrations between emission and observation on a static spatial manifold. The scalar field defines a spatiotemporal clock geometry - the Temporal Topology - whose homogeneous evolution governs cosmological calibration and whose inhomogeneous disformal connection can become non-integrable, producing synchronization holonomy. Using the canonical matter metric of the Temporal Equivalence Principle (TEP), g_tilde_{mu nu} = A^2(phi) g_{mu nu} + B(phi) nabla_mu phi nabla_nu phi, the Mount Wilson Equivalence Theorem is proven: on a homogeneous, spatially flat, static gravitational background, with universal matter coupling and A^2 - B dot_phi^2 > 0, the endpoint redshift 1 + z = A_0/A_em is observationally degenerate with the FLRW relation 1 + z = a_0/a_em at the level of the redshift observable alone. TEP is distinguished from a mere conformal rewriting by its separate matter and gravitational propagation sectors, making multi-messenger observations a principal inter-sector discriminator. The historical data from Mount Wilson Observatory are re-examined to separate the documented spectral displacements from the subsequent spatial inferences, demonstrating that the observed dynamics are consistent with a temporal reinterpretation on a static spatial manifold. Precision GNSS chronometry, pulsar scintillation, and Lunar Laser Ranging are identified as the empirical instruments capable of testing the temporal sector locally. Consequently, a globally consistent framework for an eternal, deterministic continuum is presented, supplying the common mathematical resolution to the questions that Einstein separated. Keywords: Temporal Equivalence Principle, isochrony axiom, cosmological redshift, spatial expansion, expansion degeneracy, scalar-tensor theory, static universe, eternal universe, synchronization holonomy, temporal shear, Hubble tension, JWST anomalies, dark matter, dark energy, Einstein, Hubble Website: https://mlsmawfield.com/tep/hub/Repository: https://github.com/matthewsmawfield/TEP-HUB DOI: 10.5281/zenodo.21954258 Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All analysis code, configuration files, and manuscripts are open source. Feedback and contributions to further test these results are welcome.