From Sagnac Holonomy to a Phase-Drift Model for Cosmic Expansion: Part I: A Standard Relativistic Derivation of a Fixed Clock Deficit; Part II: A Phase-Locking Hypothesis and its Testable Cosmological Implications

Abstract

Part I provides a standard relativistic derivation of the slow-clock-transport limit on a rotating Earth. In the limit of vanishing transport speed around one equatorial loop, the accumulated proper‑time difference approaches a fixed value of approximately −207 ns, identified as the Sagnac/time‑holonomy term, proportional to the rotation vector and enclosed area. Part II advances a non‑standard phase‑locking hypothesis: each completed rotational cycle fractionally rescales the local metrological baseline multiplicatively (compound‑interest law). Calibrated with the 207 ns loop scale per day and combined with a spiral‑observer Doppler readout, a conditional benchmark assigns roughly 3.92 nm of apparent CMB wavelength shift over 1965–2026 to local metrological drift, versus 0.31 nm from standard late‑time expansion—yielding a local fraction of about 93%. The paper explicitly notes that this number is a model‑dependent illustration, not an observed CMB drift, and outlines falsification tests via clock networks, GNSS, pulsar timing, and decomposition of monopole/dipole signatures.

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