This research program explores the hypothesis that proper time may be environment-dependent, testing this proposition across five scales ranging from terrestrial atomic clocks to high-redshift galaxies observed by JWST. Analysis of GNSS clock correlations suggests a characteristic length scale (λ ≈ 4,200 km) that, if confirmed, would correspond to a critical density (ρc ≈ 20 g/cm³) potentially relevant to phenomena from atomic physics to galactic structure.
The Temporal Equivalence Principle (TEP) hypothesizes that proper time is not merely a parameter along worldlines but a dynamical scalar field coupled to spacetime geometry, analogous to how the equivalence principle treats gravity as geometry rather than force. This theoretical foundation (Paper 0) yields pre-specified predictions regarding path-dependent synchronization effects and clock correlations that would manifest in precision timing systems if the hypothesis is correct.
Following the theoretical framework, a systematic empirical investigation was conducted to test these predictions through four independent GNSS analyses spanning 25 years (March 2000 to June 2025). Paper 1 analyzes 62.7 million station-pair measurements across three independent analysis centers (CODE, IGS, ESA), finding cross-center consistency. Paper 2 extends the CODE dataset to 165 million pairs over the full 25.3-year baseline, detecting signatures that appear consistent with orbital velocity coupling (r = −0.888, p < 2×10⁻⁷), CMB frame alignment (5,570× variance ratio over galactic alternative), and long-period geophysical signatures including 18.6-year lunar nutation coupling—features that TEP predicts but which also require independent confirmation. Paper 3 independently investigates these findings using 1.17 billion raw RINEX pair-samples processed via Single Point Positioning, demonstrating the signal persists in unprocessed data prior to network-level corrections. To make these findings accessible, an interactive demonstration (TEP-DEMO) allows users to process sample data directly in the browser. Paper 9 provides independent optical-domain validation using 11 years of Satellite Laser Ranging data, finding significant correlations in a system without active clocks.
Paper 4 (TEP-GL) extends the framework to gravitational lensing, examining how conformal metric couplings—unconstrained by GW170817—could produce phantom mass observationally indistinguishable from dark matter. The synthesis paper (TEP-GTE) examines whether multiple independent signatures converge, finding that seven metrics show combined significance p ≈ 2×10⁻²⁷ (>10σ), while the network's selectivity profile—sensitive to velocity-dependent dynamics but blind to GM/r² scaling—suggests it may function as an inertial interferometer rather than a gravimeter.
Analysis of the observed GNSS correlation length (λ ≈ 4,200 km) suggests a universal critical density (ρc ≈ 20 g/cm³) that, if confirmed, would organize gravitational phenomena across 40 orders of magnitude—from the Bohr radius at atomic scales through terrestrial metrology to dark matter halos in galaxies (Paper 7). This externally calibrated parameter, connected across scales through M1/3 Vainshtein screening, enables testable astrophysical predictions. Paper 8 illustrates this predictive utility through reinterpretation of the runaway black hole candidate RBH-1 as a potential gravitational soliton, offering a possible resolution to quantitative observational tensions in thermal dynamics and star formation. The convergence of terrestrial atomic clocks, optical laser ranging, galactic rotation curves, compact object behavior, and atomic physics constraints on a single density scale (ρc ≈ 20 g/cm³) suggests a possible connection between quantum mechanics, precision timekeeping, and cosmological structure formation—spanning 40 orders of magnitude in mass and 15 orders in density.
Paper 10 provides a rigorous epistemological audit of the experimental canon, identifying structural limitations in standard precision tests—specifically their reliance on reciprocity-even observables—that leave the path-dependent synchronization sector probed by TEP largely unconstrained. Paper 11 expands the empirical frontier to globular cluster dynamics, reporting a 5.8σ anomaly in millisecond pulsar timing (394 MSPs: 196 GC, 198 field). This signal exhibits "suppressed density scaling" (slope 0.39 ± 0.08 vs Newtonian 0.72; 4.1σ rejection) that appears consistent with the saturation of the TEP screening mechanism predicted by the universal critical density, establishing a tentative multi-scale evidentiary chain that connects terrestrial clock correlations to intermediate-scale astrophysical anomalies.
The empirical reach of TEP extends further to cosmological distance measurements and weak-field stellar dynamics. Paper 12 (TEP-H0) tests an environment-dependent bias in the Cepheid Period-Luminosity relation motivated by TEP, finding a statistically significant correlation (Spearman ρ = 0.434, p = 0.019) between host velocity dispersion and derived H0, with a TEP-corrected value of H0 = 68.66 ± 1.51 km/s/Mpc that reduces the Hubble tension with Planck to 0.79σ. Paper 13 (TEP-JWST) investigates whether the anomalous stellar masses, star formation efficiencies, and overmassive black holes reported by JWST at high redshift might arise from isochrony axiom violation; temporal shear is found to predict spectral age more strongly than stellar mass (ρ = +0.733, p = 1.9×10⁻³), implicating deep-potential time dilation as a possible explanation rather than exotic baryonic physics. Paper 14 (TEP-WB) tests TEP predictions in the extreme weak-field regime using the Gaia DR3 wide-binary catalog. Analysis suggests a characteristic screening transition radius R_s = 2646 ± 182 AU, with environmental ordering (halo vs. disk populations, permutation p < 10-3) that appears consistent with density-dependent conformal screening rather than a scale-free universal velocity boost.
These are working preprints shared in the spirit of open science—all manuscripts, analysis code, and data products are openly available under Creative Commons and MIT licenses. Independent scrutiny and collaboration are welcome.
