Temporal Equivalence Principle: theory, empirical evidence, and astrophysical implications
Active theoretical foundation and subsequent empirical preprints shared for open review and collaboration.
A covariant, testable reformulation of relativity in which proper time is a dynamical field and the speed of light is an emergent local invariant. Distinguishes conformal (clock-rate) from disformal (light-cone tilt) sectors, predicting synchronization holonomy as a convention-independent observable that vanishes in GR and conformal-only models.
Multi-center analysis of 62.7 million atomic clock pairs across CODE, IGS, and ESA products. Identifies an exponential correlation decay (λ ≈ 4,200 km) with cross-center consistency (R² = 0.92–0.97) and absence of classical GM/r² gravitational scaling.
Longitudinal analysis spanning 25.3 years (165M+ pairs) demonstrating temporal stability across solar cycles. Reports orbital velocity coupling (r = −0.888, 5.1σ), CMB frame alignment (5,570× variance ratio over galactic alternative), and detection of 18.6-year lunar nutation coupling.
Rigorous artifact mitigation via Single Point Positioning of 1.17 billion raw RINEX samples. Demonstrates that distance-structured correlations exist in fundamental observables prior to network corrections, with 100% detection rate across 72 metric combinations.
Demonstrates that conformal metric couplings remain unconstrained by GW170817 (common-mode for co-propagating signals). Shows how Isochrony Axiom failure creates phantom mass indistinguishable from dark matter, with M1/3 Vainshtein scaling linking terrestrial correlations to galactic halos.
Comprehensive synthesis testing general relativity's assumption of global time integrability. Seven independent signatures—including orbital coupling, CMB alignment, spatial anisotropy, planetary event responses, and nutation couplings—converge with combined significance p ≈ 2×10⁻²⁷ (>10σ). The network's selectivity profile—sensitive to velocity-dependent dynamics while blind to GM/r² scaling—characterizes it as an inertial interferometer. Specifies explicit falsification criteria for each tier of claims.
Identifies a universal critical density (ρc ≈ 20 g/cm³) from GNSS calibration, independently consistent with the atomic boundary condition. Demonstrates M1/3 scaling across SPARC rotation curves (α = 0.354 ± 0.014) and predicts magnetar anti-glitch threshold (Pcrit ≈ 6.8 s, matching 1E 2259+586 within 4%).
Applies the terrestrially-calibrated critical density to resolve the RBH-1 cooling paradox (tcool/tdyn ≈ 30). Predicts soliton radius Rsol ≈ 7.8×107 km (≈1.3 RSchwarzschild) and reinterprets the wake velocity discontinuity as a metric shock with narrow line-width signature.
Independent optical-domain investigation using 11 years of Satellite Laser Ranging data from passive retroreflector satellites. Finds 14× spectral enhancement in the TEP frequency band (10–500 μHz) and significant daily-aggregated correlations (p = 0.017), supporting the hypothesis that the signal arises from propagation physics rather than active clock systematics.
A methodological taxonomy showing why most precision tests constrain largely local, reciprocity-even observables within assumed frameworks but do not directly probe the observables that distinguish GR from two-metric disformal scalar-tensor modifications. Proposes discriminating experiments including triangle holonomy tests, interplanetary closed-loop timing, and GNSS correlation replication.
Don't just read the papers—run the code. This interactive browser-based demonstration processes GNSS clock data to replicate the distance-dependent decoherence signal. Explore the correlation decay, adjust parameters, and visualize the deviation from standard General Relativity predictions.
Reports an 8.7σ dynamical anomaly in globular cluster pulsar timing where 182 millisecond pulsars exhibit a 0.13 dex spin-down excess compared to field controls. The signal shows suppressed density scaling (slope 0.35 vs 0.82) consistent with TEP screening saturation. Complementary lensing analysis places upper limits on temporal shear (|Γ| ≤ 60 days/decade), ruling out runaway modifications while remaining consistent with the pulsar anomaly.
Resolving the Hubble Tension by demonstrating that the Cepheid Period-Luminosity relation is not universal but depends on the local gravitational potential depth, as predicted by the Temporal Equivalence Principle (TEP). Analysis of the SH0ES Cepheid sample (N=29) reveals a statistically significant correlation (Spearman ρ = 0.434, p = 0.019) between host velocity dispersion and derived H0. TEP correction yields a unified H0 = 68.66 ± 1.51 km/s/Mpc, reducing the tension with Planck to 0.79σ.
The Temporal Equivalence Principle (TEP) proposes 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) provides pre-specified predictions regarding path-dependent synchronization effects and clock correlations that should manifest in precision timing systems.
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 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. 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, demonstrating how conformal metric couplings—unconstrained by GW170817—can produce phantom mass indistinguishable from dark matter. The synthesis paper (TEP-GTE) consolidates the empirical evidence, showing that seven independent signatures converge with combined significance p ≈ 2×10⁻²⁷ (>10σ), while the network's selectivity profile—sensitive to velocity-dependent dynamics but blind to GM/r² scaling—characterizes it 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 appears to 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 constrained astrophysical applications. Paper 8 illustrates this predictive utility through reinterpretation of the runaway black hole candidate RBH-1 as a gravitational soliton, offering a 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 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 an 8.7σ anomaly in millisecond pulsar timing. This signal exhibits "suppressed density scaling" consistent with the saturation of the TEP screening mechanism predicted by the universal critical density, establishing a coherent multi-scale evidentiary chain that connects terrestrial clock correlations to intermediate-scale astrophysical anomalies.
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 warmly invited.
This interactive visualization compares distance-structured correlations across 40 independent analyses, demonstrating that the exponential decay pattern is consistent across different measurement approaches. The dual y-axes show phase alignment for processed clock products (blue, left) and magnitude squared coherence for raw RINEX data (orange, right), suggesting that both metrics follow a similar exponential decay law despite measuring on different scales.
The dotted trend lines represent averaged exponential fits with correlation lengths (λ) ranging from 600–4,500 km and fit quality (R²) of 0.87–0.99. This cross-validation across processed clock products (CODE, IGS, ESA) and raw RINEX analyses (3 station filters × 4 processing modes × 3 metrics) indicates that the correlation decay is a reproducible feature independent of measurement methodology, supporting the hypothesis of a physical phenomenon rather than a processing artifact.
This interactive visualization shows the correlation strength between GNSS clock measurements across the celestial sphere, derived from 25.3 years of CODE clock products (March 2000 to June 2025, 165 million station-pair measurements). The heatmap displays how the anisotropy pattern (East-West vs North-South correlation strength ratio) varies throughout Earth's annual orbit.
The anisotropy ratio modulates annually with Earth's orbital velocity, with the pattern aligned to the Cosmic Microwave Background dipole direction (RA 168°, Dec -7°) rather than the Solar Apex (RA 272°, Dec +30°). This annual modulation suggests that the observed correlations track Earth's motion through the universe's rest frame rather than local seasonal or environmental effects. The best-fit direction (RA 186°, Dec -4°, white marker) lies 18° from the CMB dipole (cyan marker) and 89° from the Solar Apex (orange marker), with a 5,570× variance ratio favoring CMB-frame coupling.
All analysis code, processing pipelines, and computational results are publicly available under open-source licenses. The complete analysis workflows for all four empirical studies—including data acquisition scripts, processing logs, intermediate outputs, and final results—are hosted on GitHub to enable independent verification and replication. The analysis encompasses over 1 billion individual measurements across four complementary methodologies (processed clocks, raw RINEX, optical SLR), with complete computational reproducibility from raw data to final figures.
Independent replication by other research groups is essential for validation. Researchers interested in replication may find Paper 2 (TEP-GNSS I) the most accessible entry point, using publicly available CODE/IGS/ESA clock products (compact .clk files). Paper 3 (TEP-GNSS II) extends this with 25 years of CODE clock data. Paper 4 (TEP-GNSS III) provides the most rigorous validation via raw RINEX processing but requires more substantial computational resources. All data, code, and methodologies are openly available. Feedback on methodology, interpretation, or potential collaboration is welcomed.
Core repository containing the theoretical framework, mathematical models, and LaTeX source. Includes derivation scripts, figure generation code, and the full manuscript source.
Complete analysis pipeline for Paper 2 (TEP-GNSS I). Features multi-center cross-validation scripts, processing logs, JSON statistical outputs, and generated figures for correlation decay quantification.
Research compendium for Paper 3 (TEP-GNSS II). Contains longitudinal analysis scripts, orbital coupling logs, CMB alignment data, and comprehensive JSON result files.
End-to-end pipeline for Paper 4 (TEP-GNSS III). Includes SPP processing scripts, raw RINEX analysis logs, validation datasets, and resulting anisotropy figures from 1 billion samples.
Codebase for Paper 5 (TEP-GL). Contains phantom mass modeling scripts, rotation curve data, analysis logs, and the Python notebooks used to generate manuscript figures.
Synthesis framework for Paper 6 (TEP-GTE). Includes integration scripts, cross-study correlation logs, consolidated JSON datasets, and summary figures demonstrating signal convergence.
Scaling analysis codebase for Paper 7 (TEP-UCD). Features critical density calculation scripts, scaling law verification logs, and the data pipelines used to derive Vainshtein screening effects.
Simulation suite for Paper 8 (TEP-RBH). Contains soliton wake modeling scripts, hydrodynamic simulation logs, parameter space JSONs, and the visualization tools for the RBH-1 analysis.
Complete analysis pipeline for Paper 9 (TEP-SLR). Includes SLR data parsers, residual computation logs, correlation analysis scripts, and final result figures.
Codebase for the COSMOGRAIL and Globular Cluster analysis (TEP-COS). Contains pulsar timing datasets, density scaling analysis scripts, lensing shear calculators, and N-body simulation comparisons.
Codebase for Paper 12 (TEP-H0). Includes SH0ES data processing, environment stratification, TEP correction optimization, and robustness analysis scripts demonstrating the resolution of the Hubble Tension.