Matthew Lukin Smawfield

Temporal Equivalence Principle: theory, empirical evidence, and astrophysical implications

Research Manuscripts

Temporal Equivalence Principle

Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed

A bi-metric scalar-tensor framework treating proper time as a dynamical field. Predicts testable observables including synchronization holonomy and clock anholonomy while preserving local Lorentz invariance.

18 August 2024 v0.6 Jakarta
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Global Time Echoes

Global Time Echoes: Distance-Structured Correlations in GNSS Clocks

Cross-center analysis of 62.7 million station-pair measurements across CODE, IGS, and ESA. Identifies exponential correlation decay (λ = 3,330–4,549 km) with 24–61× signal enhancement over null tests.

17 September 2024 v0.23 Jaipur
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25-Year Analysis

25-Year Analysis: Temporal-Gravitational Coupling in CODE Clock Products

Extends to 25.3 years (165 million pairs), finding decadal stability and long-period signatures consistent with orbital coupling (r = −0.888, 5.1σ), CMB frame alignment, and semiannual nutation (R² = 0.90).

3 November 2024 v0.16 Cairo
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RINEX Validation

Raw RINEX Validation: Independent Confirmation from Unprocessed GNSS Data

Examines signatures in 1.17 billion raw RINEX pair-samples via Single Point Positioning. Finds correlations present in unprocessed observables, suggesting they are not artifacts of network processing.

9 December 2024 v0.3 Kathmandu
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Gravitational Lensing

Temporal-Spatial Coupling in Gravitational Lensing

Shows that conformal time-field gradients create phantom mass indistinguishable from dark matter. Demonstrates that GW170817 speed-of-gravity constraints do not apply to conformal coupling.

18 December 2024 v0.3 Tortola
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Global Time Echoes: Empirical Validation

Global Time Echoes: Empirical Validation of the Temporal Equivalence Principle

Synthesis paper examining general relativity's assumption of global time integrability. Seven signatures appear to converge (combined p ≈ 2×10⁻²⁷) with consistent detection across 72 metric combinations in raw RINEX data.

21 December 2024 v0.1 Singapore
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About This Research

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 framework preserves local Lorentz invariance while permitting path-dependent synchronization effects that manifest as measurable correlations in precision timing systems.

The empirical validation comprises three independent analyses of GNSS atomic clock data spanning 25 years (March 2000 to June 2025). Paper I analyzes 62.7 million station-pair measurements across three independent analysis centers (CODE, IGS, ESA), demonstrating cross-center consistency. Paper II extends the CODE dataset to 165 million pairs over the full 25.3-year baseline, revealing orbital velocity coupling (r = -0.888, p < 10⁻⁷), CMB frame alignment, and long-period geophysical signatures. Paper III independently validates these findings using over 1 billion raw RINEX observation pairs processed via Single Point Positioning, confirming the signal exists in unprocessed data prior to network-level corrections. The convergence of signatures across independent datasets, processing methods, and timescales provides multi-layered validation of the theoretical predictions.

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.

Interactive CMB Frame Alignment Visualization

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.

Peak correlation occurs when Earth's velocity vector aligns with the Cosmic Microwave Background dipole direction (RA 168°, Dec -7°), reaching maximum alignment in early July. This annual modulation demonstrates that the observed correlations track Earth's motion through the universe's rest frame, not 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), demonstrating that the anisotropy modulation couples to Earth's motion through the CMB rest frame rather than galactic motion.

Open Science & Reproducibility

All analysis code, processing pipelines, and computational results are publicly available under open-source licenses. The complete analysis workflows for all three 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 three complementary methodologies, with complete computational reproducibility from raw data to final figures.

Independent replication, critical analysis, and collaborative refinement are essential to advancing our understanding. If you identify methodological concerns, alternative interpretations, or opportunities for improvement, your contributions are welcomed and valued.

TEP-GNSS

Complete pipelines, logs, and results for Paper I (multi-center cross-validation: CODE, IGS, ESA) and Paper II (25-year temporal analysis with CODE data).

TEP-GNSS-RINEX

Complete pipeline, logs, and results for Paper III (raw RINEX validation using unprocessed Single Point Positioning data).