Temporal Equivalence Principle

TEP promotes proper time from a passive parameter to a dynamical scalar field whose spatial structure is called Temporal Topology. Local Lorentz invariance and locally measured c are preserved, while global synchronization may acquire residual holonomy. Gradients in the temporal field produce Temporal Shear, a mechanism that can be tested using precision timing networks and extended astrophysical systems.

The primary empirical target is a reported distance-structured correlation pattern in global GNSS timing data. This signal has been studied in multi-center clock products, a 25-year CODE analysis, raw RINEX observations, and optical satellite laser ranging. Astrophysical applications then test whether the same temporal-field structure appears through density-dependent screening in lensing, pulsars, Cepheids, wide binaries, and high-redshift galaxies.

These manuscripts are working preprints released for open scrutiny. What is now needed is independent blinded replication of the primary timing correlations and experimental tests of synchronization holonomy.

Start here: Key Concepts · Theory Paper · GNSS I · Raw RINEX Test · Experimental Tests · Replication Code

This research programme investigates a specific assumption underlying most relativistic inference: that proper time, after standard relativistic corrections, can be transported globally without path dependence. TEP names this assumption the Isochrony Axiom and proposes a testable alternative in which proper time is a dynamical scalar field with spatial structure.

The framework is formulated as a covariant scalar-tensor theory with a gravitational metric and a matter/clock metric. Local physics remains Lorentz invariant. The new effects appear in global observables: distributed clock correlations, synchronization holonomy, temporal shear, and density-dependent screening transitions.

The empirical programme begins with GNSS because global navigation systems form a planetary-scale network of atomic clocks. The reported signal is a distance-structured correlation pattern with characteristic length λ≈4,200 km, seen in processed clock products, a 25-year longitudinal analysis, and raw RINEX-derived observables. Satellite laser ranging provides an optical-domain consistency check.

The astrophysical papers then ask whether the same temporal-field structure can organize phenomena normally treated separately: lensing mass discrepancies, globular-cluster pulsar timing, Cepheid distance-ladder biases, JWST high-redshift anomalies, and Gaia wide-binary dynamics. These applications are not presented as independent proof of TEP, but as cross-regime tests of a common screening and temporal-shear mechanism.

All papers, code, and data products are released for open review. Independent replication is essential. The clearest near-term falsification tests are external reproduction of the GNSS/RINEX correlations, multi-constellation timing checks, optical-clock or fiber-link tests, and closed-loop one-way synchronization holonomy.

What is the Temporal Equivalence Principle (TEP)?

TEP is a scalar-tensor extension of general relativity that promotes proper time to a dynamical field while preserving local Lorentz invariance. In its empirical applications, the framework emphasizes a small set of inherited parameters, especially the GNSS-derived correlation length and the critical density associated with screening.

How does TEP differ from general relativity?

TEP is a generalization of GR, not a replacement. GR is recovered in the high-density (screened) limit. TEP is constructed to recover GR to current precision in standard local, screened tests of relativity (Gravity Probe B, Cassini, binary pulsars). Differences emerge only in low-density, extended-source regimes where a scalar field introduces path-dependent synchronization holonomy.

What evidence supports TEP?

The primary evidence is a reported distance-structured correlation pattern in global GNSS timing data, observed across multi-center clock products, a 25-year CODE analysis, and raw RINEX processing. Secondary evidence includes optical-domain SLR correlations, pulsar timing trends, wide-binary screening signatures, Cepheid host-environment trends, and lensing/cosmological consistency tests. These results are presented as an open replication programme; the most important next step is independent blinded reproduction of the primary timing correlations by external groups.

How does TEP reinterpret dark matter observations?

TEP proposes that gradients in Temporal Topology can project into lensing and dynamical observables as an apparent mass component, termed Phantom Mass. In the conservative interpretation, this is a testable correction to standard lensing and timing inference. In the stronger interpretation, it could account for part of the phenomenology usually attributed to dark matter. The decisive tests are variability-dependent lensing, lensed FRB timing, and environment-dependent screening signatures.

How does TEP address the Hubble tension?

TEP predicts that Cepheid periods may acquire an environment-dependent bias in deep gravitational potentials. In the current SH0ES-host analysis, correcting for this proposed bias shifts the inferred local value toward the Planck value. This should be read as a candidate distance-ladder systematic, not as a final resolution until tested blindly on independent Cepheid, TRGB, maser, and SN host samples.

Is TEP compatible with gravitational wave observations?

Yes, in the intended parameter regime. GW170817 tightly constrains disformal light-cone differences between photons and gravitational waves. TEP’s main clock-rate effects arise in the conformal sector, where co-propagating electromagnetic and gravitational signals can share common-mode propagation effects. The disformal sector must remain small enough to satisfy multi-messenger bounds.

What are the falsification criteria for TEP?

The framework specifies six primary pathways for empirical falsification:

1. Independent GNSS replication: Reproducing the reported timing correlations using independent processing of public IGS/CODE clock products.
2. Raw-data robustness: Testing whether the timing signal persists when derived directly from raw RINEX observations using multiple GNSS processing engines (e.g., GIPSY, Bernese).
3. Technology independence: Verifying if similar spatial-temporal structure is detectable via Satellite Laser Ranging (SLR), fiber-optic time transfer, or optical-clock networks.
4. Closed-loop holonomy: Performing dedicated multi-leg timing experiments to search for residual synchronization holonomy after standard GR effects are removed.
5. Screening morphology: Testing whether the predicted density-dependent environmental ordering persists in wide-binary, globular cluster, and galaxy-scale data.
6. Astrophysical inheritance: Determining if the framework fails when timing-calibrated parameters are applied to lensing and cosmological observables without additional free parameters.

How does TEP relate to MOND?

Both TEP and MOND address phenomenology attributed to dark matter, but through distinct mechanisms. MOND proposes a universal acceleration threshold (a₀ ≈ 1.2×10⁻¹⁰ m/s²) below which gravitational behavior deviates from Newtonian predictions. TEP posits density-dependent screening via Temporal Topology governed by a universal critical density (ρ_c ≈ 20 g/cm³), which produces environmental ordering that is not a generic MOND prediction and differs from the simplest scale-free MOND expectation. The two frameworks make qualitatively different predictions for environmental stratification.

Where can I find the TEP papers, data, and analysis code?

The full manuscript series is freely available at mlsmawfield.com with Zenodo DOIs. Analysis code and data pipelines are hosted on GitHub. All manuscripts, code, and data products are released under Creative Commons CC-BY-4.0 and MIT licenses.