Temporal Equivalence Principle

This research programme develops the Temporal Equivalence Principle as a theory in which time is a dynamical field. More precisely, TEP proposes that proper-time accumulation is governed by a scalar field coupled to the matter/clock metric. The central question is whether synchronization and proper-time comparison remain globally integrable after standard relativistic corrections are modeled and removed.

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 environment-dependent Temporal Shear recovery.

The direct clock-network tests begin 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_T≈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 independently test whether the same temporal-field structure organizes 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 Temporal Topology / Temporal Shear framework.

All papers, code, and data products are released for open review. The clearest near-term tests are external reproduction of the timing-network correlations, multi-constellation checks, optical-clock or fiber-link experiments, non-GNSS timing systems, and closed-loop one-way synchronization holonomy.

What is the Temporal Equivalence Principle (TEP)?

TEP is a scalar-tensor framework proposing that time is a dynamical field. More precisely, proper-time accumulation is governed by a scalar field coupled to the matter/clock metric, while local Lorentz invariance and locally measured c are preserved.

How does TEP differ from general relativity?

TEP is proposed as a generalization of GR, not a simple replacement. GR is recovered to current experimental precision where the locally observable shear/source-charge sector is screened or saturated. Differences are expected in global or weakly screened observables: distributed clock correlations, closed-loop synchronization holonomy, and environment-dependent rate or screening transitions.

Is this just gravitational time dilation renamed?

No. GR already predicts gravitational time dilation: clocks tick differently in different gravitational potentials. TEP accepts that and does not claim it as new. The proposed new physics is residual structure after the standard GR timing model is removed: distance-structured clock covariance, environment-dependent Temporal Shear, and possible closed-loop synchronization holonomy.

What evidence motivates TEP?

TEP is first a theoretical framework, but its empirical motivation is cross-domain convergence. Engineered clock networks test distributed proper-time covariance directly; satellite laser ranging and future optical-clock or fiber-link experiments test technology independence; astrophysical systems test whether the same Temporal Topology, Temporal Shear, and screening structure appears in pulsars, Cepheids, wide binaries, lensing, flybys, lunar ranging, and high-redshift systems.

How does TEP reinterpret dark matter observations?

TEP does not deny the lensing, timing, dynamical, or cosmological phenomena usually attributed to dark matter. It challenges the assumption that those phenomena uniquely require a new invisible particulate substance. Temporal-field gradients and nontrivial proper-time transport can project into lensing, timing, and dynamical inference as an apparent mass-like component, termed Phantom Mass.

In the conservative interpretation, this is a testable correction to time-domain and variability-dependent lensing observables. In the stronger interpretation, tested across the series, part of the dark-sector phenomenology may be temporal in origin: an effect of analyzing a universe with nontrivial time transport under the assumption of global isochrony.

How does TEP address the Hubble tension?

In the Hubble-tension application, TEP predicts that Cepheid periods may acquire an environment-dependent bias in deep gravitational potentials. In the current SH0ES-host analysis, the directly identified quantity is a velocity-space environmental coefficient Γ_X. In the TEP-native pure-Cepheid gauge, Γ_X corresponds to a Cepheid clock-bias correction that shifts the local Cepheid-calibrated scale toward the CMB value. This should be read as a candidate distance-ladder resolution pending blind tests on independent Cepheid, TRGB, maser, JWST, and SN-host samples.

Is TEP compatible with gravitational wave observations?

Yes, in the intended parameter regime. GW170817 tightly constrains differential photon–graviton propagation: any disformal cone tilt must be extremely small. TEP's main conformal-sector effects are different. If electromagnetic and gravitational signals travel along the same path through the same conformal temporal landscape, the effect is common-mode rather than a photon–graviton speed split. Conformal sectors remain indirectly constrained by PPN, equivalence-principle, source-screening, redshift, and clock-comparison tests.

What would test or falsify TEP?

TEP can be challenged in several independent ways. A decisive falsifier would be showing that the reported timing-network correlations are fully reproduced by known satellite, station-network, ephemeris, clock-product, atmospheric, or environmental systematics with the same distance, direction, and time dependence. Equally important falsifiers would be failures of transfer: if timing-calibrated or screening-calibrated parameters do not carry over to pulsars, Cepheids, wide binaries, lensing, flybys, lunar ranging, or other precision datasets without arbitrary refitting, the framework weakens.

The strongest confirmations would come from independent reproduction across multiple evidence classes: non-GNSS timing networks, optical-clock or fiber-link tests, satellite laser ranging, closed-loop synchronization holonomy, and blind astrophysical predictions.

Does TEP claim GNSS is wrong?

No. GNSS works extraordinarily well. TEP does not claim navigation is failing. It asks whether residual clock-network covariance, after standard modeling and differencing, contains spatial structure normally treated as noise, covariance, or processing residual. The claim is about subdominant correlation structure, not operational GNSS accuracy.

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 instead tests environment-dependent Temporal Shear recovery organized around the Temporal Topology saturation scale ρ_T ≈ 20 g/cm³, which produces environmental ordering that differs from the MOND/EFE parameterizations tested in the wide-binary analysis. 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.