Author: Matthew Lukin Smawfield
Version: v0.4 (Istanbul)
Date: First published: 31 December 2025 · Last updated: 4 May 2026
Status: Preprint
DOI: 10.5281/zenodo.18109760
Website: https://mlsmawfield.com/tep/exp/
Paper Series: TEP Series: Paper 9 (Experimental Foundations)
Most high-precision tests of general relativity constrain reciprocity-even, largely local observables within single-metric frameworks. This leaves open a specific underdetermination between General Relativity (GR) and a class of two-metric disformal scalar-tensor modifications, exemplified here by the Temporal Equivalence Principle (TEP).
This paper formalizes a measurement taxonomy distinguishing gauge-invariant from convention-dependent observables and identifies six recurring scope limitations in the experimental canon: (1) two-way measurement dominance; (2) local/global conflation; (3) model-dependent calibration; (4) single-path multi-messenger constraints on differential propagation that do not directly test common-mode clock-sector structure; (5) theory-laden data reduction; and (6) the density-regime screening blind spot, whereby tests performed in deep potential wells probe only the screened regime where scalar-field gradients are continuously suppressed, leaving the unscreened low-density regime unexplored. These characteristics do not diminish the experimental achievements but indicate that, in many cases, the tests primarily constrain parameter space within assumed frameworks rather than systematically discriminating between alternatives.
Discriminating observables—specifically loop asymmetries, spatial correlations, and density-regime screening transitions—are proposed, together with experimental configurations capable of resolving the underdetermination. These include large-area triangle holonomy tests (targeting residual synchronization holonomy H_resid), interplanetary closed-loop timing, altitude-varying optical clock networks to map continuous geometric screening, and matter-wave interferometry.
Precision tests of GR predominantly constrain reciprocity-even, two-way observables and therefore underdetermine disformal two-metric theories that preserve local physics. Six structural blind spots are identified: two-way measurement dominance, local/global conflation, model-dependent calibration, the indirect bounds from multi-messenger constraints, theory-laden data reduction, and the density-regime screening blind spot. The paper proposes discriminating tests that directly target one-way, loop-dependent observables—triangle holonomy, interplanetary closed-loop timing, and continental-scale optical clock networks—providing falsifiable pathways to resolve the GR–TEP underdetermination.
| Paper | Repository | Title | DOI |
|---|---|---|---|
| Paper 0 | TEP | Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed | 10.5281/zenodo.16921911 |
| Paper 9 | TEP-EXP (This repo) | What Do Precision Tests of General Relativity Actually Measure? | 10.5281/zenodo.18109760 |
| Paper 1 | TEP-GNSS | Global Time Echoes: Distance-Structured Correlations in GNSS Clocks | 10.5281/zenodo.17127229 |
| Paper 2 | TEP-GNSS-II | Global Time Echoes: 25-Year Analysis of CODE Precise Clock Products | 10.5281/zenodo.17517141 |
| Paper 3 | TEP-GNSS-RINEX | Global Time Echoes: Raw RINEX Consistency Test | 10.5281/zenodo.17860166 |
| Paper 4 | TEP-GL | Temporal-Spatial Coupling in Gravitational Lensing: A Reinterpretation of Dark Matter Observations | 10.5281/zenodo.17982540 |
| Paper 5 | TEP-GTE | Global Time Echoes: Empirical Synthesis | 10.5281/zenodo.18004832 |
| Paper 6 | TEP-UCD | Universal Critical Density: Cross-Scale Consistency of ρ_T | 10.5281/zenodo.18064365 |
| Paper 7 | TEP-RBH | The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate | 10.5281/zenodo.18059250 |
| Paper 8 | TEP-SLR | Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging | 10.5281/zenodo.18064581 |
| Paper 10 | TEP-COS | Temporal Equivalence Principle: Suppressed Density Scaling in Globular Cluster Pulsars | 10.5281/zenodo.18165798 |
| Paper 11 | TEP-H0 | The Cepheid Bias: Resolving the Hubble Tension | 10.5281/zenodo.18209702 |
| Paper 12 | TEP-JWST | Temporal Equivalence Principle: A Unified Resolution to the JWST High-Redshift Anomalies | 10.5281/zenodo.19000827 |
| Paper 13 | TEP-WB | Temporal Equivalence Principle: Temporal Shear Recovery in Gaia DR3 Wide Binaries | 10.5281/zenodo.19102061 |
| Paper 15 | TEP-EFA | Temporal Equivalence Principle: Temporal Shear in the Earth Flyby Anomaly | 10.5281/zenodo.19454863 |
| Paper 16 | TEP-J0437 | Synchronization Holonomy in Pulsar Scintillation | 10.5281/zenodo.19454620 |
| Paper 17 | TEP-LLR | Lunar Laser Ranging and the Nordtvedt Effect | 10.5281/zenodo.19446029 |
The engineering success of GPS demonstrates self-consistency within the assumed framework. It does not, by itself, establish uniqueness of that framework among alternatives that reproduce the same local observables after the same class of corrections.
Almost all precision tests use two-way (round-trip) measurements. These are mathematically insensitive to reciprocity-odd, direction-dependent effects. A convention-independent residual holonomy H_resid requires one-way, direction-reversing closed loops after subtracting modeled GR loop terms.
Local tests (e.g., Pound-Rebka, optical clocks) confirm the Einstein Equivalence Principle to extraordinary precision. Agreement at the local level does not, by itself, fix global synchronization structure.
GW170817-type observations primarily constrain differential propagation speed between photons and gravitons, hence disformal cone tilt. They do not directly constrain common-mode conformal clock-rate structure along a shared path, although conformal scalar sectors remain indirectly constrained by PPN, equivalence-principle, source-screening, and clock-comparison tests.
| Experiment | Claimed Result | TEP Critique |
|---|---|---|
| Hafele-Keating (1971) | Confirms time dilation | Two-way; does not probe one-way asymmetry |
| Pound-Rebka (1960) | Gravitational redshift | Local; TEP predicts identical local result |
| GPS "works" | Proves GR corrections | Self-consistent under assumed model |
| Cassini (2003) | PPN γ = 1 to 10⁻⁵ | Two-way Shapiro; blind to odd-parity effects |
| GW170817 | c_γ = c_g to 10⁻¹⁵ | Constrains differential propagation; indirect conformal bounds from other tests |
| Gravity Probe B | Frame-dragging | Measures geodetic precession; consistent with TEP |
| Resonator MM/KT tests | Isotropy to 10⁻¹⁸ | Two-way, closed-path; blind to one-way non-reciprocity |
- Triangle Holonomy Tests: One-way timing around large-area direction-reversing loops targeting residual synchronization holonomy H_resid
- Interplanetary Closed-Loop Timing: AU-scale, direction-reversed loop measurements constructed from one-way time-tagged links
- GNSS Correlation Replication: Independent, blinded analysis of raw GNSS data to verify or refute distance-structured correlations suggested by exploratory analyses
- Optical Clock Networks: Continental-scale networks using one-way comparisons to probe synchronization structure
- Matter-Wave Interferometry: Loop asymmetries in massive particle phase accumulation
TEP-EXP/
├── site/ # Academic manuscript site
│ ├── components/ # HTML section files
│ ├── public/ # Static assets
│ └── figures/ # Generated plots
├── manuscripts/ # Related manuscripts (PDF)
├── 9-TEP-EXP-v0.4-Istanbul.md # Generated manuscript (built from site/components)
└── VERSION.json # Version metadata
cd site
npm install
npm run buildThe built site will be in site/dist/. The build also regenerates 9-TEP-EXP-v0.4-Istanbul.md at the repository root.
@misc{smawfield2025exp,
title = {What Do Precision Tests of General Relativity Actually Measure?},
author = {Smawfield, Matthew Lukin},
year = {2025},
doi = {10.5281/zenodo.18109760},
url = {https://doi.org/10.5281/zenodo.18109760},
note = {Preprint, Version v0.4 (Istanbul)}
}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 to encourage and facilitate replication. Feedback and collaboration are warmly invited and welcome.
Contact: matthew@mlsmawfield.com
ORCID: 0009-0003-8219-3159