Author: Matthew Lukin Smawfield
Version: v0.1 (Istanbul)
Date: 31 December 2025
Status: Preprint
DOI: 10.5281/zenodo.18109761
Website: https://mlsmawfield.com/tep/exp/
Paper Series: TEP Series: Paper 10 (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 five recurring scope limitations in the experimental canon: (1) two-way measurement dominance; (2) local/global conflation; (3) model-dependent calibration; (4) the conformal loophole in multi-messenger constraints; and (5) theory-laden data reduction. 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 and spatial correlations—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, and matter-wave interferometry.
| Paper | Repository | Title | DOI |
|---|---|---|---|
| Paper 1 | TEP | Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed | 10.5281/zenodo.16921911 |
| Paper 2 | TEP-GNSS | Global Time Echoes: Distance-Structured Correlations in GNSS Clocks | 10.5281/zenodo.17127229 |
| Paper 3 | TEP-GNSS-II | Global Time Echoes: 25-Year Temporal Evolution | 10.5281/zenodo.17517141 |
| Paper 4 | TEP-GNSS-RINEX | Global Time Echoes: Raw RINEX Validation | 10.5281/zenodo.17860166 |
| Paper 5 | TEP-GL | Temporal-Spatial Coupling in Gravitational Lensing | 10.5281/zenodo.17982540 |
| Paper 6 | TEP-GTE | Global Time Echoes: Empirical Validation of TEP | 10.5281/zenodo.18004832 |
| Paper 7 | TEP-UCD | Universal Critical Density | 10.5281/zenodo.18064366 |
| Paper 8 | TEP-RBH | The Soliton Wake | 10.5281/zenodo.18059251 |
| Paper 9 | TEP-SLR | Satellite Laser Ranging Validation | 10.5281/zenodo.18064582 |
| Paper 10 | TEP-EXP (This repo) | What Do Precision Tests of General Relativity Actually Measure? | 10.5281/zenodo.18109761 |
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.
Multi-messenger constraints such as GW170817 bound differential propagation speed between photons and gravitons, primarily constraining disformal cone tilts. Conformal-sector structure that rescales clock rates without splitting null cones remains comparatively weakly constrained by such common-path 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 disformal only; conformal unconstrained |
| 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)
├── manuscript-tep-exp.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 manuscript-tep-exp.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.18109761},
url = {https://doi.org/10.5281/zenodo.18109761},
note = {Preprint v0.1 (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: matthewsmawfield@gmail.com
ORCID: 0009-0003-8219-3159