Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging

Author: Matthew Lukin Smawfield
Version: v0.3 (Mombasa)
Date: 30 December 2025 · Last updated: 29 April 2026
Status: Preprint
DOI: 10.5281/zenodo.18064581
Website: https://mlsmawfield.com/tep/slr/

Abstract

An independent, optical-domain test of the Temporal Equivalence Principle (TEP) is presented using 11 years (2015–2025) of Satellite Laser Ranging (SLR) data from passive ILRS geodetic satellites (LAGEOS-1/2 and Etalon-1/2). This analysis constrains "clock-artifact" explanations by employing two-way optical ranging to passive retroreflectors—a methodology orthogonal to the microwave measurements of active atomic clocks used in Global Navigation Satellite Systems (GNSS).

Under strict 5-minute contemporaneous binning, distance-binned mean pass-correlations fluctuate with high variance. However, widening the overlap window to 15 minutes (thereby increasing multi-station overlap) reveals statistically significant, distance-structured inter-station correlations (Fisher-combined $\chi^2=15.35$ with 4 d.o.f.; $p=0.0040$) under a family-wise circular-shift test.

This signal is driven primarily by LAGEOS-2 ($p=0.0005$), which exhibits a strong negative correlation ($r \approx -0.59$) in the 5,000–7,500 km distance bin, whereas LAGEOS-1 remains consistent with the null hypothesis ($p \approx 0.93$). Although observation counts and temporal overlap are comparable, this asymmetry likely reflects a combination of orbital geometry—LAGEOS-2's prograde $52.6^\circ$ orbit versus LAGEOS-1's retrograde $109.8^\circ$ orbit—and small-number statistics in the critical distance bin.

To validate this finding with more robust statistics, a daily-aggregation analysis ($N=190$ station pairs) was performed. This confirmed a subtler but statistically significant negative correlation at shorter ranges (500–1,000 km, $p=0.017$), suggesting a persistent global background structure independent of the high-amplitude LAGEOS-2 events.

The observation of matching low-frequency structure in a system devoid of active clocks and microwave propagation challenges receiver electronics, clock steering, and ionospheric modeling errors as complete explanations. While current network sparsity limits testing to the conformal sector, this work demonstrates SLR as an independent, technology-orthogonal line of evidence for TEP phenomenology.

Key Findings

Analysis of 11 years of SLR data from passive ILRS satellites detects statistically significant distance-structured correlations (Fisher χ² = 15.35, p = 0.0040). The signal is driven primarily by LAGEOS-2 (prograde orbit, p = 0.0005), while LAGEOS-1 (retrograde orbit) shows null results—an asymmetry consistent with velocity-dependent effects. Daily aggregation confirms a persistent correlation at 500–1,000 km (p = 0.017). Critically, SLR uses passive retroreflectors with no active clocks or electronics, eliminating receiver artifacts as an explanation. This technology-orthogonal confirmation in the optical domain strengthens the case that GNSS findings reflect genuine physical phenomena rather than instrumentation effects.

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The TEP Research Program

Paper	Repository	Title	DOI
Paper 0	TEP	Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed	10.5281/zenodo.16921911
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.18059251
Paper 8	TEP-SLR (This repo)	Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging	10.5281/zenodo.18064581
Paper 9	TEP-EXP	What Do Precision Tests of General Relativity Actually Measure?	10.5281/zenodo.18109760
Paper 10	TEP-COS	The 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	The Temporal Equivalence Principle: A Unified Resolution to the JWST High-Redshift Anomalies	10.5281/zenodo.19000827
Paper 13	TEP-WB	The Temporal Equivalence Principle: Temporal Shear Recovery in Gaia DR3 Wide Binaries	10.5281/zenodo.19102061

Repository Structure

TEP-SLR/
├── scripts/
│   ├── steps/                  # Core analysis pipeline
│   │   ├── step_1_0...py       # CDDIS Data Downloader
│   │   ├── step_2_1...py       # Residual Calculation
│   │   ├── step_2_3...py       # MWPC Analysis (Main)
│   │   ├── step_2_4...py       # Plotting
│   │   └── step_3_0_sim_antiecho.py       # Anti-Echo Simulation
│   └── helpers/                # Utility scripts
│       ├── download_orbits.py  # SP3 Orbit Downloader
│       └── process_residuals_yearly.py   # Batch processing helper
├── data/                       # Input data (GitIgnored)
│   └── slr/                    # CRD observations & SP3 orbits
├── results/
│   ├── outputs/                # Analysis JSONs & CSVs
│   └── figures/                # Generated plots
├── logs/                       # Execution logs
└── reproduce_analysis.sh       # One-click reproduction script

Quick Start

1. Prerequisites

• Python 3.10+
• CDDIS Account (for data download only)

pip install -r requirements.txt

2. Reproduction

To run the full analysis pipeline (assuming data is downloaded):

chmod +x reproduce_analysis.sh
./reproduce_analysis.sh

3. Data Access

Option A: Use Pre-Processed Results (Recommended for Verification) All analysis outputs are included in results/outputs/ and results/figures/. You can verify the analysis without downloading raw data:

# View analysis results
cat results/outputs/step_2_3_mwpc_analysis.json

# Regenerate figures from existing data
python scripts/steps/step_2_4_plot_results.py

Option B: Download Raw Data from CDDIS (For Full Reproduction) To download SLR observations and orbits from NASA CDDIS:

1. Register for NASA Earthdata Account:

   • Visit: https://urs.earthdata.nasa.gov/users/new
   • Create free account (required for CDDIS access)

2. Configure Authentication:

   Option 1 - Using .netrc file (recommended):

   echo "machine urs.earthdata.nasa.gov login YOUR_USERNAME password YOUR_PASSWORD" >> ~/.netrc
   chmod 600 ~/.netrc

   Option 2 - Using environment variables:

   export CDDIS_USER="your_username"
   export CDDIS_PASS="your_password"

3. Download Data:

   # Download SLR observations (2015-2025)
   python scripts/steps/step_1_0_data_acquisition.py --start 2015-01-01 --end 2025-12-31
   
   # Download precise orbits
   for y in $(seq 2015 2025); do python scripts/helpers/download_orbits.py --year $y; done

4. Pipeline Steps

1. Data Acquisition (step_1_0): Downloads CRD (Normal Point) observation files from CDDIS.
2. Orbit Processing (download_orbits): Fetches precise SP3 orbits for LAGEOS-1 and LAGEOS-2.
3. Residual Calculation (step_2_1): Computes range residuals (Observed - Computed) using rigorous force models.
4. MWPC Analysis (step_2_3): Performs Magnitude-Weighted Phase Correlation analysis to extract spatial decay signatures.
5. Visualization (step_2_4): Generates decay plots and diagnostic figures.
6. Simulation (step_3_0): Runs the "Anti-Echo" Monte Carlo simulation to validate the sign inversion mechanism.

License

This project is licensed under Creative Commons Attribution 4.0 International (CC-BY-4.0).

Citation

If you use this code or data, please cite:

@article{smawfield2025slr,
  title={Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging},
  author={Smawfield, Matthew Lukin},
  journal={Zenodo},
  year={2025},
  doi={10.5281/zenodo.18064581},
  note={v0.3 (Mombasa)}
}

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Open Science Statement

These are working preprints shared in the spirit of open science—all manuscripts, analysis code, and data products are openly available under Creative Commons Attribution 4.0 International (CC-BY-4.0) to encourage and facilitate replication. Feedback and collaboration are warmly invited and welcome.

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Contact: matthew@mlsmawfield.com
ORCID: 0009-0003-8219-3159