24 Absolute Cross-Environment Speed-of-Light Comparison (Single External Time Standard)

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and preserves the fixed structure. For general readers: we distribute one external time standard to all terminals and perform co-source, co-window comparisons of absolute time of arrival across multiple propagation environments (vacuum cavity; near-surface free space; high-altitude paths through the troposphere; ionospheric satellite links; optical fiber; and submarine cables). After removing geometric terms (including the Sagnac effect), relativistic terms (including Shapiro delay), medium terms (refractive index/group index, wet delay, Total Electron Content), and hardware terms, we test for a frequency-independent, cross-carrier/polarization/link-consistent residual that varies monotonically with environment strength.

I. One-Sentence Goal

Using a single external time standard, compare absolute arrival times over different environment paths in the same source and observation window. After standard subtractions, test whether a band-insensitive common residual remains and increases monotonically from vacuum/high, dry air to humid boundary layers/ionospheric crossings/high-convergence paths. If the residual can be explained by dispersion, calibration drift, or time-standard divergence—or fails cross-team/facility robustness—the claim is disfavored.

II. What to Measure

• Absolute arrival-time residuals (text grades):
  With the external standard as zero, absolutely calibrate arrival times of pulses/PRN sequences per environment path. After subtractions, grade the common residual as strong / medium / weak and uplift / depression; require same-sign behavior across neighboring sub-bands and dual polarizations.
• Non-dispersion consistency:
  Across microwave/millimeter/optical carriers and dual polarizations, compare direction and strength ranking. Any λ² / 1/ν flip or rescaling, or covariance with Faraday/group delay, is classified as medium/chain dispersion.
• Cross-environment monotonicity:
  Using environment proxies—refractive/group index, precipitable water vapor/wet delay, Total Electron Content and crossing angle, path convergence near massive bodies, and intrinsic fiber/cable parameters—qualitatively grade enhanced / plateau / uncorrelated behavior. Test the vacuum → troposphere/ionosphere → high-convergence/high-humidity/high-TEC monotonic rise.
• Same-source multi-path consistency:
  For one transmitter reference observed along different environment paths (two-way and one-way Earth–space; space–space links; vacuum cavity vs free space vs fiber), normalize by geometry/medium and test curve overlap and ordering consistency.
• Zero-lag co-occurrence:
  With decoupled dual chains and multi-station parallel logging, quantify zero-lag peaks and side-lobe contrasts among residuals across environment paths to verify co-window behavior (graded strong/medium/weak).

III. How to Do It

1. Time standard and end-to-end referencing:
   Establish one external time standard (optical lattice clock or hydrogen maser) and distribute via two-way stabilized fiber/free-space time transfer. Enforce round-trip closures and co-view constraints to keep zero differences. Only this single standard may set arrival-time zero points.
2. Channels and environment families:
   • Vacuum baselines: long-path vacuum tubes/cavities, one-way and round-trip.
   • Near-surface / high-altitude free space: short LOS, mountain–mountain/tower–tower, balloon/UAV/airborne relays spanning dry/cold vs humid/hot and low/high elevation.
   • Ionosphere/satellite links: Earth–space and space–space microwave/optical links over low/mid/high latitudes and day/night/solar-cycle phases.
   • Medium references: single-mode fiber/submarine cable one-way and round-trip with real-time models of group index and thermo-elastic strain.
3. Signaling and measurement:
   • Common source: split one reference to all paths; use short pulses + PRN codes with multi-carrier / dual polarization.
   • Link calibration: unified delay/group-delay/phase calibration with switchable open/short/bypass states. Subtract geometric terms including Sagnac, relativistic/tidal/solid-Earth terms, under one convention.
   • Medium models: troposphere via met/PWV + mapping functions; ionosphere via TEC + crossing angle; fiber/cable via online thermo-strain arrays + group-index curves. Record transfer functions and residual upper limits.
4. Forward prediction, blinding, arbitration:
   • Environment team (forward): using only environment proxies and geometric masks, issue prediction cards for direction/strength, monotone profiles, and symmetry/asymmetry expectations by path/epoch.
   • Measurement teams (independent pipelines): under the single time standard and unified medium conventions, deliver absolute residuals and non-dispersion/co-occurrence verdicts.
   • Arbitration: align prediction cards and results per pre-registered rules; report hit / wrong / null rates by path/carrier/institution.
5. Sequence construction and normalization:
   Build scan sequences across environment gradients (humidity, TEC, elevation, near-mass passages). Normalize by noise floors / link stability to produce dimensionless common-term curves and compare cross-path overlaps.

IV. Positive/Negative Controls and Removal of Artifacts

1. Positive controls (supporting a path term):
   • Across multiple environment paths/carriers/polarizations/institutions, observe co-directional, non-dispersive residuals that rise monotonically with environment strength (humidity/TEC/path convergence/medium complexity).
   • Same-source multi-paths overlap after geometry/medium normalization and show significant zero-lag between paths.
   • Forward-prediction hit rates for direction/strength/monotonicity are significantly above chance, with independent-pipeline replication.
2. Negative controls (against a path term):
   • Residuals flip/scale with λ² / 1/ν or co-vary with Faraday/group delay, or track medium proxies linearly → dispersion/medium effects.
   • Significance appears in one path/carrier/institution only, or is highly sensitive to medium/geometric conventions → method/model preference.
   • Label swaps / geometric rotations / open-bypass still yield “detections” → system/selection bias.

V. Systematics and Safeguards (Three Items)

• Time-standard distribution and closure: drift can fake “absolute” differences. Safeguard: two-way transfer + co-view + triangle closures, with hold-out links for final validation; publish stability logs.
• Incomplete medium modeling and residual dispersion: leaks into the common term. Safeguard: three-line modeling—troposphere (PWV/met), ionosphere (TEC/angle), fiber (thermo-strain/index)—with transfer-function corrections and upper-bound constraints; compare de-dispersion vs raw conventions for direction consistency.
• Link asymmetry and hardware drift: asymmetric TX/RX chains and thermal drift create false offsets. Safeguard: round-trip-symmetric designs, bypass/short switches, hardware swaps/thermal shocks, and delay-spectrum monitoring; down-weight/hold out unstable epochs.

VI. Execution and Transparency

Pre-register path families and environment bins, the single external time standard and distribution links, unified geometric/relativistic/medium conventions, residual grading and non-dispersion/co-occurrence criteria, and all controls/exclusions and arbitration rules. Reserve hold-out sequences/links per environment bin. Enable cross-institution/link replication by exchanging raw time-tags/arrival-time series and scripts; run down-sampling/noise/model-perturbation robustness tests. Publicly release prediction cards, residual grade tables, non-dispersion/co-occurrence summaries, time-standard/medium/geometry logs, and key intermediates. This chapter closes a loop with Chapters 1 (cross-probe frequency-independent common term), 20 (same-source multi-path solar-grazing sequence), and 23 (21 cm non-dispersive common term—environment relation).

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more environment families and two or more institutions, detect a band-insensitive common residual whose strength increases monotonically with environment proxies.
   • Same-source multi-paths overlap after normalization, show zero-lag co-occurrence, and forward-prediction hits exceed chance.
   • Conclusions are robust to time-standard / medium / geometry conventions and to pipeline/hardware swaps.
2. Refutation (fails):
   • Residuals flip with λ² / 1/ν / Faraday laws or depend strongly on medium/bandpass/geometry choices, failing cross-institution replication.
   • Signals are confined to one path/carrier, or persist under label swaps / geometric rotations / open-bypass.
   • Monotonicity and co-occurrence fail; arbitration hit rates approach chance.