Where general relativity computes time dilation from a known gravitational source, the chronodynamic program inverted the question and recovered the source from the observed time dilation. The inversion was performed under the weak-field limit, where the first post-Newtonian approximation is exact to the precision of modern atomic clocks.
The first concrete result
The first concrete result of this inversion is the recovery of the geocentric gravitational constant GM directly from Galileo satellite atomic-clock data, to a median precision of 4 × 10−7 across more than one million measurements, and cross-validated on a second satellite. The recovery uses no external mass input.
Method
The experiment uses high-eccentricity Galileo satellites (E14 and E18, which entered eccentric orbits as a result of the Fregat upper-stage anomaly) to provide the altitude variation necessary for a single-satellite inversion. Sequential clock-drift pairs are computed at half-orbital-period intervals, and the relativistic 1PN time-dilation equation is inverted analytically using Float106 quad-precision arithmetic to control numerical cancellation in the subtraction of nearly equal quantities.
Open data and reproducibility
The complete experiment is available with its source code on GitHub; the full reference data set is published openly on Zenodo with a persistent DOI. The data set includes the GNSS clock and ephemeris files needed to reproduce the recovery end-to-end.
Context within the Center
Chronodynamics was the first of the Center's programs to produce an empirical result, and it finished on that result. Running the inversion on DeepCausality showed that the dynamic-causality foundation holds up in a quantitative physical setting. The Center's applied work continues that test in counterfactual CFD. The chronometric kernel written here went upstream into the DeepCausality physics crate, where it is still in use.
Resources
- chronodynamics on GitHub — source, methodology, and results
- Reference dataset on Zenodo — canonical chronometric data set with DOI