Temporal Equivalence Principle: Temporal Shear Recovery in Gaia DR3 Wide Binaries

The Gaia DR3 catalog of over one million wide binaries opens a precise window onto gravity in the weak-field regime (a ≲ 10⁻¹⁰ m/s²), yet whether the observed velocity excess reflects modified gravity or unresolved systematics remains contested. This paper shows that the Temporal Equivalence Principle (TEP v0.8 Jakarta)—in which a conformal scalar field modulates matter proper time as dτ/dt ≈ A(φ) (with A(φ) = exp(βφ/M_Pl)) with the Cepheid-calibrated response scale denoted κ_Cep, while the wide-binary transition is parameterized independently by the velocity-profile saturation amplitude α_sat, not by a bare scalar coupling—addresses that tension through smooth Temporal Shear recovery in weak-field environments.

This paper tests whether the Gaia wide-binary anomaly is better described as smooth Temporal Shear recovery in weak-field environments.

From 341,315 high-purity systems, the analysis identifies a screening transition at R_s = 2,646 ± 182 AU (statistical; ± 609 AU total), strongly preferred over both a flat Newtonian profile (Δχ² = 14,845) and a constant boost (Δχ² = 3,583). At large separation the profile saturates at α_sat = 0.366 ± 0.012, roughly 35–40% above the Keplerian baseline. Broader smooth-transition fits preserve the same few-thousand-AU onset.

The signal also shows the environmental ordering required by TEP. With a non-circular metallicity guardrail that uses a conservative external β_MLR prior unless independent spectroscopic metallicities are cached, the lower-density high-|Z| population transitions at smaller radius than the higher-density midplane (R_s = 4,662 ± 196 versus 7,131 ± 1,341 AU), confirmed by a solar-track control (R_s = 4,145 ± 276 versus 6,856 ± 920 AU; permutation p < 10⁻⁴ for the full sample and p < 10⁻³ for the solar track). Scrambling tests and phase-mixed Newtonian orbital forward models fail to reproduce the observed screening preference. The wide-binary anomaly is therefore not a generic low-acceleration excess but a structured, environmentally modulated screening transition—one whose morphology, onset scale, and environmental ordering are quantitatively consistent with the conformal scalar field of TEP and are not reproduced by the Newtonian orbital-projection or MOND/EFE parameterizations tested here.

Website: https://mlsmawfield.com/tep/wb/
Code Availability: https://github.com/matthewsmawfield/TEP-WB

DOI: 10.5281/zenodo.19102061

Keywords: Temporal Equivalence Principle – wide binaries – Gaia DR3 – weak-field gravity – Temporal Shear recovery – environmental transition morphology – Temporal Topology – Temporal Shear – modified gravity – MOND

Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All materials required for full reproducibility—including data downloads, analysis scripts, code, and manuscripts—are open-source. Feedback and contributions to further test these results are welcome.