Sector-Resolved Test of Local Position Invariance with Co-Located Cavity-Atom Frequency Ratios

Abstract (Theoretical Research; Preprint — proposed experimental test; Submitted)

We present a sector-resolved framework for testing local position invariance (LPI) using co-located comparisons of optical cavity and atomic clock frequencies transported across gravitational potentials. The method separates three physical contributions to the gravitational redshift: photon wave propagation, solid-state cavity length response, and atomic transition response. By measuring four independent cavity–atom frequency ratios with different cavity materials and atomic species, we obtain an over-determined system that constrains three independent parameters. General relativity predicts all sector differences vanish, corresponding to zero in this basis. Our analysis uses generalized least squares with full covariance propagation, conservative noise modeling including flicker floors, and quantitative environmental thresholds for valid measurement windows. The design includes dual-wavelength checks to suppress residual dispersion, hardware swaps to control for systematics, and orientation flips to bound elastic sag of cavities under transport. We outline realistic implementations over height differences of 30 to 100 m using current optical clock and cavity technology, with projected sensitivities competitive with existing redshift tests. Results are reported directly in the sector basis, with qualitative connections to isotropic Standard Model Extension coefficients provided as context. This approach offers a clean, falsifiable test of the universality of gravitational redshift across distinct physical systems.