Abstract (Experimental Metrology; Note; Preprint)
Local Position Invariance (LPI) is a cornerstone of General Relativity, tested via gravitational redshift with atomic clocks and matter. However, no direct test has yet compared cavity-stabilized optical frequencies (photon sector) to atomic transitions (matter sector) across a gravitational potential. We propose a protocol to close this gap: measure the fractional slope of co-located cavity–atom frequency ratios transported between two fixed altitudes. Define ξ^(M,S) = αw − α_L^(M) − α_at^(S), where αw is the photon-sector weight, α_L^(M) is cavity length sensitivity for material M, and α_at^(S) is atomic transition sensitivity for species S. GR predicts ξ^(M,S) = 0 for all materials and species. Any reproducible nonzero ξ would indicate sector-dependent deviation from LPI. For Earth gravity (g ≈ 9.8 m/s²), the natural scale is 10^−14 per 100 m altitude change, within reach of current 10^−16 optical clock precision. The protocol envisions static comparisons at two fixed altitudes using dual materials (ULE, Si) and dual species (Sr, Yb), with controls for dispersion, elastic sag, and environmental systematics.
Completing_Local_Position_Invariance_Tests__A_Cavity_Atom_Frequency_Ratio_Protocol