Completing Local Position Invariance Tests: A Cavity-Atom Frequency Ratio Protocol

Local Position Invariance (LPI) is a cornerstone of General Relativity, extensively tested via gravitational redshift measurements with atomic clocks and matter systems. 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 by measuring the fractional slope of co-located cavity–atom frequency ratios at two fixed altitudes. The observable is parameterized as ΔR/R = ξ(ΔΦ/c²), where General Relativity predicts ξ = 0 for all cavity materials and atomic species. Any reproducible nonzero slope would indicate sector-dependent deviation from LPI. Using two cavity materials (ULE, Si) and two atomic species (Sr, Yb), the protocol enables identification of three independent sector parameters through four measured slopes. The natural scale is ~10⁻¹⁴ per 100 m altitude change, within reach of current 10⁻¹⁶ optical clock precision. All required components—ultra-stable cavities, optical atomic clocks, and long-term LPI tests—have been demonstrated separately, making this cross-sector test technically feasible with existing infrastructure. The experiment would complete the phenomenological mapping of LPI across independent physical systems.