Relativistic formulation for dual one-way Doppler cancellation scheme observables for gravitational redshift tests

Abstract

Gravitational redshift is a fundamental prediction of general relativity and a sensitive probe of possible deviations from it. Motivated by recent progress in optical clocks and satellite–ground frequency transfer, we study a dual one-way optical Doppler-cancellation observable for space-based gravitational-redshift tests. The corresponding observable is constructed by combining oppositely directed one-way frequency observables, namely, an uplink and a downlink whose measurements are recorded at the receiving terminals and combined in post-processing. We derive the corresponding relativistic observable up to order

, as required for future

$$10^{-18}$$ 10 - 18

-level clock comparisons. The resulting combination suppresses the first-order Doppler contribution to second order while retaining the gravitational-redshift signal. We analyze the dominant residual effects, including higher-order Doppler terms, atmospheric delay, Shapiro delay, tidal effects, and clock synchronization. The formalism is applied to representative satellite–ground configurations, including an Atomic Clock Ensemble in Space/China Space Station (ACES/CSS)-like low-Earth-orbit configuration and a geostationary Earth-orbit satellite. The results show that the dual one-way optical DCS configuration provides a useful relativistic framework and error-modeling reference for future

$$10^{-18}$$ 10 - 18

-level space-based gravitational-redshift tests, while highlighting the need for stringent clock synchronization.