Can corner-cube absolute gravimeters sense the effects of Special Relativity?

TL;DR

This paper critically examines the relativistic corrections in absolute gravimeters, arguing that the current models lead to misleading conclusions due to the double Doppler shift and optical heterodyning effects.

Contribution

It clarifies the relativistic treatment of finite light speed corrections in gravimeters and highlights the limitations of previous approaches in detecting relativistic effects.

Findings

Double Doppler shift obscures relativistic effects in measurements.

Optical heterodyning makes quadratic Lorenz-like terms detectable.

Finite light speed disturbance includes intrinsic signal delay, not just Doppler effects.

Abstract

Relativistic treatment of the finite speed of light correction in absolute gravimeters, as evolved by Rothleitner and Francis in Metrologia 2011, 48 442-445, following the initial publication in Metrologia 2011, 48 187-195, leads to spurious conclusions. The double Doppler shift implemented in the gravimeters obliterates the difference between its relativistic and non-relativistic formulation. Optical heterodyning used in Michelson-type interferometers makes the quadratic Lorenz-like term of the double Doppler shift discernable against the linear term, while in relativistic experiments the quadratic term has to be detected against the unit. The disturbance of the registered trajectory caused by the finite speed of light includes tracking signal delay as intrinsic part not reducible to the Doppler shifts.