Can corner-cube absolute gravimeters sense the effects of Special   Relativity?
  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. 
V D Nagornyi, Y M Zanimonskiy, Y Y Zanimonskiy
physics.ins-det physics.geo-ph