The speed of light perturbation in absolute gravimeters from the viewpoint of ‘relativistic geometry’

In the past few years, the perturbation due to the finite speed of light was among the most inconsistent in corner-cube absolute gravimeters. For the relativistic treatment of the perturbation based on Lorentz transformation, the relation between Doppler shift in special relativity and time delay in classical domain is easily misunderstood, leading to spurious conclusions. To avoid these issues, we apply a 'relativistic geometrical method' based on the motion of photons to calculate the frequency shift in corner-cube absolute gravimeters, where the misunderstood relation has been corrected. Additionally, we find that the modern corner-cube absolute gravimeters cannot sense effects of the special relativity.