Relativity, Doppler shifts, and retarded times in deriving the correction for the finite speed of light: a comment on 'Second-order Doppler-shift corrections in free-fall absolute gravimeters'

摘要

In the article (Rothleitner and Francis 2011 Metrologia 48 187-195) thecorrection due to the finite speed of light in absolute gravimeters is analyzedfrom the viewpoint of special relativity. The relativistic concepts eventuallylead to the two classical approaches to the problem: analysis of the beatfrequency, and introduction of the retarded times. In the first approach, anadditional time delay has to be assumed, because the frequency of the beambounced from the accelerated reflector differs at the point of reflection fromthat at the point of interference. The retarded times formalism is equivalentto a single Doppler shift, but results in the same correction as the beatfrequency approach, even though the latter is explicitly combines two Dopplershifts. In our comments we discuss these and other problems we found with thesuggested treatment of the correction.