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’

Abstract

In the article (Rothleitner and Francis 2011 Metrologia 48 187-195) the correction due to the finite speed of light in absolute gravimeters is analyzed from the viewpoint of special relativity. The relativistic concepts eventually lead to the two classical approaches to the problem: analysis of the beat frequency, and introduction of the retarded times. In the first approach, an additional time delay has to be assumed, because the frequency of the beam bounced from the accelerated reflector differs at the point of reflection from that at the point of interference. The retarded times formalism is equivalent to a single Doppler shift, but results in the same correction as the beat frequency approach, even though the latter is explicitly combines two Doppler shifts. In our comments we discuss these and other problems we found with the suggested treatment of the correction.

Influence of chirping the Raman lasers in an atom gravimeter: Phase shifts due to the Raman light shift and to the finite speed of light

“…We have also performed a study of the influence of the finite speed of light which is the subject of recent controversy in the context of free falling corner cube gravimeters [33][34][35][36][37][38]. Our measurements confirm the validity of the analysis of [8] for the case of an atom gravimeter.…”

Experimental assessment of the speed of light perturbation in free-fall absolute gravimeters

“…This method is based on ignoring in (13) the contribution coming from the speed of light perturbation and fitting the data by the formula obtained in the limit 𝑐 → ∞. This leads to the following model function 𝑧 𝑚𝑚 (𝑡 𝑟 ) = 𝑧 𝑚𝑚 (𝑡 − ∆𝑡) = (𝑧 0 + 𝑣 0 𝑡 + 𝑔𝑡 2 /2 ) + ∆𝑧 Γ (t), (17) to which the data of each drop were fitted using the least squares method. Since the gravity gradient is known from other experiment (cf.…”

“…To single out the speed of light perturbation, and exclude any influence from time dependent gravity variations, all experimental values 𝑔 𝑚𝑒𝑎𝑠 (𝑇, 𝑣 0 ) were corrected for all classical geophysical perturbations, as well as for the self-attraction [24] and transferred to the same height. We emphasize that the perturbation due to the finite speed of light was not included into the fitted model (17). To focus on the speed of light perturbation in the measured value of the gravitational acceleration, we subtracted from 𝑔 𝑚𝑒𝑎𝑠 (𝑇, 𝑣 0 ) the minimum value of the set to obtain ∆𝑔 𝑚𝑒𝑎𝑠 (𝑇, 𝑣 0 ).…”

Measurement of thespeed-of-lightperturbation of free-fall absolute gravimeters

“…Corrections due to the finite propagation velocity of light can amount to some 10 µGal (1 µGal = 10 nm s −2 ), corresponding to 1 part in 10 8 of the absolute gravity value. The magnitude of this perturbation has been subject to an open discussion (see [3,4,5]). Until recently it was not possible to directly measure this effect, since its signal was well masked by other effects, e.g.…”