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

Abstract

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.

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

“…The controversy was deepened after the claim in [16] of the first measurement of the 'speed of light perturbation' that apparently confirmed the calculations in [15]. The results and methods of [15,16] were questioned in a series of works [17,18] (see also [19]) as well as more recently in [20].…”

A general relativistic model for free-fall absolute gravimeters

“…We review the 'relativistic geometrical method' in [15], extend it to calculate the relativistic effects in free-fall absolute gravimeters in a local-Fermi coordinates system, and consequently give a general relativistic expression of the measured gravity acceleration. Apart from the usual considered finite-speed-oflight perturbation, we discuss in particular the effects related to measuring devices: the relativistic transverse Doppler effects, gravitational redshift effects and Earth's rotation effect.…”

“…The fourth and fifth terms are related to the transverse Doppler shift, a purely relativistic effect. If the gravitational redshift effect and the Earth's rotation effect are not considered, the same formula for the beat frequency can be derived as that in [15].…”

“…The relative uncertainty of this kind of instrument is nowadays a few parts in 10 9 [1], which is smaller than the finite speed of light correction, but rather larger than the correction related to relativistic effects. Thus, to identify the local gravitational acceleration with experimental data, a lot of works on computing the finite speed of light correction have been performed in the past [2][3][4][5][6][7][8][9][10][11][12][13][14][15], while the relativistic effects are rarely considered. Although the relativistic effects are unobservable for modern measuring devices, a general relativistic model for free-fall absolute gravimeters has been missing, which is the purpose of this paper.…”

“…For ∆g FG5 , the finite speed of light effect is usually considered, while the other effects are rarely discussed. In this paper, extending the 'relativistic geometrical method' in [15], we combine the relativistic effects with the free-fall absolute gravimeters, mainly concentrating on ∆g FG5 , and consequently give a general relativistic expression of the measured gravity acceleration.…”