Abstract
In the paper by Ashby (2018 Metrologia 55 1–10) the correction due to the time delay of light propagated through the prism retroreflector of absolute gravimeters is discussed. Accordingly, the correction of about −6.8 µGal should be applied for a typical gravimeter such as the most precise FG5(X) gravimeter declaring standard uncertainty at the level of 2 µGal. In consequence, the present gravimetric results related to the Kibble balance or the global absolute gravity reference system should be significantly changed. However, such a change needs a deeper scientific consensus. In our comment, we would like to show that the proposed correction should not be applied since the author's consideration is incorrect.
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The centre of mass (CM) of a testing body in absolute gravimeters is a point where the gravitation interaction acts. Only the vertical position of the CM in the Earth's gravity field with the gradient γ has to be considered for g determination, which cannot depend on an optical index of refraction n as it is realized by the product γDn in equation (47) from [1], where the correction of g is given by the formula
where D is the cube depth from face to corner and d is the distance of the CM from the face of the retroreflector.
The vertical coordinate z in the equation of motion of a freely falling body is connected with the real position of its CM in the gravity field. This position has nothing to do with the optical distance in the interferometer, which is often considered as the distance from the beam splitter. The counting interferometer in a gravimeter measures displacements in its measuring arm and does not measure differences of measuring arm with respect to the reference arm. Therefore, measured displacements are independent of all optical paths that do not change during the free fall. These optical paths (time delays) shift only the absolute phase difference between interferometer arms, which is of course irrelevant to the measured acceleration. As sources of constant shifts, we can mention here, e.g. a reference arm, a fixed glass window to the gravimeter dropping chamber and also a glass in the falling prism retroreflector (causing shift in Dn). All these optical paths do not influence the measured position of the CM in the gravity field and thus they can not change g measurements with the sensitivity coefficient given by the gravity gradient γ, see equation (1). In fact, both terms in the correction given by (1) do not apply since the second term γd is irrelevant too, because the position of the testing body is standardly related to its CM (i.e. it is not shifted to the face by d). The correction is also not a relativistic (speed-dependent) effect, as was shown in appendix B in [1]. Thus only the finite 'speed of light' correction, which is already commonly applied by accounting for the variable time delay in the measuring arm of the interferometer, is the necessary 'relativistic' correction for the absolute gravimeters with macroscopic objects.
We should note that the optical path in a prism retroreflector slightly changes with the rotation of the prism during the free fall, as discussed, e.g. in [2]. Among others, the distance between the CM of a falling body and the optical effective position (optical centre, OC) of a retroreflector plays role in the effect of rotation-induced acceleration in absolute gravimetry and therefore the CM and OC are co-located for an FG5 falling body to within 100 µm [3].
Acknowledgment
The scientific cooperation of authors from the Czech Metrology Institute and the Research Institute of Geodesy, Topography and Cartography is funded by the Czech Science Foundation (GA ČR) in the project 'Advanced processing of absolute gravity measurements and investigation of systematic instrumental effects' as a grant no. 16-14105S.