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Relativistic theory of the falling retroreflector gravimeter

Published

Author(s)

Neil Ashby

Abstract

We develop a relativistic treatment of interference between light reflected from a falling cube retroreflector in the vertical arm of an interferometer, and light in a reference beam in the horizontal arm. Coordinates that are nearly Minkowskian, attached to the falling cube, are used to describe the penetration of the light into the cube. Relativistic effects such as the dependence of the coordinate speed of light on gravitational potential, propagation of light along null geodesics, relativity of simultaneity, and Lorentz contraction of the moving cube, are accounted for. The magnitudes of relativistic effects are estimated. The calculation is carried to first order in the gravity gradient. Analysis of data from a falling cube gravimeter shows that the propagation time of light within the cube itself causes a significant reduction in the value of the acceleration of gravity obtained from measurements, compared to assuming reflection occurs at the front face. An expression for this correction is derived and compared with experiment; depending on the instrument, the correction can be several $\mu$Gal, comparable to commonly applied corrections such as those due to polar motion and earth tides. The theory is applied to the controversial "speed of light" correction.
Citation
Metrologia

Keywords

acceleration of gravity, geodesy, relativity, retroreflectors

Citation

Ashby, N. (2017), Relativistic theory of the falling retroreflector gravimeter, Metrologia (Accessed May 26, 2024)

Issues

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Created December 12, 2017, Updated March 26, 2018