Dynamic phase shift within a falling glass cube is negligible: comment on ‘Relativistic theory of the falling retroreflector gravimeter’

Abstract

A recent paper (Ashby 2018 Metrologia 55 1) provides a rigorous relativistic treatment of the laser interferometer with a free-falling cube retroreflector. When considering the phase shift due to the light propagation within the glass cube, the associated effect was found to be 6.8 µGal. The constant phase shift was misinterpreted in the data analysis, producing a pseudo effect. We show that the time-dependent phase shift within the glass cube causes a negligible bias of the computed gravity acceleration and analyze the misconceptions that afforded a different conclusion.

Reply to ‘Dynamic phase shift within a falling glass cube is negligible: comment on ‘Relativistic theory of the falling cube gravimeter’’

“…The derived differences, equations (7), agree with differences obtained from numerical fits, showing in two ways that the optical properties of the retroreflector are significant, not negligible as claimed in the comment [2]. No substantive critique of the interference phase signal derivation, or of the steps described above that lead to the differences, equations (7), have been encountered yet.…”

“…A theoretical explanation for these differences was obtained by taking the corresponding differences for the theoretical interference signal; agreement between the numerical differences and the theoretical differences was excellent. The comment [2] contradicts the conclusions reported in [1], primarily because the comment assumes…”

“…At the end of section 2 of [2] it is claimed that the timedependent dynamical effect due to the light propagation within the cube is negligible, confirmed by the fact that the 'same number (−6.8 μGal) arises if all terms of order c −2 are neglected'. Such terms were actually not neglected in the fits; the quote from [1] only describes results of taking differences of the non-relativistic part of the signal.…”

“…where V cm is the CM velocity obtained by differentiating equation (2). Terms of degree higher than unity in the gravity gradient (γ) are neglected.…”

“…The comment [2] accepts the interference signal derived in [1], then rearranges terms, makes certain assumptions and approx imations, and revives the unnecessary 'speed of light' correction. Misunderstandings of [1] are a serious problem within [2]. Because the comment assumes Z 0 is known a priori and misunderstands statements about differences resulting from comparison with and without the optical quantity Dn − d, the comment does not provide a valid critique of [1].…”