Reply to comment by S. Svitlov [2] on "Relativistic Theory of the falling cube gravimeter"

TL;DR

This paper defends a relativistic analysis of light propagation in falling cube gravimeters, clarifying misunderstandings and emphasizing the validity of their derived interference signal expression without additional speed-of-light corrections.

Contribution

It clarifies the correct application of relativistic corrections in gravimeter signal analysis and addresses misconceptions in a recent comment.

Findings

The interference signal expression is valid without speed-of-light correction.

Corrections for initial parameters are context-dependent and not universally applicable.

Misunderstandings in the comment are clarified and corrected.

Abstract

In the subject paper [1] of the comment [2], light propagation through an absolute gravimeter was analyzed, including the propagation delay through the falling retroreflector and through the vacuum. The resulting expression for the interference signal applies without any subsequent "speed-of-light" correction. Other corrections appeared for the three fitting parameters $Z_0,\ V_0$ and $g$, which are the initial position and velocity, and the acceleration of gravity at the reference point. The comment assumes the value of $Z_0$ is known apriori, this case was not addressed in [1]. Also, the comment misunderstands statements made in [1] regarding the derivation of the relativistic/nonrelativistic parts of the corrections (Eq. (47) of [1]), and mistakenly claims they apply to the undifferenced interference signal. In this reply we show why, because of inapplicable assumptions, approximations and misunderstandings, the comment does not apply to the results of [1]\,.