Optical position meters analyzed in the non-inertial reference frames

TL;DR

This paper develops a method to analyze optical position meters within their proper non-inertial reference frames in General Relativity, revealing differences from laboratory-based analysis and implications for gravitational wave detection.

Contribution

It introduces a detector-based analysis approach for optical meters in non-inertial frames, contrasting it with traditional laboratory-based methods, and examines responses to gravitational waves.

Findings

Detector-based analysis yields measurable quantities unlike laboratory-based analysis.

Round-trip meter responses are consistent across gauges, while forward-trip responses differ.

Analysis highlights the importance of physical assumptions like clock synchronization.

Abstract

In the framework of General Relativity we develop a method for analysis of the operation of the optical position meters in their photodetectors proper reference frames. These frames are non-inertial in general due to the action of external fluctuative forces on meters test masses, including detectors. For comparison we also perform the calculations in the laboratory (globally inertial) reference frame and demonstrate that for certain optical schemes laboratory-based analysis results in unmeasurable quantities, in contrast to the detector-based analysis. We also calculate the response of the simplest optical meters to weak plane gravitational waves and fluctuative motions of their test masses. It is demonstrated that for the round-trip meter analysis in both the transverse-traceless (TT) and local Lorentz (LL) gauges produces equal results, while for the forward-trip meter corresponding results differ in accordance with different physical assumptions (e.g. procedure of clocks synchronization) implicitly underlying the construction of the TT and LL gauges.