Interferometric experiments analyzed in the non-inertial reference frames

In the framework of general relativity we develop a method for analysis of the optical position meters, which may be considered as constituents of interferometers, in the proper reference frames of their photodetectors. Such reference frames are non-inertial in general due to the action of external forces. We explicitly demonstrate that the proper-frame-analysis always results in a measurable quantity, while the analysis in the laboratory (globally inertial) frame, widely used in literature, results in a contradiction with the relativity principle for certain schemes of position meters. The difference between the results may be explained by different mechanisms of clocks synchronization implicitly underlying the construction of the laboratory and proper frames. We also calculate the responses of the simplest position meters to weak plane gravitational wave and fluctuative displacements of their test masses in both the transverse-traceless and local Lorentz and demonstrate the similarity with Newtonian physics.