Light speed and the LIGO experiment

[RockyMarciano]

Just to clarify: in the LIGO team's coordinates, the coordinates of the mirrors at the ends of the arms are constant, but the metric coefficients change as the GW passes in such a way that the lengths of the arms change (because those lengths depend on both the coordinates of the ends and the metric coefficients). The alternate set of coordinates I was imagining, in the interpretation where the arm lengths don't change, still assigns constant coordinates to the mirrors at the ends of the arms, but is set up so that a different set of metric coefficients changes as the GW passes, the ones that govern the coordinate speed of light. But this is only a heuristic description; I have not done any computations.

As discussed in a previous thread, even if the alternate set of coordinates you mention is routinely used in interferometry for instance in the maesurent of refraction variations, in the GW case only the LIGO team's class of coordinates( the family of harmonic coordinates) are mathematically compatible with the linearized EFE expressed as a wave equation with plane gravitational wave solutions(see for example Efstathiou's "General relativity" section 17.5). This is a particularity of general relativity as a mathematical model that has no bearing on the general principle which always prevails, i.e.: that the physics must be independent of the coordinates.