Please note that this is not an inquiry into the mechanisms of technology that LIGO uses to detect gravitational waves. Also, I am not a flat-earther.
I was watching physicists vs. flat-earthers debate (who knew reality could be up for debate) and a point was brought up by a flat-earther:
"A core aspect of Einstein's relativity is that time and space are woven into a 4D spacetime. So gravitational waves warp space (the distance of LIGO arms that light must travel) and time (ticking of clocks slows for light). If the speed of light is constant, and time and space warp accordingly to keep it constant, therefore you won't be able to detect an interference pattern --> Einstein was wrong (if they detect something that means the speed of light wasn't constant, and if they don't then general relativity is wrong)."
tl;dr the warping of space is cancelled out by dilation of time (to keep light's speed constant) so the photon will always be in phase and no interference pattern will be seen.
I know that there is something VERY wrong with this argument, but sadly I am not well-studied enough in special and general relativity to figure it out. My hunch is that the warping of the time component of spacetime is irrelevant for photon as they do not experience time...they move purely through space. I find unsatisfactory because the measurements are made in our reference frame, not that of the photons.
I'm not even sure if that's what the man is getting out so I included the link: https://www.youtube.com/watch?v=_ZnAvjzjTBY (The argument beings at 20:35)