I LIGO Discovery - A question about space-time properties

[RockyMarciano]

The (relevant) motion of light is orthogonal to the direction of the gravitational wave.

I'm afraid I can't relate this sentence to what I wrote in #25.
I think I understand that you referred above(when mentioning the different scales of microseconds to miliseconds, and "The light that "sees" the maximal amplitude") to the effect of the GW frequency on the amplitude detected from the phase shift at the photodetector, which certainly can never cancel the amplitude at such low GW frequencies, so certainly the arms stretching is measured, that is understood, a much higher frequency of GWs would be needed to achieve such amplitude cancelling you correctly discard.

But what I was saying in reply to phyzguy post has nothing to do with the above. I was simply explaining that if the wavelength of a light wave is altered so is its frequency/period and this change of frequency must be accounted for when using the interferometer as a clock to detect phase shift build-up between the arms as it delays or rushes time of flight by laser light in the arms in proportion to any shrinking/stretching in the arms.

Compare it to the case with interferometer phase shift build-up in response to other causes different from GWs like seismic vibrations, where there is obviously no change of wavelength/frequency of the laser light from spacetime ripples.

 

[PeterDonis]

how can the constancy of c be taken as the very premise of the experiment?

That isn't the premise. The premise is that light travels on null worldlines. "Constancy of c" in the sense of a constant coordinate speed of light only follows from that premise if you choose appropriate coordinates. The standard coordinates that are used to analyze LIGO are such coordinates. But you could choose coordinates in which the coordinate speed of light was not constant.

What you can't do is make the actual observed result change by changing coordinates. The actual observed result is that the passage of a gravitational wave causes interference fringes in the LIGO detector. The fundamental reason for that is that the gravitational wave changes the geometry of spacetime as it passes (more precisely, the change in spacetime geometry is the gravitational wave), and the change is different in the different arms. The difference in the spacetime geometry in the different arms causes the laser beams to not be precisely in phase when they return after a round trip, so interference is produced.

All of these different ordinary language descriptions in terms of "distance changing", "time changing", "speed of light changing", "wavelength of light changing", "frequency of light changing", are not different possible explanations of the above results that are in competition with each other. They are just different ways of translating the fundamental reason I just gave--different changing spacetime geometry in the different arms--into terms that seem more intuitive to people. They are different ways of trying to describe the same underlying reality. So much of the argument over how to interpret LIGO is not an argument over the actual physics at all; it's an argument over which ordinary language descriptions people prefer.

The ordinary language description that says "the speed of light stays the same, but the arm lengths change differently, so the round-trip travel time of the light changes" is the one that seems to work best for the people who are actually working on LIGO, so that's the one you see in the stuff they write. That ordinary language description is also backed up by a detailed mathematical model, based on linearized GR in the TT gauge, which correctly predicts observations. That doesn't necessarily make other ordinary language descriptions wrong. It does, however, mean that if you want to use a different ordinary language description, it's not enough to just say you don't like the standard one; you need to have your own detailed mathematical model, based on some different choice of coordinates in which your ordinary language description makes sense, that also correctly predicts observations. This is not in principle impossible, but it's certainly not easy, and AFAIK nobody has done it.