Gravitational Waves: Time, Synchronization, Speed

[Karl Coryat]

Hi folks. I see there is a similar thread on grav waves and time, but I have a few specific questions.

Everyone talks about grav waves "in space" -- even Brian Greene was saying this on Colbert, whereas Colbert was saying spacetime. I would like to make a video on how GWs are indeed "waves in time" as well, (a) to shed additional light on GWs for lay people and (b) connect it back to relativity.

Ignoring the obvious technological limitations, if there were clocks at the end of the LIGO arms, we would see their rates fluctuate as the GW passes, yes? If they were centrally synchronized and each sending signals, the signals would go out of phase momentarily...I assume they would return to phase and be re-synchronized once the GW has passed?

Also, is it true that the signal would seem to speed up on an arm that's otherwise seen to "lengthen," and slow down when "shortening"?

It strikes me that this would be a nice way to demonstrate how space and time are intimately linked in spacetime, and the invariance of c. Incidentally I had a lot of success with my last physics video, "How Gravity Makes Things Fall," which also began as a question right here. Thanks!

 

[Karl Coryat]

Sorry, I am past the editing time limit. I meant to say, "is it true that the rate of the signal would seem to speed up on an arm that's otherwise seen to lengthen" -- which, when phrased this way, makes me think the rate of the ticks would actually be slower or redshifted on the arm that would be observed as having lengthened. Is that right?