Regarding the wonderful 2016 news about gravitational waves.
Travel time in one arm of the LIGO is ~ 30μs.
A gravitational wave affects the arm for some few hundred of these laps.
Then for example as RobJ explains "the arm changes length ... subsequent wavecrests will have had successively further to travel and so there is a phase lag that builds up ..."
But we always use the language that gravitational waves are affecting the spacetime metric. I just don't see how the phase ("speed") can change if the spacetime metric is changing.
Let me put it this way:
Say I said (A) "gravitational waves stretch and squash objects - amazing!". Say a physicist says (B) "gravitational waves stretch and squash the spacetime metric - amazing!"
What really is the difference between saying "A" versus "B", and, what is it in the experiment that shows us "B" happened, not "A"?
In other words, say we deliberately merely did "A" - using say a really precise bulldozer chained to one end of the tube - what specifically would we look at in the signal and conclude "oh, that was merely 'A' - not actually 'B'".
Or indeed are "A" and "B" indistinguishable?