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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?

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Fattie
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1 Answers1

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I've extended my answer to the question I linked to address this, but for completeness I'll also post the answer here.

In the LIGO experiment light is continually being shone into the arms, and the travel time along an arm and back is about 27 $\mu$s. The maximum frequency of the gravitational wave is 250Hz making the period 4 ms. So the gravitational wave is changing the length of the arm more than a factor of a hundred times more slowly than the light is measuring that length change.

The changes in the metric caused by the gravitational wave do indeed affect light, but because they are so slow the light is (to a first approximation) unchanged by them. The light simply doesn't hang around for long enough to be stretched.

John Rennie
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