# LIGO discovery: if the space “time” metric is changed, how is it measured? [duplicate]

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?

• You are asking why the wavelengths of light aren't affected in the same way as the arms of the interferometer? they are, but there are GR subtleties going on... – innisfree Feb 12 '16 at 14:23
• Hi Innisfree (btw - Morar??!) - that sounds tantalizing, but deserves a very long answer! :O – Fattie Feb 12 '16 at 14:47
• Related and/or dupe: physics.stackexchange.com/q/153657 – Kyle Kanos Feb 12 '16 at 15:28
• Hi @innisfree .. Hmm, you mention "GR subtleties". Can you elaborate? In the linked answer, JR I believe is essentially saying "photons don't change with the metric". Is that what you mean by "GR subtleties" or do you mean some further point? – Fattie Feb 12 '16 at 18:48
• "since it would be deforming the space and time of the photons equally." the photon is a point in space and time, it cannot be deformed. It can be red shifted or blue shifted , but the experiment is measuring phases , not frequencies, and phases enter in the way the photons build the electromagnetic wave. John is saying that the amplitude changes of the gravitational wave is much slower then the return track of the laser light, where the phases should cancel if spacetime is quiet. Did you see the webcast? – anna v Feb 13 '16 at 14:09

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.