Detecting Gravitational Waves: Is My Understanding Wrong?

[wvphysicist]

Something is wrong in my understanding of Relativity. There is an equivalence idea running around, which says that gravity and the distortion of space time by gravity waves acts the same way on all things. That would mean that all objects and light and space experience the same distortion from a gravity wave. Then the tunnel in the LIGO machine and the space in it and the laser beam must all distort the same amount. If there is no difference in these distortions than a gravity wave antenna cannot work. But it has. So where have I been misinformed?

 

[Grinkle]

https://www.physicsforums.com/threads/what-is-a-gravity-wave-detector-measuring.839079/#post-5266713

That helped me out with a similar question.

 

[A.T.]

Then the tunnel in the LIGO machine and the space in it and the laser beam must all distort the same amount. If there is no difference in these distortions than a gravity wave antenna cannot work. But it has. So where have I been misinformed?

This is discussed here too:

 

[PeterDonis]

There is an equivalence idea running around, which says that gravity and the distortion of space time by gravity waves acts the same way on all things.

That's not what the equivalence principle says. It says (at least this is one way of putting it) that a freely falling object's path through spacetime depends only on the geometry of spacetime, not on the object's shape or composition. But it does not say that the geometry of spacetime is the same everywhere, nor does it say that that geometry is static and unchanging. Gravitational waves are distortions in the spacetime geometry, and those distortions vary in both space and time. So two objects that are not at the exact same point in space will be acted on differently by gravitational waves. That is how GW detectors work.

 

[Paul Colby]

I find it actually quite strange when I try to visualize it. The mirrors in LIGO are made inertial along the beam direction by a very clever suspension system. As the GW passes the mirrors don't "move" in a classical sense of gaining kinetic energy relative to their initial position. It's the distance between mirrors that changes as the wave passes. Hope I haven't butchered this too badly.

 

[PeterDonis]

As the GW passes the mirrors don't "move" in a classical sense of gaining kinetic energy relative to their initial position. It's the distance between mirrors that changes as the wave passes

This is one way of looking at it, but it's worth pointing out that it's coordinate dependent. The coordinates that are usually used to describe GW detectors like LIGO put all of the effects of the GW into the transverse metric coefficients; that is, each of the detector masses and mirrors are at fixed coordinates, but the metric varies with time so the physical distance between objects at fixed coordinates changes. (If you think about it, you will see that this also means the coordinate speed of light changes.)

It is perfectly possible to adopt different coordinates, in which the masses/mirrors do move, in the sense of changing spatial coordinates with time. It just turns out that coordinates like these would be harder to work with mathematically, so they aren't used.