Can gravitational waves do work on matter?
Feynman answered this with a yes, using a thought experiment with a rod strung with beads that move with friction. He reasoned that a passing wave would result in the beads releasing friction heat.
Would it, though? The beads and the rod are in the same metric, wouldn't they (for lack of a better word) "move" together?
On the other hand, if a gravitational wave set a Weber bar to ringing, there would certainly be energy dissipated.
One practical application for the question is Big Bang astronomy. The universe was opaque to electromagnetic radiation for its first 400,000 years. I have heard a hope that gravitational waves would allow probing those early years. But that would depend on them not coupling with matter.
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I don't know the specific thought experiment, but generally, matter tries to follow spacetime geodesics if nothing forces it not to. So if a gravitational wave passes though a gas or other medium in which the particles can move freely, I would expect the gravitational waves not to produce work. I'd expect that to be the case in the early universe (though I'm definitely no expert in that).
But beads and strings are definitively not in that category; rather they are solid matter where the relative locations are mostly determined by the electromagnetic forces acting between them, and the corresponding quantum properties.
I think a good analogy should be tidal friction. Tidal friction happens when a massive, solid object rotates in an inhomogeneous gravitational field, that is, its solidity forces its atoms to move along trajectories that do not agree with the spacetime geodesics they would otherwise follow. The tidal forces cause changing deformations as the body rotates (and relative movements, e.g. of the water relative to the earth), and since those deformations are not perfectly elastic, that means friction.
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