From Wikipedia:

"Feynman’s gravitational wave detector: It is simply two beads sliding freely (but with a small amount of friction) on a rigid rod. As the wave passes over the rod, atomic forces hold the length of the rod fixed, but the proper distance between the two beads oscillates. Thus, the beads rub against the rod, dissipating heat."

Why the argument of atomic forces does not hold in the case of interferometers? Am I wrong on thinking of them as chemically bound structures with fixed mirrors at the end? In this case I do not see what is playing the role of the bead, here. I treat the laser beam as merely the meaning to measure change in a arm via interference. In simple words, why a passing GW should oscillate the arm(s) of the interferometer but does not if a rod (that of the sticky bead argument) is considered? Please try to answer at the same level at which my question is posed, if possible.

EDIT: perhaps I should take the quote from Wikipedia less literally. I would say that both the rod and the beads of the sticky bead machinery oscillate. Just the beads do so more freely as there are almost free masses (ideal little friction). But the rod does oscillate to, just in less extent... Is this the key to dissolve my doubt?

  • $\begingroup$ Thanks @John Rennie. I thought of that but it only shift my doubt to a bound object larger than the interferometer. I. E why Earth responds to GW but the rod of the sticky bead ideal machinery does not? $\endgroup$ – Alchimista Oct 4 '17 at 13:20
  • $\begingroup$ Look at my edit please. Perhaps I ve got it. $\endgroup$ – Alchimista Oct 4 '17 at 13:35
  • $\begingroup$ Ah! This means the shortcut I have found is wrong? $\endgroup$ – Alchimista Oct 4 '17 at 13:41
  • $\begingroup$ @John Ronnie. Basically each arm behaves as in the sticky beads, whit even less friction. Thanks but plz have a look at the edit too. $\endgroup$ – Alchimista Oct 4 '17 at 13:43
  • $\begingroup$ @John Rennie. Sorry shortcut meant my way to solve the doubt, as in the edit. Thanks again. $\endgroup$ – Alchimista Oct 4 '17 at 13:45

The interferometer arms look roughly like this:

Interferometer arm

There is a housing made up of the vacuum tube and the building around the tube, and this housing is rigid. That means when the gravitational wave passes through the length of the housing, $\ell$, does not change. This is analogous to Feynman's rigid rod.

The mirrors are suspended as delicately as possible inside the housing, so they are free to move to and fro. So as the gravitational wave passes through the mirrors move and the distance between the mirrors, $d$, changes. The light beam measures the distance between the mirrors, so as the mirrors move in response to the gravitational wave the light beam measures the change in their spacing. The mirrors are analogous to Feynman's beads.

You might wonder how something as heavy as the mirrors can move in response to the tiny forces created by the gravitational wave. The, perhaps surprising, answer is that the mirrors don't move. The mirrors remain exactly where they are and the gravitational wave in effect creates and removes extra space in between the mirrors.

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  • $\begingroup$ Your final remarks induced a new puzzling consideration : in the sticky beads the GW does work on the bead, as seen by dissipation of heat. How / where I can see this in the interferometer? Is the acceleration / movement of the mirrors with respect of the fixed tunnel? In such a frame the mirrors indeed move, right? $\endgroup$ – Alchimista Oct 5 '17 at 12:26
  • $\begingroup$ The mirrors move relative to the tunnel, so if you had some form of linkage between the mirrors and the tunnel the length of that linkage would change as the GW passed through and you could use that length change to do work. $\endgroup$ – John Rennie Oct 5 '17 at 12:40

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