Gravitational waves are measured by interferometers, in particular by the change in length of one of the arms, with respect to the other. In this scenario, the light that has always the same speed, measures a delay by traveling one of the arms. My question is: if an arm pass from length $L$ to length $L+dL$, and if I am inside the arm and measure it with my ruler, I will measure from my point of view always the same length $L$, because also my ruler will be distorted like the arm. This means that the delay of light is related to the different "speed" of time between the two arms?
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The ruler resists attempts to change its length, due to electrostatic forces between atoms in the ruler (eg see Young's modulus). This means the ruler will not change as length to the same extent as space, when a gravitational wave passes.
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1$\begingroup$ If the ruler doesn't change its length to the same extent of space, means that for me that am inside the arm, the arm remains at the same original length, that makes sense for me. My question was about the fact that the light has a "delay" with respect to the light that traveled the other arm, and this can appens only if my time in my arm has a different speed with respect to the other arm. $\endgroup$ Commented Jul 26, 2022 at 12:51
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$\begingroup$ @blackhole Yes, that's one way of looking at what is happening. $\endgroup$– AndrewCommented Jul 26, 2022 at 13:34
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$\begingroup$ @ Andrew I don't undertand well your previous answer: if the space will become longer, there aren't electrostatic forces in the ruler because from its point of view, the ruler remain always of the same length. It is not so? $\endgroup$ Commented Aug 1, 2022 at 16:21
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$\begingroup$ @blackhole Empty space expands, but the ruler itself is held together by electrostatic forces and doesn't expand by the same amount as empty space. $\endgroup$– AndrewCommented Aug 1, 2022 at 18:22
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$\begingroup$ Do you mean that the empty space becomes longer, but the "full" space not? It this the reason why the two mirrors in the antennas are suspended? $\endgroup$ Commented Aug 2, 2022 at 7:39