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A friend and I were having a discussion about the LIGO experiments and were wondering if there is any issue with the laser light undergoing a wavelength shift as a result of the gravitational wave? Akin to the red/blue shift we see in the galactic sense but on a much smaller level.

Wouldn't this make it "impossible" to measure the length contraction since the "ruler" itself contracts within the space also?

Feel free to go into detail, but we are just looking for a simple explanation.

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  • $\begingroup$ I will reserve an answer for someone with expertise in this subject, but you might look at this presentation (pdf): aapt.org/doorway/tgrutalks/Saulson/… $\endgroup$
    – Rococo
    Commented Feb 12, 2016 at 18:59
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    $\begingroup$ It should be reassuring that the spokesperson of LIGO also admits that he was confused by this for years :) $\endgroup$
    – Rococo
    Commented Feb 12, 2016 at 19:00

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Light is stretched by the gravitational wave and you are quite correct that this is the reason we see the cosmological red shift.

However the arms of the LIGO interferometer are only 4km long so light takes only 27 microseconds to make the round trip. The maximum frequency of the observed gravitational waves was 250Hz making the period 4 milliseconds. So the length of the arm is changing more than a hundred times more slowly than the time the light takes to probe that length change.

The result is that the gravitational wave has essentially no effect on the light beam, and that's why the light can detect the change in the length of the arm.

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