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I wonder why detectors for gravitational waves have only two perpendicular arms, not three. Having three arms appears to allow for better detection of direction, or may even increase sensitivity (I may be wrong). So far I came up with a few guesses, but I'm by no means an expert.

  • two arms are cheaper than three
  • a 600m tower is a no-go (stability), a 600m deep hole is a challenge to build and operate
  • two arms is all we need, three would not guarantee significantly better results
  • photons going down and up would gain and lose energy; those in the surface arms do not or much less so. Signal evaluation would be messy.

What are the true reasons?

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LIGO's arms are 4km long, which makes the problem even worse. Besides, you can just move a quarter of the way around the planet and build another 2-arm facility there, and it'll automatically be at right angles to your first facility (and as long as you do know their relative positions and orientations precisely, you don't have to put them at exactly right angles to each other).

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The basic idea is that you have destructive interference. This is hard(-er) to achieve with three photons as well as I don't see a trivial way to do the beam-splitting.

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    $\begingroup$ I like the trivial pun :) $\endgroup$ – Amphibio Feb 12 '16 at 16:17
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    $\begingroup$ What about a 3-in-1 device: 3 pairwise perpendicular two arm interferometers? $\endgroup$ – Jens Feb 12 '16 at 17:24
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    $\begingroup$ @Jens - That's probably the proper way to do it. But that really increases the cost and complexity of the setup, and one would still have the problem you mentioned about photons going up and down in one of the arms against gravity. It would probably be a better use of money to just build another 2-arm LIGO site somewhere else on the planet. $\endgroup$ – Samuel Weir Feb 12 '16 at 18:32

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