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I understood that the basic idea of the interferometric detectors is the michelson interferometer experiment, in which the change in the position of the mirrors will cause the interferometer ( constructive or destructive)which causes the changin the detected wave's intensity.the question is how do the gravitational waves cause the change in the arm length? here is the sentence I can't understand

"Gravitational waves lead to rhythmic distortions of space. This distortion influences the time it takes a light signal to travel back and forth between two freely falling test masses. As the distance the light signal has to travel is stretched or squeezed, it takes the light a little more or a little less time to travel from one test mass to the other." from EISTEIN ONLINE site Catching the wave with light

I think the reason that I can't understand this because I can't imagine how these distortion in space take place and how does the distance is stretched or squeezed.I hope someone can help!

Zeinab Mabrouk
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  • Related: http://physics.stackexchange.com/questions/153657/ (possible dupe?), http://physics.stackexchange.com/questions/25643/, http://physics.stackexchange.com/questions/18584/ – Kyle Kanos Jun 16 '15 at 13:38
  • From my own questions on this site, I have stopped trying to get a mental picture of GR for 3 reasons: 1. It was nearly always wrong, and led me astray in the problem, 2. It was impossible to do anyway and 3. I treat the math like electrical engineers treat complex numbers, you start with a REAL problem, then you use complex numbers as an intermediate step, then in the end you go back to a REAL answer. Best of luck with your studies. –  Jun 16 '15 at 15:39

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I hope the following makes sense to you.

Gravity waves are thought to distort spacetime , but trying to get a mental picture of it will make you go well, mental.

So difficult as it may be, try to stop thinking of a 4 D space, it won't work, for you, me or anybody.

We can only imagine 3 D space, but we can (fairly!) easily calculate the distortion due to gravity on spacetime using math.

Imagine the waves on water making the surface of the ocean distort periodically. Now you want to measure a certain length, it will differ, roughly speaking, depending on whether a wave is passing by at the time of measurement or not.

Now extend that idea to spacetime being distorted so that our measurement of it, using light waves, also changes with time, as the gravity waves pass by.

So if the light rays are out of phase, because one of them travels a different distance compared to the other, this will show up in the interference pattern of the interferometer.

You can see from the picture below how the arms of the LIGO detector are set at 90 degrees apart, to maximise our chances of detecting the distortion, as the math , not just our mental pictures, tells us this is the best way to line them up for possible detection of gravity waves.

Ligo Interferometer

  • There is a technical detail. The time for the laser beam to travel back and forth must be much shorter than the period of the gravitational wave. So that the "stretching of space" barely changes at all during the laser's trip. LIGO is 4km long so a round trip is in the order of $10^{-4}$. It's designed to detect waves between 10 and 100 Hz. So it's fine. – Petra Axolotl Mar 23 '23 at 17:55