Laser interferometry and the search for gravitational waves

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When viewing the light coming from distant galaxies, it is my understanding that there are 2 redshifts occurring, the doppler effect from the galaxies' peculiar motions, and the cosmological redshift from space itself expanding.

For the cosmological redshift, I visualize a square of space, say 1 meter long, and a light wave sitting inside with a wavelength of 1 meter. When space stretches, lets say by a factor of 2, then the light wave sitting inside also gets stretched, and so now its wavelength is 2 meters long. I imagine space stretching and compressing due to gravitational waves is similar, and it is this stretching and compressing that will allow http://lisa.nasa.gov/" [Broken] to detect gravitational waves due to the changes in the wavelengths of the light waves hitting the LISA detectors, causing a change in the constructive/destructive interference.

But lets say we have a square of space the same length as the distance between 2 of the LISA detectors/transmitters. If they are setup so the laser light is in perfect constructive interference, and a gravitational wave passes by, wont they stay in perfect constructive interference? The space will get stretched and then compressed, depending on the direction of the wave as I understand it, but so will the light waves sitting inside the space by the same factor, so there wouldn't be a change in the interference. The way I see it the detectors get moved say 1 meter farther from each other, but at the same time the wavelength of light gets stretched by 1 meter (if the distance between the detectors were 1 wavelength). So I'm obviously missing something.

If I have 2 protons being held a certain distance apart so they are exerting a force of 1 newton on each other, and a gravitational wave passes through them in such a way that space compresses, do they move closer together, so I would then momentarily detect a force larger than 1 newton? Or do they somehow stay the same distance apart, even when the space between them is being compressed?
 
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Matterwave

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For the interferometry question: Gravity waves only compress/expand in 1 direction. This is why LIGO uses 2 laser beams perpendicular to each other. Only one of them will stretch/contract and this will cause an interference pattern because it no longer matches the other beam. I suppose if the gravity wave comes in at exactly 45 degrees then one may see uniform stretching/expanding (although I'm not sure), but for any other configuration, one beam will stretch/expand more than the other.
 
But lets say we have a square of space the same length as the distance between 2 of the LISA detectors/transmitters. If they are setup so the laser light is in perfect constructive interference, and a gravitational wave passes by, wont they stay in perfect constructive interference? The space will get stretched and then compressed, depending on the direction of the wave as I understand it, but so will the light waves sitting inside the space by the same factor, so there wouldn't be a change in the interference. The way I see it the detectors get moved say 1 meter farther from each other, but at the same time the wavelength of light gets stretched by 1 meter (if the distance between the detectors were 1 wavelength). So I'm obviously missing something.
The answer is that the wavelength of light is not a physical object that can get stretched; rather, it is the length over which the phase of the electromagnetic fields oscillate through a cycle, for radiation of a given frequency. Remember that the light waves are not "sitting" alongside the LISA arms, but propagating across them. As they do so, while a gravitational wave is passing by, they will experience a shorter or longer path, and therefore have time to "unroll" through a few less or more wavelengths.

Another way to think about it is to visualize individual photons moving between the spacecraft... because of the constancy of the speed of light, the time they will take will depend on the instantaneous armlength (which changes with the gravitational waves), and the total "phase" that they acquire will change accordingly.

If I have 2 protons being held a certain distance apart so they are exerting a force of 1 newton on each other, and a gravitational wave passes through them in such a way that space compresses, do they move closer together, so I would then momentarily detect a force larger than 1 newton? Or do they somehow stay the same distance apart, even when the space between them is being compressed?
Indeed, they move closer together. The distance (as can be measured by light) is smaller, and therefore the force is stronger. This is the principle of operation of the resonant-mass gravitational-wave detectors.
 

Mentz114

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For the interferometry question: Gravity waves only compress/expand in 1 direction. This is why LIGO uses 2 laser beams perpendicular to each other. Only one of them will stretch/contract and this will cause an interference pattern because it no longer matches the other beam. I suppose if the gravity wave comes in at exactly 45 degrees then one may see uniform stretching/expanding (although I'm not sure), but for any other configuration, one beam will stretch/expand more than the other.
A grav wave travelling perpendicular to both arms will

* stretch along x while compressing along y
* stretch along y while compressing along x

See for instance http://arxiv.org/abs/1005.4735" [Broken].
 
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