Laser interferometry and the search for gravitational waves

[PiTHON]

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, let's 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/" 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 let's 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, won't 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?

 

[Matterwave]

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.

 

[vallis]

But let's 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, won't 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]

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 traveling 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" .

 

[sardar]

I find your understanding of laser interferometry and the search for gravitational waves to be quite accurate. The two redshifts you mentioned, the doppler effect and the cosmological redshift, are indeed important factors in our observations of distant galaxies.

Your visualization of the cosmological redshift as a stretching of space is also correct. In fact, this is one of the key principles of general relativity, which describes how space and time are affected by the presence of massive objects. In the case of gravitational waves, it is not just the space itself that is stretching and compressing, but also the geometry of space and time. This leads to changes in the wavelengths of light waves, which is what we are trying to detect with instruments like LISA.

However, your question about the interference of light waves in a square of space is a valid one. While it is true that the distance between the detectors and transmitters would increase or decrease by the same factor as the light waves, there are other factors at play. For example, the gravitational wave may not affect the entire square of space uniformly, leading to a differential stretching and compressing of the light waves. This would result in a change in the interference pattern, which can be detected by sensitive instruments like LISA.

As for your example with two protons, the answer is not as straightforward. The force between two particles is not solely determined by their distance, but also by other factors such as their masses and the strength of the gravitational field. So even if the space between them is being compressed, the force between them may not change significantly. It is also worth noting that gravitational waves have a very small amplitude, so the effect on the distance between two particles may not be noticeable at all.

In conclusion, your understanding of laser interferometry and gravitational waves is quite impressive. However, these are complex concepts and there are still many questions and uncertainties in this field of study. That is why we continue to conduct experiments and research in order to deepen our understanding of the universe and its workings.