Can Gravitational Waves Affect Light Wavelengths?

[cianfa72]

Hi,
a simple question related to the gravitational wave detection.

The net effect of gravitational wave is basically the stretching of the space including all the measurements tools (meter sticks just to illustrate the concept) that could be used to detect it. I am aware of laser interferometer techniques (e.g. LIGO) are employed for the detection. From this point of view can we assume light wavelength is not affected by the gravitation wave itself ?

Thanks

 

[Wrichik Basu]

Quoting LIGO:

If a gravitational wave stretches the distance between the LIGO mirrors, doesn't it also stretch the wavelength of the laser light?

While it's true that a gravitational wave does stretch and squeeze the wavelength of the light in the arms ever so slightly, it does NOT affect how fast the light beams travel (the speed of light). And the only thing that matters to LIGO is the time it takes each laser beam to travel through its arm before being merged with the beam from the other arm.

LIGO is designed such that as long as the distance the laser beams travel is exactly the same in both arms, they will make their trips in exactly the same time, and recombine nicely when merged. When recombined, the light waves actually completely cancel each other out in a phenomenon called "total destructive interference". When this is occurring, we know the interferometer and its components are stable.

 

[Ibix]

There are different ways to describe how an interferometer like LIGO detects gravitational waves. One way is to note that the lengths of the arms vary, and the wavelength of the light in flight is similarly affected. However, the light is in flight for a very short time, much less than the period of the gravitational wave. New unstretched light is continually being injected, while the interferometer continues to change length.

Imagine ants walking along a rubber band. One ant enters per second, one ant leaves per second. Sloooowly stretch the band. The spacing between ants (analogous to the wavelength) is increased the same as the band stretches. But the time taken for the ants to walk the length of the band (analogous to the reason for interference fringes) grows and grows as you stretch the band further and further.

 

[cianfa72]

Thanks for answers...
A point about the following: I know the speed of the light is taken as the constant c in each local Lorentz frame thus I believe we can assume it constant also during the wave detection. But what about the time "stretching/dilatation" due to the gravitational wave "impact" ? Could it affect the measurements ?

 

[Ibix]

I believe we can assume it constant also during the wave detection.

You can't treat the whole experiment as covered by approximately flat spacetime, because it's the non-flatness you are measuring.

I think whether or not the speed of light is constant through the experiment depends on the coordinate system you use. You may regard the appearance of interference fringes as due to a change in length of the arms or due to a change in the speed of light along the arms, or a bit of both. The first seems to be conventional, and that's what Wrichik's quote from LIGO is based on. Possibly the maths is simpler in this coordinate system. I'm not familiar enough with the details of the analysis to know.

 

[cianfa72]

You can't treat the whole experiment as covered by approximately flat spacetime, because it's the non-flatness you are measuring. I think whether or not the speed of light is constant through the experiment depends on the coordinate system you use.

Which coordinate system are you referring to ? Can you elaborate it a bit ?

 

[PeterDonis]

I think whether or not the speed of light is constant through the experiment depends on the coordinate system you use.

More precisely, the coordinate speed of light depends on the coordinate system you use.

You may regard the appearance of interference fringes as due to a change in length of the arms or due to a change in the speed of light along the arms, or a bit of both. The first seems to be conventional, and that's what Wrichik's quote from LIGO is based on.

That's basically correct, but note that the change in length is due to the change in the metric, not any change in the coordinate locations of the ends of the arms. The standard coordinates used to analyze experiments like LIGO are called "transverse-traceless" coordinates in the literature. In these coordinates, the metric only changes in the spatial components that are transverse to the direction of gravitational wave propagation: the spatial component in the direction of propagation, and the time component, do not change. In these coordinates, the coordinate lengths of the arms do not change, but the physical lengths change because the metric transverse to the direction of propagation changes. The change in the metric is the gravitational wave.

 

[gmax137]

arent the arm lengths changing all the time, due to changes in temperature along the arms (warm breezes and sunny spots), tidal effects in the planet, trucks rumbling by? the articles on LIGO always talk about changes in length the size of a proton, how can that be measured over the noise in the lengths? seems like a butterfly flying by would upset that degree of accuracy.

 

[PeterDonis]

arent the arm lengths changing all the time, due to changes in temperature along the arms (warm breezes and sunny spots), tidal effects in the planet, trucks rumbling by?

Yes, and LIGO takes measures to isolate the test masses in the arms from such disturbances as far as possible. Also, LIGO does not accept a signal unless it is seen in at least two detectors (there are three total in the network right now, one in Hanford, WA, one in Livingston, LA, and one in Italy, the last one is referred to as VIRGO but it's part of the same overall detection network); the external disturbances you describe will not be correlated between different detectors separated by hundreds or thousands of miles.

 

[gmax137]

Thanks, but it seems like the nominally 4 km mirror spacing must be constantly changing over some range, due to these effects. By how much? I don't know, but it must be at least a few thousandths of an inch (maybe +- 0.1 mm) which is gigantic compared to the 10^-17 meter signal. Do you know where the signal to noise is discussed? I have searched the web but so far all I find are popular "gee-whiz" accounts. There must something about the actual method that I don't know about that takes care of these global influences.

I seem to be hijacking this thread, maybe it should be split off.

 

[PeterDonis]

t seems like the nominally 4 km mirror spacing must be constantly changing over some range, due to these effects.

The purpose of the various isolation methods is to keep this from happening. Note that some of these methods are active, i.e., they sense outside disturbances and move the mirrors in response to keep the mirror spacing constant.

By how much? I don't know, but it must be at least a few thousandths of an inch

Rather than guess, you should read what the LIGO project has to say:

https://www.ligo.caltech.edu/page/ligo-technology

https://www.ligo.caltech.edu/page/vibration-isolation

 

[gmax137]

thanks @PeterDonis