# How can one know, that the length of one arm is exactly 4km (or so)?

Garfiulia
Joined: 11 Mar 05
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Topic 188524

I came to think about how they have measured that the both arms of LIGO are excactly 4km long, or at least equal in length.

I supposed that if they had tried to measure the absolute length of one arm by laser, the graviotational waves would have distorted the measurement. Well, of course they could have tried to get the average of one arm to exactly 4km and that should be the "true" length of the arm.

Anyway, I have understood that nobody really knows how many gravitational waves hit the earth per second. Because the frequencies of the hitting waves are different, one might suppose that their superposed wave would have very, very long time of period. And this would of course make it difficult to get the right average of length. So the question is, how is it done or am I completly wrong?

In LIGO they also reflect the beam back and forth about 100 times to get it more easy to measure the difference in length. This is appropriate due to the gravitational wavelengths are approximately 1000 km in length, so that the length of an arm can't really change in that time. Once again I came to think about, that due to very large number of gravitational waves hitting earth, how one can be sure that the superposed wave of them all doesn't have the time to change the length of one arm?

Anyway, I would be more than delighted if somebody could enlighten me a bit.

Ben Owen
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### How can one know, that the length of one arm is exactly 4km (or

Garfiulia,

Actually what the interferometer measures is the difference between the lengths of the two arms. They're not actually both exactly 4km long in the absence of a gravitational wave, and that doesn't hurt the sensitivity at all.

LIGO doesn't even really measure the length difference so much as changes in the length difference. And it's much more sensitive to changes on some timescales than on others. For example, if you shake it at 100Hz (cycles per second), which is what the best pulsars do, it is quite sensitive to that. If you shake it at 10Hz or 10kHz, it's much less sensitive.

Why?

At high frequencies you see fluctuations in the light that drown out your sensitivity to gravitational waves anyway. These are basically the vacuum fluctuations of quantum mechanics, which are normally equally small at all frequencies, but because of the way the mirrors are set up they get worse at high frequencies (fed back through several mirrors).

At low frequencies, you get drowned out by seismic noise (ground rattling from earthquakes, cars, footsteps, ocean waves hitting the coast hundreds of miles away, you name it). It is possible to put in various insulating mechanisms. They are there, and they are incredibly good (LIGO inspired the cutting edge here). But as you get down toward 10Hz the Earth just gets too noisy; thus the plans for LISA (a space-based LIGO).

Hope this helps,
Ben