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I think I have understood properly the principle of LIGO, however the sensitivity is around $10^{-18}~\rm m$ of accuracy of distortion. That looks pretty small... just starting with simpler phenomena, for example, thermal expansion. In order to avoid thermal expansion, the temperature needs to be control within a variation of $10^{-10}~\rm K$ or $10^{-11}~\rm K$ along the tubes.

I guess that the tubes do not need to be exactly $4~\rm{km}$ equal as the lasers can be synchronized although the distance is not exactly 4km within the range of $\left[10^{-18}~\rm m\right]$

How is the thermal noise avoided currently in LIGO, related to suspension and not complete vacuum?

It is already demonstrated that the frequency cut-off is low, but, how is that achieved? Which materials and isolation supported it?

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Trebia Project.
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  • You can read it in all detail in the technical design report and other documents relating to the instrument: https://dcc.ligo.org/cgi-bin/DocDB/ListTopics. The effective length of the interferometer arms is 1600km, by the way, not 4km, so I am not sure your estimate about the temperature control is correct. Having said that, the instrument doesn't need DC stability and the noise increases very quickly below its intended operating frequency range. – CuriousOne Feb 13 '16 at 10:51
  • I used their web https://www.ligo.caltech.edu/page/ligos-ifo , anyhow for a difference of factor 2 or 3 my argument is not challenged... – Trebia Project. Feb 13 '16 at 10:56
  • The length of the tubes is not the relevant factor. The light in these interferometer arms goes forth and back 400 times to make the effective size of the instrument much larger than its physical size. That's also explained on the same page, by the way. They key to the stability of the instrument is, as I said, that it only works at fairly high frequencies, where all terrestrial noise sources can be controlled. Future space based gravitational wave observatories will not suffer from that limitation. – CuriousOne Feb 13 '16 at 10:59
  • How is this argument challenging my argument about temperature?, it will amplify its effect as amplifies the effect of the gravitational wave. – Trebia Project. Feb 13 '16 at 11:15
  • That was my point, exactly. The problem is harder, not easier. It is probably also less relevant than you think, because what matters is not the absolute control of the temperature but the differential control of its drift between two arms over the design bandwidth. The thermal masses are certainly large, the average distance of mirrors can be controlled by the interferometer itself, which greatly reduces the drift problem. What can not be reduced by the interferometer so easily is the in-band seismic noise, and I believe that was the major problem with the initial LIGO design. – CuriousOne Feb 13 '16 at 11:20
  • I understand your argument about the difficulties for seismic noise, which is also a challenge, and how the interferometer can avoid an stable temperature difference. However, each measurement takes around 5ms the laser to move and we need to ensure that no arm of the LIGO modifies is temperature around $10^{-10}K$ in that period of time. Looks to me really challenging – Trebia Project. Feb 13 '16 at 11:43
  • Temperature only changes if the radiation balance changes. Keep in imd that all of these things are in vacuum and they are being controlled extremely well. LIGO's test masses are 40kg fused silica mirrors... that's a lot of thermal mass, which only gets larger as one moves out towards the mirror mounts and then the foundations on which the experiment rests. – CuriousOne Feb 13 '16 at 11:48
  • The tubes are covered to isolate from the external environment, so the radiation will not affect the internal vacuum. Still, we are talking about the movement of the size of an atom in 5ms. The mirror will be mounted in an structure that will conduct termal energy, and still can that small temperature variation be secured? How either we measure that is not happening? – Trebia Project. Feb 13 '16 at 12:26
  • I haven't read the technical documents, but it seems obvious that they use a negative feedback circuit to continually null the signal over time scales of a few tens of seconds. That scale is much slower than the signals they are sensitive to (so it doesn't interfere with getting the data) but much faster than issues like thermal variation on the arms and other environmental variations (so that the system is always in a usable state). @CuriousOne tried to point that out by talking about bandwidth but you may not have followed that point. – dmckee --- ex-moderator kitten Feb 13 '16 at 17:27
  • When the interferometer drifts it will produce an output signal in form of noise. If that noise is too high, you know that your thermal insulation etc. is not working. We aren't talking about the movement of single atoms here, we are talking about the average movement of a large thermal mass. If you look at Avogadro's number (it's LARGE!), averaging out over that many atoms is surprisingly effective. But seriously, if you want to know how to build one of these, simply read the documentation. It's all public, nothing is classified. – CuriousOne Feb 13 '16 at 18:23
  • The distance measures is much smaller than the size of an atom. I understand the point of ten of seconds, but what I am trying to mean is that the variation of temperature we are talking about in order to notice a difference in the signal is so small that and small perturbation in one edge will be notice at that level in the other edge. I know there is vacum, but finally the mirrors will have supports that will be exposed to conduction. – Trebia Project. Feb 13 '16 at 19:22
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    Possible duplicate of How does LIGO remove the effects of environmental noise? – Danu Feb 16 '16 at 17:09
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    Definitely not a duplicate -- thermal expansion and seismic vibrations are unrelated. –  Feb 18 '16 at 01:06
  • My question was an overall question about all effects and highlighting an specific problem related to temperature. That question is only answering one part of the question related to vibration but not the temperature one. Actually this question has been asked earlier, the duplicated one is the other. – Trebia Project. Feb 18 '16 at 20:53
  • How can I get an answer to my question? How thermal errors are avoided? – Trebia Project. Feb 18 '16 at 22:31

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The LIGO experiment doesn't measure the length of the tubes, it measures the changes in the length of the tubes.

It also has a lower frequency cut-off of 10Hz, so any perturbation that is slower than 10Hz won't affect the measurements. In particular temperatures changes will happen on a timescale of hours so if they change the length of the tube that doesn't matter. When LIGO measures the $10^{-18}$ m change in the tube length it doesn't matter if that length is a bit longer at midday than at midnight.

The accepted answer to the question suggested as a duplicate, How does LIGO remove the effects of environmental noise?, includes a graph of possible perturbations as a function of frequency, and you'll note that the frequency scale doesn't go below 1Hz because frequencies below that don't matter.

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John Rennie
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  • My question is how currently we are avoiding the thermal noise. The link provided (and all the links included in the answer) refer to the current level of noise and only describes the approach for the sismic noise. My question is , how are we able to reach that level of noise? The answer is incomplete – Trebia Project. Feb 18 '16 at 21:15
  • LIGO isn't measuring the length of the arms, it's measuring the time it takes, as stated in my answer here – Kyle Kanos Feb 18 '16 at 22:30
  • @TrebiaProject.: the point is the frequency of the thermal noise is too low to affect LIGO - the temperature changes happen too slowly. – John Rennie Feb 19 '16 at 06:09
  • I understood that, but that is why, not how. I mean, if you introduce copper instead of the material used for sure the frequency will grow. My question is how they are able to reach that low frequency, which materials and which suspension isolation was used? – Trebia Project. Feb 20 '16 at 10:09