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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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  • $\begingroup$ You can read it in all detail in the technical design report and other documents relating to the instrument: 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. $\endgroup$
    – CuriousOne
    Commented Feb 13, 2016 at 10:51
  • $\begingroup$ I used their web ligo.caltech.edu/page/ligos-ifo , anyhow for a difference of factor 2 or 3 my argument is not challenged... $\endgroup$
    – Trebia Project.
    Commented Feb 13, 2016 at 10:56
  • $\begingroup$ 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. $\endgroup$
    – CuriousOne
    Commented Feb 13, 2016 at 10:59
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    $\begingroup$ Possible duplicate of How does LIGO remove the effects of environmental noise? $\endgroup$
    – Danu
    Commented Feb 16, 2016 at 17:09
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    $\begingroup$ Definitely not a duplicate -- thermal expansion and seismic vibrations are unrelated. $\endgroup$
    – user10851
    Commented Feb 18, 2016 at 1:06

1 Answer 1

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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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  • $\begingroup$ 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 $\endgroup$
    – Trebia Project.
    Commented Feb 18, 2016 at 21:15
  • $\begingroup$ LIGO isn't measuring the length of the arms, it's measuring the time it takes, as stated in my answer here $\endgroup$
    – Kyle Kanos
    Commented Feb 18, 2016 at 22:30
  • $\begingroup$ @TrebiaProject.: the point is the frequency of the thermal noise is too low to affect LIGO - the temperature changes happen too slowly. $\endgroup$
    – John Rennie
    Commented Feb 19, 2016 at 6:09
  • $\begingroup$ 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? $\endgroup$
    – Trebia Project.
    Commented Feb 20, 2016 at 10:09

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