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Comment by nharada | Hacker News Reader

LIGO blows my mind whenever I hear news about it. The sensitivity alone is insane -- it can detect a change in distance between its mirrors 1/10000th the width of a proton. This is the equivalent of measuring the distance to the nearest star (4.2 light years) to an accuracy of 1 human hair. Those are bonkers numbers. How the hell did we even come up with this thing?

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Speaking of which, I can understand how interferometry gets you to, say, 1/1000th of a wavelength, but the wavelength is 1000nm. How do they go from 1nm to 1/10000th the width of a proton? What's the trick?

Is it an integral transform thing, like how spectrum analyzers can claim super low noise floors if you sort of gloss over the "noise is proportional to badwidth" part and look in a tiny bandwidth without normalizing?

Cavities. We trade off bandwidth for peak sensitivity by sending the same light back and forth between mirrors in the arms of the interferometer hundreds of times. As the gravitational wave passes, the same light samples it over and over and picks up additional phase shift, enhancing the signal. The downside is that we can't see gravitational waves at signals far above the cavity pole frequencies at a few 10s of kHz, but the most promising sources we aimed at when the detectors were designed were considered to be below that.

We also use techniques called power and signal recycling to enhance this bandwidth-sensitivity tradeoff even more. Combined these techniques give you what remains between your 1/1000th wavelength and the actual sensitivity of LIGO and Virgo.

That sounds like a block & tackle [1] for light.

[1] https://en.wikipedia.org/wiki/Block_and_tackle

In addition they've been using squeezed light[1] since 2019 to help increase the sensitivity.

[1]: https://www.optica-opn.org/home/newsroom/2019/december/squee...

I wonder if twisting light is similar to this (now useful in fiber optics) or if this would be another dimension to explore.

Cool! Thanks for the explanation, it makes sense!

Great question! The precision is not just better than the wavelength of the light. It's also way smaller than the surface roughness of the mirrors! How does it work?!

Like you suggest, and adding to what sleavey mentioned above, I would say the answer is: averaging over time and space. The laser beam is pretty wide, so it averages over a significant area of mirror surface. (The optical system also selects one spatial mode of the laser beam.) And the stated displacement sensitivity ("1/10000 the width of a proton") only occurs when you integrate over the sensitive frequency band.

Neat! Thanks for that puzzle piece. Even knowing the tricks, it's an astounding piece of work!

Interferometry has a long history in experimental physics. The Michelson–Morley experimental design scaled up to large distances and using modern technology, like lasers and computers, gets you LIGO.

And resonant cavities, the best mirrors ever made, and a huge amount of cleverness and work over 40+ years.

*the second nearest star

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