I have no idea how it works, I don't have an explanation, I just know the one spouted by people doesn't make sense

Well, if you're uncomfortable with LIGO, you're in good company. Once a whole decade went by in physics where people couldn't agree if it would work in principle or not. And it is true that a lot of common explanations are bad (e.g. "it's just a ruler" is not complete by itself because "why doesn't the light get stretched too?"). Nonetheless, today we have a variety of independent explanations.

Maybe you'll find this paper helpful: https://aapt.scitation.org/doi/10.1119/1.18578

Would you say it's accurate to say LIGO is a big interferometer measuring changes in lengths of the arms due to gravitational waves, with some extra analysis to figure why it still works even though the light waves get stretched? Or is OP correct that such an explanation means I "don't have even a slight understanding of how it works" and a correct explanation must "involve higher spatial dimensions (not time)?"

I'd say that's a perfectly fine explanation. And in fact the light does get stretched. For sufficiently low frequencies, that's fine because there's enough time for new (unstretched) light to enter and exit the apparatus. At higher frequencies this causes the sensitivity of LIGO to fall.

Part of the popular confusion around how LIGO works is the freedom in coordinates: there are different, perfectly good definitions of space and time you can use, and the explanation sounds different in each one. So people can get them mixed up. For example, my previous paragraph makes sense in "transverse traceless gauge", but not in others.

I'm not sure what GP was referring to with "higher spatial dimensions".

Thank you for this link. I read it once and think I've gotten more of the picture and I'm going to re-read it to see if I can get more. What's baffling to me is everyone who has tried to explain the LIGO detector doesn't even realize this question exists. I've independently thought this question and when people start explaining LIGO to me, and I take the time to spell out the question, they realize they don't understand LIGO either.

If light is emitted at a constant wavelength independent of the stretching of the universe, doesn't that imply light is traveling through a higher spatial dimension, otherwise the emitter itself would be stretched with the universe and we'd never be able to observe differences in the speed of light? If I understand this paper, once light is emitted, it's "stuck" to space and will stretch along with it. But if the emitter wavelength stays constant doesn't that imply it's waving through a higher dimension?

> If light is emitted at a constant wavelength independent of the stretching of the universe, doesn't that imply light is traveling through a higher spatial dimension, otherwise the emitter itself would be stretched with the universe and we'd never be able to observe differences in the speed of light? If I understand this paper, once light is emitted, it's "stuck" to space and will stretch along with it. But if the emitter wavelength stays constant doesn't that imply it's waving through a higher dimension?

I'm not totally sure what you mean by a higher dimension. The properties of the emitter (which is, e.g. a laser cavity) aren't affected by the gravitational wave because the emitter is a rigid body, which doesn't get stretched. (It's the same thing as described here: https://news.ycombinator.com/item?id=22990753 ) So it puts out light of a given frequency.

By contrast, LIGO is not a rigid body, because the mirrors at the ends of the arms hang freely, hence allowing gravitational waves to change the distance between them.

> What's baffling to me is everyone who has tried to explain the LIGO detector doesn't even realize this question exists. I've independently thought this question and when people start explaining LIGO to me, and I take the time to spell out the question, they realize they don't understand LIGO either.

Yup, it generally is the case in physics that over 95% of people who claim they can explain any given thing don't actually understand it! But the professionals are aware. I even know a LIGO guy who goes to popular talks armed with a pile of copies of the paper I linked.

I've read this paper twice now and it's very good. I still don't have a fundamental understanding, I'm having trouble visualizing what happens over time with the stretching and squashing of space vs the light in the tunnel. I've come away with this paper with more questions than answers, but I think all of it is there if I study it hard enough.

- It sounds like (based on the answer you linked) the "expansion" of the universe is a lie in the sense that the fabric of space is not actually expanding, things are just moving farther away from each other via motion. So it's not points on a balloon being blown up (in which case the points themselves are also growing in size), but a force pushing things apart

- If that's true, then I don't understand why the paper talks about light waves expanding with the cosmological expansion, implying that the fabric of space itself is indeed expanding, and talks about how that makes the doppler effect make no sense since the light wavelength expands with the universe. It sounds like there's a fundamental incompatibility with your explanation ("this doesn't expand small objects") and the paper ("the wave itself expands with the expanding space in which it travels, so that its wavelength grows with the cosmic scale factor"), which implies the fabric of space, eg all particles, is expanding

- It sounds like light "sticks" to space as space expands, but new light emitted after an expansion will still have some constant wavelength. So in this way in an expanding universe, light which has a constant wavelength will have further to go between particles, so light will appear to slow down as the universe expands

- If light does stick to space, and the fabric of space is expanding, then I never realized that the doppler effect makes no sense for measuring cosmological expansion, because we wouldn't be able to see it (hinted at in the paper)

- Maybe I don't fully understand why LIGO needs two arms. If you had a clock that could accurately measure light wave crests, could you do it only with one arm? i'll take a leap of faith in believing that a gravitaional wave compresses in one dimension and expands another (maybe not if the wave hits it exactly at 45 degrees?). Maybe the two arms are just for convenience to get phase difference for free?

- I think what I'm missing still is what is actually being measured and how it happens. Space expands, the wave gets longer in one direction, so it has further to go (only for a fraction of time), and it will take longer for the next crest to get to the detector, (I guess the crest itself is still moving at C? but through a farther distance?) so for a tiny blip of time, there will be a phase difference, not for all the light in the arm but just for the one or few crests that make it back along the further length until the wave resets the overall distance?

- Does space compressing and expanding prove that its compressing and expanding through a higher dimension? Especially if new light emitted is at some constant wavelength independent of the stretching of the spacetime it enters? Does that also imply this constant wavelength is happening independent of our (3d) space stretch, so it's a constant through some higher dimension?

Hi, sorry, but I don't have time to answer all the questions (because each answer would have to be at least 10x longer than the question, so my answer would have to add up to at least 5000 words)! However, these are all good questions and I would urge you to check out a resource like Physics StackExchange (the physicist's equivalent of StackOverflow). Many of these have been asked before, and the new ones could get very informative answers.

> - Maybe I don't fully understand why LIGO needs two arms. If you had a clock that could accurately measure light wave crests, could you do it only with one arm?

Yes, that's absolutely right. The two arms cancel out the frequency fluctuations of the laser itself. If we had a perfectly stable laser, we could make do with just one arm.

Regarding the question about what stretches and what doesn't, I think the general rule is that rigidity prevents "stretching". For example, a hydrogen atom in expanding space would lose momentum over time, because it redshifts, but the atom itself wouldn't get any bigger. There's no need to invoke a higher dimension here, just some things are rigid (like laser cavities and the Earth) and some things aren't (like electromagnetic waves). In fact, in general invoking higher dimensions without a strong reason to is discouraged when discussing general relativity, simply because the math is already very complicated in 4D.