Comment by bzbarsky | Hacker News Reader

Comment by bzbarsky | Hacker News Reader

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This thing was a billion light years away. Say it were closer; let's put it at a single light year away.

LIGO measures wave amplitude, as far as I can tell, which goes down linearly with distance (unlike wave energy, which goes down quadratically, since it's proportional to square of the amplitude). So we could expect to see an effect about a billion times bigger.

The detected effect was a change in metric of one part in 6e20 if I'm not mistaken: (4e-3 * (diameter of proton))/4km based on the article's claim of "four one-thousandths of the diameter of a proton". So at one light year distance we could expect an effect of one part in 6e11.

Not really visible on the human scale, seems to me. You could detect it easily with something like the Mössbauer effect, I expect. Your typical lab bench laser interferometer has errors on the order of 1 in 1e6 as far as I can tell, so probably wouldn't be able to pick this up.

Disclaimer: I could be totally off on what a lab bench laser interferometer can do. I'm pretty confident in the rest of the numbers above.

On the other hand, we may well detect the 3 solar masses radiated away as energy. That decreases as an inverse square law, so as one solar mass is about 10^30kg, and 1kg gives off about 10^17 J, we're talking about an explosion releasing something around 10^47 J. For comparison, a 1 kiloton nuclear bomb gives off about 10^15 J.

So, inverse square that explosion... 1 light year is about 10^16m, so we square that and get 10^32m, so we're now talking about ... 10^15 J.

So, unless my maths is all off (which is possible), if this happened about a light year away, whoever's on the side facing towards the blast wouldn't get to observe very much because they'd feel as if a 1kt nuke just went off above their head. Not a great way to start the day.

Chances are it would wipe out life on Earth too, through the ensuing side-effects like lighting the atmosphere on fire, sterilising half the planet, significantly heating up the oceans, possibly even stripping part of the atmosphere away, etc.

For a great novel based around a strikingly similar premise to what was just observed (and the main reason I even bothered to calculate this), Diaspora by Greg Egan is a fantastic book.

The big question is how much of the energy would get transferred in practice.

I agree that 3 solar masses worth of electromagnetic radiation at 1 light year distance would feel like a nuke going off. What I don't know is to what extent the energy of the equivalent gravitational waves (which _would_ have a lot of energy I agree) would actually get transferred to things we care about, like the atmosphere and us. If it's a few percent, say, we'd clearly be in trouble. If it's more like what neutrinos do, it would probably be detectable but probably not by unaided human senses.

I tried doing some quick looking around for estimates of gravitational wave coupling and energy transfer and didn't find anything so far...

I would like to understand why a gravitational wave distorts length in relation to normal gravity wells; specifically is this particular to waves? Why don't lengths get distorted in a normal gravity well, or do they? In essence, what is different between a gravity wave and a gravity well, which i understand both distort space, but only the wave distorts it in a way we can measure? Does the gravity well change lengths proportionally in all directions and thus isnt measurable?

A gravity well also distorts lengths, as best I understand (which is not very well, to be honest; take everything I'm saying here with a big grain of salt).

The difference in terms of detection is that the wave does this in a time-varying, periodic fashion.

For something like LIGO, we're trying to measure length changes on the order of 1e-18 meters. We're not actually measuring the lengths of LIGO's arms to that accuracy, though. What we're measuring is the difference between the times light takes to travel down those arms. And even that's hard to measure on an absolute scale, so what we really measure is how that difference changes in time.

Or put another way, the effect of Earth's gravitational well is not really distinguishable from inaccuracies in making the two legs of the interferometer equal length to start with, and is a much smaller effect than those inaccuracies. Again, if I understand this right...

Actually, we have ample proof of the distortion of spacetime in a gravity well - gravitational lensing. It's an observed effect around very massive objects and we have been able to see it at work very well. Also, arguably, the fact that we're not falling towards the sky is itself evidence of a spacetime gradient near the Earth, but that was also explained by Newton's Law of Gravitation.

But back in 1916, Einstein also theorised, as part of his general theory of gravitation, that there would be such things as gravity waves, caused by very massive objects moving through spacetime making 4-dimensional ripples appear in spacetime. Until today, that was just an unproven theory, though everyone believed it was likely to be true. There is now solid evidence to back it.

Agree... my question, though poorly worded, is less about proof of spacetime gradients (they do in the ways you describe).

It's more about understanding what the measurable effects of a gravitational well on earth has on the LIGO experimental setup (or a similar one with infinite precision), in the absence of gravitational waves.

Well, something like LIGO can only measure gravitational waves, because it looks for changes in the geometry of spacetime. If you were to move the LIGO in and out of Earth's gravitational well, I guess then it would record a shift.

If the gradient is small (as it should be 1 ly away) then the coupling ought to be very weak.

That is a good point - perhaps it would all come out as neutrinos or gravitons... then we'd be fine. I doubt such an event would result in no electromagnetic radiation at all however... Why would it? The creation of a new black hole typically releases enormous amounts of all kinds of energy, electromagnetic as well as in the form of neutrinos.

I really don't have any good answers here; this just isn't something I know very much about....

The energy was all dumped into the gravitational waves we detected, not into electromagnetic radiation: Gravity waves don’t interact with matter very much (the cross section of the graviton is believed to be extremely small) so the quantity of energy transferred to matter as the wave passes through is likewise extremely small. I haven’t run the numbers, but I’m not sure you’d notice this even from a light year away without fairly sensitive detectors.

What I didn't understand after reading the article is how do they separate out a set of waves for one specific thing vs. the many other objects sending out waves. Is it just that the set of blackholes are the strongest set of waves and thus the ones we can detect?

That, and the high frequency. For example, the Earth orbiting the Sun produces gravitational waves at a frequency that's about (factors of 2 and pi here and there) the orbital frequency; order of 1e-8 Hz. The black holes were producing 250Hz waves if I read the article right.

The longer the interferometer arms, the better you can do in sensitivity. The reason LIGO has 4000 m long arms is that it makes the experiment 4000x more sensitive than something you can do on a bench. (and their laser stabilization is excellent, improving things further)

Sure, but LIGO is sensitive at something like 1 part in 1e20, which is a lot more than 4000x better than 1 part in 1e6. I agree that their laser stabilization is likely much better, their vacuum is likely a lot better, etc. I was just surprised by how much better, I guess; 10 orders of magnitude is a lot.

Part of the reason for that is that LIGO isn't exactly a Michaelson interferometer in that it has an extra pair of mirrors in each arm. If you look at this schematic [1] then in a traditional Michaelson interferometer you would only have the mirrors that are at the end of both arms.

With LIGO there is an extra set of mirrors within the arms this allows the light from the laser to bounce between them ~100 times or so increasing the effective path length greatly.

[1] https://www.nsf.gov/news/speeches/colwell/rc03_ligo/img009.j...

Ah, neat. Did not know that!

I see, thanks.

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