This is super exciting stuff! We know that the two most accurate models of the physical world, Quantum Mechanics and General Relativity, contradict each other so at least one, and probably both, are approximations to the real laws that govern our universe. Since the QM and GR disagree about what happens for small massive objects, and in particular black hole event horizons, this is a place to look for divergence to existing theories. If these echos holds up under repeated measurements, it could be one of the most consequential measurements of this century. This is another example of how taking measurements to verify a theory you think you know can lead you in completely unexpected directions.
Though, for now, the LIGO team is apparently saying that these results could be the result of noise which would occur 1 out of 270 times. That's not strong enough evidence (in my mind) to overcome the overwhelmingly likely prior that General Relativity is correct. In time, we'll see.
Also, the article mentions that LIGO has witnessed 3 black hole mergers. Last I heard LIGO had only witnessed 2.
> Also, the article mentions that LIGO has witnessed 3 black hole mergers. Last I heard LIGO had only witnessed 2.
Two have been published as bona fide BH mergers. The third is a signal in the LIGO data that doesn't formally meet the statistical significance criteria, and so is classified as a "GW candidate" rather than a detection. Unfortunately I don't have a reference for it, but this was discussed during a seminar I attended last month, given by Pedro Marronetti (NSF Program Director for LIGO, I believe).
While writing the original comment, I quickly browsed the LIGO publications list[0], but nothing jumped out at me as being about the candidate, specifically. The papers with "candidate" in the titles are pre-upgrade, so I don't think they include the candidate that was referenced in the seminar I attended.
EDIT: Found something. The third candidate event (LVT151012) is mentioned in this paper, in the 2nd paragraph of the introduction and discussed in more detail in Section C (beginning on page 11): https://arxiv.org/abs/1606.04856 ("Binary Black Hole Mergers in the first Advanced LIGO Observing Run", LIGO+VIRGO).
For reference, at least in particle physics the standard for a discovery is usually taken to be five-sigma, a 1 out of 1.7 million error probability, plus an independent verification to eliminate systematic errors that would not show up in the statistics.
From someone who hasn't worked with statistics in awhile, isn't sigma partly dependent on the number of independent events? If so, and LIGO detects occur infrequently, how long are we talking about, even assuming the data supports?
We use a technique called time sliding to generate more background data to understand our detector noise better, and thus set better upper limits on the false alarm rate. So even with a 3 month observation time we can claim 5+ sigma.
If so, would it be fair to say (as a simplification) that instead of increasing the confidence in GW events by collecting more of them, you're doing so by holding the number of collected events almost constant and increasing the confidence in the characteristics of noise the detector is reporting?
Yes, exactly that. We don't have the luxury of many events, so to increase our confidence we generate more background. One of the problems is what to do with data that contains more than one event. In the second detection paper, one of the plots contains the background with and without the other event taken into account. This is because during the time sliding process you will necessarily slide the time series from one detector across a gravitational wave signal in the other, producing false background noise.
There's no real standard way of dealing with this, so we show both cases - but both claim 5+ sigma.
First a bit of background on QM vs GR, then I'll return to your point about horizons.
It's not that they disagree, it's just that when you do perturbative quantization of General Relativity you find out you can't use the renormalization (by power-set counting) that is done on other perturbatively quantized field theories. This is only a problem in strong gravity -- where in this context, "strong" means more than one loop of gravitons on a Feynman diagram. With multi-loop Feynman diagrams involving other massless propagators we can use a number of techniques to reduce the integrals; these techniques do not work with (massless) gravitons.
One could describe this form of renormalization as a enabling a reduction of infinite modes by making a finite set of measurements at high energy to fix a parameter; this works well for light, for example. Einstein gravity, on the other hand, is perturbatively non-renormalizable, at least using the same techniques, because you need to make an ever increasing set of these types of parameter-fixing measurements at higher energies, and ultimately in strong gravity (as defined above) you need an infinite number of them.
Since there is an overwhelming amount of evidence for Einstein gravity everywhere we have been able to look so far, this poses a problem: how do you quantize gravity in a way that makes useful predictions about systems in strong gravity? There are lots of research programmes looking at this problem.
(The opposite side of the coin is that programmes to geometrize the fields of the Standard Model exist, but they run into difficulty too. Taken together, this is the underlying situation supporting the claim that QM and GR disagree about QM scale physics where local curvature distorts lengths and times at the scale of SM scatterings.)
Outside of strong gravity, however, perturbatively quantized gravity on the one hand, and semiclassical gravity on the other, are perfectly fine effective field theories (effective field theories in the Kenneth G Wilson sense; General Relativity as an effective field theory in this sense I'll call "the EFT" below).
One of the features of black holes generically is that strong curvature is found only very near the (unremovable by change of coordinates in General Relativity, gravitational) singularity. The event horizon or horizons, depending on metric the black hole sources, are found further from the singularity as the black hole's mass increases. Around an arbitrarily high mass black hole, one will find the horizon is in a region of arbitrarily flat spacetime. If the compact massive objects we observe to date are astrophysical black holes, they do not have strong gravity at the horizon.
This is one of the critical parts of the AMPS firewalls "paradox", wherein one of the set of properties of a black hole which cannot all be true is the no-drama conjecture: an infaller at a sufficiently massive black hole will experience no tidal stresses.
Afshordi, one of the authors of the paper that's the topic of the article has been doing productive phenomenology in his various collaborations, and his argument that there are classes of quantum gravity theory that can be excluded if the observations do not disappear under analysis (e.g., they're not systematic errors, and aren't "lucky" low-sigma correlations).
It's more than a bit provocative to suggest that the observations suggest that the EFT fails outside the horizon (one of the possibilities that has been discussed by Polchinski and others in the wake of AMPS (he's the "P")), which is fine, since the point will stand or fall on the basis of evidence rather than the consequences for various QG research programmes. :-)
For now it's pretty safe to work on the assumption that the EFT is fine at least everywhere outside the event horizon and the extremely hot dense early universe, and that a UV completion to GR will be completely compatible with the EFT outside strong gravity and inside a region at least a little bigger than the observable universe.
Finally, all this means that although I won't exactly endorse your wording in your third last sentence, I do certainly agree with the sentiment.
Any reading suggestions for someone who wants to understand this and has a very strong math background but no physics background beyond basic second-year QM?
It's hard to gauge (pardon the pun) where to start you based on that.
I'll guess that you're keen on understanding the General Relativity part in detail.
Carroll and ‘t Hooft have kindly put up lecture notes that might be a good starting place. Stefan Waner has made available good lecture notes on differential geometry in the GR context.
If you can wrap your head around those you could proceed to any of the standard grad texts on GR (MTW, Wald, Weinberg mainly). Weinberg is popular with people who like concise maths.
If it's all too novel, then Hartle, Schutz and Carroll all have excellent introductory texts aimed at grad students.
Once you understand how General Relativity works as a general background to any field theory -- classical or quantum -- then you'd be ready for semiclassical gravity or various quantizations of GR.
An alternative approach might be to aim you instead towards QFTs via group theory, Lie groups, Yang-Mills theory, renormalization, renormalization group flow, and so forth.
Eventually you hit on gauge/group correspondence arguments in general, which will equip you to understand the attractions of AdS/CFT in moving the tedious calculations from one setting to another setting in which they're a lot less tedious, and hopefully not fall too hard for the idea that AdS/CFT automatically helps us with gravity and matter theories in our universe.
There is certainly ample scope for talented mathematicians to test the correspondence argument (and especially whether AdS/CFT specifically or gauge/gravity generally really is a duality) rigourously.
I think that'd cover all the ideas touched on in comment you replied to.
PS: Sorry I meant to list off some QFT resources for you but I have run out of time today. :(
I think that as you have some rough exposure to relativity already, you could first absorb the idea that Minkowski (flat) spacetime is a theory where at every point the Poincaré group is the isometry group. That's a good way to hit on representation theory.
However, Lancaster and Blundell's book has some reviews suggesting that someone good at math should be able to work through it without the background needed by textbooks like Srednicki's https://www.dur.ac.uk/physics/qftgabook/ (I have not read it though).
Thanks again. Your suggestions led me to scan the QC174.45 shelves at a nearby university library. I settled on Maggiore's A Modern Introduction to Quantum Field Theory, which seems to be almost all Math.
If a Markov chain could generate something that long and coherent, it would be a much greater find than a simple explanation of gravity in General Relativity.
If it's any help, I can, and it's not. I just learned a ton from that post, in terms of clarifying the framework for things I already know a little about.
>"Quantum Mechanics and General Relativity, contradict each other so at least one, and probably both, are approximations to the real laws that govern our universe.
[...]
overwhelmingly likely prior that General Relativity is correct"
If you think both QM and GR are likely incorrect, then why do you use "a overwhelmingly likely prior" that GR is correct?
Neither is "incorrect"; the Standard Model and General Relativity are two of our best physical theories in that they both accord entirely with observational and experimental evidence to date.
Either or both may be incomplete, however. Correctness and completeness of any theory in mathematical physics are esentially orthogonal. You can have a complete theory that is just wrong, for example.
As I wrote a bit earlier in this thread, the most straightforward approach to quantizing General Relativity fails in strong gravity. Additionally, the classical field theory that is General Relativity is defined on a smooth manifold and yet so far we have been unable to escape the conclusion that some systems of mass-energy inevitably produce a non-smooth discontinuity. A completion of classical General Relativity requires the smoothing of these regions. Sharpening this, the problem with GR is the prediction of a gravitational singularity; if singularities are physical at all (even if they are in a region of spacetime that is inaccessible outside event horizons), then General Relativity is incomplete in its own terms.
The Standard Model as a paradigm of quantum field theory, on the other hand, is defined against a flat spacetime and thus relies on the result from General Relativity that the flat spacetime metric is induced on the tangent space of every point in a smooth spacetime. So if GR is incomplete, so is the Standard Model, in its own terms. (This is not just an academic point; any theory of gravity that does not reproduce the Poincaré invariance of flat spacetime in the energy scales of the Standard Model has a terrible correctness problem.) Additionally, the Standard Model is not especially well-defined at GUT energy scales. Additionally, the Standard Model does not describe the whole of the non-gravitational content of the universe; for example, it is silent on dark matter.
The Standard Model is highly correct, however, in the limits where it is effectively complete. It's a pity it has so many free parameters that have to be determined by experiment.
Likewise, General Relativity is both highly correct in the limits of present observability, and it is complete in its own terms if one admits the possibility that gravitational singularities only arise in our idealized models and that, for example, there are no exactly Schwarzschild black holes anywhere in the past, present or future of our universe. (One have to show that, and also that there are no other physically realizable systems of matter that can generate non-smoothness in our spacetime. That's not an easy ask. Although General Relativity has only one of the free paramaters complained about in the previous paragraph, it doesn't offer much guidance about how to show that you can't actually generate a low-Q Kerr-Newman metric in reality, and worse, some of that guidance must come from the high-energy behaviour of matter fields -- we can only be as complete as the Standard Model right now.)
Just a heads up: the authors of the paper this article is talking about are not part of the LIGO collaboration. They ran their own analysis on the publicly available data.
Theory is the operative word here both theories could be, and likely are to some degree, false. It's a common human bias to being to believe one's theories as fact.
What does this possibly have to do with creationism? I guess you think that because I'm calling modern scientific thought into question that I must be a creationist. Sorry but that's not the case.
I mean that your understanding of what a scientific theory is inaccurate. It's a misunderstanding that is most common among creationists so that's where you see it discussed most. Here's one overview:
You are confused about my understanding. However, scientific theory does not mean "really it's true". It means we think it's true. Or, this is our best guess so far. To believe anything else is science as religion.
Though, for now, the LIGO team is apparently saying that these results could be the result of noise which would occur 1 out of 270 times. That's not strong enough evidence (in my mind) to overcome the overwhelmingly likely prior that General Relativity is correct. In time, we'll see.
Also, the article mentions that LIGO has witnessed 3 black hole mergers. Last I heard LIGO had only witnessed 2.