Wednesday, April 25, 2018

A black hole merger... merger... merger

For my 40th birthday I got a special gift: 2.5 σ evidence for quantum gravity. It came courtesy of Niayesh Afshordi, Professor of astrophysics at Perimeter Institute, and in contrast to what you might think he didn’t get the 2.5 σ on Ebay. No, he got it from a LIGO-data analysis, results of which he presented at the 2016 conference on “Experimental Search for Quantum Gravity.”

Frankly I expected the 2.5 σ gift to quickly join the list of forgotten anomalies. But so far it has persisted, and it seems about time I unwrap this for you.

Evidence for quantum gravity is hard to come by because quantum fluctuations of space-time are so damn tiny you can’t measure them. To overcome this impasse, Afshordi and his collaborators looked at a case where the effects of quantum gravity can become large: Gravitational waves produced by black hole mergers.

Their idea is that General Relativity may not correctly describe black hole horizons. In General Relativity, the horizon bounds a region that, once entered, cannot be left again. The horizon itself has no substance and indeed you would not notice crossing it. But quantum effects may change the situation.

Afshordi and his group therefore studied that quantum effects turn the horizon into a physical obstacle that partly reflects gravitational waves. If that was so, the gravitational waves produced in a black hole merger would bounce back and forth between the horizon and the black hole’s photon sphere (a potential barrier at about 1.5 times the Schwarzschild radius). This means the waves would slowly leak out in each iteration rather than escape in one bang. If that’s what’s really going on, gravitational wave interferometers like LIGO should detect echoes of the original merger signal.

2.5 σ means that roughly one-in-a-hundred times random fluctuations conspire to look like the observed echo. It’s not a great level of significance, at least not by physics standards. But it’s still 2.5σ better than nothing.

Afshordi’s group extracted the echo signal from the LIGO data with their own analysis methods. Some members of the LIGO collaboration criticized this method and did their own analysis, concluding that the significance is somewhat lower. Afshordi’s group promptly complained the LIGO people make misleading statements and the results are actually consistent. You see they’re having fun.

Bottomline is there’s some quarrel about exactly what the level of significance is, and exactly what’s the right way to analyze the data, but the results of both groups are by and large comparable. Something is there, but at this point we cannot be sure it’s a real signal.

I will admit that as a theorist, I am not enthusiastic about black hole echoes because there are no compelling mathematical reasons to expect them. We know that quantum gravitational effects become important towards the center of the black hole. But that’s hidden deep inside the horizon and the gravitational waves we detect are not sensitive to this. That quantum gravitational effects are also relevant at the horizon is speculative and pure conjecture, and yet that’s what it takes to have black hole echoes.

But theoretical misgivings aside, we have never tested the properties of black hole horizons before, and on unexplored territory all stones should be turned. Indeed the LIGO collaboration has now included the search for echoes into their agenda.

There is even another group, this one in Toronto, which has done their own scan of the LIGO data. They found echoes at 3 σ. The Toronto group’s analysis has the benefit of being largely model-independent. But they advocate the use of periodic window-functions which induce spurious periodic signals. The authors show that in certain frequency regimes the side-effect of the windowing can be neglected and that in simulations they were able to extract the actual signal. But I suspect it will take more than this to convince anyone that imposing a periodic signal on data is a good way to look for a periodic signal.

Afshordi and his collaborators meanwhile have put out another paper, claiming that indeed the evidence is as high as 4.2 σ. That’s a pretty high significance, inching close to an actual discovery. I am, however, not convinced by their latest study. The reason is that the more they doctor on their model, the better they will get at finding specific types of echo in the noise. To correctly evaluate the significance they’d then have to take into account the number of different models which they tried. Without doing that, the significance is bound to increase simply because they’ve tested more hypotheses.

So I’d advise you to not read too much into the 4.2 σ. On the other hand, the LIGO people probably tried very hard to make the signal go away but didn’t manage to. Therefore I think at this point we can be confident there is something in the data. But to find out whether it’s more than just funny-looking random fluctuations, we will have to wait for more black hole mergers.

[I wrote about black hole echoes previously for Aeon and more recently for Quanta Magazine, and the story will probably come back a few times more.]


  1. Hello Sabine,

    On a related subject, is it relevant to talk about the inside of a black hole ? Since basically the inside lies outside the hypersurface defined by the Scharzschild metric. How about a bimetric representation of the black hole (you did an article about bimetric if I recall) where particles travel from one metric to the other as they reach the horizon (or should we call it throat sphere?). Retired researcher JP Petit did some work on this (he is a special guy but equations don't lie).

    Thank you for your post,

  2. Shouldn't the radius of the photon sphere be 1.5 times the Schwarzschild radius? (Just nitpicking...)

  3. Wow! Hope hope hope! And LIGO will be back online pretty soon! Great days ahead! Wheeeee!

  4. I only read Afshordi’s group paper, but I did not see a discussion about the possibility that this kind of echo could just be some lensing effect. I can't wait for more events and better data!

  5. I wait for the first StringT to came out of their cave and claim. This is proof of ....

  6. Live long and prosper, Bee!

  7. Alex,

    I have no idea what it means for an inside to lie outside a hypersurface defined by a metric, sorry. Also, I certainly never wrote anything about particles traveling from one metric to another.

  8. Luca,

    Yes, you are right. I meant 3M. Thanks for pointing out, I have fixed that.

  9. Wouldn’t some reflections back from the photon sphere lense around the black hole and a small part reflecting again on the other side? It seems like this would produce a ringing echo alone without considering additional reflections at the horizon.

  10. "gravitational waves produced in a black hole merger would bounce back and forth between the horizon and the black hole’s photon sphere "

    There are validated rules for spherical optical etalons. There are validated rules (atomic s-orbitals and harmonics; orthogonal polynomials) for spherical shell waveguides. Classical GR is the only validated gravitation. Consider classical prior fits before applying "accepted" theory. Evolved "beauty" absent curve fitting fails versus observation.

  11. "We know that quantum gravitational effects become important towards the center of the black hole."

    I'm curious how we could possibly *know* this?

    Happy birthday!

  12. It’s understandable that the LIGO group would be unenthused about an echo in the data. If a genuine echo were found, one possible explanation might be that it is some artifact of the measuring apparatus. This may be improbable, but it seems (to me) more probable than a gross violation of the equivalence principle at the horizon (where, for sufficiently large black holes, gravity could be arbitrarily weak).

    If the equivalence principle were grossly invalid near the horizon of a black hole, then general relativity would be grossly wrong in that regime, and in that case what theoretical basis would we have for modeling black holes and gravitational wave production in the first place?

  13. Fluctuations in the Ligo data (WOW!). No one is really sure what it means (crap, more stuff to wonder about). As if there weren't enough questions already. Answers, we want answers (<-jokingly and earnestly).

  14. The 2.5 \sigma and the 4.2 \sigma claims correspond to different signals. The former is from one of the BBH events and the latter is from the BNS event.

  15. 4 sigma echos should be blatant to the eye, with the same data cleaning as the signal. They are not. Waiting will solve this puzzle, as new data will be cleaner. Re evaluating old data fells like busy work.

  16. Matthew,

    Because we know the weak field limit and we can use it to estimate when the effects become comparably large as the quantum effects of other interactions.

  17. @Amos
    "This may be improbable, but it seems (to me) more probable than a gross violation of the equivalence principle at the horizon (where, for sufficiently large black holes, gravity could be arbitrarily weak)."

    But for us, far far away, the horizon is real. So, if I understand correctly, the fact that we, far away, see an effect of the horizon on the propagation of gravitational waves should not be a violation of the equivalence principle.

  18. I have similar ideas about detecting quantum hair on a black hole event horizon in gravitational wave signatures. The idea is similar to this, but the difficulty I have with Afshordi's approach is that this runs into some trouble with the equivalence principle. If there is some reflection of gravitational waves off the event horizon it means this r = 2GM/c^2 region is detected. The argument of course is this is a quantum correction to classical physics that has been "amplified" by curvature or gravitational effects. So this is subtle and might play into questions of where quantum and classical physics meet.

  19. It is just rather fun to see this conversation between the believers in the event horizon.

  20. LISA (Laser Interferometer Space Antenna) cannot come soon enough. The satellites will properly open up the field of gravitational astronomy. Now can I wait till 2034?

  21. Is there at least any sketch of a model that would produce such echos? Extra credit for explaining how an event horizon can have a measurable effect when the position of an event horizon at time t0 can be influenced by the amount of matter thrown into a black hole at time t1>t0!

  22. As far as I can tell by a quick glance, that paper discusses quasi-normal modes in a purely classical situation, i.e. hbar=0. I meant any quantum model that would produce the echos. And no, just saying "firewalls" doesn't do the job.

  23. Robert,

    If I knew of a convincing model I'd have mentioned it.

  24. Does the echo carry some of the energy of the original event? (I guess it does). If so, could it explain why the merger between two black holes we have observed (GW150914) was unexpectedly massive?

  25. But for us, far far away, the horizon is real. So, if I understand correctly, the fact that we, far away, see an effect of the horizon on the propagation of gravitational waves should not be a violation of the equivalence principle.

    I don’t understand what you mean. The gravitational wave that is allegedly "reflected" at r=2m is not located “far far away”, it is located at r=2m, where the local forward light cones all point to lesser r. There is nothing to cause a wave to be reflected at that location. If the wave continues to propagate locally in empty space along the forward light-like direction (and why wouldn’t it?), it must continue to go to smaller r. It’s true that, in terms of the Schwarzschild coordinate time, the crossing at r=2m occurs at infinite t, but that’s an artifact of the Schwarzschild coordinates, and it certainly doesn’t imply that the wave would ever “turn around”. Any reflection at r=2m (causing the wave to switch from decreasing r to increasing r) would be a gross violation of the equivalence principle and ordinary continuity.

    I’m not saying that coalescing black holes can’t produce some “echoing” in their emitted gravitational waves, I just don’t see how it could be attributed to waves being reflected between 2m and 3m. (Of course, for two coalescing black holes, the spherically symmetrical Schwarzschild solution is not relevant, so expressions like 2m, 3m, “light sphere”, etc., are only notional at best.)

  26. Thank you. Now that we have seen gravity waves maybe we can at last find out what it is an thereby understand it better.

  27. We will eventually have lots of data from neutron star (NS) mergers with other NS and black hole candidates (BHC) as well as BHC-BHC mergers. My bet is that the concept of an event horizon won't survive the scrutiny.

  28. Greatmag,

    Gravity waves are a phenomenon in clouds (or similar). The things under question here are called gravitational waves. And we understand them pretty well.

  29. Hi Sabine and Friends,

    Thanks again for the post and discussion. I just wanted to respond to your skepticism as to why we used a different method for detecting echoes following a binary neutron star merger, and whether that could bias our statistics. While this could be a real concern, to get a p-value of 10^-5 by fitting random noise, we had to try O(10^5) different methods! We did not!

    The fact is mergers of neutron stars at 2*1.4 Msun and black holes at 2* 30 Msun, as seen by LIGO, are entirely different beasts and their echoes cannot be probed using the same methods. It's like trying to catch a mouse with a racoon trap! This is why we had to invent a new method.

  30. @nafshordi: It is my understanding this physics is due to the replacement of an event horizon by a shell of matter or some other barrier such as in a gravastar. This with the photon ring form a potential well where gravitational waves may be trapped in an analogue of light in a material with an index of refraction. This does mean the equivalence principle is violated by quantum physics that forms this barrier. With the firewall issue this is of course an open possibility. Is violation of the EP a necessary aspect of this?

  31. Everyone:

    Yes, of course this violates the equivalence principle. I just recently wrote a long post about this.

  32. Niayesh,

    Accounting for different methods isn't as easy as just counting how many you tried because of course these are not independent trials, given that you learn from your failures (or I hope you do). And you don't need a factor 10^5 to get above p=0.01. But look, I don't mean to say it's what's going on, I am just saying it's a worry with any a posteriori analysis, so take those 4.2 \sigma with some grains of salt.

  33. Sabine,

    Can you avoid the violation of EP with radiation (echoes) if there would exist no event horizon? The simplest solution, isn't it?

  34. Sabine,

    Thanks a lot. We Iranian love salt. In fact we put it on everything, from our drinks to our oranges, which many Westerners find shocking.

  35. @Sabine "Yes, of course this violates the equivalence principle.?" Equivalence Principle (EP) violation requires test masses differentially vacuum embed, pursuing non-identical minimum action trajectories, Einstein-Cartan gravitation.

    No measurable observable violates the EP. Geometric chirality cannot be measured, only compared[1] for maximum divergence. Baryogenesis requires ~ppb chiral anisotropic vacuum toward hadrons. Beauty demands achiral isotropic vacuum, then prediction suffers chiral curve fitting. microwave spectrometer 40,000:1 S/N detects enantiomer[2] divergent vacuum embedment as ppb-displaced rotational spectra[3]. Fifty years of arrogant theory failure, one hour of spectrometry; look[4].

    [1] (DOI:10.1007/s11590-017-1189-7, DOI:10.1063/1.1484559
    [2] DOI:10.2174/138527212804004508, DOI:10.1016/S0040-4020(98)00211-7
    [3] DOI:10.1515/zna-1986-1107; exemplar with internal hyperfine coupling calibration, 30:1 S/N. Test enantiomers are 3:1 -R:S 2-cyano-D_3-trishomocubane.
    [4] DOI:10.3847/0004-637X/829/1/47

  36. @Sabine "Yes, of course this violates the equivalence principle." Test masses must differentially vacuum embed, pursuing non-identical minimum action trajectories – Casimir etalon spacing.

    Repeatedly layer 70 nm of (93% reflectivity 100 to 120 nm) aluminum with 37 nm of 60:40 MgF2:LiF (linear thermal coefficient of expansion match), refractive index 1.628 at 121 nm. This obtains 37 wt-% Casimatter. The excluded vacuum zero point fluctuation fraction is not optimistic. Thinner fabrications are not functional.

    Graphene plane spacing in single crystal graphite is 0.3354 nm. Perhaps (but not likely) single crystal graphite is active as one side of an Eötvös experiment. Active smectic meta-materials require fabrication for deep x-ray. Current fabrications in the visible are not obtainable.

  37. Eusa,

    No, because removing the event horizon requires violating the equivalence principle.

  38. If there was "something" with gravitation interactions at the event horizon, wouldn't one expect this to undergo tidal deformation, whit significant effects on the inspiral?

  39. The idea that quantum gravity becomes important only near the center is based on the assumption that the equivalence principle holds. If it is violated in QG (which is quite probable, given that up to now there is not even a single consistent candidate for QG with equivalence principle) the situation is quite different. Then the natural thing is some preferred time coordinate, and then the time dilation - the relation between the preferred time coordinate and proper time - becomes infinite near the horizon. And infinities are certainly the place where you have to expect a change. One possibility would be an upper bound for this relation. This would be a stable star with that maximal surface time dilation. Or think about harmonic time as the most beautiful candidate for a preferred time, which gives you a continuity equation \(\partial_{\mu} (g^{0\mu}\sqrt{-g})=0\). Then \(g^{00}\sqrt{-g}\) cries for an interpretation as a density, which would become infinite at the horizon too, and asks for remaining finite. Bimetric theories, where one metric serves as a background, are examples of such theories, thus, will often lead to stable frozen stars.

  40. Ilja,

    The redshift from infinity to the horizon is not a local property. There is zero reason to think that the divergence of this quantity bears any relevance for the breakdown of GR.

  41. Sabine, to think that all what is relevant to identify the breakdown of GR are infinities of things which are physical according to the leading GR interpretation is unjustified. The place where QG becomes relevant is defined by QG, that means, by what is physical according to QG.

    Of course, we don't know QG, thus, cannot tell what is physical in QG. But we know that all quantum theories up to now have a fixed background, and we also know that to make a quantum theory background-independent is a hard problem. (I have argued that it is impossible, using a quantum variant of the hole argument.) So, a background is at least a reasonable candidate for a physical QG structure not present in GR.

    Moreover, if you introduce a fixed background and throw away diff invariance with some non-covariant gauge-fixing terms, the quantization of gravity itself is not even really a problem. You can obtain a non-degenerated Lagrange formalism, a well-defined local energy and momentum, a corresponding non-degenerate Hamilton formalism, use a lattice regularization to get a regular lattice theory which gives QG as an effective field theory in the large distance limit. So, introducing a fixed background allows to solve all the problems of quantization of GR (problem of time, quantum foam and so on).

    I understand that those who value the beauty of GR as a deep insight do not like this idea. But up to now they have not delivered, there is no well-defined QG without a background, LQG is imho not more than a hope.

    So, up to now all quantum theories are theories with background, and in a theory with background the horizon is critical. I think this is a quite good indication that we have to expect a breakdown of GR near the horizon.



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