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.

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[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.]