Tuesday, October 23, 2018

Loud black holes

Stephen Hawking's most famous contribution to physics was the proposal that black holes might actually glow, like any hot object even if it is perfectly black, when Einstein's General Theory of Relativity is combined with quantum mechanics. It's not just that black holes could be hot and glow, but that they are inherently hot (or at least a little bit warmer than absolute zero), with a temperature inversely proportional to their mass. It remains unclear whether Hawking's theory is actually true, but even just as a hypothesis it has inspired a generation of theoreticians, because it suggests some kind of profound connection between relativity, quantum mechanics, and thermodynamics. 

We haven't yet been able to test Hawking's hypothesis astronomically, because even though we've found things far out in space that we're sure are black holes, the thermal glow they would have if Hawking were right would still be too faint to see. If we could get a little black hole in a lab here on Earth, we might make revolutionary observations ... but we probably shouldn't try this.
 
Let's not do this.


An idea from William G. Unruh might let us study black holes here on Earth in a safe way, however, by simulating them with fluid dynamics. What Unruh pointed out is that sound waves in a flowing fluid behave mathematically just like light waves in the curved spacetime of General Relativity. The sonic analog of a black hole—a sonic ergoregion—is a region in which the fluid itself is flowing faster than its own speed of sound. Sound waves can pass into this region, but cannot get back out again, because the supersonic fluid drags them along faster than they can run.

Unruh's fluid analog idea has been pursued by quite a few people over the years. Back in 2001 Luis Garay, Ignacio Cirac, Peter Zoller and I initiated the theoretical study of how to make sonic black holes in Bose-Einstein condensates. BECs would be great candidates, we thought, because they are very controllable (so we might get a supersonic flow going), they are superfluid (so no friction to slow down the flow), and they are quantum mechanical (so Hawking's effects might show up). Other people have greatly extended this work, and just a few years ago Jeff Steinhauer actually did some experiments on supersonic condensates and found quantum-correlated sound waves coming out of the sonic black hole, very much like the quantum radiance of Hawking's theory.

"Beyond the mountains, more mountains" is a Haitian saying. Now that we've seen Hawking effects in a lab here on Earth, we have new questions. One concerns a simple geometrical issue. Our 2001 work assumed a one-dimensional model for simplicity, and everyone after us seems to have maintained this convention, even up to Steinhauer's experiments, which use long, thin clouds of ultracold gas. A subtlety that we and everyone else seem to have ignored, however, is that Unruh's analogy between fluid flow and curved spacetime really needs at least two spatial dimensions. In 1D it only kind of works, roughly.

There are other good reasons to look at black holes in more dimensions as well. Bekenstein's tantalizing concept of purely geometrical entropy in black holes needs at least two dimensions. So in the past year we finally bit the computational bullet and did some theoretical simulations of two-dimensional sonic black holes. What we found is an instability that doesn't show up in one dimension: the formation of vortices. Our sonic ergoregion became a turbulent sea of quantized whirlpools. It generated plenty of sound waves, but not the kind of sound predicted by Hawking.

Vortices and sound waves from a sonic black hole. The power spectrum is not thermal.
So is this bad news for analog black holes? That depends on how you look at it, because the analogy between fluid flow and curved spacetime only ever works as far as mild sonic ripples. Once the fluid starts doing violent things like forming vortices, the analogy breaks down. There's no reason to expect nonlinear quantum fluid dynamics to reproduce nonlinear quantum gravity.

So one interpretation of our results would be to say that the appearance of vortices marks the end of the experiment, and only everything up to that point counts as a black hole simulation. As long as we only have low-amplitude sound waves moving through a smooth, steady flow, Unruh's analogy still works, and Hawking's theory should still be confirmed.

The problem with this, though, is that the low-amplitude regime in which everything works is not the regime that holds mysteries. We don't need cutting-edge experiments to solve linear equations, and anyway there was never any doubt about Hawking's linear calculations as far as they went. The big question is whether black hole thermodynamics survives in fully nonlinear quantum gravity. 

Unruh's analogy was never supposed to go beyond the linear regime, though. So why have we even been bothering with analog black holes at all, if they are inherently incapable of answering our only real questions? 

Well, when it comes to quantum gravity, we are desperate. We've stopped hoping for reliable answers. We'd be glad if we could just get some hints. And although nonlinear quantum fluid dynamics certainly won't reproduce nonlinear quantum gravity, it does at least give us a real, physical system which has nonlinear quantum dynamics and can also look like curved spacetime in some situations. 

We don't actually know anything more than that about real quantum gravity. Recent calculations based on string theory have suggested that real black holes out in space may be quantum "fuzzballs" that are quite different, inside their ergoregions, from the classical black holes of General Relativity. Our turbulent ergoregions do happen to look something like this.

And that may well be a meaningless fluke. It still means that experiments on sonic black holes in Bose-Einstein condensates will be able to put some data points on the big empty graph of nonlinear quantum systems with even limited resemblance to General Relativity. We know so little about quantum gravity, and it would be so wonderful to learn about black hole thermodynamics. It's well worth listening to what the sonic black holes have to say.

Interested readers can find our paper in the open-access online journal New Journal of Physics. (NJP is a joint venture of the Institute of Physics and the Deutsche Physikalische Gesellschaft. It's a mainstream peer-reviewed journal that is one of the standard examples to show that not all open-access online journals are scams.)