Dumb Holes Leak

Tl;dr: A new experiment demonstrates that Hawking radiation in a fluid is entangled, but only in the high frequency end. This result might be useful to solve the black hole information loss problem.

In August I went to Stephen Hawking’s public lecture in the fully packed Stockholm Opera. Hawking was wheeled onto the stage, placed in the spotlight, and delivered an entertaining presentation about black holes. The silence of the audience was interrupted only by laughter to Hawking’s well-placed jokes. It was a flawless performance with standing ovations.

In his lecture, Hawking expressed hope that he will win the Nobelprize for the discovery that black holes emit radiation. Now called “Hawking radiation,” this effect should have been detected at the LHC had black holes been produced there. But time has come, I think, for Hawking to update his slides. The ship to the promised land of micro black holes has long left the harbor, and it sunk – the LHC hasn’t seen black holes, has not, in fact, seen anything besides the Higgs.

But you don’t need black holes to see Hawking radiation. The radiation is a consequence of applying quantum field theory in a space- and time-dependent background, and you can use some other background to see the same effect. This can be done, for example, by measuring the propagation of quantum excitations in Bose-Einstein condensates. These condensates are clouds of about a billion or so ultra-cold atoms that form a fluid with basically zero viscosity. It’s as clean a system as it gets to see this effect. Handling and measuring the condensate is a big experimental challenge, but what wouldn’t you do to create a black hole in the lab?

The analogy between the propagation of excitations on background fluids and in a curved space-time background was first pointed out by Bill Unruh in the 1980s. Since then, many concrete examples have been found for condensed-matter systems that can be used as stand-ins for gravitational fields; they are summarily known as “analogue gravity system” – this is “analogue” as in “analogy,” not as opposed to “digital.”

In these analogue gravity systems, the quantum excitations are sound waves, and the corresponding quantum particles are called “phonons.” A horizon in such a space-time is created at the boundary of a region in which the velocity of the background fluid exceeds the speed of sound, thereby preventing the sound waves from escaping. Since these fluids trap sound rather than light, such gravitational analogues are also called “dumb,” rather than “black” holes.

Hawking radiation was detected in fluids a few years ago. But these measurements only confirmed the thermal spectrum of the radiation and not its most relevant property: the entanglement across the horizon. The entanglement of the Hawking radiation connects pairs of particles, one inside and one outside the horizon. It is a pure quantum effect: The state of either particle separately is unknown and unknowable. One only knows that their states are related, so that measuring one of the particles determines the measurement outcome of the other particle – this is Einstein’s “spooky action at a distance.”

The entanglement of Hawking radiation across the horizon is origin of the black hole information loss problem. In a real black hole, the inside partner of the entangled pair eventually falls into the singularity, where it gets irretrievably lost, leaving the state of its partner undetermined. In this process, information is destroyed, but this is incompatible with quantum mechanics. Thus, by combining gravity with quantum mechanics, one arrives at a result that cannot happen in quantum mechanics. It’s a classical proof by contradiction, and signals a paradox. This headache is believed to be remedied by the, still missing, theory of quantum gravity, but exactly what the remedy is nobody knows.

In a new experiment, Jeff Steinhauer from the Israel Institute of Technology measured the entanglement of the Hawking radiation in an analogue black hole; his results are available on the arxiv.

For this new experiment, the Bose Einstein condensate was trapped and put in motion with laser light, making it an effectively one-dimensional system in flow. In this trap, the condensate had low density on one half and a higher density in the other half, achieved by a potential step from a second laser. The speed of sound in such a condensate depends on the density, so that a higher density corresponds to a higher speed of sound. The high density region thus allowed the phonons to escape and corresponds to the outside of the horizon, whereas the low density region corresponds to the inside of the horizon.

The figure below shows the density profile of the condensate:

Figure 1 from 1510.00621. The density profile of the condensate. 

In this system then, Steinhauer measured correlations of fluctuations. These flowing condensates don’t last very long, so to get useful data, the same setting must be reproduced several thousand times. The analysis clearly shows a correlation between the excitations inside and outside the horizon, as can be seen in the figure below. The entanglement appears in the grey lines on the diagonal from top left to bottom right. I have marked the relevant feature with red arrows (ignore the green ones, they indicate matches between the measured angles and the theoretical prediction).

When Steinhauer analyzed the dependence on the frequency, he found a correlation only in the high frequency end, not in the low frequency end. This is as intriguing as confusing. In a real black hole all frequencies should be entangled. But if the Hawking radiation was not entirely entangled across the horizon, that might allow information to escape. One has to be careful, however, to not read too much into this finding.

To begin with, let us be clear, this is not a gravitational system. It’s a system that shares some properties with the gravitational case. But when it comes to the quantum behavior of the background, that may or may not be a useful comparison. Even if it was, the condensate studied here is not rotationally symmetric, as a real black hole would be. Since the rotational symmetry is essential for the red-shift in the gravitational potential, I actually don’t know how to interpret the low frequencies. Possibly they correspond to a regime that real black holes just don’t have. And then the correlation might just have gotten lost in experimental uncertainties – limitations by finite system size, number of particles, noise, etc – on which the paper doesn’t have much detail.

The difference between the analogue gravity system, which is the condensate, and the real gravity system is that we do have a theory for the quantum properties of the condensate. If gravity was quantized in a similar way, then studies like the one done by Steinhauer, might indicate where Hawking’s calculation fails – for it must fail if the information paradox is to be solved. So I find this a very interesting development.

Will Hawking and Steinhauer get a Nobelprize for the discovery and detection of the thermality and entanglement of the radiation? I think this is very unlikely, for right now it isn’t clear whether this is even relevant for anything. Should this finding turn out to be key to developing a theory of quantum gravity however, that would be groundbreaking. And who knows, maybe Hawking will again be invited to Stockholm.