Sonic Black Holes

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Here’s something interesting that came up on Slashdot today: scientists at the Israel Institute of Technology report having created an “acoustic black hole”, a region from which no sound waves can escape, just as a normal black hole is a region from which no light waves can escape.

How did they do it? Well, whenever sound travels through a medium, it does so at a characteristic speed — about \(\unit{343}{\frac{\meter}{\second}}\) in air, for example. That speed is relative to the medium, though, so if you can get the medium to move through your lab at a faster speed, the sound waves won’t be able to propagate fast enough to move against it (relative to the lab). If you had a wind tunnel blowing air to the right at \(\unit{400}{\frac{\meter}{\second}}\), the air would carry along all sound waves traveling through it, even those emitted in the leftward direction. Any sound waves produced at the right end of the tunnel would be stuck there — in effect, it’s a one-dimensional acoustic black hole, with an event horizon at the point (surface, really) where the air accelerates past the speed of sound as it’s drawn into the tunnel.

Building a supersonic wind tunnel is no easy task, though — and even if you did it, you’d run into problems with turbulence messing up the propagation of sound waves through the air. The acoustic black hole actually reported was created in a Bose–Einstein condensate, a special low-temperature state, of rubidium. This has two advantages: first, you don’t have to deal with turbulence, and also, the speed of sound is much slower, typically less than \(\unit{1}{\frac{\milli\meter}{\second}}\) according to the paper. Although creating and stabilizing a Bose-Einstein condensate in the first place is no easy matter, it’s a lot easier to control than a wind tunnel.

The reason everyone is so excited about this is that it paves the way for experimental detection of Hawking radiation. In real black holes, Hawking radiation occurs when a particle and an antiparticle spring into existence near the event horizon of a black hole; one of them falls in, and the other is “radiated” away. But in an acoustic black hole, instead of particles and antiparticles, you can get sound waves (“phonons”) radiating in opposite directions, one heading into the acoustic black hole and one heading away. Here’s how that works: the energy of a phonon, relative to the medium (the air or BEC), is given by

$$E = pc$$

where \(p\) is the momentum carried by the wave and \(c\) is the speed of sound (it’s not a coincidence that this looks just like the formula for the energy of a photon). But when that whole medium is moving with a speed \(v\) relative to your lab, you see sound moving at the speed \(c - v\), so you would calculate the energy as

$$E = p(c - v)$$

So if two phonons are created with the same momentum, but on opposite sides of the event horizon, the one inside the horizon has \(v > c\), giving it negative energy, and the other has \(v < c\), giving it positive energy. And for waves created in the right positions, the energies add up to zero, meaning that these waves can be created at virtually no cost to the universe.

Why is Hawking radiation so special? Nearly all physicists are very confident that it exists, but the fact remains that nobody has ever directly observed Hawking radiation, simply because nobody has been able to get up close to an event horizon to study it. So seeing the stuff for the first time will be an exciting moment in the history of physics. Plus, when you can create small, easily controllable systems that mimic black holes, you could potentially discover all sorts of other cool things that could be happening out in space.

Probably of more interest to the public is the way Hawking radiation is relevant to the whole LHC “doomsday” myth. There’s been a lot of hype about the idea that the LHC could produce a black hole which could destroy the world, and Hawking radiation is the favorite explanation for why that can’t happen. Simply put, any black hole that might be produced on Earth would evaporate due to Hawking radiation long before anything could fall into it. (Of course, there’s also the fact that the LHC just reproduces processes that occur in the upper atmosphere. So even if Hawking radiation isn’t going to save us from black holes, something else will.)