Hyper-intelligent fish and black hole thermodynamics

Bill Unruh's recent collection on black hole analogues begins,

Deep beneath the great encircling seas of the Discworld lived a species of hyper-intelligent fish. (Unruh 2007, p.1)

Unusual, but inspiring: Unruh compares Hawking radiation -- the thermal heat bath emitted by black holes -- to a scenario he imagines in Terry Pratchett's Discworld. Pratchett's world is basically a big dish, with water flowing over the edges.

On Unruh's take, the dish-water is filled with little physicist fish, who are trying to determine the laws of physics. The fish are blind, but use sound waves to interpret their environment. And they are mostly successful. However, as water falls off the edge of the world, it reaches speeds faster than the speed of sound. Events beyond this "sound horizon" are thus inaccessible to the fish in the ocean.

One day, a graduate-student-fish goes flying off the edge while the professor-fish observes. (Professor Unruh apparently expects a lot of his students.) The graduate student yells "Help," while falling off. Then he plunges to his doom. But, from the professor's perspective, the sound of the graduate student's scream persists forever, getting ever more bass-shifted, as the student approaches the horizon.

The point is, the unlucky graduate-student-fish is directly analogous to an astronaut falling into a black hole. From the astronaut's perspective, nothing special happens as she crosses the event horizon. But from an outside observer's perspective, the astronaut appears to be forever approaching (but never crossing) the event horizon, and the light she emits getts ever more red-shifted.

Of course, the astronaut will get ripped to shreds by tidal forces, while the fish will not.

And so the "black hole analogue" debate begins. Black holes are widely believed to have a number of thermal properties -- for example, black holes have a temperature proportional to their surface gravity. Analogously, soundless "dumb-holes" (as Unruh calls them) in water can be shown to have interesting thermal properties as well. And -- tantalizingly -- it appears possible to carry out experiments that would actually test the properties of "dumb-holes," even though black holes remain outside our reach.

But does evidence for a sound-based analogue somehow provide us evidence about a real black hole?

I see no plausible way that it can. Although a black hole is mathematically similar to a "dumb hole," it is not the same thing. And history has something to teach us here: gas and fluid vortices are "mathematically similar" to Descartes' aether vortices. But experiments with the former do not provide evidence for the latter. After all, aether vortices don't exist! So, in spite of some interesting recent experiments (see here), we still don't have any new evidence that black holes have thermal properties.

Nevertheless, there might be one thing that sound-based experiments can still teach us about black holes, according to Unruh:

such successful experiments would greatly increase the confidence in the approximation which were being made in both the gravitational and the analogue situations. ... Certainly the suggestions from the sonic case are that Planckian physics is irrelevant to black hole evaporation, and that the radiation emitted by a black hole is due to low energy processes, processes on the length scale set by the black hole, and not by quantum gravity. (Unruh 2007, p.3.)

This to me seems very plausible: an analogy can tell us whether or not scale is relevant to the effect. According to Unruh, sound-based experiments are really teaching us that black hole thermodynamics is about essentially macroscopic effects. So, our prediction of thermal effects like Hawking radiation won't change when a new theory of quantum gravity comes along, and modifies our picture of the (microscopic, high-energy) Planck scale.

It's a bold and intriguing suggestion, but I'll wait for the iron hand of history to decide.
(If you have a Springer subscription, you can see a version of Unruh's article here.)

LHC Black Holes: Why I'm Not Holding My Breath

The attention that these two nut-jobs are receiving is a bit discouraging.

Some people do hope to see mini-black-holes at CERN, it's true. Some calculate that we will see thousands. But: (1) if you have any empiricist scruples, then you won't believe in these mini-black-holes at CERN; alternatively, (2) if you have no such empiricist scruples, then you'll agree that all mini-black-holes at CERN are short-lived and harmless. Here's why:

Let's begin with (2), and suppose that you're not too hardcore about your empiricism. Consider a Schwarzschild blackhole (spherically symmetric and non-rotating, simplified idealization of what is expected at CERN) with mass M. Then dM/dt = -K/M^2, where K is a (very large) constant (See Hobson et al, pp. 277). Let M get very, very small, since we are dealing with particle collisions and not collapsing super-structures. Then dM/dt will become an enormous negative number. In other words, any emergent mini-black-hole will quickly decay into a boring everyday particle. These black holes are harmless and short-lived!

This effect is called Hawking radiation. But should we really believe it will happen? It hasn't ever been observed. However, the result is far from speculative. It is derived from well-verified results of basic quantum theory and of general relativity. From GR, we need only the causal structure of black holes (which is now well accepted, and if we're wrong about it, then there are no black holes anyway). And from QT we need little more than quantum fluctuations (consisting of particle/anti-particle pairs), which we have good empirical reason to believe in. So this isn't one of those weird fringe cases where "quantum theory and gravity don't mix." As things currently stand, there are great betting odds in favor of Hawking radiation.


Image Credit: Universe Review (2008)

But now let's suppose that you're a hardcore empiricist and you still don't buy it. If that's the case, then you don't have to worry about mini-black-holes at CERN in the first place, as there is absolutely no empirical reason to believe they will appear.

Black holes appear when a sufficiently large mass-energy to be crammed into a sufficiently small radius, which in our example is called the Schwarzschild radius (R_s) of that mass. This is not expected to happen at CERN according to any well-confirmed quantum theory, for reasons that have to do with uncertainty, and our consequent inability to squish that much mass-energy into lengths of the order of a very small R_s.

However, some string theorists think that our four dimensions are just one surface of a many-dimensional world that we apparently can't access. One consequence they derive is a much larger value for R_s for a given mass in these situations (from what I understand, they think it gets stretched out into these extra dimensions). This is the reason people have recently decided to hype up the hope that mini-black-holes might appear at CERN -- string theory says there is a larger R_s, so it's easier to cram sufficient mass into the region. (This idea was sketched in a CERN press release a few years back.) But of course, there is zero empirical evidence for this (and all) string theory. So your empiricist scruples set you free here -- mini-black-holes at CERN are little more than a fancy speculation. Maybe there's monsters in the closet too, but I'm not holding my breath.

Whew. Do you feel liberated? I feel liberated.

For more information, download the expert safety reports at the CERN website.