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.)
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I doubt that it amounts to anything, but the fact that an analogy does not provide evidence for [the existence of] its analogue does not entail that the analogy does not provide information about its analogue, under the assumption that the analogue actually exists. Had the ether turned out to exist, I suspect that the fluid mechanics of “ordinary” fluids would have provided some useful information about Descartes’ vortices.