Pedagoguery

I've mentioned many times before in these columns that the two pillars of modern physics, general relativity and quantum mechanics, are mutually exclusive. Evidence of this fact lies in a subtle flaw in Stephen Hawking's explanation of why black holes emit radiation. Hawking's triumph is a partial combination of the two theories. Quantum mechanics states that at small scales, virtual pairs of particles are being created and annihilating in the vacuum all the time. Hawking visualized this process taking place at the event horizon of a black hole. If one of the pairs of virtual particles fell into the black hole before it annihilated with its counterpart, that counterpart would become real, and the energy for it to do so would come from the black hole itself. The problem arises from the fact that any particle traveling from the event horizon of a black hole would have its wavelength redshifted to an infinite extent; so for it to be visible at any distance from the black hole, it would have to start with a wavelength of zero. However, zero is smaller than the Planck length, below which relativity theory is invalid. How to resolve this conflict? Some surprising insights are coming from the study of the flow of sound in a flowing fluid.

There is an acoustic equivalent to a black hole. You take a fluid flowing along in a pipe and you insert something called a Laval nozzle into the pipe. A Laval nozzle is found at the end of rockets. It contains a constriction that forces the fluid to go supersonic as it flows past. That transition where the fluid goes supersonic is analogous to the event horizon of a black hole. In the subsonic portion, sound waves can travel in all directions, but once a sound wave passes through the nozzle into the supersonic region, it cannot travel fast enough to reenter the subsonic region, since the medium through which its passing is going faster than it is. There is even a region just short of the sonic event horizon where quantum effects produce low volume sound analogous to Hawking radiation. A microphone placed just upstream from the nozzle will pick up a faint hiss, energy that is being drawn from the fluid flow.

The interesting thing about this “Hawking sound” is that the wavelengths produced at the sonic event horizon are very small, comparable to the separation distance between the molecules within the fluid. This tells us that the granularity of the fluid plays an important role.

When sound waves are very short (on the order of the molecular distance), they behave differently than when they are much longer. In particular, their speed of propagation depends on the wavelength. Depending on the specifics of the fluid, the velocity can either decrease with shorter wavelengths, or increase. The first type is referred to as Type II dispersion, and the second as Type III. Type I is the case in a perfect fluid where the speed never changes. In a Type II fluid, if you take the sonic equivalent of a photon, called a phonon, and follow it backwards in time as it travels back to the sonic event horizon. Initially, it simply travels back, its wavelength getting shorter and shorter until dispersion effects start to matter. Then a strange thing happens; it starts to slow down, and eventually reverse direction. In a Type III fluid, they would accelerate, go faster than the local speed of sound, and pass through the event horizon.

What does this tell us about spacetime? We can consider it to be a fluid with particles on the order of the Planck length. When the wavelength of a photon gets down to that length, dispersion type effects would govern its behavior. This gives us a possible fix for the flaw in Hawking's model. If spacetime exhibits Type II dispersion, then Hawking radiation originates from just outside the event horizon, and one of the photons, curves back and around to escape. If spacetime exhibits Type III dispersion, then Hawking radiation originates from inside the event horizon, and one of the photons momentarily exceeds the velocity of light to escape. Either way, it points to a granular structure for spacetime that meshes nicely with many quantum gravity theories.

Next issue: The origins of brown dwarf stars.