Jillian's Guide to Black Holes: Forming - Types - Outside - Inside - Finding - References - Websites
The very small quantum mechanics bit
Pretty odd, isn't it? First I tell you that nothing can leave a static black hole once it has passed the event horizon, but now I say that sometimes it can! I think most of quantum mechanics seems contradictory. While classical physics said protons and electrons and all of those funky little particles could be visualized like little marbles rolling around 3D tracks. Quantum mechanics says it will have none of this! Those particles are more like groups of waves than little balls of matter. This fit in with an experimentally-proven idea called the Heisenberg uncertainty principle, that it was impossible to predict with absolute certainty a particle's location, just give probabilities of where it could be. The wave-packet view incorporates this uncertainty, while the marbles-in-tracks does not. Chalk one up for quantum mechanics.
Then again, two classic experiments can be performed simultaneously to demonstrate the wave nature and particle nature of the photon. The first is called the double slit experiment, for obvious reasons. Set up a wall with two small slits (small meaning relevant to the size of the photon packet, not slits that are two centimeters wide) rather close to one another. Set a photon source on one side of the wall and a photon detector on the other side. One would expect that, in order to pass through the wall, a photon would go through one or the other slit and hit the detector, if photons acted like particles. One would then see two bands of particles on the detector, each from a slit. What actually happens is that the photons act like waves and interfere with each other going through the slits. Or perhaps the photons could not decide which slit to go through and went through both. At the same time. What the detector will show is an interference pattern from the two slits. Pretty cool.
The second experiment is the photo-electric effect. It is a known effect that light of a special frequency shone on a piece of metal will induce a current. A certain amount of energy must be given to the metal for it to conduct. One would expect, with light behaving like a wave, that one would need to expose a certain area of metal to light for a certain length of time, and the light rays would impart enough energy to the metal. If one had light that was lower energy, one would simply have to expose the metal for a longer time. Makes sense, neh? What actually happens is that, if one has light that isn't high enough in energy to induce a current in the metal, the metal will not show a current no matter how long you shine the light on it. You could shine it for a whole day and not see a single electronic peep. Einstein came up with a nifty solution for that: he said, what if light arrived in little packets of a certain energy level? Each time a metal atom got hit with a little packet (of the right energy), it would have enough energy to kick out an electron and do the current thing. If the little packet did not have sufficient energy, no matter how many one threw at the metal atom, it would not have enough energy to kick out an electron. I suppose it might be like the fission reaction of uranium. If a lump of uranium does not have the critical mass, it just doesn't have the critical mass. You could look at 50 lumps of uranium that were under critical mass, and each one would still sit there like a lump.
There you go. That's a particle acting like a wave and like a particle in two different experiments. Wacky.
Turns out that the wave-like probability is also important in electrical circuit devices like diodes. A diode creates a wall, a potential barrier, so no electricity can flow in certain instances. However, quantum mechanics predicts that there is some probability that particle-waves can get through. Guess what---electrons do get through this barrier, even though classical mechanics says they can't! What does this have to do with static black holes?? The gravity field of the black hole can be thought of as a potential barrier preventing stuff from leaving. For large black holes that barrier is so thick that the probability of something getting through is pretty much zero. But, but ,but --- for small black holes that barrier is very thin! In 1975 Hawking proved that particles can be created within the event horizon and escape to the outside world!