Hawking's Speech
Here is the problem, as Hawking saw it in the past: Things fall into a black hole, and once they pass the event horizon, they are out of communication with the outside world, and the information in them in unavailable, although it hasn't been lost to the whole world, since it still exists inside the horizon. But now, the black hole emits Hawking radiation and loses mass. Hawking had proved that the radiation was "thermal", or "uncorrelated", meaning that it contains no information beyond its temperature.
Eventually the black hole loses all its mass to this non informational radiation and vanishes, and at that point all the information that went into it is completely lost. This might not seem important to many, but it really bothers quantum physicists, for whom unitarity is a prime directive. Unitarity is the principle that information is conserved in all physical interactions; if it fails some of their key math won't work.
This is where things stood for maybe 20 years. But now Hawking comes out with a new idea and says maybe the information is eventually preserved after all. His idea, based on some recent work in string physics, is that we should analyze the black hole from far away, and use the techniques of adding up all possible physical contributions from varying geometries of spacetime to see what happens in the far future. The technique was first thought up by the famous physicist Richard Feynmann, and is called path integrals or sum over histories.
In this sum there will be contributions from simple geometries where the black hole never formed, plus contributions from spacetimes that do have the black hole. And you have to add them up. But now Hawking says he can prove that the part of the sum with a fully formed black hole just dies out, and never reaches the far furure. So the sum in the end only includes the contributions from no-black-hole universe states. And thus the information will reach the far future, possible modified, but not lost.
Hawking has not published his proof yet, and everyone is waiting to see it.
Some things I have seen that I think misrepresent him:
1. The black hole never forms. He didn't say that; he said it has no physical effect on the physics passing from far away to far in the future.
2. The information comes out of the black hole again. He didn't say that either. He said it arrived at the future in possibly modified or distorted form.
You have to understand that by staying far away from the black hole, he essentially winds up saying that the future can't SEE the black hole, even if it formed, and the future CAN see the information, whatever happened to it in between.
:surprise: 
