One of the big puzzles in theoretical physics is the question of what happens to information when it falls into a black hole. Although a very important tenet of quantum mechanics says that no process can ever destroy information, black holes appear to do just that.
In a practical sense, information can be destroyed by, for example, burning an encyclopedia. However, its information has not really been destroyed, but, instead, has been transferred into the detailed arrangement of ash and smoke. If we could measure the position and velocity of every ash and smoke particle, we could run time backwards using the laws of physics and a very large computer to calculate the original contents of the encyclopedia.
However, black holes appear to violate this principle. According to our current understanding, if we throw an encyclopedia into a black hole and wait a long time, the black hole will slowly evaporate and disappear without emitting any of the tell-tale ``smoke.'' One way of phrasing this problem is to note that ``Hawking radiation violates the Bousso bound.'' In the paper ``Quantum Bousso Bound,'' Andy Strominger and I show that a modification of the Bousso Bound resolves this violation in a particular quantum theory of gravity in which the relevant calculations can be made.