Ideas for resolving the black hole information paradox
Per Kraus, University of California, Los Angeles
In classical physics black holes are, by definition, objects that can swallow an arbitrary amount of matter, rendering it inaccessible to an outside observer. Quantum mechanically, black holes are also found to emit matter via ``Hawking radiation", thereby losing mass and eventually shrinking to a microscopic size, and then most likely disappearing entirely. At our present level of understanding we are only able to compute the character of this radiation in an approximation whose precise regime of validity is subject to debate. In a regime where we have good reason to trust the approximation we find that the spectrum of emitted radiation is uncorrelated with the details of any matter that was earlier absorbed by the black hole. This is information loss, because an outside observer is unable to reconstruct the past history of the black hole even by carefully collecting all of the radiation into which the black hole decays. Complete knowledge of the present is insufficient to reconstruct the past.
In quantum mechanics all information about the world is packaged in a wavefunction which evolves deterministically (although the wavefunction itself is then used to make probabilistic predictions). Therefore, quantum mechanics apparently is incompatible with information loss, since by knowing the wavefunction now one can run the equations backwards to determine the wavefunction at any earlier time.
Solving the black hole information paradox means finding out where the apparently lost information is in fact hidden. It is widely believed that the resolution of this paradox will play a central role in the unification of gravity with quantum mechanics. I will mainly discuss recent ideas coming from string theory indicating that our naive notions of spacetime geometry in the presence of black holes requires drastic revision.