Lecture 22: Black Hole Complementarity

Both the cloning and the strong subadditivity paradox can be resolved by black hole complementarity. The phrase "complementarity" is used by different people to mean different things! However, broadly speaking, there are two perspectives on the issue:

1) The degrees of freedom inside the black hole are "scrambled versions" of degrees of freedom outside the black hole. So the Hilbert space of the theory does not factorize into an interior and exterior. This resolves the cloning paradox by positing that there is no duplication on information --- even though the interior and exterior appear to be separated on the nice slice, suitably complicated operators in the exterior (polynomials with a very large number of local insertions) literally equal simple operators in the interior. The strong subadditivity paradox also relies on the factorization of the Hilbert space, and if this is not true, then there is no paradox.

2) A somewhat older perspective is that the outside and inside observers have different perspectives on the black hole, and no experiment that avoids Planck-scale physics can detect the conflict between these two perspectives. Susskind and Thorlacius analyzed some Gedanken experiments related to this in hep-th/9308100, which we reviewed in class.

Lecture 22 notes