Quantum information and information loss in General Relativity

Abstract

When it comes to performing thought experiments with black holes, Einstein-Bohr like discussions have to be re-opened. For instance one can ask what happens to the quantum state of a black hole when the wave function of a single ingoing particle is replaced by an other one that is orthogonal to the first, while keeping the total energy and momentum unaffected. Observers at $t\rightarrow\infty$ will not notice any difference, or so it seems in certain calculational schemes. If one argues that this cannot be correct for the complete theory because a black hole should behave in accordance with conventional quantum mechanics, implying a unitary evolution, one is forced to believe that local quantum field theory near the black hole horizon is very different from what had hitherto been accepted. This would give us very valuable information concerning physics in the Planck length region, notably a mathematical structure very close to that of super string theory, but it does lead to conceptual difficulties. An approach that is somewhat related to this is to suspect a breakdown of General Relativity for quantum mechanical systems. It is to some extent unavoidable that Hilbert space is not invariant under general coordinate transformations because such transformations add and remove some states. Finally the cosmological constant problem also suggests that flat space-time has some special significance in a quantum theory. We suggest that a new causality principle could lead to further clues on how to handle this problem.