Quantum Purity at a Small Price: Easing a Black Hole Paradox

Abstract

Following Hawking, it is usual to mimic the effect of collapse space-time geometry on quantum fields in a semi-classical approximation by imposing suitable boundary conditions at the origin of coordinates, which effectively becomes a moving mirror. Suitable mirror trajectories induces a close analogue to the radiance of black holes, including a flux of outgoing radiation that appears accurately thermal. If the acceleration of the mirror eventually ceases the complete state of the radiation field is a pure quantum state, even though it is indistinguishable from an accurately thermal state for an arbitrarily long period of time and in a precise sense differs little from ``pure thermal'' closely followed by ``vacuum''. Suspicions that the semiclassical calculation of black hole radiance gives evidence for the evolution of pure into mixed states are criticized on this basis. Possible extensions of the model to mimic black holes more accurately (including the effects of back reaction and partial transparency), while remaining within the realm of tractable models, are suggested.