Bob in a black hole, or: On Decoherence from Horizons
Abstract: Danielson, Satishchandran, and Wald (DSW) derived the remarkable result that the mere presence of a black hole induces a fundamental rate of decoherence on all nearby quantum superpositions. The effect can be understood from measurement and causality: An observer (Bob) in the black hole should be able to disturb outside quantum superpositions by measuring their superposed gravitational fields, but since his actions cannot (by causality) have this effect, the superpositions must automatically disturb themselves! DSW calculated the rate of decoherence up to an unknown numerical factor for distant observers in Schwarzschild spacetime. Working in the electromagnetic analog, we flesh out and generalize their calculation to obtain the precise decoherence rate for an observer at an arbitrary location on the symmetry axis of a Kerr black hole. We find that the decoherence vanishes entirely in the extremal limit, due to the ``Black hole Meissner effect'' screening the Coulomb field from entering the black hole. This supports the causality picture: Since Bob is unable to measure the field of the outside superposition, no decoherence is necessary---and indeed none occurs.