http://arxiv.org/abs/1304.1899
In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state” (Verbatim from ref. 2.) This was the starting point of the popular “black hole (BH) information paradox”. On the other hand, during one of his famous quantum field theory lectures at Harvard, S. Coleman claimed that “The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.” One of the highest levels of abstraction concerning the harmonic oscillator in Nature is surely represented by BH quasi-normal modes (QNMs), which are a countable set of damped oscillations representing the BH’s reaction to perturbations. In a series of papers, together with collaborators, I naturally interpreted BH QNMs in terms of quantum levels. Here I explicitly write down a time dependent Schr\”odinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave-function are written in terms of an unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of mixed one. Hence, Hawking’s claim is falsified by an application of Coleman’s claim. Information comes out in BH evaporation in terms of pure states in an unitary time dependent evolution. The assumption by ‘t Hooft that Schr\”oedinger equations can be used universally for all dynamics in the universe is in turn confirmed, further endorsing the conclusion that BH evaporation must be information preserving.
C. Corda
Mon, 3 Mar 14
44/55