An Interdisciplinary Journal

2004, Vol.7, No.3, pp.283-290

Unitarity in Generalized Quantum Mechanics and Hawking's Information Problem for Black Holes.
A.E. Shalyt-Margolin

Hawkings problem of information loss at black holes is a unitarity problem in Quantum Theory involving such objects as black holes. The present work is a study of this problem in Quantum Mechanics of the early and current Universe. Therewith the Early Universe Quantum Mechanics (at Planck scale) is treated as a deformation of the well-known Current Universe Quantum Mechanics. Owing to the generalized Uncertainty Relations, in the first case it may be considered as Quantum Mechanics with Fundamental Length. And the above-mentioned problem could be studied in two ways. Note that similar to previous works of the author, the primary approach is based on deformation of the density matrix (density pro-matrix) with concurrent development of the wave function deformation in the respective Schrodinger picture. In parallel this problem is considered in the deformation terms of Heisenberg algebra. It is demonstrated that the involvement of black holes in the suggested approaches in the end twice results in non-unitary transitions (first after the Big Bang of Quantum Mechanics with Fundamental Length to Quantum Mechanics, and then when on trapping of the matter into the black hole the situation is just the opposite - from Quantum Mechanics to Quantum Mechanics with Fundamental Length)and hence in recovery of the unitarity. From this an explicit solution for Hawking's Information Paradox has been derived.
Key words: density matrix deformation, wave-function deformation, Heisenberg algebra deformation, unitarity, information problem

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