An Interdisciplinary Journal

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

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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Last updated: *November 8, 2004*