2003/09/25 by Alexander Shalyt-Margolin, A. E. Shalyt-Margolin, Shalyt-Margolin, A. E.
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0309121
Latex,12 pages,no figures,some corrections
openalex publication_date 2003/09/25 · arxiv created 2003/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present work is a study of the unitarity problem for Quantum Mechanics at Planck Scale considered as Quantum Mechanics with Fundamental Length (QMFL).In the process QMFL is described as deformation of a well-known Quantum Mechanics (QM). Similar to previous works of the author, the basic 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. It is demonstrated that the existence of black holes in the suggested approach in the end twice results in nonunitary transitions (first after the Big Bang of QMFL to QM, and then when on trapping of the matter into the black hole the situation is just the opposite - from QM to QMFL)and hence in recovery of the unitarity. In parallel this problem is considered in the deformation terms of Heisenberg algebra, showing the identity of the basic results. From this an explicit solution for Hawking's informaion paradox has been derived