Non-Unitary and Unitary Transitions in Generalized Quantum Mechanics, New Small Parameter and Information Problem Solving

TL;DR

This paper introduces a deformed quantum mechanics framework with a new small parameter to address the information paradox, demonstrating nonunitary-unity transitions and providing an explicit solution to Hawking's paradox.

Contribution

It develops a deformed quantum mechanics approach with a novel small parameter, offering a new perspective on black hole information loss and unitarity restoration.

Findings

Black holes induce nonunitary transitions leading to unitarity.

Deformation of density matrix and wave function explains information preservation.

Explicit solution to Hawking's information paradox is derived.

Abstract

Quantum Mechanics of the Early Universe is considered as deformation of a well-known Quantum Mechanics. Similar to previous works of the author, the principal approach is based on deformation of the density matrix with concurrent development of the wave function deformation in the respective Schr{\"o}dinger picture, the associated deformation parameter being interpreted as a new small parameter. It is demonstrated that the existence of black holes in the suggested approach in the end twice causes nonunitary transitions resulting in the unitarity. In parallel this problem is considered in other terms: entropy density, Heisenberg algebra deformation terms, respective deformations of Statistical Mechanics, - all showing the identity of the basic results. From this an explicit solution for Hawking's informaion paradox has been derived.