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

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{ö}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.

18 pages

References in corpus (8)

• Do black holes radiate?
• Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics
• Quantum Mechanics at Planck's scale and Density Matrix
• Quantum Mechanics of the Early Universe and its Limiting Transition
• Density matrix and dynamical aspects of Quantum Mechanics with Fundamental Length
• Fundamental Length,Deformed Density Matrix and New View on the Black Hole Information Paradox
• Generalized Uncertainty Relations,Fundamental Length and Density Matrix
• Deformed density matrix, Density of entropy and Information problem

Cited by in corpus (15)

• Deformed Density Matrix and Quantum Entropy of the Black Hole
• Entropy In The Present And Early Universe: New Small Parameters And Dark Energy Problem
• The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration
• Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics
• The Density Matrix Deformation in Physics of the Early Universe and Some of its Implications
• Minimal Length, Measurability and Gravity
• Quantum Theory at Planck Scale, Limiting Values, Deformed Gravity and Dark Energy Problem
• Deformed Quantum Field Theory, Thermodynamics at Low and High Energies, and Gravity. I
• Some Implications of the Density Matrix Deformation in Statistical Mechanics of the Early Universe
• The Black Hole Quantum Entropy and Its Minimal Value
• Probable Entropic Nature of Gravity in Ultraviolet and Infrared Limits, Part I. An Ultraviolet Case
• Spacetime Quantum Fluctuations, Minimal Length and Einstein Equations
• Two Approaches to Measurability Concept and Quantum Theory
• The Quantum and Statistical Theory of Early Universe and Its Possible Applications to Cosmology
• Minimal Length and the Existence of Some Infinitesimal Quantities in Quantum Theory and Gravity