Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics

TL;DR

This paper explores the black hole information paradox using a deformed density matrix in generalized quantum mechanics, demonstrating that pure states evolve into mixed states and linking entropy with holography and uncertainty principles.

Contribution

It introduces a deformed density matrix framework to analyze black hole information loss and connects generalized uncertainty relations with holographic entropy bounds.

Findings

Pure states become mixed in black hole processes.

High entropy of black hole remnants explained via density matrix entropy.

Consistency with the Holographic Principle and derivation of uncertainty relations from entropy bounds.

Abstract

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As previously, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck remnants of black holes appearing in the assumption of the Generalized Uncertainty Relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the Holographic Principle. Because of this, a conjecture is made about the possibility for obtaining the Generalized Uncertainty Relations from the covariant entropy bound at high energies in the same way as R. Bousso has derived Heisenberg uncertainty principle for the flat space.