Fundamental Length,Deformed Density Matrix and New View on the Black Hole Information Paradox

TL;DR

This paper proposes a novel approach to quantum mechanics at Planck scale by deforming the density matrix, offering new insights into the black hole information paradox and connecting quantum mechanics with fundamental length.

Contribution

It introduces a deformation of the quantum density matrix instead of commutators, providing a new framework for quantum mechanics with fundamental length and its implications for black hole information.

Findings

Density pro-matrix reduces to standard density matrix at low energies

Deformation leads to non-unitary transition from GUR-based quantum mechanics

New perspective on black hole information paradox

Abstract

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations (GUR). Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies on the fact that here density matrix subjects to deformation whereas so far commutators have been deformed. The density matrix obtained by deformation of quantum-mechanical density one is named throughout this paper density pro-matrix, which at low energy limit turns to the density matrix. This transition corresponds to non-unitary one from Quantum Mechanics with GUR to Quantum mechanics. Below the implications of obtained results are enumerated.New view on the Black Holes Information Paradox are discussed