2010/01/01 by Konstantin G. Zloshchastiev · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Black Holes and Theoretical Physics
paper · doi:10.1063/1.3292518
openalex publication_date 2010/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
Within the framework of a generic generally covariant quantum theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra governed by this non‐linear correction. It turns out that such time parametrization is essentially energy‐dependent and becomes global only asymptotically—when the energies get very small comparing to the effective quantum gravity scale. We show how the logarithmic non‐linearity deforms the vacuum wave dispersion relations and explains certain features of the astrophysical data coming from recent observations of high‐energy cosmic rays. In general, the estimates imply that ceteris paribus the particles with higher energy propagate slower than those with lower one, therefore, for a high‐energy particle the mean free path, lifetime in a high‐energy state and, therefore, travel distance from the source can be significantly larger than one would expect from the conventional theory.