Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences
Abstract
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 nonlinear correction. It turns out that such time parametrization is essentially energydependent and becomes global only asymptoticallywhen the energies get very small comparing to the effective quantum gravity scale. We show how the logarithmic nonlinearity deforms the vacuum wave dispersion relations and explains certain features of the astrophysical data coming from recent observations of highenergy 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 highenergy particle the mean free path, lifetime in a highenergy state and, therefore, travel distance from the source can be significantly larger than one would expect from the conventional theory.
 Publication:

American Institute of Physics Conference Series
 Pub Date:
 January 2010
 DOI:
 10.1063/1.3292518
 Bibcode:
 2010AIPC.1206..112Z
 Keywords:

 quantum theory;
 wave equations;
 linear algebra;
 quantum gravity;
 05.30.Ch;
 03.65.Pm;
 02.10.Ud;
 04.60.m;
 Quantum ensemble theory;
 Relativistic wave equations;
 Linear algebra;
 Quantum gravity