Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences
- National Institute for Theoretical Physics (NITheP), University of Stellenbosch, Stellenbosch (South Africa)
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.
- OSTI ID:
- 21371504
- Journal Information:
- AIP Conference Proceedings, Vol. 1206, Issue 1; Conference: 4. Gamow international conference on astrophysics and cosmology after Gamow;9. Gamow summer school on astronomy and beyond: Astrophysics, cosmology, radio astronomy, high energy physics and astrobiology, Odessa (Ukraine);Odessa (Ukraine), 17-23 Aug 200917-23 Aug 2009; Other Information: DOI: 10.1063/1.3292518; (c) 2009 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ALGEBRA
ASTROPHYSICS
CORRECTIONS
COSMIC RADIATION
DISPERSION RELATIONS
DISTANCE
ENERGY DEPENDENCE
LIFETIME
MEAN FREE PATH
NONLINEAR PROBLEMS
QUANTUM GRAVITY
VACUUM STATES
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
IONIZING RADIATIONS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICS
QUANTUM FIELD THEORY
RADIATIONS