Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences |
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Authors: | K G Zloshchastiev |
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Affiliation: | 1.National Institute for Theoretical Physics (NITheP), Department of Physics and Centre for Theoretical Physics,University of Witwatersrand,Johannesburg,South Africa |
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Abstract: | Starting from a generic generally covariant quantum theory, we introduce a logarithmic correction to the quantum wave equation.
We demonstrate the emergence of evolution time from the group of automorphisms of the von Neumann algebra governed by this
nonlinear correction. It turns out that such a parametrization of time is essentially energy-dependent and becomes global
only asymptotically, as the energies become very small as compared to the effective quantum gravity scale. A similar thing
happens to Lorentz invariance: in the resulting theory it becomes an asymptotic low-energy phenomenon. We show how the logarithmic
nonlinearity deforms the vacuum wave dispersion relations and explains certain features of the astrophysical data coming from
the recent observations of high-energy cosmic rays. In general, the estimates imply that, ceteris paribus, particles with higher energy propagate slower than those with lower energy, therefore, for a high-energy particle the mean
free path, lifetime in a high-energy state and thus the travel distance from the source can be significantly larger than one
would expect from the conventional theory. In addition, we discuss the possibility and conditions of transluminal phenomena
in the physical vacuum such as Cherenkov-type shock waves. |
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