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There are well-documented models of a system of interest
coupled to an environment whose details are ignored. These unmeasured
modes carry away phase information about the system and induce
decoherence which allows probabilities to be assigned to the possible
outcomes of measurements of the system. In the case of the
gravitational field, if only the macroscopic modes are involved in the
definitions of alternatives, to what extent to the short-wavelength
modes act as an "environment" to induce decoherence in the
long-wavelength modes? (Previous work, for example by Halliwell
[Phys Rev **D39**, 2912 (1989)] and
Padmanabhan [Phys Rev **D39**, 2924 (1989)],
used an additional field to obtain decoherence of the gravitational
field in cosmological models. The present enterprise differs in that
it examines decoherence which is induced by other modes of the
gravitational field itself.)

Examining a scalar field action with some of the same properties as the action for General Relativity, I use a perturbative approach to determine when the off-diagonal elements of the decoherence functional for coarse graining only by the long-wavelength modes are suppressed by the influence functional. An important limitation of the result is that the perturbative approach is only applicable when the temperature describing the state of the short-wavelength modes is high compared to the inverse of the length scale dividing long and short wavelengths.

This work has been published as Phys
Rev **D57**, 768 (1998) and is also
available as a
preprint from the XXX
e-print database at Los Alamos. There is also a short summary,
written for the proceedings of the 18th
Texas Symposium on Relativistic Astrophysics.

Last Modified: 2011 April 6

Dr. John T. Whelan / john.whelan@astro.rit.edu / Professor, School of Mathematical Sciences & Center for Computational Relativity and Gravitation, Rochester Institute of TechnologyThe contents of this communication are the sole responsibility of Prof. John T. Whelan and do not necessarily represent the opinions or policies of RIT, SMS, or CCRG.