Quantum Fluctuations and Semiclassical Gravity Theory

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Casimir Force, Gravity

Scientific paper

Semiclassical gravity theory should serve as a working model before the final theory of quantized gravity is known, or as an approximation for manageable calculations even when the final theory is known. We deal with the important issue of the applicability of the semiclassical theory of gravity, specifically considering the effects of quantum fluctuations of the matter fields and the induced metric perturbations. The quantum fields with negative energy densities are proposed to be the cases where the semiclassical theory is no longer valid. We start with a discussion of the basic notions and developments of semiclassical gravity theory, and continue with a discussion of the establishment of a meaningful measurement of the deviation from semiclassical theory. The measure is a normalized dispersion of the energy density. The non-positive-definiteness of the energy density of quantum fields is derived and discussed. Important cases, like squeezed states and the Casimir effect, which exhibit negative energy densities, are discussed and the deviations from semiclassical theory are checked. A test particle method using a generalized Langevin equation is formulated for the physical description of systems for which the semiclassical theory can not be used. Quantum fields around straight infinite cosmic string is another example of where the negative energy densities may arise. We examine the validity of semiclassical theory for this case. The Casimir force due to the zero-point fluctuations of the electromagnetic fields in the presence of a conducting plate is another case where the quantum fluctuations are large and naive classical consideration should be modified. Using the test particle method, we are able to show that it is a relaxation phenomenon and that a notion of effective temperature can be associated with it.

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