Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps

Gravitons and Lightcone Fluctuations II: Correlation Functions

A model of a fluctuating lightcone due to a bath of gravitons is further investigated. The flight times of photons between a source and a detector may be either longer or shorter than the light propagation time in the background classical spacetime, and will form a Gaussian distribution centered around the classical flight time. However, a pair of photons emitted in rapid succession will tend to have correlated flight times. We derive and discuss a correlation function which describes this effect. This enables us to understand more fully the operational significance of a fluctuating lightcone. Our results may be combined with observational data on pulsar timing to place some constraints on the quantum state of cosmological gravitons.Comment: 16 pages and two figures, uses eps

Semiclassical Gravity Theory and Quantum Fluctuations

We discuss the limits of validity of the semiclassical theory of gravity in which a classical metric is coupled to the expectation value of the stress tensor. It is argued that this theory is a good approximation only when the fluctuations in the stress tensor are small. We calculate a dimensionless measure of these fluctuations for a scalar field on a flat background in particular cases, including squeezed states and the Casimir vacuum state. It is found that the fluctuations are small for states which are close to a coherent state, which describes classical behavior, but tend to be large otherwise. We find in all cases studied that the energy density fluctuations are large whenever the local energy density is negative. This is taken to mean that the gravitational field of a system with negative energy density, such as the Casimir vacuum, is not described by a fixed classical metric but is undergoing large metric fluctuations. We propose an operational scheme by which one can describe a fluctuating gravitational field in terms of the statistical behavior of test particles. For this purpose we obtain an equation of the form of the Langevin equation used to describe Brownian motion.Comment: In REVTEX. 20pp + 4 figures(not included, available upon request) TUTP-93-

Decoherence and Vacuum Fluctuations

The interference pattern of coherent electrons is effected by coupling to the quantized electromagnetic field. The amplitudes of the interference maxima are changed by a factor which depends upon a double line integral of the photon two-point function around the closed path of the electrons. The interference pattern is sensitive to shifts in the vacuum fluctuations in regions from which the electrons are excluded. Thus this effect combines aspects of both the Casimir and the Aharonov-Bohm effects. The coupling to the quantized electromagnetic field tends to decrease the amplitude of the interference oscillations, and hence is a form of decoherence. The contributions due to photon emission and to vacuum fluctuations may be separately identified. It is to be expected that photon emission leads to decoherence, as it can reveal which path an electron takes. It is less obvious that vacuum fluctuations also can cause decoherence. What is directly observable is a shift in the fluctuations due, for example, to the presence of a conducting plate. In the case of electrons moving parallel to conducting boundaries, the dominant decohering influence is that of the vacuum fluctuations. The shift in the interference amplitudes can be of the order of a few percent, so experimental verification of this effect may be possible. The possibility of using this effect to probe the interior of matter, e.g., to determine the electrical conductivity of a rod by means of electrons encircling it is discussed. (Presented at the Conference on Fundamental Problems in Quantum Theory, University of Maryland, Baltimore County, June 18-22, 1994.)Comment: 7pp +2 Figs.(not included), TUTP-94-1