Quantum Field Fluctuations and the Motion of Test Particles

Abstract: This talk will explore the use of classical or semiclassical test particles as a probes of the fluctuations of quantum fields. The resulting motion is a variety of Brownian motion, which is well-known in statistical physics. However, in the absence of dissipation, random force fluctuations will lead to a velocity variance which grows linearly in time. In statistical physics, this linear growth describes the approach to equilibrium before dissipation effects become important. However, in the case of a quantum field in its vacuum state, there is no obvious source of energy. This apparent paradox is resolved by the presence of anti-correlations. Thus the particle can acquire a limited amount of energy from a field fluctuation, but a short time later, an anti-correlated fluctuation will take back this energy. We will explore several physical systems in which this type of Brownian motion is predicted to occur, and give some estimates of the magnitude of the effect and discuss its observability. These systems will include motion of electrons in the Casimir vacuum near conducting boundaries and in a fluctuating electric field produced by zero point density fluctuations in a dielectric material. We will discuss when the motion due to zero point fluctuations can exceed the thermal motion and may be observable. Test particles need not be electrons or other massive particles, but could also be photons. Photon Brownian motion in a fluctuating gravitational field leads to quantum light cone fluctuations, which is a prediction of quantum gravity. It will be argued that tensor inflationary perturbations in the Cosmic Microwave Background (CBM, which have not yet been observed, can be interpreted as an example of photon Brownian motion.

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