Electromagnetic vacuum fluctuations and topologically induced motion of a charged particle

Abstract

We show that nontrivial topologies of the spatial section of Minkowski space–time allow for motion of a charged particle under quantum vacuum fluctuations of the electromagnetic field. This is a potentially observable effect of these fluctuations. We derive the mean squared velocity dispersion when the charged particle lies in Minkowski space–time with compact spatial sections in one, two and/or three directions. We concretely examine the details of these stochastic motions when the spatial section is endowed with different globally homogeneous and inhomogeneous topologies. We also show that compactification in just one direction of the spatial section of Minkowski space–time is sufficient to give rise to velocity dispersion components in the compact and noncompact directions. The question as to whether these stochastic motions under vacuum fluctuations can locally be used to unveil global (topological) homogeneity and inhomogeneity is discussed. In globally homogeneous space topologically induced velocity dispersion of a charged particle is the same regardless of the particle’s position, whereas in globally inhomogeneous the time-evolution of the velocity depends on the particle’s position. Finally, by using the Minkowskian topological limit of globally homogeneous spaces we show that the greater is the value of the compact topological length the longer is the time interval within which the velocity dispersion of a charged particle is negligible. This means that no motion of a charged particle under electromagnetic quantum fluctuations is allowed when Minkowski space–time is endowed with the simply-connected spatial topology. The ultimate ground for such stochastic motion of charged particle under electromagnetic quantum vacuum fluctuations is a nontrivial space topology.