  We show that a 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 vacuum fluctuations. We derive 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.
