  The effects of small extra dimensions upon quantum fluctuations of the
lightcone are examined. We argue that compactified extra dimensions modify the
quantum fluctuations of gravitational field so as to induce lightcone
fluctuations. This phenomenon can be viewed as being related to the Casimir
effect. The observable manifestation of the lightcone fluctuations is
broadening of spectral lines from distant sources. In this paper, we further
develop the formalism used to describe the lightcone fluctuations, and then
perform explicit calculations for several models with flat extra dimensions. In
the case of one extra compactified dimension, we find a large effect which
places severe constraints on such models. When there is more than one
compactified dimension, the effect is much weaker and does not place a
meaningful constraint. We also discuss some brane worlds scenarios, in which
gravitons satisfy Dirichlet or Neumann boundary conditions on parallel
four-dimensional branes, separated by one or more flat extra dimensions.

General Relativity and Quantum Cosmology;High Energy Physics - Theory