Quantum Lightcone Fluctuations in Theories with Extra Dimensions

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.