The physical measurable vacuum energy density in rectangular geometries and the Scharnhorst effect

Following the approach developed by Actor (Ann. Phys. 230 (1994) 303) on how to extract global results from the divergent local description, we obtained physical measurable vacuum energy density associated with the electromagnetic and conformally coupled scalar fields in rectangular cavities. For the electromagnetic field, we show that this quantity has no position dependence in a rectangular waveguide (as between parallel plates) but has a position dependence in the interior of a rectangular cavity. As an application we derive the Scharnhorst effect in a rectangular cavity. We show that the shift in the refractive index acquire a position dependence and the light velocity can be greater or smaller than c depending on the space point in the interior of the rectangular cavity and on the global length parameters.