  Recently Randjbar-Daemi and Shaposhnikov put forward a 4-dimensional
effective QED coming from a Nielsen-Olesen vortex solution of the abelian Higgs
model with fermions coupled to gravity in D=6. However, exploring possible
physical consequences of such an effective QED was left open. In this letter we
study the corresponding effective Casimir effect. We find that the extra
dimensions yield fifth and third inverse powers in the separation between
plates for the modified Casimir force which are in conflict with known
experiments, thus reducing the phenomenological viability of the model.
