Is the physical vacuum a preferred frame ?

It is generally assumed that the physical vacuum of particle physics should be characterized by an energy momentum tensor in such a way to preserve exact Lorentz invariance. On the other hand, if the ground state were characterized by its energy-momentum vector, with zero spatial momentum and a non-zero energy, the vacuum would represent a preferred frame. Since both theoretical approaches have their own good motivations, we propose an experimental test to decide between the two scenarios.