# Spontaneous breaking of Lorentz invariance

Is it possible to spontaneously break Lorentz invariance, i.e., have a Lagrangian that respects LI but a vacuum which does not? If it is possible, why isn't there even the slightest hint of the Minkowski vacuum not being Lorentz invariant? (Or in other words, would this pose another fine-tuning problem?)

Dear D-brane, yes, in principle, one could have theories that spontaneously break the Lorentz symmetry. Just add a vector field (or another non-scalar field) and some potential of the form $$(V_\mu V^\mu - v^2)^2$$ which will drive $V_\mu$ towards a vector of the right length, i.e. $(v,0,0,0)$ which would pick a preferred reference frame at each point much like the Higgs boson picks the "right" direction in the space of doublets.
As far as I can say, this is clearly excluded, at least for any microscopic value of $v$.