  We study bounds and signatures of models where the Higgs doublet has an
inhomo- geneous mass or vacuum expectation value, being coupled to a hidden
sector that breaks Lorentz invariance. This physics is best described by a
low-energy effective Lagrangian in which the Higgs speed-of-light is smaller
than c; such effect is naturally small because it is suppressed by four powers
of the inhomogeneity scale. The Lorentz violation in the Higgs sector is
communicated at tree level to fermions (via Yukawa interactions) and to massive
gauge bosons, although the most important effect comes from one-loop dia- grams
for photons and from two-loop diagrams for fermions. We calculate these effects
by deriving the renormalization-group equations for the speed-of-light of the
Standard Model particles. An interesting feature is that the strong coupling
dynamically makes the speed-of-light equal for all colored particles.
