Motivated by ideas from quantum gravity, Lorentz invariance has undergone
many stringent tests over the past decade and passed every one. Since there is
no conclusive reason from quantum gravity that the symmetry \textit{must} be
violated at some point we should ask the questions: a) are the existing tests
sufficient that the symmetry is already likely exact at the Planck scale? b)
Are further tests simply blind searches for new physics without reasonable
expectation of a positive signal? Here we argue that the existing tests are not
quite sufficient and describe some theoretically interesting areas of existing
parameterizations for Lorentz violation in the infrared that are not yet ruled
out but are accessible (or almost accessible) by current experiments. We
illustrate this point using a vector field model for Lorentz violation
containing operators up to mass dimension six and analyzing how terrestrial
experiments, neutrino observatories, and Auger results on ultra-high energy
cosmic rays limit this model.
