  We discuss the applicability of the argument of Collins, P\'erez, Sudarsky,
Urrutia and Vucetich to loop quantum gravity. This argument suggests that
Lorentz violations, even ones that only manifest themselves at energies close
to the Planck scale, have significant observational consequences at low
energies when one considers perturbative quantum field theory and
renormalization. We show that non-perturbative treatments like those of loop
quantum gravity may generate deviations of Lorentz invariance of a different
type than those considered by Collins et al. that do not necessarily imply
observational consequences at low energy.
