  We display several examples of how fields with different limiting velocities
(the "speed of light") at a high energy scale can nevertheless have a common
limiting velocity at low energies due to the effects of interactions. We
evaluate the interplay of the velocities through the self-energy diagrams and
use the renormalization group to evolve the system to low energy. The
differences normally vanish only logarithmically, so that an exponentially
large energy trajectory is required in order to satisfy experimental
constraints. However, we also display a model in which the running is
power-law, which could be more phenomenologically useful. The largest velocity
difference should be in system with the weakest interaction, which suggests
that the study of the speed of gravitational waves would be the most stringent
test of this phenomenon.
