  We apply the Lieb-Robinson bounds technique to find the maximum speed of
interaction in a spin model with topological order whose low-energy effective
theory describes light [see X.-G. Wen, \prb {\bf 68}, 115413 (2003)]. The
maximum speed of interactions is found in two dimensions is bounded from above
less than $\sqrt{2} e$ times the speed of emerging light, giving a strong
indication that light is indeed the maximum speed of interactions. This result
does not rely on mean field theoretic methods. In higher spatial dimensions,
the Lieb-Robinson speed is conjectured to increase linearly with the dimension
itself. Implications for the horizon problem in cosmology are discussed.
