  Within loop quantum gravity we construct a coarse-grained approximation for
the Einstein-Maxwell theory that yields effective Maxwell equations in flat
spacetime comprising Planck scale corrections.
  The corresponding Hamiltonian is defined as the expectation value of the
electromagnetic term in the Einstein-Maxwell Hamiltonian constraint,
regularized a la Thiemann, with respect to a would-be semiclassical state. The
resulting energy dispersion relations entail Planck scale corrections to those
in flat spacetime. Both the helicity dependent contribution of Gambini and
Pullin [GP] and, for a value of a parameter of our approximation, that of Ellis
et. al. [ELLISETAL] are recovered. The electric/magnetic asymmetry in the
regularization procedure yields nonlinearities only in the magnetic sector
which are briefly discussed. Observations of cosmological Gamma Ray Bursts
might eventually lead to the needed accuracy to study some of these quantum
gravity effects.
