  We find dispersion laws for the photon propagating in the presence of
mutually orthogonal constant external electric and magnetic fields in the
context of the $\theta $-expanded noncommutative QED. We show that there is no
birefringence to the first order in the noncommutativity parameter $% \theta .$
By analyzing the group velocities of the photon eigenmodes we show that there
occurs superluminal propagation for any direction. This phenomenon depends on
the mutual orientation of the external electromagnetic fields and the
noncommutativity vector. We argue that the propagation of signals with
superluminal group velocity violates causality in spite of the fact that the
noncommutative theory is not Lorentz-invariant and speculate about possible
workarounds.

High Energy Physics - Theory