It is shown that (a) both the dispersion relations between the mean frequency θ0 and the mean wave number k 0 are invariant under the Lorentz transformation; and (b) the relativistic Doppler effects on θ 0 and k 0 differ. In the suboptic packet there is anomalous red shift in the mean wave number k' 0 received from a source receding with speed v: k′ 0 changes sign through zero as v goes through the value vg, the mean group velocity (...) in the packet. In the superoptic packet the anomalous red shift is in the mean frequency θ′ 0 which reverses sign through zero as v goes through the value vp, the mean phase velocity in the packet. This last finding indicates a blackout of the superoptic signal when propagated toward a receiver moving away from the source at a speed greater than vp. There is no violation of causality involved, and the final conclusion of the paper is that it is not a fundamental axiom of “special relativity,” as usually believed, to deny that information can be transmitted at speeds greater than c. (shrink)