Serious difficulties from extinction are shown to exist in the interpretation of past experiments on γ rays from moving sources. We have measured the relative speed of the two γ rays emitted forward and backward by a π0 meson decaying in flight. The velocity of the neutral pions, which were produced in the reaction π-+p-->π0+n, was v=0.2c. We have compared our results with what would have been expected, taking account of extinction, on the assumption that the initial photon velocities were c+v and c-v. The results were in complete disagreement with this assumption.