The question has now been amended to:
"Is there a systematic causal link between the direction of a photon and the direction the mass from which it emerges is moving in?
I'm not talking about the direction of the electron involved in radiating the photon, but the direction of the overall mass (atom or larger) from which the photon emerges, and asking whether such direction of such overall mass will systematically determine the path a photon takes when it flies off on its trip.
So let's say the mass is doing 0.5c along the x-axis, will this systematically determine the angle of trajectory which the photons which emerge from it take, or will they simply find their own trajectory independently according to other random factors? If it will systematically determine the trajectory of the photons, please state whether such determination will be in part or in full, and what the mechanism for such will be."