[Moderator's note: thread spun off from a previous one on a related but different topic.] Well that's another question that has been puzzling me for quite some time and would love to know the answer to it... Imagine 4 tubes of equal length, making a square, with 4 identical photons running around in the same direction, and hitting the corners at the same time. So we have an object with some angular momentum, which is constant with time. But when the square is viewed from a moving coordinate system, the photons no longer hit the corners in sync. It means that the angular momentum will oscillate around some average value. Also, the center of mass of the object is moving periodically, so the momentum and energy can not even be defined. (Imagine the square standing on one of its sides, moving to the right. Then the center of mass is certainly moving up and down). This leads me to the conclusion that 3-angular momentum and energy is only defined -and conserved- in a frame co-moving with the center of mass of the system under consideration, or some similar condition. Is that not correct? It seems to contradict Mfb's answer.