I have a basic question about the trajectory of a photon. As can be seen in the figure above, lets suppose there is a stationary frame F and a cylinder sealed with two sided mirror is located at the origin of F. Then lets consider two cases; First is the velocity of cylinder is 0 with regard to F and second is constant v=v0. For the first case, at initial time t=t0, single photon is emitted from the center of bottom mirror to the positive y direction with velocity c so that the x position of the photon is not changed. Because of zero velocity of cylinder, the photon will bounce off from side to side forever so the trajectory of the photon will be like the red dotted line at bottom of the figure. So far so good. Here comes my question concerning the second case v=v0. If the velocity of cylinder with regard to F is non-zero v0 and travel from x=0 to x=v0*(t1-t0), then what will the trajectory of the photon look like? the diagonal path or path parallel y axis of F? Is the x position of the photon 0 or v0*(t1-t0) at t=t1? Which one is correct? According to the link here, the answer seems to be x=v0*(t1-t0) when measured in frame F. Do I understand correctly? If so, I doubt where does x changes come from although the photon is emitted to a perpendicular direction to the x axis?