A single source of light exists at a fixed point in space relative to two observers. The two observers move on the surface of a shell with a fixed radius with the light source at its centre. They move along a circular path on the sphere. They move at different velocities u and v. Will they experience time dilation relative to each other?
If relativity says that there will be time dilation on the shell of a sphere with a fixed radius with a light source at its centre, then there is a problem. Let's say the light blinks once every 10 secs. Then that light will reach all observers on the shell at the same time no matter what their relative velocity to each other. All observers would agree the light blinks once every 10 secs, no matter what their velocity is as long as they are on the shell.