Relativity of Simultaneity seems to be about OBSERVING two events simultaneously (please correct me if I am wrong).
However, as long as the two events are separated by a distance (any distance) then two observers (in the same frame) cannot agree that they happen simultaneously unless they are equidistant from the two events within the frame.
Consider the example of A and B at rest with respect to another observer C. A and B are stationary in space but separated by 1 light second of distance.
An event occurs simultaneously at A and B, the time should be the same since they are at rest with respect to each other. However, A will OBSERVE event at A and exactly after 1 second, the event at B. B will OBSERVE the event at B and exactly after 1 second, the event at A.
C may observe A first, B first or A and B simultaneously (which is fine).
My questions are:
- Are A and B in the same inertial frame? And if so, if simultaneity is about OBSERVING an event, then how do we account for the different observation times within the same frame? An event can never be simultaneous for A and B unless they are at the same location.
- If A and B are not in the same frame, then they are not in inertial frames as there is no motion with respect to each other.
- If simultaneity is not about OBSERVING two events, then how do we separate the visual aspect (time taken for light to travel) from the temporal aspects (time at which the two events actually occurred.