Relativity of simultaneity
Two events occurring at different space co-ordinates x_{1} and x_{2} in an inertial frame S, are said to be simultaneous, if they occur at the same time t. The time t is recorded by two synchronized clocks fixed at x_{1} and x_{2} in S. The same events are observed from another moving Lorentz frame S' at (x_{1}', t_{1}') and (x_{2}', t_{2}') respectively. We have,
x_{1}' = (x_{1} - vt), t_{1}' = (t - vx_{1}/c^{2})
x_{2}' = (x_{2} - vt), t_{2}' = (t - vx_{2}/c^{2})
We have assumed the case of standard Lorentz transformations. Note that the two events do not occur simultaneously in frame S', t_{2}' ≠ t_{1}', and the time interval is given by,
The simultaneity is therefore not absolute but relative to frame of reference. Two events that occur simultaneously in one frame are not simultaneous in another frame.