6.2. Simultaneity of events in different reference systems

Let the system K at the points with coordinates and two things happen at the same time . According to the Lorentz transformations in the system K ', the coordinates will correspond to these events.

and time points

Where

From the written formulas it is clear that if events in system K occur in the same place in space , then they will match in space and in time also in system K '.

If the events in system K are spatially separated then the system they will also be spatially separated but will be simultaneous. Difference sign determined by the sign of the expression . From this it follows that in different systems (at different v) difference will be different in magnitude and may differ in sign. This means that in some systems event 1 will precede event 2, in other systems, on the contrary, event 2 will precede event 1. This only applies to events between which there is no causal relationship.

Causally related events (for example, a shot and a bullet hit a target) will not be simultaneous in any frame of reference and in all systems the event that is the cause will precede the result