Simultaneity

Simultaneity: We have an intuitive idea of what is meant when we say that two events are simultaneous. With respect to a given coordinate system two events are simultaneous if their time coordinates have the same value. However events which are simultaneous in one coordinate system are not necessarily simultaneous in another coordinate system.

For an example, consider a railway man standing at the middle of a freight car (stationary)length 2L. He flicks his lantern and light pulse travels in all directions with velocity c. Light arrives at the two ends of the car after a time interval L/c. In this system, the freight cars rest system light arrives simultaneously at A and B.

Let us observe the same situation from a different system, where the observer moves towards the right with a velocity v. In the frame of observer, the freight car moves towards left with a velocity v. Light travels with same velocity, c in both systems. During the transit time of light A moves to A* and B moves to B*. So in the second frame it is apparent that light reaches at B* before A* and the events are not simultaneous.

Let us apply the Lorentz transformation for the above problem.

Freight car system : Let us take the origin at the position of railway man (middle of car).

         Event I     ( Pulse arrives at A )

         Event II    ( Pulse arrives at B )

Second car system :
         Event I     ( Pulse arrives at A )

Event Pulse arrives at B

. The pulse arrives at B earlier than A.

Thus simultaneity is not particularly fundamental property of events, it depends on the coordinate system.