## Simultaneity Demonstration

A lightning bolt hits the center of a flatbed railcar at t = 0 seconds as shown in the animations (position is given in meters and time is given in seconds)Restart.  There is a relative velocity between the reference frame of the ground, called S in the lower panel of the animation, and the reference frame of the railcar, called S' in the lower panel of the animation.  In the animation From the Frame of the Ground, the event of the lightning strike and the subsequent transmission of this information are shown as seen from the reference frame of the ground.  Alternatively in the animation, From the Frame of the Railcar, the same event is depicted as seen from the reference frame of the railcar.

For ease of viewing, there is an offset in the y direction shown between S and S' in the animations. Likewise there is an offset in the y direction shown between the people on the railcar and the people on the ground.

Begin by reconsidering what is seen in the  From the Frame of the Ground by playing and pausing the animation.  In this frame of reference, the railcar is moving to the right at a given speed as depicted in the lower panel by S' moving to the right.  As the circle representing the path of a spherical light wave expands, it first encounters the observer (the man) at A'.  This means according to any intelligent observer in reference frame S, no matter where he or she is in the reference frame, this event (the light reaching A') happens first.  Next the outgoing spherical light wave reaches the observers at A and B simultaneously (again as seen by an intelligent observer in reference frame S no matter where he or she is in the reference frame).  Finally, the light reaches the observer at B'.

Now consider what is seen in the From the Frame of the Railcar by again playing and pausing the animation.  In this frame of reference (S') the railcar is stationary and the ground is moving to the left at a given speed as depicted in the lower panel by S moving to the left.  As the circle representing the path of a spherical light wave expands it first encounters the observer (the woman) at B.  This means according to an intelligent observer in reference frame S', no matter where he or she is in the reference frame, this event (the light reaching B) happens first.  Next the outgoing spherical light wave reaches the observers at A' and B' simultaneously (again as seen by any intelligent observer in reference frame S' no matter where he or she is in the reference frame).  Finally, the light reaches the observer at A.

So who is right? After all it cannot possibly be true that in one frame of reference events A and B are simultaneous and then in the other events A' and B' are simultaneous?  Or can it?  When we are dealing with moving reference frames we must modify our idea of simultaneity to include the idea that events that are simultaneous in one reference frame are not simultaneous in another reference frame as shown by the animations: From the Frame of the Ground and From the Frame of the Railcar.  This is perhaps one of the most important things to keep in mind when considering the apparent paradoxes that arise in special relativity.  Almost all of these apparent paradoxes can be understood by remembering that events simultaneous in one reference frame are not simultaneous in another reference frame.

Another way to describe the events depicted in the View from the Ground animation is with a spacetime diagram as shown in the Show the Spacetime Diagram animation.  In the top panel is a spacetime diagram.  As the animation is played, the blue worldlines represent the light pulse moving to the left and to the right from the center of the railcar.  The green and red lines represent the worldlines of the 4 intelligent observers (two on the rail car and two stationary).  So which lines are which?  In the reference frame of the ground, the two observers on the ground are stationary and therefore do not move in the x direction.  Consequently their worldlines are vertical and must be the red ones.  The observers on the train are seen by an observer on the ground to be moving to the right and therefore have worldlines with horizontal components and are the green lines.  Reset the animation and play again.  Watch for the events A, B, A', and B' to occur.  How do you know when and where they occur on the spacetime diagram?  When the worldline of the light intersects a world line of an intelligent observer, the intelligent observer sees the light (the light and the observer are at the same space-time point; they are at the very same place at the very same time).  Also note the sequence of events as described by the space time diagram.  A and B are simultaneous (as we found above).  Horizontal lines on the space time diagram, Show the Spacetime Diagram with Equal Time, represent simultaneous events in that reference frame (they happen at the exact same time).  Note that events A and B are simultaneous for all intelligent observers in the stationary reference frames irrespective of his or her position (any point on the horizontal line).

Authored by Mario Belloni and Wolfgang Christian.
© 2004 by Mario Belloni and Wolfgang Christian.