Please wait for the animation to completely load.
A lightning bolt hits the center of a flatbed railcar at t = 0 seconds as shown in the above animations (position is given in meters and time is given in seconds). Restart. There is a relative velocity between the frame of the ground, called S in the lower panel of the animation, and the frame of the railcar, called S' in the lower panel of the animation. In the animation, View from Ground, the event of the lightning strike and the subsequent transmission of this information is shown as seen from the reference frame of the ground. Alternatively in the animation, View from Railcar, the same event is depicted as seen from the reference frame of the railcar.
Begin by reconsidering what is seen in the View from 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 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 an omnipresent observer in reference frame S, 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 omnipresent observer in reference frame S). Finally, the light reaches B'.
Now consider what is seen in the View from Railcar by 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 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 omnipresent observer in reference frame S', 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 an omnipresent observer in reference frame S'). Finally, the light reaches 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 above animations. 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 depict the above event from the reference frame of the ground is with a spacetime diagram as shown in the Show 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 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 observer the 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 not the sequence of events as described by the space time diagram. Note that A and B are simultaneous (as we found above). We know this by realizing that horizontal lines on the space time diagram, Show Spacetime Diagram with Equal Time, represent simultaneous events in that reference frame (they happen at the exact same time).