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# Section 2.3: Simultaneity

In these animations, a lightning bolt hits the center of two different flatbed railcars at t = 0 seconds (position is given in meters and time is given in in the time it takes light to travel one meter or 3.33 × 10−9 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 Experiment 1: From the Frame of the Ground, the event of the lightning strike and the subsequent transmission of this information are shown as observed from the reference frame of the ground. Alternatively, in the animation Experiment 2: From the Frame of the Railcar, a second, and different, experiment is depicted as observed from the reference frame of a second 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 between the observers on the railcars and the people on the ground.

Begin by reconsidering what is observed 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 observed 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 observed 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.

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. 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.

Also note that there are two different experiments depicted. To see why this must be the case, we first need to discuss length contraction, which follows in Section 2.4.

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