Sullivan Stockwell said:
My question is based around the popular thought experiment regarding Einstein's relativity of simultaneity. That is, the one regarding two lightning strikes and two observers. Observer 1 is stationary relative to the ground, and is located equidistant between lightning strikes A and B. Observer 2 is moving on a train parallel to the lightning strikes and observer 1. It is said that observer 2 will judge the lighting strikes to happen at different times, and observer 1 will say they happen at the same time. This is true. But often times the explanation goes beyond addressing that the perceptions will indeed view the lighting strikes as happening at different times and claim that the lighting actually happens at different times. If you had a sensor under lighting strikes A and B, could you not prove that they do happen at the same time? The perceptions are different, but the events themselves can be proven as to their time. Maybe I just don't fully understand the interpretations people give regarding it. Thanks.
Here's a pair of animations I created a while back to help to visualize what is happening.
We start in with the ground observers frame:
He is halfway between the red dots and when each end of train aligns with a dot, the lightning strikes both the dot and end of the train. The flashes expand outward from the strikes reaching the ground observer simultaneously, as the started simultaneously and traveled at the same speed relative to the ground observer. They reach the train observer at different times (and when he is adjacent to different points of the tracks).
Now we switch to the train observer's frame. One thing to note first is that in the last animation the train was moving relative to the observer's frame, Thus the train will be measured to be length contracted: Thus is is this contracted length for the train that just fits between the red dots. When we switch to the train's frame, the train will measure as having its normal proper length. Now it is the ground that is moving and is length contracted. Thus from the train we would measure our train length as being greater than the distance between the two red dots and can never fit between them;
Here, the right end of the train reaches the right dot before the left end reaches the left dot. The strikes still occur when the dots and ends of the trains align. (an observer at the right end of the train and an observer at the right dot both will agree that they were hit by a lightning strike simultaneously. The same can be said for observers at the other end of the train and other dot.) The flashes expand outward from the ends of the train. Each have to travel an equal distance to reach the train observer at the train midpoint. The rightmost flash reaches him first, then the leftmost flash. Since they traveled the same distance at the same speed, they only could have left at different times.
Also note that in this second animation the two flashes still reach the ground observer simultaneously.
In fact, any observer anywhere on the train or by the the tracks would have to agree as to what part of the train was next to what part of the track at the moment either of the flashes reached that point. In other words, no matter how many observers or sensors you put on the train or the ground, all the ground sensors would conclude that the strikes occurred simultaneously and all the train mounted ones would say that they did not.
