The question is extention of thought experiment proposed by Einstein of light pulses in a train cart called Einstein's train. Assume that light pulses are emitted from the end of cart, instead from the center, such that stationary observer, sees the light pulses at the center crossing each other at the same time. image of this case from real experiment is given here And now let there a new observer which has a relative motion between cart and himself. So similarly to this case, the new observer will see that two pulses, coming at the center, in two different instants of time. Now there are two things

  1. I can consider two pulses crossing each other at the center as a single event because they have same spacetime coordinates. So events don't change in relativity but here they are apparently. Because now the event is non-existential here in any other frame than the stationary one. (Light pulses don't reach at the center at the same time) So where is that, I am getting wrong?
  2. It's consequences can change reality. For example if I place a detector at the center and what it does is, it (making it dramatic) kills the schrodinger's cat (I know the name looks familiar) in the glass box placed at the center, if it records that two pulses have reached at it simultaneously. (Since it is placed in the cart at the same spatial point with the center, we can approximately say that detection and killing is simultaneous). But for everyother observer the cat would be alive. Why?
  • $\begingroup$ Your question says light pulses are emitted from ends but your image shows that it's emitted from the center. $\endgroup$ Jul 30 '20 at 20:13

You're assuming that events that are simultaneous in one frame will be simultaneous in another frame too which is not the case. That is the whole point of the Einstein's train thought experiment. If in the train's frame, the light pulses are emitted at the same time from the ends, then to an observer in the train the light pulses will meet at the center. To an observer outside the train moving with a velocity relative to the train, the light pulses will still meet at the center of the train but the outside observer will say that the light pulses at the ends were not emitted at the same time. To the outside observer, light from one side was emitted earlier than light from the other side so that the two pulses meet at the center of the train.


The problem that we face here is that you are asking a question that appeals to intuition, but SR is unintuitive. Specifically, what I mean is that there are assumptions which hold in Newtonian physics that do not hold in relativistic physics.

Lets make your example even more dramatic, replace our laser pulses with super fast moving missiles. They are shot from both ends of the train, such that they arrive and explode in the center, leaving a mark. This action has consequence. Now suppose the train is moving very fast, with one observer watching the missiles on the train, and one observer watching from outside, not moving with the train.

Now if the observers on the outside sees that one missile is moving faster relative to the train than the other (due to velocity addition), then the missiles should pass the center at different times, as you say. It should also explode at a different point, leaving a different mark. This must be a contradiction right?

The resolution to this problem is simple, the observer on the tracks does not see the missiles being fired at the same time, one appears to be fired before the other. There is no contradiction to this observer. However, this is highly unintuitive. We want to think that this is wrong, because we naturally assume that if one frame sees the missiles firing together, then all frames should, but this simply is not the case.


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