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I know similar questions have been asked multiple times, hence I'll get straight to my doubt which I couldn't find cleared in the other ones.

The earth frame observer sees the lightning flashes simultaneously and he sees that the person in the middle of the train would receive the flash from the ahead one before the rear one. Now the thought experiment continues by saying that the observer on the train would also see the ahead one before the rear one and hence conclude that the ahead flash occured first.

My question is why is it being assumed that the earth frame observer seeing that the ahead flash hits the observer in the train first imply that the train observer would also see the ahead flash first.

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    $\begingroup$ Suppose the first flash knocks the train passenger to the floor, causing the second flash to pass completely over him. Surely both observers must agree on that sequence of events. $\endgroup$
    – WillO
    Dec 18, 2020 at 19:28
  • $\begingroup$ What if when the observer was centered between the two flashes His train was moving east as the earth rotated At 1000MPH? As well as orbiting the sun at 67,000 mph as it rotated around the galaxy at 490,000 MPH. Add to that 3,600,000 mph rushing toward other galaxies. If they all lineup the observer could be moving over 4,000,000 miles per hour. Would that make a difference? $\endgroup$ Dec 18, 2020 at 23:24

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My question is why is it being assumed that the earth frame observer seeing that the ahead flash hits the observer in the train first imply that the train observer would also see the ahead flash first.

Notice that at some instant the two light fronts reach each other. At that moment the front light pulse has already passed the train observer and the back light pulse has yet to reach the train observer. The order of events on a worldline of a massive or massless particle is frame invariant (causality). So the light pulses crossing each other happens after the front light pulse crosses the train observer in every frame, and it happens before the rear light pulse crosses the train observer in every frame. So in every frame there is some time when the front pulse has reached the train observer and the back pulse has not.

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You are right to question this assumption, as that's a good way to gain understanding and we know in relativity that observers can differ about measurements e.g. lengths, time intervals and simultaneity.

But let's suppose the train occupant has an instrument at his location with front and rear sensors that will ring a bell if a light beam hits the front sensor followed by one hitting the rear sensor, with the timing determined in the train frame of reference where the instrument is located. The platform observer expects the bell to ring, and it does. It can't be that the sound exists only in the platform frame of reference and not the train frame. So the train occupant would also observe the ahead flash to reach him first.

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