In the lightning bolt example, what if the the bolts are simultaneous in the train?
In this example we assumed that saw the equidistant flashes at the same time, and so the bolts were simultaneous on the ground. If we assume instead they are simultaneous in the train, they will not be simultaneous on the ground! It works symmetrically: to the person on the train, it looks as if the ground is moving. The analysis goes the same way: suppose is at the center of the train and sees the flashes arrive at the same time. She’s read Einstein’s paper, so she concludes that because the ends of the train are equidistant, the flashes must have been simultaneous. The train moves to the right during the time the light is traveling. So, the flashes will meet to the right of . The light from will arrive at before the light from . So, observer , also having read Einstein’s paper and knowing that the speed of light is always , concludes that in his frame, the lightning bolt hit first. The flashes are not simultaneous in if they are simultaneous in .
