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Feb13-12, 06:17 AM
P: 152

From wikipedia:

"A popular picture for understanding this idea is provided by a thought experiment consisting of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past. It is similar to thought experiments suggested by Daniel Frost Comstock in 1910[1] and Einstein in 1917.[2][3]

A flash of light is given off at the center of the traincar just as the two observers pass each other. The observer onboard the train sees the front and back of the traincar at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the traincar at the same time.

The observer standing on the platform, on the other hand, sees the rear of the traincar moving (catching up) toward the point at which the flash was given off and the front of the traincar moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times."
Is this helpful? According to SR the speed of light on earth is not c in relation to the gravitational field of the earth but relative to "any inertial frame". Thus the observer on the platform sees the front- and the backside of the wagon lit up at different times but the guy on the train will think that the front and the backside of the train are lit up simultanesously, because the light coming back from the rear and the front end of the wagon walls will hit him simultaneously.

I think this type of thought experiments are always what is meant when someone talks about "relativity of simultaneity", but I might be wrong...