Relativity of simultaneity

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according to the relativity of simultaneity, when two people are at opposite ends of a moving train, and in their reference frame sign a paper at the same time when a beam of light emitted from the center of the train reaches them, observers on the outside of the train will say that the person on the back of the train signed first. The reason being that the speed of light is constant and the back of the train moves toward the light while the front of the train moves away from the light. Why is it that the signing of the papers does not have to occur at the same time for the observer on the outside of the train, but the paper being signed and the light reaching the person signing the paper must occur at the same time?
 

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Simon Bridge
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Why is it that the signing of the papers does not have to occur at the same time for the observer on the outside of the train, but the paper being signed and the light reaching the person signing the paper must occur at the same time?
Because the speed of light is invariant.
 
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If something happens six light-seconds away, the light from that event will reach your eyes six light-seconds after it happened. Therefore, the only sensible definition of when it happened is "six light-seconds before the light hit my eyes".

The point of the train thought experiment is that observers in motion relative to one another but applying this altogether sensible definition of when events happen will come to different conclusions about which events happened "at the same time".
 

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