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Consider two fixed points A and B in a frame S. In this frame a person P moves towards the point A and does an event EA. After that, this person moves to the point B and does an event EB.

Based on Lorentz's transformations, it is very easy to find a frame S' where events EA and EB occur simultaneously. The problem is that this leads to that the person P exists in both positions A and B simultaneously! (according to S').

How is this possible?