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You don't need a rocket ship to dislocate your there-and-now rather violently, if the “there” is far enough away, because the effect increases with distance. Suppose you put down this book, get up from your chair, and walk across the room. You have just changed your there-and-now in the Andromeda galaxy by a whole day! What I mean by this statement is that, while sedentary, you can deduce that a certain event E on a certain planet in Andromeda is happening at the same moment (as judged by you, in your particular frame of reference) as the act of “you reading this passage.” When you walk across the room, the event on that distant planet which is simultaneous with your ambulation suddenly changes from “just after E” to some other event which differs from E by a day. It jumps either into the future or past of E, depending on whether you are walking towards or away from Andromeda at the time. Thus simultaneity, like motion, is relative.
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Paul C.W. Davies (About Time: Einstein's Unfinished Revolution)