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Re: Twin Paradox (I know...not again)
Relativity of Simulteneity: Different sets of events are simultaneous in different frames.
Suppose that the spacecraft goes to Vega 10 light-years away at nearly c, and that there is a clock on Vega synchronized with Earth's in the Vega-Earth rest frame. Suppose that when the ship gets to Vega, its clock reads 10.1 years.
In neither of the ship's two frames are the Earth's Clock and Vega's Clock synchronized, and they are mis-synchronized in opposite senses in the two frames. In the outgoing frame, the event simultaneous with "Vega's Clock Reads 10.1 years" is "Earth's clock reads 0.01 years." In the returning frame, the event simultaneous with "Vega's Clock Reads 10.1 years" is "Earth's Clock Reads 20.19 years." And that's it.
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