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 Quote by ZikZak The reason depends on which observer you are. The unaccelerated observer attributes the disagreement in the clocks as being due to time dilation while the spacecraft was in motion. The accelerated observer attributes the difference to a combination of factors, but mainly failure of simultaneity. Suppose your rest observer, with clocks stationed everywhere, in particular has a clock next to himself where the race begins, and a clock at the "finish line" where the traveling observer slows down and stops, and that these clocks are synchronized in his frame. Then they will not be synchronized in the traveling frame. The traveling observer observes both clocks running at the same slow rate, but the finish line clock will read a value that is vastly ahead of the starting line clock. So it is no surprise to him that when he gets there, it is reading many years ahead of his own clock, even though it runs more slowly.
Why will he read that the clock at the finish line is years ahead of his own clock, even if it is running the same speed as the one at the starting line? If there was a person in the rest frame, he would predict that time went slower for the person in the space ship. If this was true as well, why isn't he the one who is younger than the person who traveled?

 Quote by ZikZak No it isn't.
The theory says that time goes slower for both the person in the space ship and in the rest frame. It says that time goes slower in rest frame relative to space ship frame, and time goes slower in space ship frame relative to rest frame. This can't be true if there is only one truth. Also when the two frames arrives at equal velocity, they predict only one truth. However it seems like some kind of acceleration is necessary for them to predict and arrive at the same truth. Thus I am curious about the role of acceleration as well.