Without acceleration, the system is symmetrical, so each observer thinks the other's time is passing more slowly. But that also means they can never meet up ag

Without acceleration, the system is symmetrical, so each observer thinks the other's time is passing more slowly. But that also means they can never meet up again to compare ages and see who's "right". The observer who accelerates is the one who breaks the symmetry, and thus travels into the other's future. I haven't done the math, but Wikipedia has pictures: http://en.wikipedia.org/wiki/Twin_paradox http://en.wikipedia.org/wiki/Twin_paradox