The point is, and this is something I just learned, that in a finite universe one of the twins would know there was something wrong with his spaceship. Let's say that it's a simple uniformly curved finite universe. Julian's flashbulb goes off sending light rays in all directions, just as Joaquin passes by, say heading east. After waiting a very long time, Julian sees the light returning from all the directions simultaneously. That tells him he has nice simple laws of physics in his frame. In a uniform universe, light travels the same speed in all directions.
Now what does Joaquin see? He's also traveling without acceleration, at less than the speed of light according to Julian. So he hasn't gotten back to Julian when all the light gets there. Joaquin sees the light which had been going east, and now is wrapping around from the west, after he sees the light that had been heading west and now is wrapping around from the east. If he tries to say that the universe is uniform (as it looks) and that light travels the same speed in all directions, he can't explain why he sees one direction before the other. His reference frame just doesn't allow the same simple laws of physics.
So we can't use those simple laws to figure out how things look to Joaquin. We know how things look to Julian, so that's how we figure out that Joaquin is the younger of the two when they get back together.
Mike W.
(published on 09/05/2012)