Again, you're talking about the Twin Paradox, which is only applicable to General Relativity. Newtype is talking about Special Relativity. :bitch:
So fricken annoying to see the two so constantly conflated, which is why I despise the twin paradox.
No, the twin paradox comes from special
relativity, which had no trouble explaining that the twins wouldn't be the same age, just trouble explaining why A should be older B instead of B older than A, if there wasn't a preferred reference frame, which special relativity said there wasn't. That's why it was called a paradox
As I recall, Einstein had largely resolved it around 1910, before general relativity, by distinguishing btween the non-accelerated reference frame and the accelerated one, which initially would also seem to be relative (which one is accelerating? Wouldn't it depend on your point of view?), but only one twin feels like he's pulling some serious G's somewhere along the way, leading to the importance of the non-accelerated reference frame's proper time, etc.
But for the twins paradox to occur, one has to change your inertial frame of reference, which is the domain of general
relativity. Otherwise, one twin sees the other as aging more slowly, and vice versa.
But the paradox is only a paradox under special relativity, which couldn't initially explain why one reference frame would be prefered over the other, accept by noting that one of the twins underwent acceleration (that was bouncing around somewhere near 1910). That brought up the question of why an acceleration should matter, and given that acceleration and gravity are the same thing to the twin (he can't tell which is which inside a sealed box), gravity must be doing something weird to time, too, leading to general relativity.
The twins paradox isn't a paradox under general relativity because it explained why it occured (thus no longer a paradox), but the fact that the twins clocks don't match was apparent in special relativity, where it of course created a paradox (all reference frames are not equal - but they are - except they're not - damn).
The interesting thing about this new warp drive is that the twins paradox doesn't occur because their clocks stay the same. Both twins stay in a non-accelerating inertial reference frame the whole time. There's no time-dilation for either of them, just a seperation of distance (along with the doppler effect of moving relative to the transmission speed of a whatever they use to send signals back and forth).
Whenever they meet up, their clocks will still be in sync.