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 trouble with this is General Relativity never formalized the MECHANISM involved. While gravitational time dilation can be inferred by the behavior of light (e.g. light still moves at C even when it's coming from a neutron star) that still wouldn't apply to the acceleration of a spacecraft, since even while accelerating it is still transitioning between inertial reference frames as parts of the ship collide with other parts of the ship and experience velocity changes (impulse and inertia).
Gravity is a special case in GR because, because it's an example of a constantly moving frame of reference (as opposed to movement BETWEEN frames). A rotating reference frame (a space station, for example) is sometimes said to be non-inertial as well, but in this case only locally (.e.g if you fall off the wheel you are immediately in an inertial frame in which the space station is rotating).
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.
But that's just it: a warp drive is using an accelerated reference frame by definition
. Strictly speaking, it's a situation in which the ship has created a stationary reference frame that it itself in motion in an arbitrary direction. This is similar to gravity -- a reference frame that is constantly moving towards the center of mass -- and should have some similar implications for time dilation.
The thing is, gravitational time dilation is only a consequence of the fact that light retains its native velocity regardless of acceleration, and time dilation should persist because the gravitational field never STOPS accelerating and the Earthbound twin never enters an inertial one. I'm trying to think whether this would actually be true of a warp drive, since in that case the drive can be SHUT OFF and the ship reenters an inertial frame anyway.
It's probably worth keeping in mind that photons only ARRIVE at their target at the speed of light; GR allows that from the transmitter to the receiver, over a distance of one light second, the photon can do whatever the hell it wants -- slow down, speed up, change directions, go into orbit around a black hole, move backwards, do some jumping jacks, double its energy or halve its energy etc -- but it will always reach you exactly one second after it leaves the transmitter. In a way, even gravitational time dilation is only apparent
, but it only seems not to be because you can never create a situation where you wouldn't observe it.