I jotted down a quick post on the Alcubierre Drive and faster than light travel. I had assumed that like many FTL misconceptions, the media had been confused by speed measured as proper velocity, (space in the Earth's rest frame divided by time in the spaceships frame), as opposed to lab velocity. +Jonah Miller quickly pointed out, however, that the claims for the drive were that it could go faster than the speed of light with regard to the laboratory frame, and hence with laboratory velocity. I found the original paper by Alcubierre on arxiv, and...
Jonah's absolutely right!
The paper is amazingly well written and anyone that's had a grad level general relativity class should be able to easily traipse through it. Alcubierre even shows that causality won't be violated. I haven't had time to digest the material enough to say why causality isn't violated except with the very unsatisfying statement, "Well, the math works out." Alcubierre was also quick to point out that he felt that with a bit of effort he could come up with an example that would violate causality:
"As a ﬁnal comment, I will just mention the fact that even though the spacetime described by the metric (8) is globally hyperbolic, and hence contains no closed causal curves, it is probably not very diﬃcult to construct a spacetime that does contain such curves using a similar idea to the one presented here."
OK, so to summarize. The math explanation and associated formulas I wrote down are correct. With uniform acceleration and no exotic matter whatsoever, you can travel more than x light years in x proper time years. In the case of the Alcubierre drive, however, that's not the trick they're playing. I hope to have more details soon, but in the meantime I'll leave you with this quote from Schild regarding the twin paradox and general relativity.
"A good many physicists believe that this paradox can only be resolved by the general theory of relativity. They find great comfort in this, because they don't know any general relativity and feel that they don't have to worry about the problem until they decide to learn general relativity."
Alcubierre's original warp drive paper