The idea of interstellar travel has always intrigued me. As I understand it, as one approaches the speed of light, passage of time from the perspective of the traveller would dilate. Therefore assuming one can devise a way to make travel at relativistic speeds possible, the major drawback to human space travel is a difference in the passage of time for a stationary observer on Earth (I realize that the Earth is not stationary) compared to the people moving in the proposed spaceship. That is to say, while from the travellers perspective only a few days (or weeks) has passed, a much larger period of time would have elapsed for the people left behind. Therefore humanity is unlikely to colonize any system other than our own due to the disparity in time.

That being said, my understanding of how a theoretical warp drive would work is via the Alcubierre metric. From Wikipedia:

This is a Lorentzian manifold which, if interpreted in the context of general relativity, allows a warp bubble to appear in previously flat spacetime and move off at effectively superluminal speed.

My interpretation of the drive stated very simply is that the ship is in a "bubble" and remains stationary. The bubble is able to move at superluminal speeds and thus the ship is able to move as well.

So my question is, if the ship is still moving at a great velocity through space (although enclosed in a bubble), why doesn't time dilation apply? Is the reason as simple as they seem to make it in the article or is the explanation more entrenched in the mathematics of the drive?

Just an addendum to take care of responses that might arise from this post:

I understand (or think I do) that an Alcubierre drive is very unlikely due to energy requirements.

I understand that anything with mass can't travel at or faster than the speed of light because an infinite amount of energy is needed (or an infinite amount of acceleration is needed).