That only applies if when traveling faster than light within flat spacetime. A consequence of high speed travel is time dilation, where the elapsed time is noticeably different between, say, the earth and a traveler going at say 1/10th the speed of light.
While the math is beyond me, the Alcubierre drive apparently works around this mess (while introducing others) by contracting spacetime itself. The most notable mess is the requirement of negative mass exotic matter, which we have no way of proving or disproving can even exist. This is the same type of exotic matter which can also be used to open worm-holes.
That said, I would happily fund this sort of research out of my own pocket for the rest of my life. Maybe it's because I've watched/read too much sci-fi but I'd like to think humanity can accomplish far more than than the the Internet and combustion-based travel.