Of course, our only hope would be to travel at much, much greater speeds. As MIT astronomer Sara Seager explained here at The Atlantic to Ross Andersen:

There are a lot of people who think we have the capabilities to get to a tenth of the speed of light. People are using that number as a benchmark of what they think is attainable, whether it's with a solar sail or nuclear pulse propulsion. If we could achieve that speed, then we could get to Alpha Centauri in just over 40 years. Whenever I give a talk to a public audience I explain the hazards of living on a spacecraft for 40 years, the fact that life could be extremely tedious, and could possibly even include some kind of induced hibernation. But then I always ask if anyone in the audience would volunteer for a 40+ year journey, and every single time I get a show of hands. And then I say "oh I forgot to mention, it's a one way trip," and even then I get the same show of hands. This tells me that our drive to explore is so great that if and when engineers succeed at traveling at least 10 percent of the speed of light, there will be people willing to make the journey. It's just a matter of time.

So, one-tenth the speed of light and we could be there in 40 years. That's not half bad. As Seager notes, many people would be willing to give up Earth and make that assuredly miserable journey for the privilege of being the first humans to explore another solar system. But still: 40 years, it's no cakewalk.

That's why a new number, care of NASA physicist Harold White, is so stunning: Two weeks. Two weeks to Alpha Centauri, he told io9, if only we can travel by warping space-time.

Of course, of course, easier said than done, but White thinks it's possible, and he and a team at NASA are at the very early stages of making it so. io9's George Dvorsky explains:

The idea came to White while he was considering a rather remarkable equation formulated by physicist Miguel Alcubierre. In his 1994 paper titled, "The Warp Drive: Hyper-Fast Travel Within General Relativity," Alcubierre suggested a mechanism by which space-time could be "warped" both in front of and behind a spacecraft. Michio Kaku dubbed Alcubierre's notion a "passport to the universe." It takes advantage of a quirk in the cosmological code that allows for the expansion and contraction of space-time, and could allow for hyper-fast travel between interstellar destinations. Essentially, the empty space behind a starship would be made to expand rapidly, pushing the craft in a forward direction -- passengers would perceive it as movement despite the complete lack of acceleration. ... In terms of the engine's mechanics, a spheroid object would be placed between two regions of space-time (one expanding and one contracting). A "warp bubble" would then be generated that moves space-time around the object, effectively repositioning it -- the end result being faster-than-light travel without the spheroid (or spacecraft) having to move with respect to its local frame of reference.

And that's not even the hard part: Ever since this idea was floated, the catch has been the absolutely enormous amount of energy such an event would require. As White explains, "Space-time is really stiff, so to create the expansion and contraction effect in a useful manner in order for us to reach interstellar destinations in reasonable time periods would require a lot of energy." When he says a lot, he doesn't mean a couple of nuclear-power plants' worth; he means energy equal to the mass-energy of Jupiter, the biggest planet in our solar system. So that's not going to work.