Leaving aside my skepticism about our ability to do that sort of thing, a bigger question should be -- how would that even help? It seems impossible to get to the edge of our Galaxy in 80 years no matter how fast we go. The Milky Way is thousands of light years in diameter. Even going at the speed of light, crossing it would take thousands of years, so what could Hawking be talking about?
The answer is again relativity. In my previous post, I talked about how objects going near the speed of light experience relativistic effects. One of those effects is time dilation: clocks of moving objects go slower when viewed by (relatively) stationary observers. Another is Lorentz contraction: an observer will measure the length of a moving object as shorter in the direction of its relative motion.
So while we can't hope to go faster than the speed of light, we wouldn't really have to traverse thousands of light years either, at least not from our point of view. Because of Lorentz contraction, we would see the entire galaxy contract into a more manageable distance. So, in some sense, we can travel a light year in under a year. And if we then turn around and come home to Earth, we will also have traveled into the future, killing two birds with one giant fuel-filled spaceship.
This also answers the question from my previous post. From their point of view, muons halve only thrice between airplane height and the Earth's surface because to them it's 3000 feet, not 30000.
The Milky Way image is under a Creative Commons Attribution-Share Alike 2.5 Generic license. Its author is Digital Sky LLC.