This is an interesting one. More interesting than you might think. Let's assume that in the next twenty years somebody works out some new fundamental principle, and effectively invents a spacedrive where fuel is not an issue. Let's also assume that for a manned flight, we want to limit the acceleration and deceleration to 1g.
OK, if you accelerate at 1g, after a year you're travelling at fairly close to the speed of light. Assuming that you have some very good shielding and you don't hit anything major, to go 30 light years is going to take you about 31 years. Let's call it 32 years for luck. Then you'd have to decelerate at 1g, so you'd get to your planet 60 light years away in 64 years. But here's the rub: that's 64
earth years. It didn't take you 64 of
your years. For the moment let's say that your average velocity was .99c. Then we can use 1/√(1-v²/c²) to work out that you experienced a sevenfold time dilation. (Multiply .99 by itself to get .98 and subtract this from one to get a fiftieth, which is roughly a seventh multiplied by a seventh). So
if your average velocity was .99c, the trip would have taken you 9 years of your time. But actually, your average velocity would have been
higher than that. Search google on "accelerate at 1g" to find some decent maths because I gotta go:
http://www.google.co.uk/search?hl=en...erate+at+1g%22
The way it pans out, if you don't care about going back, if you don't
care how many years have passed on earth while you've experienced your time-dilated years, you can keep on accelerating. You get closer and closer to the speed of light, and your time dilation increases and increases. In the end, it means you can cross the whole galaxy in maybe twenty years of your time. Did you get that?
You travel 100,000 light years in twenty years. It means that whilst you can't actually travel faster than light, in a weird kind of cheaty way...
you can.