What still blows my mind is the fact that the Speed of Light is a constant. Meaning: if you're on a train moving a 0.9c, any light emitting from you will STILL travel at c in your reference frame, while at the same time an observer outside of the train will also see the beam of light travelling at c.

As for time dilation, it's a very simple formula called Lorentz Contraction: http://en.wikipedia.org/wiki/Length_contraction. At 0.99996c, you can cross the Milky Way (100,000 ly) in one year.

Consider this. It is impossible for matter to travel at the speed of light, yes? However, imagine a cannon on a train travelling (speed_of_light - 10 MPH). The cannon shoots a cannonball at 210 MPH. So when the cannon fires, you'd expect the cannonball to go (speed_of_light + 200 MPH), right? Well, no... matter cannot exceed the speed of light. What actually happens (afaik) is time itself is altered as one approaches the speed of light. So the closer you are to the speed of light, the more time is altered.

I don't know any of the details though.

Not only that, but you could go 2M ly in less than 30 years (ship time), at 1g acceleration. http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.h... for more.

Yes, it is. At light speed, time dilation brings the high-speed observer to see the trip as instantaneous : http://en.wikipedia.org/wiki/File:Time_dilation.svg

You can choose ANY time dilation factor and determine a velocity accordingly, because the graph is asymptotic and continuous.

[EDIT: I mean, obviously, the whole thing breaks down with an observer actually AT light speed; assume above that I'm talking about taking limits of the Lorentz factor as velocity approaches 1]

I don't know, but the Wikipedia article claims that "a constant 1 g acceleration would permit humans to travel as far as light has been able to travel since the big bang (some 13.7 billion light years)".

So I would guess, hell, yes!

(I recommend "The Forever War" by Joe Haldeman for serious time dilation fun.)