[gradschool]

If the ship's means of propulsion is set to impart a constant force, then I understand that the passengers could experience a constant acceleration indefinitely, but that constant acceleration would be with respect to the ship's reference frame, not ours. A constant acceleration of 1g in our reference frame would mean by definition that the speed reaches 2c in two years, which can't be right. Subject again to the disclaimer that I'm not a physicist and haven't done the math, the only outcome I can picture is that in our reference frame the speed asymptotically approaches c in some interesting way.

[methodover]

Oh I see! 1G from our reference frame! Fascinating! That’s a perspective I haven’t seen before, I didn’t realize that that’s what you meant. Indeed, it isn’t possible. We’d see the ship slowly approach but never reach the speed of light, no matter how hard or long they step on the accelerator.