Relativistic Rockets?

Question

How much time would pass in a rocket from here to Alpha Centaury where the occupants experience 1G of acceleration up and 1G of acceleration down?

Answer 1

Around 4 years. About 5.5 years as measured from the outside.
In each of the first and last years they'd go about half a light year, and most of a light year per year in the middle.
The first years are the longest. They could get across the galaxy in 20 years or so.

Answer 2

Not much. Time would slow down to a stop. Actually it is not possible to have a constant acceleration up to the speed of light.