Could we build a starship using current technology?

[jeff_wilson]

Originally Posted by Humabout

For what it's worth, accelerating that much for that long would run headlong into relativistic effects that would sap all efficiency. After three or four months, you'll probably be going plenty fast enough to achieve your goal, and without using up nearly so much fuel.
[...]

This is not correct; the mass of the ship remains constant wrt itself, regardless.