Originally Posted by Rock Chalk
The anti-matter is the key and the mathematics is not only possible but, given a sufficient amount of anti-matter, are likely.
With an "endless" supply of anti-matter, or the ability to create it on the go from galactic "debris" or whatever, one could accelerate a spaceship indefinitely. Never reaching the speed of light but continuing to incrementally get closer to it (99.9%, 99.99%, 99.999%). Mathematically, accelerating this way one could travel the ENTIRE universe in roughly 12 local years (relativistic effects would mean quadrillions of years on Earth, closer to the speed of light you get, slower time moves for you locally though). Acceleration at 1G, which solves the lack of gravity issue.
Anyone who said "No, Mathematically impossible" sould read this post. However, the amount of time passage outside the ship would be a problem.