In a general astronomy class, the professor said that Andromeda, being 2 million light years from the Milky Way, would never be reached by humans. But it seems to me that we may be able to reach a significant fraction of light speed using technology like what was envisioned in the Orion project -- we would have to improve on Orion technology but the point is, near light speed does not seem out of the question.
If this is so, then with relativistic time-dilation, some brave astronauts would experience an arbitrary short amount of subjective time and so could reach Andromeda or even galaxies farther away than that. Given near light speed, is there any reason a spacecraft could not travel that far?
EDIT: I want to clarify that given the technology to reach the closest star in a reasonable length of time and return, it seems like we get any distance as a "free" side effect -- is that the case? I realize that the big difference is that while a trip at .99c to Alpha Centauri can even be in theory a roundtrip, to Andromeda the astronauts would know millions of years had passed on Earth so the return would probably not be undertaken but as far as reaching the nearest galaxy, that seems almost as feasible as reaching the nearest star.