For a hard science fictional version of this, check out Poul Anderson’s “Tau Zero”, from 1970, according to Wikipedia. I read it a few years after that, and it

For a hard science fictional version of this, check out Poul Anderson’s “Tau Zero”, from 1970, according to Wikipedia. I read it a few years after that, and it’s stuck with me since. A ship with a Bussard ramjet runs into troubles and has to keep accelerating, into the far future.