Time dilation means that you can get anywhere while experiencing an arbitrarily small amount of time. You can cross the galaxy in a second as far as special relativity is concerned. (With the expenditure of insanely vast amounts of energy,
ofc.)
To an observer back home you'd look like you're travelling at merely extremely close to the speed of light, but to you the journey would take a second.
> You can cross the galaxy in a second as far as special relativity is concerned.
Sure, but the rest of the universe will keep on changing. In 90 billion years it’s going to be a very old universe. Galaxies will become consolidated and isolated, fewer young stars will be born. Only the dim light of red dwarf stars will shine among a graveyard of dead stars.
Tau-Zero by Poul Anderson explores this, BTW. It's a great little sci fi novel about a spaceship doomed to accelerate at 1G indefinitely.
It is significant
from a colonisation PoV. With sufficient acceleration capability and the ability to survive travelling through the interstellar medium at extreme velocity (rather than getting vaporised by a mote of dust), a single generation of humans could in theory colonise the whole galaxy within their own lifespans. Indeed, some of them could even come back together and meet again after visiting those distant worlds, on an Earth many millions of years older, if their worldlines end up with similar proper times.
The observable universe is ~93B LY - unless you're assuming FTL (and MUCH faster than light), I don't see how that's possible?