Right, which is why many of the theoretical propulsion systems proposed for interstellar travel generally don’t involve the ship carrying its own fuel.
Besides solar sails, another theoretical interstellar propulsion system (introduced to me by science fiction writer Larry Niven) is the Bussard ramjet.
Note that the transmitter experiences the same thrust as as the receiver, which means it has to be counter-balanced to maintain orbit.
I’m probably missing something obvious, but why does the ship have to keep accelerating the whole way there? Couldn’t it stop accelerating once its reached 99 plus percent of the speed of light relative to its destination?
Sure you could. But as @Chronos pointed out in another thread, continuous acceleration increases the time dilation for the ship. The Andromeda Galaxy is 2.5 million light years away. So there’s no way to get there in a human lifetime without continuous acceleration.
(The amount of time dilation and duration of the trip as experienced by the crew of the ship is left as an exercise for the reader. 
Of course, to an outside observer here on Earth, the journey will take at least 2.5 million years.)
Depending on how you define ‘human lifetime’, it wouldn’t necessarily have to be continuous acceleration the entire way. But it would still be several years of 1g acceleration at a minimum to get close enough to c for sufficient time dilation.
But for the edge of the observable Universe? Yeah, that’s more like decades of 1g acceleration to get there within a normal human lifetime.
The other caveats about fuel ratio and engineering challenges still apply, of course, which should include the human physiological need for gravity, which a constant 1g acceleration would artificially provide.
Yep. With truly uniform acceleration, the time dilation can reach absurd values. The farther the destination, the more it matters.
It won’t feel that long to the accelerating travellers.
I mean, yeah, that’s a pleasant side effect, but if that’s your only reason for constant acceleration, there are much cheaper ways to get the same effect.
Hey, I’ll take it, as long as we’re ignoring only some but not all physically realistic constraints on space travel
It should be mentioned, by the way, that we know for sure that zero g is bad for humans: We’ve had lots of experience with lots of humans at 0 g, some of them for over a year at a time. But we don’t know how much gravity is necessary for health, since the longest any human has ever spent at any gravity between 0 and 1 is the few days the Apollo astronauts spent on the Moon. So maybe your starship only needs to maintain a fraction of a g.
Time again to mention Poul Anderson’s Tau Zero, which explores time dilation in spades.
Indeed! Larry Niven also had several stories that featured a Bussard ramjet that experienced extreme time dilation, but not to the extent of Tau Zero.
One of them (The Ethics of Madness from 1967) was a story about a murderer who tries to escape the consequences of his crimes by taking off in a Bussard ramjet, chased by a grieving relative of the deceased in another ship. The murderer can’t outrun the ship chasing him, so the two ships accelerate to extreme relativistic speeds toward the edge of the universe.
Of course, a real Bussard ramjet (assuming it’s fusion-powered and maximally efficient) couldn’t get to more than 0.12 c, due to the necessary drag force from collecting the hydrogen.
Which is still an impressive speed, of course, but relativistic effects are still small at that speed.
The perils of creating a setting in the 1960s that keeps being read into the 2020s.
Right from the start, it could have been anticipated that a ramscoop would produce drag, and everything needed to do the calculation of maximum speed derived therefrom was known in the 1960s.
I’d be more worried about the 5.7 GeV proton (hydrogen nuclei) flux being constantly encountered at .99c…
At some point in the acceleration, it might be possible to use the incoming particles to take X rays to help diagnose the cancers they are also causing.