For the comments saying we "just" need to maintain a 1G acceleration, should point out that as the ship approaches the speed of light, its mass increases [0].
And as the mass increases, so does the thrust required to maintain that acceleration. So that engine better be able to tap into some magical energy source, otherwise it can't maintain the acceleration at the higher speeds. :)
The last time I studied special relativity was a while ago, but I think your mass only increases in other frames of reference.
If, for example, we consider the speed of your ship from the point of view of someone left on earth, then your ship should appear heavier from that person's perspective as you accelerate. But from your point of view, you still weigh the same, and so does your ship. In fact, you would see earth going through the dramatic "weight gain".
Is the ship gaining mass (and shortening, and having its time slowed) in its own frame of reference? No, right? So wouldn't it be that the 1G acceleration from the viewpoint of the ship remains from the internal perspective, even though near the speed of light, more and more of that energy goes into higher mass and slower time?
I'm reading up again to refresh my relativity knowledge. Though:
> even though near the speed of light, more and more of that energy goes into higher mass and slower time?
This to me does not sound very different from saying the (relativistic) mass to be accelerated is larger, and is what's stopping a 1G (or any constant) acceleration to be maintained to bring the ship to the speed of light.
The concept may have been an overly simplified pedagogical tool though that I need to upgrade from. (I'll keep the comment chain intact since it's educational to me).
My (previously unexamined) assumption was that the slower time exactly offsets the lower acceleration in terms of speed gained, such that in the reference frame of the accelerating ship, experiments would continue to show 1G acceleration.
The "increasing mass" stuff is more to make it easier for calculations and learning (with imo terrible consequence to physical intuition) than an actual physical concept.
For the comments saying we "just" need to maintain a 1G acceleration, should point out that as the ship approaches the speed of light, its mass increases [0].
And as the mass increases, so does the thrust required to maintain that acceleration. So that engine better be able to tap into some magical energy source, otherwise it can't maintain the acceleration at the higher speeds. :)
[0] https://en.wikipedia.org/wiki/Mass_in_special_relativity#Rel...
Edit: this interpretation may not be entirely accurate (comments below).