Actually, even if space is Euclidean, the effects of special relativity still mean that we can expand exponentially (for as long as we’re able to maintain some constant amount of acceleration in any direction we choose, that is).
I’m curious what would be the requirements in terms of energy and mass to maintain this motion under special relativity. In Newtonian physics, constant acceleration of a constant mass requires power increasing linearly with time—are things substantially different under SR? Also, even if free energy is somehow given, is it possible to maintain constant acceleration without constantly losing mass in the other direction due to momentum conservation (assuming you’re not moving along infinite-mass rails of some sort)?
Well, the amount of energy needed seems to be linear in the Lorentz factor, which is rate of change of co-ordinate time with respect to proper time. But the latter is increasing exponentially, so I think you need power increasing exponentially with time to maintain constant acceleration.
Also, even if free energy is somehow given, is it possible to maintain constant acceleration without constantly losing mass in the other direction due to momentum conservation (assuming you’re not moving along infinite-mass rails of some sort)?
No—you’d need to somehow keep on propelling yourself. I suppose in theory you could harvest forward momentum from any stars and galaxies you meet, no matter how rapidly you’re whizzing past them. That’s what’s going to need exponentially increasing power.
I’m curious what would be the requirements in terms of energy and mass to maintain this motion under special relativity. In Newtonian physics, constant acceleration of a constant mass requires power increasing linearly with time—are things substantially different under SR? Also, even if free energy is somehow given, is it possible to maintain constant acceleration without constantly losing mass in the other direction due to momentum conservation (assuming you’re not moving along infinite-mass rails of some sort)?
Well, the amount of energy needed seems to be linear in the Lorentz factor, which is rate of change of co-ordinate time with respect to proper time. But the latter is increasing exponentially, so I think you need power increasing exponentially with time to maintain constant acceleration.
No—you’d need to somehow keep on propelling yourself. I suppose in theory you could harvest forward momentum from any stars and galaxies you meet, no matter how rapidly you’re whizzing past them. That’s what’s going to need exponentially increasing power.
(Somehow I don’t think this is going to work!)