It currently is, but there's no suggestion that it 'breaks physics'. Even resorting to generation ships, there's nothing in physical law that prevents colonization of the universe.

That's not really true. Even if you have infinite time, you can't sustain 1g indefinitely without infinite amounts of fuel. You're still subject to the rocket equation, so even without the problem of relativistic mass increase the amount of fuel you have to carry scales exponentially with your final velocity.

I would think HN readers would appreciate the futility of scaling up using algorithms that go as O(exp(N)) even if there's nothing in principle that says it won't work. Just saying "we'll wait until the computers are fast enough" is not going to work. Plus, when it comes to rockets, you're much more bound by practical constraints.

Just as an order of magnitude exercise: Suppose you want to accelerate with a super-efficient ion thruster with 16km/s exhaust velocity. To get 1km/s, you need 6% fuel. 10km/s: 87%. 100km/s: a fuel of 518times the payload. 1000km/s: 1e27 times the payload. For comparison, that means to accelerate a ton to that speed, you need a fuel amount equal to the mass of the Sun. (And at that speed, it would still take a millenium to go a parsec. Space is really effing big.)