Like it or not, we as a species are stuck here, likely forever.
Once humanity has had perhaps centuries of experience with orbital habitats then the idea of a large "generational" starship won't seem so unlikely. With functional fusion power and highly efficient recycling systems the ability to have an interstellar city ship which spends hundreds or thousands of years isolated from the rest of civilization may not seem so unlikely.
Also consider that interstellar space holds far more destinations than we have currently cataloged. Begin with a colony near a comet out in the deepths of the Oort cloud. Then make a hop to another comet, free roaming planet, brown dwarf, or red dwarf that is very likely to be within a single light year distant. At each destination repair, refuel, resupply and move on.
In a time span of only a fraction of the age of human civilization significant populations of humans will spread out from our Solar System and diffuse through interstellar space.
http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsi...
It would be unbelievably expensive right now however.
But give it a century or two and things could well change. If a space elevator was built it would slash the cost.
Constant 1g acceleration makes nearby galaxies accessible, nevermind nearby solar systems.
Returning from exploration? Reporting results? That isn't going to happen.
Colonizing the universe? There's nothing at all stopping it in physical law.
"Break physics" is relative -- things which can be allowed by the laws of physics can be so humanly implausible as to be useless to discuss.
I mean, let me just be totally clear about this. In relativity, to get your time dilation factor γ up, you need a lot of kinetic energy K. How much? Well E = γ m c² = m c² + K, so K = (γ − 1) m c².
If you wanted to go to the nearest galaxy -- which is 25,000 light years away on the other side of the Milky Way -- and you wanted to do it with any sort of vehicle in 25 years -- you would have to take along about 1000 times the mass of your vehicle as fuel. More importantly, whatever fuel you're using to accelerate you're also using to decelerate, so you actually need 1,000,000x fuel to start with, to get your 1,000x fuel up to speed for most of the journey. So your 10^5 kg shuttle orbiter would need to come with 10^8 kg slowdown fuel. That's what we're sending around, you've got to build the Great Pyramid at Giza out of antimatter and find a way to carry it with you, just to get the shuttle to do this in a reasonable time.
Now c² is about 10^17 J/kg so we need about 10^25 J to slow down, and to send this would require 10^28 J. For perspective, our largest nuclear blasts (Tsar Bomba's 50 megaton yield) are 2 * 10^17 J, so you'd need fifty million of those to launch. Or you could just carry the US with you, that has an annual power consumption of 10^22 J -- wait, make that a million copies of the United States, before you could launch.
Of course, antimatter is unstable and you might want to carry the Tsar Bomba around as a massive fuel source instead, but the Tsar Bomba actually only carried an energy yield of around 10^-4 m c², so you would need to have 10,000 times more mass (10 million space shuttles to decelerate your one) if you wanted to do it with nuclear bombs.
I appreciate you doing the mathematics, but you don't base it on the 1g acceleration I mentioned, as far as I can tell.
"You're sort of right -- since rapidities are linear in relativity one also has v/c = tanh(a t / c), γ = cosh(a t / c), and that's in principle an exponential growth, so if you can keep up a constant acceleration at this rate for 8 years, you could get to γ ~= 2,000. But here's why maintaining a constant acceleration for 8 years is pretty much totally unfeasible: getting a γ around 2,000 requires carrying 2,000 times as much fuel as spaceship."
At some point I edited this out to focus on that main point without editing out the quote at the front. Sorry if that's confusing.
You're way off, it requires much more than that. See my post.
If you're making a mathematical argument, be sure to do the math. Nothing's going to be receding at >exponential< speeds. (It would be nice if we could do that trick.)
to get around the diffraction limit you'd need an exponentially increasingly large collimation mechanism.
Yes, this gets pretty freaking huge. Robert Forward worked out the mathematics for this: http://en.wikipedia.org/wiki/Solar_sail#Interstellar_flight
Change targets to Proxima Centauri, use magsails to decelerate instead of jettisoning the outer mirror, and the power and lens requirements go down by a lot. I suppose your point would be that they remain freakishly huge. True, but if humanity continues to progress into the solar system, it should be feasible for the much larger and more advanced economy.
Yeah, my bad. Momentary loss of order-of-magnitude sense. Speed will go as t, distance as t^2, so solid angle subtended as t^-4. That's still pretty rapidly shrinking, though nowhere near exponential of course.
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.)