5 ms·

This is remarkably negative. There are a number of ways to explore without having to break physics. Constant 1g acceleration makes nearby galaxies accessible,

This is remarkably negative. There are a number of ways to explore without having to break physics. 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.

drostie 15y ago
Constant 1g acceleration makes nearby galaxies accessible, nevermind nearby solar systems. "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.
- hahainternet 15y ago
  The reason I mentioned no returning of data is that it obviously is not plausible within 25 years. I appreciate you doing the mathematics, but you don't base it on the 1g acceleration I mentioned, as far as I can tell.
  - drostie 15y ago
    Yeah, sorry if that was misleading. I wrote something to this effect and then pulled it out: "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.
    - lutorm 15y ago
      getting a γ around 2,000 requires carrying 2,000 times as much fuel as spaceship. You're way off, it requires much more than that. See my post.
      - drostie 15y ago
        Well, I'm stating a basic constraint of physics: you have to carry around this much energy and it will require this much mass. You're making a certain assumption about the kind of engine and its exhaust velocity, and finding that there's a problem with low exhaust velocities. That's mostly correct, but in principle there are probably fuel sources which could achieve an exhaust velocity near c -- I'm thinking in particular if you were carrying matter and antimatter, and annihilated them in an ultrahigh-Q cavity with a small aperture to let the light out in only one direction -- or some really crazy futuristic application of lasing. You will still not get better than carrying thousands of times the mass of your spaceship for the deceleration phase, due to a basic constraint of physics.
lutorm 15y ago
Except that constant 1g acceleration is totally infeasible.
- hahainternet 15y ago
  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.
  - lutorm 15y ago
    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.)

drostie 15y ago

Constant 1g acceleration makes nearby galaxies accessible, nevermind nearby solar systems. "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.

hahainternet 15y ago
The reason I mentioned no returning of data is that it obviously is not plausible within 25 years. I appreciate you doing the mathematics, but you don't base it on the 1g acceleration I mentioned, as far as I can tell.
- drostie 15y ago
  Yeah, sorry if that was misleading. I wrote something to this effect and then pulled it out: "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.
  - lutorm 15y ago
    getting a γ around 2,000 requires carrying 2,000 times as much fuel as spaceship. You're way off, it requires much more than that. See my post.
    - drostie 15y ago
      Well, I'm stating a basic constraint of physics: you have to carry around this much energy and it will require this much mass. You're making a certain assumption about the kind of engine and its exhaust velocity, and finding that there's a problem with low exhaust velocities. That's mostly correct, but in principle there are probably fuel sources which could achieve an exhaust velocity near c -- I'm thinking in particular if you were carrying matter and antimatter, and annihilated them in an ultrahigh-Q cavity with a small aperture to let the light out in only one direction -- or some really crazy futuristic application of lasing. You will still not get better than carrying thousands of times the mass of your spaceship for the deceleration phase, due to a basic constraint of physics.

lutorm 15y ago

Except that constant 1g acceleration is totally infeasible.

hahainternet 15y ago
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.
- lutorm 15y ago
  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.)