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.
I don't think rockets are feasible for interstellar travel for the reasons you state. Beamed propulsion is probably the way to accelerate. Magsails can be used for deceleration. This gets around the nastiness of the rocket equation.
Beamed propulsion gets around the rocket equation, but trying to beam energy to something receding at exponential speeds doesn't sound that much easier. It would pose an exponentially decreasing target, so to get around the diffraction limit you'd need an exponentially increasingly large collimation mechanism.
Beamed propulsion gets around the rocket equation, but trying to beam energy to something receding at exponential speeds doesn't sound that much easier.
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.
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.
be sure to do the math. Nothing's going to be receding at >exponential< speeds
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.
Well that'd be a nice thing about relativity: from the point of view of the beamer, of course they're receding at a constant distance and their surface area decays like 1/t^2. ^_^
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.
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.
"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.