If you can convince me the colonization speed is definitely >0.9c, I agree this question is moot. I’m currently putting significantly probability on <2/3 c speed.
The numbers are in the paper (including intergalactic dust). Allowing nuclear fusion reaches 80%c no problem. The most distant galaxies can be colonised at 99%c, because the Hubble drag means you don’t have to decelerate much—it’s deceleration that’s the problem.
Now, if you’re allowed to go beyond the very conservative assumptions of our paper, you can do a lot more to decelerate—for example, sucking in hydrogen from space to fuel your deceleration. Or you could use more way-points: not aim directly for each galaxy, but for one galaxy in each super-cluster. Or aim for nearby galaxies to construct a massive second wave.
Do you want me to summarise the paper here, or do you prefer to read it?
PS: the article was peer reviewed and published in Acta Astronautica, if that’s relevant to your assessment.
I like the calculations in the paper. I don’t see how to get high confidence about colonization speeds getting close to c, rather than e.g. retaining 10% on colonization at <2/3c and 30% on <0.9c. It seems to me like a priori we have a reasonable chance that colonization occurs near c. The calculation in the paper pushes it further, by addressing a few possible defeaters (esp. slowing down, dust), but doesn’t seem decisive since there are likely unanticipated difficulties. (Anders also gave guesstimates in line with this intuition in private correspondence, so it’s not just me here.)
I believe you can get better-than-fusion densities, so that slowing down probably isn’t a bottleneck.
(I’m not sure I understand your remarks about hubble drag though. The goal is getting to the destination quickly, doesn’t that mean we need to be traveling near c for the entire trip? Can’t afford to slow down to 0.5c for the second half, or else your average speed is < 2/3c...)
The Hubble drag means that for the most distant galaxies, you can launch at 99%c and arrive with almost null velocity. If you prioritise speed (rather than distance) the best strategy would be to wait till the Hubble drag has reduced (co-moving) velocity to about 80%c, decelerate, Dyson a star, and then re-launch at 99%c. Dysoning and re-launch take a decade or two at most, so that barely changes the average speed.
The reason I feel that defeaters will not be an issue (apart from dust), is because of the huge margin this method has. Launching ten thousand times more probes is very doable. Operating in a series of short hops from galaxy to galaxy, is also doable. Sending ten thousand mini probes to accompany the payload probe is also doable (these mini probes would not decelerate, they would just backup the payload’s data and check it as we arrived to a destination; or they might replace the payload probe if this one had been damaged). Eric Drexler has many ideas to make the process much more efficient; it seems that using a gun rather than a rocket to decelerate is a better idea.
But the whole setup does require some form of automation/weak AI assumptions. Without those, then this become slower/less likely.
I need to talk with Anders about these other defeaters :-)
Overall I still think that you can’t get to >90% confidence of >0.9c colonization speed (our understanding of physics/cosmology just doesn’t seem high enough to get to those confidences), but I agree with you that my initial estimate was too pessimistic about fast colonization and it’s pretty unlikely that colonization is slow enough for this question to matter.
If you assume that Dysoning and re-launch take 500 years, this barely changes the speed either, so you are very robust.
I’d be interested in more exploration of deceleration strategies. It seems obvious that braking against the interstellar medium (either dust or magnetic field) is viable to some large degree; at the very least if you are willing to eat a 10k year deceleration phase. I have taken a look at the two papers you linked in your bibliography, but would prefer a more systematic study. Important is: Do we know ways that are definitely not harder than building a dyson swarm, and is one galaxy’s width (along smallest dimension) enough to decelerate? Or is the intergalactic medium dense enough for meaningful deceleration?
I would also be interested in a more systematic study of acceleration strategies. Your arguments absolutely rely on circumventing the rocket equation for acceleration; break this assumption, and your argument dies.
It does not appear obvious to me that this is possible: Say, coil guns would need a ridiculously long barrel and mass, or would be difficult to maneuver (you want to point the coil gun at all parts of the sky). Or, say, laser acceleration turns out to be very hard because of (1) lasers are fundamentally inefficient (high thermal losses), and cannot be made efficient if you want very tight beams and (2) cooling requirement for the probes during acceleration turn out to be unreasonable. [*]
I could imagine a world where you need to fall back to the rocket equation for a large part of the acceleration delta-v, even if you are a technologically mature superintelligence with dyson swarm. Your paper does not convince me that such a world is impossble (and it tries to convince me that hypothetical worlds are impossible, where it would be hard to rapidly colonize the entire universe if you have reasonably-general AI).
Obviously both points are running counter to each other: If braking against the interstellar medium allows you to get the delta-v for deceleration down to 0.05 c from, say 0.9 c, but acceleration turns out to be so hard that you need to get 0.8 c with rockets (you can only do 0.1c with coil guns / lasers, instead of 0.9 c), then we have not really changed the delta-v calculus; but we have significantly changed the amount of available matter for shielding during the voyage (we now need to burn most of the mass during acceleration instead of deceleration, which means that we are lighter during the long voyage).
[*] Superconductors can only support a limited amount of current / field-strength. This limits the acceleration. Hence, if you want larger delta-v, you need a longer barrel. How long, if you take the best known superconductors? At which fraction of your launch probe consisting of superconducting coils, instead of fusion fuel? Someone must do all these calculations, and then discuss how the resulting coil gun is still low-enough mass compared to the mass of a dyson swarm, and how to stabilize, power, cool and maneuver this gun. Otherwise, the argument is not convincing.
edit: If someone proposes a rigid barrel that is one light-hour long then I will call BS.
Thanks, those are some good points. I feel that the laser acceleration option is the most viable in theory, because the solar sail or whatever is used does not need to be connected to the probe via something that transmits a lot of heat. I remember Anders vaguely calculating the amount of dispersion of a laser up to half a light-year, and finding it acceptable, but we’ll probably have to do the exercise again.
I would not fret too much about slight overheating of the payload; most of the launch mass is propulsion fuel anyway, and in worst-case the payload can rendezvous with the fuel in-flight, after the fuel has cooled down.
I would be very afraid of the launch mass, including solar sail / reflector loosing (1) reflectivity (you need a very good mirror that continues to be a good mirror when hot; imperfections will heat it) and (2) structural integrity.
I would guess that, even assuming technological maturity (can do anything that physics permits), you cannot keep structural integrity above, say, 3000K, for a launch mass that is mostly hydrogen. I think that this is still icy cold, compared to the power output you want.
So someone would need to come up with either
1. amazing schemes for radiative heat-dissipation and heat pumping (cannot use evaporative cooling, would cost mass),
2. something weird like a plasma mirror (very hot plasma contained by magnetic fields; this would be hit by the laser, which pushes it via radiation pressure and heats it; momentum is transferred from plasma to launch probe via magnetic field; must not loose too many particles, and might need to maintain a temperature gradient so that most radiation is emitted away from the probe; not sure whether you can use dynamo flow to extract energy from the plasma in order to run heat pumps, because the plasma will radiate a lot of energy in direction of the probe),
3. show that limiting the power so that the sail has relatively low equilibrium temperature allows for enough transmission of momentum.
No 3 would be the simplest and most convincing answer.
I am not sure whether a plasma mirror is even thermo-dynamically possible. I am not sure whether sufficient heat-pumps plus radiators are “speculative engineering”-possible, if you have a contraption where your laser pushes against a shiny surface (necessitating very good focus of the laser). If you have a large solar sail (high surface, low mass) connected by tethers, then you probably cannot use active cooling on the sail; therefore there is limited room for fancy future-tech engineering, and we should be able to compute some limits now.
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Since I already started raising objections to your paper, I’ll raise a second point: You compute the required launch mass from rocket-equation times final payload, with the final payload having very low weight. This assumes that you can actually build such a tiny rocket! While I am willing to suspend disbelieve and assume that a super efficient fusion-powered rocket of 500 tons might be built, I am more skeptical if your rocket, including fusion reactor but excluding fuel, is limited to 30 gram of weight.
Or did I miss something? While this would affect your argument, my heart is not really in it: Braking against the interstellar medium appears, to me, to circumvent a lot of problems.
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Because I forgot and you know your paper better than me: Do any implicit or explicit assumptions break if we lose access to most of the fuel mass for shielding during the long voyage?
If you could answer with a confident “no, our assumptions do not beak when cannot use the deceleration fuel as shielding”, then we can really trade-off acceleration delta-v against deceleration delta-v, and I stay much more convinced about your greater point about the Fermi paradox.
Thanks for these critiques! They are useful to hear and think about.
> I think that this is still icy cold, compared to the power output you want.
I think it’s not so much the power, but the range of the laser. If the target is large enough that a laser can hit it over distance of light years, for example, then we can get away with mild radiation pressure for a long time (eg a few years). But I haven’t run the numbers yet.
>I am more skeptical if your rocket, including fusion reactor but excluding fuel, is limited to 30 gram of weight.
I was imagining a sort of staged rocket, where you ejected the casing of the previous rockets as you slow, so that the mass of the rocket was always a small fraction of the mass of the fuel.
But Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
>Do any implicit or explicit assumptions break if we lose access to most of the fuel mass for shielding during the long voyage?
We didn’t do the shielding very well, just arbitrarily assumed that impacts less energetic than a grenade could be repaired/ignored, and that anything larger would destroy the probe entirely.
As usual, Eric Drexler had a lot of fun shielding ideas (eg large masses ahead of the probe to inonise incoming matter and permanent electromagnetic fields to deflect them), but these were too “speculative” to include in our “conservative” paper.
>I was imagining a sort of staged rocket, where you ejected the casing of the previous rockets as you slow, so that the mass of the rocket was always a small fraction of the mass of the fuel.
Of course, but your very last stage is still a rocket with a reactor. And if you cannot build a rocket with 30g motor+reactor weight, then you cannot go to such small stages and your final mass on arrival includes the smallest efficient rocket motor / reactor you can build, zero fuel, and a velocity that is below escape velocity of your target solar system (once you are below escape velocity I’ll grant you maneuvers with zero mass cost, using solar sails; regardless, tiny solar-powered ion-drives appear reasonable, but generate not enough thrust to slow down from relativistic to below-escape in the time-frame before you have passed though your target system).
>But Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
That does solve the “cannot build a small motor” argument, potentially at the cost of some inefficiency.
It still obeys the rocket equation. The rocket equation is like the 2nd law of thermodynamics: It is not something you can trick by clever calculations. It applies for all propulsion systems that work in a vacuum.
You can only evade the rocket equation by finding (non-vacuum) stuff to push against; whether it be the air in the atmosphere (airplane or ramjet is more efficient than rocket!), the solar system (gigantic launch contraption), various planets (gravitational slingshot), the cosmic microwave background, the solar wind, or the interstellar medium. Once you have found something, you have three choices: Either you want to increase relative velocity and expend energy (airplane, ramjet), or you want to decrease relative velocities (air-braking, use of drag/friction, solar sails when trying to go with the solar wind, braking against the interstellar medium, etc), or you want an elastic collision, e.g. keep absolute relative velocity the same but reverse direction (gravitational slingshot).
Slingshots are cool because you extract energy from the fact that the planets have different velocities: Having multiple planets is not thermodynamic ground state, so you steal from the potential energy / negative entropy left over from the formation of the solar system. Alas, slingshots can’t bring you too much above escape velocity, nor slow you down to below escape if you are significantly faster.
Edit: probably stupid idea, wasn’t thinking straight <strike> Someone should tell me whether you can reach relativistic speeds by slingshotting in a binary or trinary of black holes. That would be quite elegant (unbounded escape velocity, yay! But you have time dilation when close to the horizon, so unclear whether this takes too long from the viewpoint of outside observers; also, too large shear will pull you apart).</strike>
edit2: You can afaik also push against a curved background space-time, if you have one. Gravity waves technically count as vacuum, but not for the purpose of the rocket equation. Doesn’t help, though, because space-time is pretty flat out there, not just Ricci-flat (=vacuum).
That’s what I used to believe. But now, on closer analysis, it seems that it doesn’t. The rocket equation holds when you are continuously ejecting a thin stream of mass; it doesn’t hold when you are ejecting a large amount of mass all at once, or transferring energy to a large amount of mass.
The thought experiment that convinced me of this: assume you have a gun with two barrels; you start at rest, and use the gun to propel yourself (ignore issues of torque and tumble). If you shoot both barrels at once, that’s two bullets, each of mass m, and each of velocity v. But now assume that you shoot one bullet, then the other. The first is of mass m and velocity v, as before. But now the gun is moving at some velocity v’. The second bullet will have mass m, but will be shot with velocity v-v’. Thus the momentum of the two bullets is lower in the second case; thus the forward momentum of the gun is also lower in that case.
(The more bullets you shoot, and the smaller they are, the more the gun equations start to resemble the rocket equation).
But when you eject the payload and blast it with a laser beam, you’re essentially just doing one shot (though one extended over a long time, so that the payload doesn’t have huge acceleration). It’s not *exactly* the same as a one shot, because the laser itself will accelerate a bit, because of the beam. But it you assume that, say, the laser is a 100 times more massive than the payload, then the gain in velocity of the laser will be insignificant compared with the deceleration of the payload—it’s essentially a single shot, extended over a period of time. And a laser/payload ratio of 100 is way below what the rocket equation would imply.
If you disbelieve in 30g fusion reactors and set a minimum viable weight of 500t for an efficient propulsion system (plus negligible weight for replicators) then you get an additional factor of 1e7.
Combining both for fusion at 0.8c would give you a factor of 5e12, which is significantly larger than the factor between “single solar system” and “entire galaxy”. These are totally pessimistic assumptions, though: Deceleration probably can be done cheaper, and with lower minimal mass for efficient propulsion systems. And you almost surely can cut off quite a bit of rocket-delta-v on acceleration (Stuart assumed you can cut 100% on acceleration and 0% on deceleration; the above numbers assumed you can cut 0% on acceleration and 0% on deceleration).
Also, as Stuart noted, you don’t need to aim at every reachable galaxy, you can aim at every cluster and spread from there.
So, I’m not arguing with Stuart’s greater claim (which is a really nice point!), I’m just arguing about local validity of his arguments and assumptions.
Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
(if the probe is very robust, we might be able to railgun it instead of using a laser—and railgunning a single mass, once is clearly not subject to the rocket equation).
If you can convince me the colonization speed is definitely >0.9c, I agree this question is moot. I’m currently putting significantly probability on <2/3 c speed.
The numbers are in the paper (including intergalactic dust). Allowing nuclear fusion reaches 80%c no problem. The most distant galaxies can be colonised at 99%c, because the Hubble drag means you don’t have to decelerate much—it’s deceleration that’s the problem.
Now, if you’re allowed to go beyond the very conservative assumptions of our paper, you can do a lot more to decelerate—for example, sucking in hydrogen from space to fuel your deceleration. Or you could use more way-points: not aim directly for each galaxy, but for one galaxy in each super-cluster. Or aim for nearby galaxies to construct a massive second wave.
Do you want me to summarise the paper here, or do you prefer to read it?
PS: the article was peer reviewed and published in Acta Astronautica, if that’s relevant to your assessment.
I like the calculations in the paper. I don’t see how to get high confidence about colonization speeds getting close to c, rather than e.g. retaining 10% on colonization at <2/3c and 30% on <0.9c. It seems to me like a priori we have a reasonable chance that colonization occurs near c. The calculation in the paper pushes it further, by addressing a few possible defeaters (esp. slowing down, dust), but doesn’t seem decisive since there are likely unanticipated difficulties. (Anders also gave guesstimates in line with this intuition in private correspondence, so it’s not just me here.)
I believe you can get better-than-fusion densities, so that slowing down probably isn’t a bottleneck.
(I’m not sure I understand your remarks about hubble drag though. The goal is getting to the destination quickly, doesn’t that mean we need to be traveling near c for the entire trip? Can’t afford to slow down to 0.5c for the second half, or else your average speed is < 2/3c...)
The Hubble drag means that for the most distant galaxies, you can launch at 99%c and arrive with almost null velocity. If you prioritise speed (rather than distance) the best strategy would be to wait till the Hubble drag has reduced (co-moving) velocity to about 80%c, decelerate, Dyson a star, and then re-launch at 99%c. Dysoning and re-launch take a decade or two at most, so that barely changes the average speed.
The reason I feel that defeaters will not be an issue (apart from dust), is because of the huge margin this method has. Launching ten thousand times more probes is very doable. Operating in a series of short hops from galaxy to galaxy, is also doable. Sending ten thousand mini probes to accompany the payload probe is also doable (these mini probes would not decelerate, they would just backup the payload’s data and check it as we arrived to a destination; or they might replace the payload probe if this one had been damaged). Eric Drexler has many ideas to make the process much more efficient; it seems that using a gun rather than a rocket to decelerate is a better idea.
But the whole setup does require some form of automation/weak AI assumptions. Without those, then this become slower/less likely.
I need to talk with Anders about these other defeaters :-)
Overall I still think that you can’t get to >90% confidence of >0.9c colonization speed (our understanding of physics/cosmology just doesn’t seem high enough to get to those confidences), but I agree with you that my initial estimate was too pessimistic about fast colonization and it’s pretty unlikely that colonization is slow enough for this question to matter.
If you assume that Dysoning and re-launch take 500 years, this barely changes the speed either, so you are very robust.
I’d be interested in more exploration of deceleration strategies. It seems obvious that braking against the interstellar medium (either dust or magnetic field) is viable to some large degree; at the very least if you are willing to eat a 10k year deceleration phase. I have taken a look at the two papers you linked in your bibliography, but would prefer a more systematic study. Important is: Do we know ways that are definitely not harder than building a dyson swarm, and is one galaxy’s width (along smallest dimension) enough to decelerate? Or is the intergalactic medium dense enough for meaningful deceleration?
I would also be interested in a more systematic study of acceleration strategies. Your arguments absolutely rely on circumventing the rocket equation for acceleration; break this assumption, and your argument dies.
It does not appear obvious to me that this is possible: Say, coil guns would need a ridiculously long barrel and mass, or would be difficult to maneuver (you want to point the coil gun at all parts of the sky). Or, say, laser acceleration turns out to be very hard because of (1) lasers are fundamentally inefficient (high thermal losses), and cannot be made efficient if you want very tight beams and (2) cooling requirement for the probes during acceleration turn out to be unreasonable. [*]
I could imagine a world where you need to fall back to the rocket equation for a large part of the acceleration delta-v, even if you are a technologically mature superintelligence with dyson swarm. Your paper does not convince me that such a world is impossble (and it tries to convince me that hypothetical worlds are impossible, where it would be hard to rapidly colonize the entire universe if you have reasonably-general AI).
Obviously both points are running counter to each other: If braking against the interstellar medium allows you to get the delta-v for deceleration down to 0.05 c from, say 0.9 c, but acceleration turns out to be so hard that you need to get 0.8 c with rockets (you can only do 0.1c with coil guns / lasers, instead of 0.9 c), then we have not really changed the delta-v calculus; but we have significantly changed the amount of available matter for shielding during the voyage (we now need to burn most of the mass during acceleration instead of deceleration, which means that we are lighter during the long voyage).
[*] Superconductors can only support a limited amount of current / field-strength. This limits the acceleration. Hence, if you want larger delta-v, you need a longer barrel. How long, if you take the best known superconductors? At which fraction of your launch probe consisting of superconducting coils, instead of fusion fuel? Someone must do all these calculations, and then discuss how the resulting coil gun is still low-enough mass compared to the mass of a dyson swarm, and how to stabilize, power, cool and maneuver this gun. Otherwise, the argument is not convincing.
edit: If someone proposes a rigid barrel that is one light-hour long then I will call BS.
Thanks, those are some good points. I feel that the laser acceleration option is the most viable in theory, because the solar sail or whatever is used does not need to be connected to the probe via something that transmits a lot of heat. I remember Anders vaguely calculating the amount of dispersion of a laser up to half a light-year, and finding it acceptable, but we’ll probably have to do the exercise again.
I would not fret too much about slight overheating of the payload; most of the launch mass is propulsion fuel anyway, and in worst-case the payload can rendezvous with the fuel in-flight, after the fuel has cooled down.
I would be very afraid of the launch mass, including solar sail / reflector loosing (1) reflectivity (you need a very good mirror that continues to be a good mirror when hot; imperfections will heat it) and (2) structural integrity.
I would guess that, even assuming technological maturity (can do anything that physics permits), you cannot keep structural integrity above, say, 3000K, for a launch mass that is mostly hydrogen. I think that this is still icy cold, compared to the power output you want.
So someone would need to come up with either
1. amazing schemes for radiative heat-dissipation and heat pumping (cannot use evaporative cooling, would cost mass),
2. something weird like a plasma mirror (very hot plasma contained by magnetic fields; this would be hit by the laser, which pushes it via radiation pressure and heats it; momentum is transferred from plasma to launch probe via magnetic field; must not loose too many particles, and might need to maintain a temperature gradient so that most radiation is emitted away from the probe; not sure whether you can use dynamo flow to extract energy from the plasma in order to run heat pumps, because the plasma will radiate a lot of energy in direction of the probe),
3. show that limiting the power so that the sail has relatively low equilibrium temperature allows for enough transmission of momentum.
No 3 would be the simplest and most convincing answer.
I am not sure whether a plasma mirror is even thermo-dynamically possible. I am not sure whether sufficient heat-pumps plus radiators are “speculative engineering”-possible, if you have a contraption where your laser pushes against a shiny surface (necessitating very good focus of the laser). If you have a large solar sail (high surface, low mass) connected by tethers, then you probably cannot use active cooling on the sail; therefore there is limited room for fancy future-tech engineering, and we should be able to compute some limits now.
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Since I already started raising objections to your paper, I’ll raise a second point: You compute the required launch mass from rocket-equation times final payload, with the final payload having very low weight. This assumes that you can actually build such a tiny rocket! While I am willing to suspend disbelieve and assume that a super efficient fusion-powered rocket of 500 tons might be built, I am more skeptical if your rocket, including fusion reactor but excluding fuel, is limited to 30 gram of weight.
Or did I miss something? While this would affect your argument, my heart is not really in it: Braking against the interstellar medium appears, to me, to circumvent a lot of problems.
---------------------
Because I forgot and you know your paper better than me: Do any implicit or explicit assumptions break if we lose access to most of the fuel mass for shielding during the long voyage?
If you could answer with a confident “no, our assumptions do not beak when cannot use the deceleration fuel as shielding”, then we can really trade-off acceleration delta-v against deceleration delta-v, and I stay much more convinced about your greater point about the Fermi paradox.
Thanks for these critiques! They are useful to hear and think about.
> I think that this is still icy cold, compared to the power output you want.
I think it’s not so much the power, but the range of the laser. If the target is large enough that a laser can hit it over distance of light years, for example, then we can get away with mild radiation pressure for a long time (eg a few years). But I haven’t run the numbers yet.
>I am more skeptical if your rocket, including fusion reactor but excluding fuel, is limited to 30 gram of weight.
I was imagining a sort of staged rocket, where you ejected the casing of the previous rockets as you slow, so that the mass of the rocket was always a small fraction of the mass of the fuel.
But Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
>Do any implicit or explicit assumptions break if we lose access to most of the fuel mass for shielding during the long voyage?
We didn’t do the shielding very well, just arbitrarily assumed that impacts less energetic than a grenade could be repaired/ignored, and that anything larger would destroy the probe entirely.
As usual, Eric Drexler had a lot of fun shielding ideas (eg large masses ahead of the probe to inonise incoming matter and permanent electromagnetic fields to deflect them), but these were too “speculative” to include in our “conservative” paper.
>I was imagining a sort of staged rocket, where you ejected the casing of the previous rockets as you slow, so that the mass of the rocket was always a small fraction of the mass of the fuel.
Of course, but your very last stage is still a rocket with a reactor. And if you cannot build a rocket with 30g motor+reactor weight, then you cannot go to such small stages and your final mass on arrival includes the smallest efficient rocket motor / reactor you can build, zero fuel, and a velocity that is below escape velocity of your target solar system (once you are below escape velocity I’ll grant you maneuvers with zero mass cost, using solar sails; regardless, tiny solar-powered ion-drives appear reasonable, but generate not enough thrust to slow down from relativistic to below-escape in the time-frame before you have passed though your target system).
>But Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
That does solve the “cannot build a small motor” argument, potentially at the cost of some inefficiency.
It still obeys the rocket equation. The rocket equation is like the 2nd law of thermodynamics: It is not something you can trick by clever calculations. It applies for all propulsion systems that work in a vacuum.
You can only evade the rocket equation by finding (non-vacuum) stuff to push against; whether it be the air in the atmosphere (airplane or ramjet is more efficient than rocket!), the solar system (gigantic launch contraption), various planets (gravitational slingshot), the cosmic microwave background, the solar wind, or the interstellar medium. Once you have found something, you have three choices: Either you want to increase relative velocity and expend energy (airplane, ramjet), or you want to decrease relative velocities (air-braking, use of drag/friction, solar sails when trying to go with the solar wind, braking against the interstellar medium, etc), or you want an elastic collision, e.g. keep absolute relative velocity the same but reverse direction (gravitational slingshot).
Slingshots are cool because you extract energy from the fact that the planets have different velocities: Having multiple planets is not thermodynamic ground state, so you steal from the potential energy / negative entropy left over from the formation of the solar system. Alas, slingshots can’t bring you too much above escape velocity, nor slow you down to below escape if you are significantly faster.
Edit: probably stupid idea, wasn’t thinking straight <strike> Someone should tell me whether you can reach relativistic speeds by slingshotting in a binary or trinary of black holes. That would be quite elegant (unbounded escape velocity, yay! But you have time dilation when close to the horizon, so unclear whether this takes too long from the viewpoint of outside observers; also, too large shear will pull you apart).</strike>
edit2: You can afaik also push against a curved background space-time, if you have one. Gravity waves technically count as vacuum, but not for the purpose of the rocket equation. Doesn’t help, though, because space-time is pretty flat out there, not just Ricci-flat (=vacuum).
>It still obeys the rocket equation.
That’s what I used to believe. But now, on closer analysis, it seems that it doesn’t. The rocket equation holds when you are continuously ejecting a thin stream of mass; it doesn’t hold when you are ejecting a large amount of mass all at once, or transferring energy to a large amount of mass.
The thought experiment that convinced me of this: assume you have a gun with two barrels; you start at rest, and use the gun to propel yourself (ignore issues of torque and tumble). If you shoot both barrels at once, that’s two bullets, each of mass m, and each of velocity v. But now assume that you shoot one bullet, then the other. The first is of mass m and velocity v, as before. But now the gun is moving at some velocity v’. The second bullet will have mass m, but will be shot with velocity v-v’. Thus the momentum of the two bullets is lower in the second case; thus the forward momentum of the gun is also lower in that case.
(The more bullets you shoot, and the smaller they are, the more the gun equations start to resemble the rocket equation).
But when you eject the payload and blast it with a laser beam, you’re essentially just doing one shot (though one extended over a long time, so that the payload doesn’t have huge acceleration). It’s not *exactly* the same as a one shot, because the laser itself will accelerate a bit, because of the beam. But it you assume that, say, the laser is a 100 times more massive than the payload, then the gain in velocity of the laser will be insignificant compared with the deceleration of the payload—it’s essentially a single shot, extended over a period of time. And a laser/payload ratio of 100 is way below what the rocket equation would imply.
How much does the argument break down if we use the rocket equation? I apologize for being a lazy reader.
I assume that if you are using a galaxy’s power for colonization, then it doesn’t matter at all.
In that case contacting us would still be mostly-useless.
If you have to use the rocket equation twice, then you effectively double delta-v requirements and square the launch-mass / payload-mass factor.
Using Stuart’s numbers, this makes colonization more expensive by the following factors:
0.5 c: Antimatter 2.6 / fusion 660 / fission 1e6
0.8 c: Antimatter 7 / fusion 4.5e5 / fission 1e12
0.99c Antimatter 100 / fusion 4.3e12 / fission 1e29
If you disbelieve in 30g fusion reactors and set a minimum viable weight of 500t for an efficient propulsion system (plus negligible weight for replicators) then you get an additional factor of 1e7.
Combining both for fusion at 0.8c would give you a factor of 5e12, which is significantly larger than the factor between “single solar system” and “entire galaxy”. These are totally pessimistic assumptions, though: Deceleration probably can be done cheaper, and with lower minimal mass for efficient propulsion systems. And you almost surely can cut off quite a bit of rocket-delta-v on acceleration (Stuart assumed you can cut 100% on acceleration and 0% on deceleration; the above numbers assumed you can cut 0% on acceleration and 0% on deceleration).
Also, as Stuart noted, you don’t need to aim at every reachable galaxy, you can aim at every cluster and spread from there.
So, I’m not arguing with Stuart’s greater claim (which is a really nice point!), I’m just arguing about local validity of his arguments and assumptions.
Eric Drexler is making some strong arguments that if you eject the payload and then decelerate the payload with a laser fired from the rest of the “ship”, then this doesn’t obey the rocket equation. The argument seems very plausible (the deceleration of the payload is *not* akin to ejecting a continuous stream of small particles—though the (tiny) acceleration of the laser/ship is). I’ll have to crunch the number on it.
(if the probe is very robust, we might be able to railgun it instead of using a laser—and railgunning a single mass, once is clearly not subject to the rocket equation).