The Power density they deliver to Mercury exceeds the power density of radiation exiting the sun by 6 orders of magnitude!
I don’t follow. What does power density have to do with anything and how can any merely geometrical theorem matter? You are concentrating the power of the sun by the megaengineering (solar panels in this case), so the density can be whatever you want to pay for. (My CPU chip has much higher power density than the equivalent square inches of Earth’s atmosphere receiving sunlight, but no one says it ‘violates the laws of thermodynamics’.) Surely only the total power matters.
The sun emits light because it is hot. You can’t concentrate thermal emission to be brighter than the source. (if you could, you could build a perpetual motion machine).
Eternity in Six Hours describes very large lightweight mirrors concentrating solar radiation onto planet Mercury.
The most power you could deliver from the sun to Mercury is the power of the sun times the square of the ratio of the radius of Mercury to the radius of the sun.
The total solar output is 4*10^26 Watts. The ratio of the sun’s radius to that of mercury is half a million. So you can focus about 10^15 Watts onto Mercury at most.
Figure 2 of Eternity in Six Hours projects getting 10^24 Watts to do the job.
We do not assume mirrors. As you say, there are big limits due to conservation of etendué. We are assuming (if I remember right) photovoltaic conversion into electricity and/or microwave beams received by rectennas. Now, all that conversion back and forth induces losses, but they are not orders of magnitude large.
In the years since we wrote that paper I have become much more fond of solar thermal conversion (use the whole spectrum rather than just part of it), and lightweight statite-style foil Dyson swarms rather than heavier collectors. The solar thermal conversion doesn’t change things much (but allows for a more clean-cut analysis of entropy and efficiency; see Badescu’s work). The statite style however reduces the material requirements many orders of magnitude: Mercury is safe, I only need the biggest asteroids.
Still, detailed modelling of the actual raw material conversion process would be nice. My main headache is not so much the energy input/waste heat removal (although they are by no means trivial and may slow things down for too concentrated mining operations—another reason to do it in the asteroid belt in many places), but how to solve the operations management problem of how many units of machine X to build at time t. Would love to do this in more detail!
The conservation of etendué is merely a particular version of the second law of thermodynamics. Now, You are trying to invoke a multistep photovoltaic/microwave/rectenna method of concentrating energy, but you are still violating the second law of thermodynamics.
If one could concentrate the energy as you propose, one could build a perpetual motion machine.
I don’t see how they are violating the second law of thermodynamics—“all that conversion back and forth induces losses.” They are concentrating some of the power of the Sun in one small point, at the expense of further dissipating the rest of the power. No?
DK> “I don’t see how they are violating the second law of thermodynamics”
Take a large body C, and a small body H. Collect the thermal radiation from C in some manner and deposit that energy on H. The power density emitted from C grows with temperature. The temperature of H grows with the power density deposited. If, without adding external energy, we concentrate the power density from the large body C to a higher power density on the small body H, H gets hotter than C. We may then use a heat engine between H an C to make free energy. This is not possible, therefore we cannot do the concentration.
The Etendue argument is just a special case where the concentration is attempted with mirrors or lenses. Changing the method to involve photovoltaic/microwave/rectenna power concentration doesn’t fix the issue, because the argument from the second law is broader, and encompasses any method of concentrating the power density as shown above.
When we extrapolate exponential growth, we must take care to look for where the extrapolation fails. Nothing in real life grows exponentially without bounds. “Eternity in Six Hours” relies on power which is 9 orders of magnitude greater than the limit of fundamental physical law.
But in laboratory experiments, haven’t we produced temperatures greater than that of the surface of the sun? A quick google seems to confirm this. So, it is possible to take the power of the sun and concentrate it to a point H so as to make that point much hotter than the sun. (Since I assume that whatever experiment we ran, could have been run powered by solar panels if we wanted to)
I think the key idea here is that we can add external energy—specifically, we can lose energy. We collect X amount of energy from the sun, and use X/100 of it to heat our desired H, at the expense of the remaining 99X/100. If our scheme does something like this then no perpetual motion or infinite power generation is entailed.
How much extra energy external energy is required to get an energy flux on Mercury of a billion times that leaving the sun? I have an idea, but my statmech is rusty. (the fourth root of a billion?)
And do we have to receive the energy and convert it to useful work with 99.999999999% efficiency to avoid melting the apparatus on Mercury?
I have no idea, I never took the relevant physics classes.
For concreteness, suppose we do something like this: We have lots of solar panels orbiting the sun. They collect electricity (producing plenty of waste heat etc. in the process, they aren’t 100% efficient) and then send it to lasers, which beam it at Mercury (producing plenty more waste heat etc. in the process, they aren’t 100% efficient either). Let’s suppose the efficiency is 10% in each case, for a total efficiency of 1%. So that means that if you completely surrounded the sun with a swarm of these things, you could get approximately 1% of the total power output of the sun concentrated down on Mercury in particular, in the form of laser beams.
What’s wrong with this plan? As far as I can tell it couldn’t be used to make infinite power, because of the aforementioned efficiency losses.
To answer your second question: Also an interesting objection! I agree melting the machinery is a problem & the authors should take that into account. I wonder what they’d say about it & hope they respond.
Yeah, though not for the reason you originally said.
I think I’d like to see someone make a revised proposal that addresses the thermal management problem, which does indeed seem to be a tricky though perhaps not insoluble problem.
Ok, I could be that someone. here goes. You and the paper author suggest a heat engine. That needs a cold side and a hot side. We build a heat engine where the hot side is kept hot by the incoming energy as described in this paper. The cold side is a surface we have in radiative communication with the 3 degrees Kelvin temperature of deep space. In order to keep the cold side from melting, we need to keep it below a few thousand degrees, so we have to make it really large so that it can still radiate the energy.
From here, we can use Stefan–Boltzmann law, to show that we need to build a radiator much bigger than a billion times the surface area of Mercury. It goes as the fourth power of the ratio of temperatures in our heat engine.
The paper’s contribution is the suggestion of a self replicating factory with exponential growth. That is cool. But the problem with all exponentials is that, in real life, they fail to grow indefinitely. Extrapolating an exponential a dozen orders of magnitude, without entertaining such limits, is just silly.
I’m still interested in this question. I don’t think you really did what I asked—it seems like you were thinking ‘how can I convince him that this is impossible’ not ‘how can I find a way to build a dyson swarm.’ I’m interested in both but was hoping to have someone with more engineering and physics background than me take a stab at the latter.
My current understanding of the situation is: There’s no reason why we can’t concentrate enough energy on the surface of Mercury, given enough orbiting solar panels and lasers; the problem instead seems to be that we need to avoid melting all the equipment on the surface. Or, in other words, the maximum amount of material we can launch off Mercury per second is limited by the maximum amount of heat that can be radiated outwards from Mercury (for a given operating temperature of the local equipment?) And you are claiming that this amount of heat radiation ability, for radiators only the size of Mercury’s surface, is OOMs too small to enable dyson swarm construction. Is this right?
Interesting. I googled “eternity in six hours” and found http://www.fhi.ox.ac.uk/wp-content/uploads/intergalactic-spreading.pdf , which looks to be a preprint of the same paper (dated March 12, 2013); the preprint version does say “The lightest design would be to have very large lightweight mirrors concentrating solar radiation down on focal points” and contains the phrase “disassembly of Mercury” 3 times; while the published article Daniel Kokotajlo linked to lacks all of that. Indeed, in the published article, the entire 8-page “The launch phase” section has been cut down to one paragraph.
Maybe you should read the preprint too. I’ll excuse him for reading the wrong obsolete preprint even though that search would also show him that it was published at #3 and so he should be checking his preprint criticisms against the published version (I don’t always bother to jailbreak a published version either), but you are still failing to read the next sentence after the one you quoted, which you left out. In full (and emphasis added):
The lightest design would be to have very large lightweight mirrors concentrating solar radiation down on focal points, where it would be transformed into useful work (and possibly beamed across space for use elsewhere). The focal point would most likely some sort of heat engine, possibly combined with solar cells (to extract work from the low entropy solar radiation).
If he read that version, personally, I think that reading error is even more embarrassing, so I’m happy to agree with you that that’s the version weverka misread in his attempt to dunk on the paper… Even worse than the time weverka accused me of not reading a paper published 2 years later, IMO.
(And it should be no surprise that you screwed up the reading in a different way when the preprint was different, because either way, you are claiming Sandberg, a physicist who works with thermodynamic stuff all the time, made a trivial error of physics; however, it is more likely you made a trivial error of reading than he made a trivial error of physics, so the only question is what specific reading error you made… cf. Muphry’s law.)
So, to reiterate: his geometric point is irrelevant and relies on him (and you) being bad at reading and attacking a strawman, because he ignored the fact that the solar mirrors are merely harvesting energy before concentrating it with ordinary losses, and aren’t some giant magnifying glass to magically losslessly melt Mercury. There are doubtless problems with the mega-engineering proposal, which may even bump the time required materially from 6 hours to, say, 600 hours instead—but you’re going to need to do more work than that.
For the record, I find that scientists make such errors routinely. In public conferences when optical scientists propose systems that violate the constant radiance theorem, I have no trouble standing up and saying so. It happens often enough that when I see a scientist propose such a system, It does not diminish my opinion of that scientist. I have fallen into this trap myself at times. Making this error should not be a source of embarrassment.
either way, you are claiming Sandberg, a physicist who works with thermodynamic stuff all the time, made a trivial error of physics;
I did not expect this to revert to credentialism. If you were to find out that my credentials exceed this other guy’s, would you change your position? If not, why appeal to credentials in your argument?
Basically, no amount of mirrors and lenses can result in the energy beaming down on Mercury being denser per square meter than the energy beaming out of a square meter of Sun surface. The best you can do is make it so that Mercury is effectively surrounded entirely by Sun. And if that’s not good enough, then you are out of luck… I notice I’m a bit confused, because surely that is good enough. Wouldn’t that be enough to melt, and then evaporate, the entirety of Mercury within a few hours? After all isn’t that what would happen if you dropped Mercury into the Sun?
>Kokotajlo writes:Wouldn’t that be enough to melt, and then evaporate, the entirety of Mercury within a few hours? After all isn’t that what would happen if you dropped Mercury into the Sun?
It would cause a severe heat dissipation problem. All that energy is going to be radiated as waste heat and, in equilibrium, will be radiated as fast as it comes in. The temperature required to radiate at the requisite power level would be in excess of the temperature at the surface of the sun, any harvesting machinery on the surface of the planet would melt unless it is built from something unknown to modern chemistry.
I don’t follow. What does power density have to do with anything and how can any merely geometrical theorem matter? You are concentrating the power of the sun by the megaengineering (solar panels in this case), so the density can be whatever you want to pay for. (My CPU chip has much higher power density than the equivalent square inches of Earth’s atmosphere receiving sunlight, but no one says it ‘violates the laws of thermodynamics’.) Surely only the total power matters.
The sun emits light because it is hot. You can’t concentrate thermal emission to be brighter than the source. (if you could, you could build a perpetual motion machine).
Eternity in Six Hours describes very large lightweight mirrors concentrating solar radiation onto planet Mercury.
The most power you could deliver from the sun to Mercury is the power of the sun times the square of the ratio of the radius of Mercury to the radius of the sun.
The total solar output is 4*10^26 Watts. The ratio of the sun’s radius to that of mercury is half a million. So you can focus about 10^15 Watts onto Mercury at most.
Figure 2 of Eternity in Six Hours projects getting 10^24 Watts to do the job.
We do not assume mirrors. As you say, there are big limits due to conservation of etendué. We are assuming (if I remember right) photovoltaic conversion into electricity and/or microwave beams received by rectennas. Now, all that conversion back and forth induces losses, but they are not orders of magnitude large.
In the years since we wrote that paper I have become much more fond of solar thermal conversion (use the whole spectrum rather than just part of it), and lightweight statite-style foil Dyson swarms rather than heavier collectors. The solar thermal conversion doesn’t change things much (but allows for a more clean-cut analysis of entropy and efficiency; see Badescu’s work). The statite style however reduces the material requirements many orders of magnitude: Mercury is safe, I only need the biggest asteroids.
Still, detailed modelling of the actual raw material conversion process would be nice. My main headache is not so much the energy input/waste heat removal (although they are by no means trivial and may slow things down for too concentrated mining operations—another reason to do it in the asteroid belt in many places), but how to solve the operations management problem of how many units of machine X to build at time t. Would love to do this in more detail!
The conservation of etendué is merely a particular version of the second law of thermodynamics. Now, You are trying to invoke a multistep photovoltaic/microwave/rectenna method of concentrating energy, but you are still violating the second law of thermodynamics.
If one could concentrate the energy as you propose, one could build a perpetual motion machine.
I don’t see how they are violating the second law of thermodynamics—“all that conversion back and forth induces losses.” They are concentrating some of the power of the Sun in one small point, at the expense of further dissipating the rest of the power. No?
DK> “I don’t see how they are violating the second law of thermodynamics”
Take a large body C, and a small body H. Collect the thermal radiation from C in some manner and deposit that energy on H. The power density emitted from C grows with temperature. The temperature of H grows with the power density deposited. If, without adding external energy, we concentrate the power density from the large body C to a higher power density on the small body H, H gets hotter than C. We may then use a heat engine between H an C to make free energy. This is not possible, therefore we cannot do the concentration.
The Etendue argument is just a special case where the concentration is attempted with mirrors or lenses. Changing the method to involve photovoltaic/microwave/rectenna power concentration doesn’t fix the issue, because the argument from the second law is broader, and encompasses any method of concentrating the power density as shown above.
When we extrapolate exponential growth, we must take care to look for where the extrapolation fails. Nothing in real life grows exponentially without bounds. “Eternity in Six Hours” relies on power which is 9 orders of magnitude greater than the limit of fundamental physical law.
But in laboratory experiments, haven’t we produced temperatures greater than that of the surface of the sun? A quick google seems to confirm this. So, it is possible to take the power of the sun and concentrate it to a point H so as to make that point much hotter than the sun. (Since I assume that whatever experiment we ran, could have been run powered by solar panels if we wanted to)
I think the key idea here is that we can add external energy—specifically, we can lose energy. We collect X amount of energy from the sun, and use X/100 of it to heat our desired H, at the expense of the remaining 99X/100. If our scheme does something like this then no perpetual motion or infinite power generation is entailed.
How much extra energy external energy is required to get an energy flux on Mercury of a billion times that leaving the sun? I have an idea, but my statmech is rusty. (the fourth root of a billion?)
And do we have to receive the energy and convert it to useful work with 99.999999999% efficiency to avoid melting the apparatus on Mercury?
I have no idea, I never took the relevant physics classes.
For concreteness, suppose we do something like this: We have lots of solar panels orbiting the sun. They collect electricity (producing plenty of waste heat etc. in the process, they aren’t 100% efficient) and then send it to lasers, which beam it at Mercury (producing plenty more waste heat etc. in the process, they aren’t 100% efficient either). Let’s suppose the efficiency is 10% in each case, for a total efficiency of 1%. So that means that if you completely surrounded the sun with a swarm of these things, you could get approximately 1% of the total power output of the sun concentrated down on Mercury in particular, in the form of laser beams.
What’s wrong with this plan? As far as I can tell it couldn’t be used to make infinite power, because of the aforementioned efficiency losses.
To answer your second question: Also an interesting objection! I agree melting the machinery is a problem & the authors should take that into account. I wonder what they’d say about it & hope they respond.
A billion times the energy flux from the surface of the sun, over any extended area is a lot to deal with. It is hard to take this proposal seriously.
Yeah, though not for the reason you originally said.
I think I’d like to see someone make a revised proposal that addresses the thermal management problem, which does indeed seem to be a tricky though perhaps not insoluble problem.
Ok, I could be that someone. here goes. You and the paper author suggest a heat engine. That needs a cold side and a hot side. We build a heat engine where the hot side is kept hot by the incoming energy as described in this paper. The cold side is a surface we have in radiative communication with the 3 degrees Kelvin temperature of deep space. In order to keep the cold side from melting, we need to keep it below a few thousand degrees, so we have to make it really large so that it can still radiate the energy.
From here, we can use Stefan–Boltzmann law, to show that we need to build a radiator much bigger than a billion times the surface area of Mercury. It goes as the fourth power of the ratio of temperatures in our heat engine.
The paper’s contribution is the suggestion of a self replicating factory with exponential growth. That is cool. But the problem with all exponentials is that, in real life, they fail to grow indefinitely. Extrapolating an exponential a dozen orders of magnitude, without entertaining such limits, is just silly.
I’m still interested in this question. I don’t think you really did what I asked—it seems like you were thinking ‘how can I convince him that this is impossible’ not ‘how can I find a way to build a dyson swarm.’ I’m interested in both but was hoping to have someone with more engineering and physics background than me take a stab at the latter.
My current understanding of the situation is: There’s no reason why we can’t concentrate enough energy on the surface of Mercury, given enough orbiting solar panels and lasers; the problem instead seems to be that we need to avoid melting all the equipment on the surface. Or, in other words, the maximum amount of material we can launch off Mercury per second is limited by the maximum amount of heat that can be radiated outwards from Mercury (for a given operating temperature of the local equipment?) And you are claiming that this amount of heat radiation ability, for radiators only the size of Mercury’s surface, is OOMs too small to enable dyson swarm construction. Is this right?
Awesome critique, thanks! I’m going to email the authors and ask what they think of this. I’ll credit you of course.
Ah, so you’re just bad at reading. I thought that was why you were wrong (it does not describe mirrors), but I didn’t want to say it upfront.
Interesting. I googled “eternity in six hours” and found http://www.fhi.ox.ac.uk/wp-content/uploads/intergalactic-spreading.pdf , which looks to be a preprint of the same paper (dated March 12, 2013); the preprint version does say “The lightest design would be to have very large lightweight mirrors concentrating solar radiation down on focal points” and contains the phrase “disassembly of Mercury” 3 times; while the published article Daniel Kokotajlo linked to lacks all of that. Indeed, in the published article, the entire 8-page “The launch phase” section has been cut down to one paragraph.
Perhaps weverka read the preprint.
thanks for showing that Gwern’s statement that I am “bad at reading” is misplaced.
Maybe you should read the preprint too. I’ll excuse him for reading the wrong obsolete preprint even though that search would also show him that it was published at #3 and so he should be checking his preprint criticisms against the published version (I don’t always bother to jailbreak a published version either), but you are still failing to read the next sentence after the one you quoted, which you left out. In full (and emphasis added):
If he read that version, personally, I think that reading error is even more embarrassing, so I’m happy to agree with you that that’s the version weverka misread in his attempt to dunk on the paper… Even worse than the time weverka accused me of not reading a paper published 2 years later, IMO.
(And it should be no surprise that you screwed up the reading in a different way when the preprint was different, because either way, you are claiming Sandberg, a physicist who works with thermodynamic stuff all the time, made a trivial error of physics; however, it is more likely you made a trivial error of reading than he made a trivial error of physics, so the only question is what specific reading error you made… cf. Muphry’s law.)
So, to reiterate: his geometric point is irrelevant and relies on him (and you) being bad at reading and attacking a strawman, because he ignored the fact that the solar mirrors are merely harvesting energy before concentrating it with ordinary losses, and aren’t some giant magnifying glass to magically losslessly melt Mercury. There are doubtless problems with the mega-engineering proposal, which may even bump the time required materially from 6 hours to, say, 600 hours instead—but you’re going to need to do more work than that.
For the record, I find that scientists make such errors routinely. In public conferences when optical scientists propose systems that violate the constant radiance theorem, I have no trouble standing up and saying so. It happens often enough that when I see a scientist propose such a system, It does not diminish my opinion of that scientist. I have fallen into this trap myself at times. Making this error should not be a source of embarrassment.
I did not expect this to revert to credentialism. If you were to find out that my credentials exceed this other guy’s, would you change your position? If not, why appeal to credentials in your argument?
I think weverka is referring to the phenomenon explained here: https://what-if.xkcd.com/145/
Basically, no amount of mirrors and lenses can result in the energy beaming down on Mercury being denser per square meter than the energy beaming out of a square meter of Sun surface. The best you can do is make it so that Mercury is effectively surrounded entirely by Sun. And if that’s not good enough, then you are out of luck… I notice I’m a bit confused, because surely that is good enough. Wouldn’t that be enough to melt, and then evaporate, the entirety of Mercury within a few hours? After all isn’t that what would happen if you dropped Mercury into the Sun?
weverka, care to elaborate further?
>Kokotajlo writes:Wouldn’t that be enough to melt, and then evaporate, the entirety of Mercury within a few hours? After all isn’t that what would happen if you dropped Mercury into the Sun?
How do you get hours?
I didn’t do any calculation at all, I just visualized Mercury falling into the sun lol. Not the most scientific method.
Yeah, that’s where you got things wrong.
I have sinned! I repent and learn my lesson.
Specifically, you can focus 10^15 watts on mercury, but Eternity in 6 hours proposes 10^24 watts to be used. It’s a 9 order of magnitude difference.
It would cause a severe heat dissipation problem. All that energy is going to be radiated as waste heat and, in equilibrium, will be radiated as fast as it comes in. The temperature required to radiate at the requisite power level would be in excess of the temperature at the surface of the sun, any harvesting machinery on the surface of the planet would melt unless it is built from something unknown to modern chemistry.
Seems like a good point. I’d be interested to hear what the authors have to say about that.