Speaker 1: Another topic I know you studied a lot is how one might mine a black hole.

Speaker 2: Oh, yeah, right. I read a paper about that. Very good. Yeah, um, tell me about it.

Speaker 1: So, uh, what do you mean by "mining a black hole"? Mining a black hole means taking the energy out of a black hole that used to be in a black hole. Obviously, if our distant descendants have used up all of the energy and stars and everything else, the black hole might be the last thing they turn their eye to. So, can you get energy out of black holes at all?

Speaker 1: Uh, the old story, pre-1970s, is no. Like, it's just a black hole. Matter falls in, it never comes out, it's stuck. Uh, the thing that Hawking and Beckenstein discovered in the 70s is that once quantum mechanics is involved, that's not true anymore. Once quantum mechanics is involved, in fact, energy, even without you doing anything, starts to leave black holes. Uh, the problem, as far as our distant descendants will be concerned, is that it leaves black holes extremely slowly. So, if you took a solar mass black hole, same mass as the sun, just collapsed to form a black hole, there'll be this little quantum, what's called Hawking radiation nowadays, little quantum Hawking radiation in which the energy will leech out again very, very slowly. And the temperature of a solar mass black hole is measured in nanokelvins, so very low temperature, and that's bad news because it means the energy comes out super duper slowly. A solar mass black hole, if you don't help it, will take about 10 to the 55 times the current age of the universe to have given out all its energy back into the universe.

Speaker 1: Can you make that faster? The mining question is, can you speed that up? And there was this proposal that you could, you know, reach in with a mechanical claw, obviously not crossing the horizon because otherwise you've lost the claw and you're somewhat counterproductive, but like, just just outside the horizon, just grab some of that Hawking radiation and just drag it a long way away from the black hole, and then, and then feast on it, or do whatever it is you want to do with it. Now, from one point of view, that's just like a space elevator, or all be at a very high performance space elevator. Space elevators, you'll remember, are these ideas for how we might get things off the surface of the Earth without using rockets. And the idea is that you have, uh, some massive orbiting object, sort of very long way away, beyond geostationary orbit, and then you dangle off that rope down to the surface of the Earth, and then you can essentially just climb up the rope to get out. That's a space elevator idea. And already around Earth, it, it's hitting pretty hard material science constraints. The trouble with making a space elevator isn't so much supporting the payload that you're trying to have climb up it, it is merely just the rope supporting its own weight, because each bit of the rope needs to support not only its own weight, but also the weight of all of the rope beneath it. Uh, so the tension that you require keeps getting more and more and more as you as you go up. At the bottom, there is no tension effect, it doesn't even touch the Earth. It's not like a compression structure, that's like a skyscraper that's pushed up from below. It's a tension structure that's held up from above. Uh, but as you go up, because the T, you need more and more tension, you also need to make the rope thicker and thicker and thicker. And if you try and on Earth, or around Earth, build a space elevator out of steel, say, it just doesn't work. Steel is not strong enough. Uh, you need to keep doubling the thickness until by the time you get to geostationary orbit, the thickness of the steel rope is more than the size of the Earth. Like the whole thing just doesn't, just doesn't work at all. Uh, but carbon nanotubes are this material that we just, we've discovered that are much stronger than steel. So in fact, around Earth, carbon nanotubes will just about work if we can make them long enough and pure enough. And, uh, then they will be strong enough, we will be able to build a space elevator around Earth in, you know, maybe sometime in the next, next century. That you only need a couple of doublings of the thickness of the carbon nanotubes, uh, along its entire, entire length. So carbon nanotubes work great around Earth, but they are totally inadequate for black holes. For black holes, you know, the CR, the critical material science property you need for this, for this rope, is the tensile strength to mass per unit length ratio. IO, it needs to be strong, high tensile strength, but low weight, like light, low mass per unit length. And that's the critical ratio. And carbon nanotubes is, you know, 10 to the minus, uh, 12 or something on that, on that scale. And that is simply not strong enough at all. Uh, in fact, what I showed in my paper is that you need a tensile strength to weight ratio that is as strong as is consistent with the laws of nature. So in fact, the laws of nature bound this quantity. The finiteness of the speed of light means you cannot have an arbitrarily strong rope with a given mass per unit length. There is a bound set by the C squared, uh, in some, in some units, that bounds the maximum possible tensile strength that any rope can have. Any rope, in fact, that has that. An example of a rope that has that is a string. So a string is, um, I mean, a fundamental string from string theory is an example of a hypothetical rope that is just strong enough to, to violate, to saturate that bound, that strength bound. And then the problem is, is the following. The problem is that if you have a rope, uh, that saturates the bound, as strong as any rope can be, uh, it is just strong enough to support all of its own weight with exactly no strength left over to support any payload it might wish to carry. And that's ultimately what dooms these mining black holes, you know, these rapid mining black hole proposals.

Speaker 2: Okay, so we can't get the material out of the black hole in a, at a pace that would make it like reasonably useful to us. What can we do with black holes? What, what are they good for? If you have a small black hole, uh, you can get stuff out of them, uh, more rapidly. The, the temperature of a black hole is inversely proportional to size. So one thing that people have talked about with black holes is using them to extract all of the energy from matter. As you know, most chemical reactions are pretty inefficient. You, you, you burn gasoline, and you extract, as a, as a function of the rest mass of the gasoline that that you started with, you extract one part in 10 billion of of energy from the, from the gasoline that you started with. So that, that's bad. From the point of view, you know, you have MC squared worth in, in a gallon of gasoline, you've got a full MC squared worth of energy in there, and you can only get out one part in 10, 10. That's a pretty unsatisfactory situation. Roughly speaking, the reason that all chemical processes are so inefficient, uh, is that they only address the electromagnetic energy in the electrons. And very small fraction of the electromagnetic energy in an electron, in, in atoms, is stored in the electromagnetic interaction between the, between the electrons, and between the nucleus and the electrons. Most of it is stored in the nucleus itself, in the strong nuclear forces, and particularly in the rest mass of the protons and neutrons that constitute it. So you could do much better if instead of doing electromagnetic interactions, you use nuclear interactions. That, that can probe the energy in, uh, turning protons into neutrons. That's why nuclear power plants are so much more efficient on a per mass basis than chemical power plants like coal plants or or gas plants. Uh, because you're getting a much higher fraction. You, you know, best case scenario, you're getting one part in 10 to the three, um, or 10 to the four of the rest mass of the uranium that you start with, uh, you're extracting as energy. But even there, uh, in even in that process, uh, it's still only, you know, absolute best, one part in a thousand of the rest mass. And the reason is that you are using where much more of the energy is stored, which is the strong and weak interactions between the protons and the neutrons. So much more is available to you. But still, at the end of whatever the process you finish with, there, there's a number that'll be conserved. And that is the, what's called the baryon number. So it's the total number of protons plus the total number of neutrons. You can transmute protons into neutrons or vice versa in, in nuclear processes, which is part of the reason they're so much more, uh, use, much more better energy than things that just affect the chemistry. But still, uh, most of the energy is stored in the rest mass of the protons and the neutrons. And you want to get that. And nuclear processes conserve that. Um, beta decay will maybe turn a proton into a neutron or vice versa, but the total number of protons plus neutrons is not changing. And so therefore, 99.9% of the energy is inaccessible to you. So what you need to do to get that energy and try and get most of the MC squared out of the matter that you have, what you need to do is is use a process that eats baryon number. That can, in which you can start off with a proton or a neutron and end up with no proton or neutron. And instead, all of that energy unleashed in high energy radiation that you can use for purposes. So electromagnetic interactions won't do that. Strong interactions also won't do that. Weak interactions won't do that. The only force of nature that will do that, um, with a small caveat, the only force of nature that, that we know that will do that is the gravitational interaction. And so you, it is a property of black holes that you can stand outside the black hole and throw protons and neutrons into the black holes, and then it'll process it, uh, and then spit out photons at the end in Hawking radiation and and and gravitons. Which is going to be slightly annoying to have to capture. And and neutrinos. But like, they're there in principle, uh, and in principle you could capture them. So one thing that black holes might be technologically useful for in the future is you start off with a much smaller black hole than, uh, than what I've just, than, uh, the size of the sun. Be very careful about making sure it doesn't grow. And, yeah, you could be super duper careful, um, and throw in protons and neutrons, uh, and then get out photons. And in principle, if you could capture the, everything that's emitted from the black hole, including the gravitons and the, in the neutrinos, uh, that gets rid of the baryon number conservation problem, and allows you to build power plants that approach 100% efficiency. And by 100%, I mean, uh, not the way we measure gas turbine efficiency where we talk about the total available chemical energy in the gas. I mean, 100% of the MC squared of the entire gas you're you're putting in.