Adam Brown: evaluation

Transcript context

…ula. The first order term is just the old Newtonian formula. It better be. It better be that the long-distance limit of general relativity recovers the Newtonian physics that we originally discovered. But as you get closer and closer to the black hole, this starts to deviate from the Newtonian answer, in a way that exactly is going to end up resolving our original thought experiment to do with lowering a brick down towards a black hole. So how much, then, looking at this formula, have I extracted from the brick as I lower it down towards the black hole? If r equals infinity—if the brick’s still a long way from the black hole—then I’ve extracted 1-1=0. I haven’t extracted any energy. As I lower it closer and closer to the black hole, initially I just get the Newtonian formula. So in fact, these are pretty close to correct in general relativity as well, because the corrections are only going to start getting large when this term becomes order one, and it’s still very small here. So these are all essentially correct. But once I get closer and closer to the black hole, they stop being correct. What I see is that as r approaches the black hole event horizon, as this formula goes to zero, I have extracted exactly all of the energy from the brick. So I start off with a brick a very, very long way from the black hole, attach it to a rope, slowly lower the brick down towards the event horizon. Of course, I can’t lower it past the event horizon, otherwise I’ll lose control of the brick. But I lower it right above the event horizon—the last possible place I can lower it to—and then just let go of it with zero velocity. The brick falls into the black hole and I have extracted the entire mc2 that used to be in the brick in my pulley system out there. So it exactly resolves this question we had. Is it possible to extract more than mc2 from the brick? No. Is it possible to extract the full mc2 from the brick using a black hole? Yes, it is. That’s actually pretty neat, and why people talk about using black holes as power plants. Most power plants today operate by burning chemical energy. That is not very efficient. You have to pay a factor of 10-10, because chemical bonds are super weak compared to the rest masses of objects. You’re really only extracting a tiny fraction of the rest mass of the fuel that you’re considering. You can level up from there by going to nuclear energy, which instead of dealing with the feeble electromagnetic bonds between atoms, starts to concern itself with the nuclear forces between the protons and the neutrons within the nucleus. So you can go up from about 10-10 to about 10-3 for fission, or 10-2 for fusion. But that’s about as good as you can go, even with fission and fusion. Because even though you can extract energy from the strong nuclear force, neither fission nor fusion changes the total number of protons plus neutrons in your process. The bulk of the energy—99% of the energy—is stored not in the electromagnetic interaction, not in the strong interaction, but in the rest mass energy of the protons and neutrons, something that neither chemical reactions nor nuclear reactions can touch. But gravity can touch them. eraction, not in the strong interaction, but in the rest mass energy of the protons and neutrons, something that neither chemical reactions nor nuclear reactions can touch. But gravity can touch them. If I start off with a mass object of m, I can extract, up to quantum corrections, essentially 100% of the rest mass energy that I’ve gone in with. It is the most efficient possible power plant, because by building an apparatus like this, in principle, I could extract 100% of the energy of whatever I started with. I intuitively get how energy equals mass. There’s these chemical bonds. Those get dissolved, they release energy. The thing weighs less if those bonds are released. I even get that if the bonds between the protons and the neutrons are broken, that releases energy and makes the thing have less mass. But if something with protons and neutrons is just slightly above the event horizon, is the interpretation that those protons and neutrons stop existing right at that point? What does it even mean for them to have 1% or 2% or 5% of their original mass?…

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