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Can we make a black hole?
🕑 Added 2022-05-14 12:01:01 +0000 UTC[This is a transcript of the video.]
Wouldn’t it be cool to have a little black hole in your office? You know, maybe as a trash bin. Or to move around the furniture. Or just as a kind of nerdy gimmick. Why can we not make black holes? Or can we? If we could, what could we do with them? And what’s a black hole laser? That’s what we’ll talk about today.
Everything has a gravitational pull, the sun and earth but also you and I and every single molecule. You might think that it’s the mass of the object that determines how strong the gravitational pull is, but this isn’t quite correct.
If you remember Newton’s gravitational law, then, sure, a higher mass means a higher gravitational pull. But a smaller radius also means a higher gravitational pull. So, if you hold the mass fixed and compress an object into a smaller and smaller radius, then the gravitational pull gets stronger. Eventually, it becomes so strong that not even light can escape. You’ve made a black hole.
This happens when the mass is compressed inside a radius known as the Schwarzschild-radius. Every object has a Schwarzschild radius, and you can calculate it from the mass. For the things around us the Schwarzschild-radius is much much smaller than the actual radius.
For example, the actual radius of earth is about 6000 kilometers, but the Schwarzschild-radius is only about 9 millimeters. Your actual radius is maybe something like a meter, but your Schwarzschild radius is about 10 to the minus 24 meters, that’s about a billion times smaller than a proton.
And the Schwarzschild radius of an atom is about 10 to the minus 53 meters, that’s even smaller than the Planck length which is widely regarded to be the smallest possible length, though I personally think this is nonsense, but that’s a different story.
So the reason we can’t just make a black hole is that the Schwarzschild radius of stuff we can handle is tiny, and it would take a lot of energy to compress matter sufficiently. It happens out there in the universe because if you have really huge amounts of matter with little internal pressure, like burned out stars, then gravity compressed it for you. But we can’t do this ourselves down here on earth. It’s basically the same problem like making nuclear fusion work, just many orders of magnitude more difficult.
But wait. Einstein said that mass is really a type of energy, and energy also has a gravitational pull. Yes, that guy again. Doesn’t this mean, if we want to create a black hole, we can just speed up particles to really high velocity, so that they have a high energy, and then bang them into each other. For example, hmm, with a really big collider.
Indeed, we could do this. But even the biggest collider we have built so far, which is currently the Large Hadron Collider at CERN, is nowhere near reaching the required energy to make a black hole. Let’s just put in the numbers.
In the collisions at the LHC we can reach energies about 10 TeV, that corresponds to a Schwarzschild radius of about 10 to the minus 50 meters. But the region in which the LHC compresses this energy is more like 10 to the minus 19 meters. We’re far far away from making a black hole.
So why were people so worried 10 years ago that the LHC might create a black hole? This is only possible if gravity doesn’t work the way Einstein said. If gravity for whatever reason would be much stronger on short distances than Einstein’s theory predicts, then it’d become much easier to make black holes. And 10 years ago the idea that gravity could indeed get stronger on very short distances was popular for a while. But there’s no reason to think this is actually correct and, as you’ve noticed, the LHC didn’t produce any black holes.
Alright, so far it doesn’t sound like you’ll get your black hole trash can. But what if we built a much bigger collider? Yes, well, with current technology it’d have to have a diameter about the size of the milky-way. It’s not going to happen. Something else we can do?
We could try to focus a lot of lasers on a point. If we used the world’s currently most powerful lasers and focused them on an area about 1 nanometer wide, we’d need about 10 to the 37 of those lasers. It’s not strictly speaking impossible, but clearly it’s not going to happen any time soon.
Ok, good, but what if we could make a black hole? What could we do with it? Well, surprise, there’s a couple of problems. Black holes have a reputation for sucking stuff in, but actually if they’re small, the problem is the opposite. They throw stuff out. That stuff is Hawking radiation.
Stephen Hawking discovered in the early 1970s that all black holes emit radiation due to quantum effects, so they lose mass and evaporate. The smaller the black holes, the hotter, and the faster they evaporate. A black hole with a mass of about 100 kilograms would entirely evaporate in less than a nanosecond.
Now “Evaporation” sounds rather innocent and might make you think of a puddle turning into water vapor. But for the black hole it’s far from innocent. And if the black hole’s temperature is high, the radiation is composed of all elementary particles, photons, electrons, quarks, and so on. It’s really unhealthy. And a small black hole converts energy into a lot of those particles very quickly. This means a small black hole is black basically a bomb. So it wouldn’t quite work out the way it looks in the Simpson’s clip. Rather than eating up the city it’d blast it apart.
But if you’d manage to make a black hole with masses about a million tons, those would live a few years, so that’d make more sense. Hawking suggested to surround them with mirrors and use them to generate power. It’d be very climate friendly, too. Louis Crane suggested to put such a medium sized black hole in the focus of a half mirror and use its radiation to propel a spaceship.
Slight problem with this is that you can’t touch black holes, so there’s nothing to hold them with. A black hole isn’t really anything, it’s just strongly curved space. They can be electrically charged but since they radiate they’ll shed their electric charge quickly, and then they are neutral again and electric fields won’t hold them. So some engineering challenges that remain to be solved.
What if we don’t make a black hole but just use one that’s out there? Are those good for anything? The astrophysical black holes which we know exist are very heavy. This means their Hawking temperature is very small, so small indeed that we can’t measure it, as I just explained in a recent video. But if we could reach such a black hole it might be useful for something else.
Roger Penrose already pointed out in the early 1970s that it’s possible to extract energy from a big, spinning black hole by throwing an object just past it. This slows down the black hole by a tiny bit, but speeds up the object you’ve thrown. So energy is conserved in total, but you get something out of it. It’s a little like a swing-by that’s used in space-flight to speed up space missions by using a path that goes by near a planet.
And that too can be used to build a bomb… This was pointed out in 1972 in a letter to Nature by Press and Teukolsky. They said, look, we’ll take the black hole, surround it with mirrors, and then we send in a laser beam, just past the black hole. That gets bend around and comes back with a somewhat higher energy, like Penrose said. But then it bounces off the mirror, goes around the black hole again, gains a little more energy, and so on. This exponentially increases the energy in the laser light until the whole thing blasts apart.
Ok, so now that we’ve talked about blowing things up with bombs that we can’t actually build, let us talk about something that we can actually build, which is called an analogue black hole. The word “analogue” refers to “analogy” and not to the opposite of digital. Analogue black holes are simulations of black holes in fluids or solids where you can “trap” some kind of radiation.
In some cases, what you trap are sound waves in a fluid, rather than light. I should add here that “sound waves” in physics don’t necessarily have something to do with what you can hear. They are just periodic density changes, like the sound you can hear, but not necessarily something your ears can detect.
You can trap sounds waves in a similar way to how a black hole traps light. This can happen if a fluid flows faster than the sound speed in that fluid. You see, in this case there’s some region from within which the sound waves can’t escape.
Those fluids aren’t really black holes of course, they don’t actually trap light. But they affect sound very much like real black holes affect light. If you want to observe Hawking radiation in such fluids, they need to have quantum properties, so in practice one uses superfluids. Another way to create a black hole analogue it is with solids in which the speed of light changes from one place to another.
And those analogue black holes can be used to amplify radiation too. It works a little differently than the amplifications we already discussed because one needs two horizons, but the outcome is pretty much the same: you send in radiation with some energy, and get out radiation with more energy. Of course the total energy is conserved, you take that from the background field which is the analogy for the black hole. This radiation which you amplify isn’t necessarily light, as I said it could be sound waves, but it’s an “amplified stimulated emission”, which is why this is called a black hole laser.
Black hole lasers aren’t just a theoretical speculation. It’s reasonably well confirmed that analogue black holes actually act much like real black holes and do indeed emit Hawking radiation. And there have been claims that black hole lasing has been observed as well. It has remained somewhat controversial exactly what the experiment measured, but either way it shows that black hole lasers are within experimental reach. They’re basically a new method to amplify radiation. This isn’t going to result in new technology in the near future, but it serves to show that speculations about what we could do with black holes aren’t as far removed from reality as you may have thought.
Comments
Rad Antonov
Thanks Tracey. Yes, that video summed it up well.
Ta. 🙂 I'd forgotten that video except for the haircut bit. Sabine's hair needs its own platform, I think.
Hey Colleen and Rad, this video of Sabine's from early 2020 discusses the Planck length: https://www.youtube.com/watch?v=nyPdIBnWOCM
Seconding Rad: what *is* that other story?
Rad Antonov
Fun episode,I really enjoyed all the Schwarzschild radius comparisons. Now you have me curious to hear your take on that dimensional analysis that seems to have become a standard for minimum length.
Of course, it might be easier to build a plasma-arc incinerator. It could be self powered by capturing the heat energy of the materials that fall into it. When it reaches planned obsolescence, it should incinerate itself. (~;
Happy you like it!
Sounds pretty accurate! Easy to underestimate just how mindbogglingly massive even tiny black holes are.
Notwithstanding Robert Dicke's idle conjectures of mathematical convenience (the so-called Einstein and Strong equivalence principles), according to Einstein's General Relativity the speed of light diminishes in an increasing gravitational field. That GR effect has been observed. Consequently, since E/m=c^2, a body undergoing gravitational collapse will begin to emit electromagnetic radiation until the collapse is stabilized. The resulting body would resemble a quasar, a compact gravitating body with a significant gravitational redshift, emitting copious amounts of EMR. The only problem with that model, of course, is that it is realistic and so not as much fun as the mathematical fantasy of black holes with their woo-woo, singularities and event horizons. Black holes may not be physics but they nonetheless support a whole cottage industry of black hole theorists, which makes BHs good for something, I guess.
This video is really cool. I'm going to make another bangin' science dance track from it. ✨🌌
My nerdy Saturday morning task: examine Lisa Simpson's black hole more closely... The size of the event horizon looked to be about that of a softball (radius of 2 in ~ 5 cm). Given that Earth's Schwarzschild radius is about 0.9 cm and R and M are proportional, this means that Lisa's black hole had a mass of about 5.6 Earth masses. The Hawking evaporation time goes as the cube of the mass, so the lifetime of Lisa's black hole is about 10^62 years. The moral of this exercise is that you should always wait until a baby black hole is properly weaned before separating it from its mother. That way your pet black hole will grow and act normally rather than have behavioral issues that will blow up your town.
