Singularities in Space-Time Prove Hard to Kill
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I'm Lauren Good. I'm a senior writer at Wired. I'm Michael Calori, Wired's director of consumer tech and culture. And I'm Zoe Schiffer, director of business and industry. And we're the hosts of Wired's Uncanny Valley. It's a show about the people, power, and influence of Silicon Valley. Every week, we get together to talk about how technology and culture from the Valley are influencing our everyday lives. The internet really was no longer about the early days. It was about minting money.

money. He was swapping out the hoodie for a suit. And it just became like the shorthand for I'm the Silicon Valley hustle coder guy. Or we'll dive deep into the history of some of Silicon Valley's most important institutions and figures. So a lot of people point to parallels between Sam Altman and Steve Jobs. Very good for engagement for Meta for its bottom line, possibly or probably bad for humanity. I don't know if there's any single person that I would trust with this.

Whether you're optimistic or absolutely terrified about what Silicon Valley will do next, this is the podcast for you. We'll be there to bring the analysis and reporting you can only get from Wired. Listen to and follow Wired's Uncanny Valley wherever you get your podcasts. One of the biggest mysteries in physics is what happens when the field's two most advanced established theories collide.

Einstein gave us a theory for how gravity works, that objects with mass curve space-time itself. And that's why the Earth goes around the Sun and apples fall to the ground. We call it general relativity. And a century of work by many scientists has given us another theory, quantum mechanics, which explains very consistently and accurately how atomic and subatomic particles work.

So there are two internally consistent visions of reality, one for kind of the fabric of reality itself and one for the particles that fill it. And each of them works beautifully. The problem is that mathematically, they don't agree with each other.

Getting these two ideas together is the so-called theory of quantum gravity. And one way to get closer to that idea might be to, well, push Einstein's gravity until it breaks. And when that happens, something monstrous and a little terrifying happens. A place where matter vanishes and time stops the literal edge of the cosmic map.

Welcome to the Quanta podcast, where we explore the frontiers of science and math. I'm Samir Patel, editor-in-chief of Quanta magazine. A quantum-based description of gravity, a way to bring these two theoretical frameworks together, is a problem that comes up regularly in our physics stories, in part because lots of folks are still trying to figure it out.

Our physics writer, Charlie Wood, is with us today to talk about one approach to getting closer and closer to quantum gravity that he explored in a recent story on quantummagazine.org called Singularities in Space-Time Prove Hard to Kill. Welcome, Charlie. Hi, Samir. Happy to be here. We'd like to ask at the beginning of these interviews, what's the big idea? Where are we going with this conversation?

Like you said, we have these two theories that just describe so much of our universe. General relativity, as you said, encapsulates everything we know about space and time, or space-time together. So that's how light rays bend as they travel near the sun. That's why clocks tick more slowly on GPS satellites in deep space.

And we have this other theory, quantum theory, which encapsulates everything we know about matter. That's why atoms are stable, why neon lights have the colors they do, why superconductivity is possible. But we don't really know what happens when you put quantum matter in spacetime and let these two things fully converse with each other. And that leads to a couple of notable blind spots.

But reality exists as we know it now, right? We have gravity. We have quantum materials and particles, but they are together in the universe that we live in. We're not able to get them to agree theoretically, right?

Right. So usually you can use one theory and ignore the other one. So either you can focus on the quantum matter and ignore gravity, or you can focus on gravitational and space-time phenomena and ignore the quantum stuff. It's in the couple of rare situations where you need to know about both the quantum matter properties and the space-time together that we don't really know what to do. So is it helpful to start at the beginning of time, at the Big Bang?

That's a great place to start. Because, you know, if we use general relativity and we play the universe backwards, like a movie. Right now, we know the universe is expanding, so we play things backwards. It kind of contracts in a way, and the density of matter goes up and up and up. And we know from general relativity that should affect space-time. It should curve space-time more and more and more. Toward that place where everything is contracting, too. Exactly.

And so eventually we get to this point where we can no longer just focus on the matter or the space-time, we really need both. And the theory kind of glitches and doesn't tell us what happens. Something similar happens deep inside black holes, and physicists would just love to know what goes on in these kind of the last two kind of unknown frontiers. Black holes and the beginning of the universe. Exactly.

When you say glitches, what do you mean? Okay. So I say glitches, I mean like the mathematical framework gives you infinite answers. Now that might sound mysterious, but it's actually not that exotic. Okay. So, you know, to put space-time and black holes aside for a second, just think about a water droplet. Let's go to your kitchen sink and watch a water droplet falling from your sink. We might use fluid dynamics to describe the water. Fluid dynamics treats the water like it's this smooth, continuous thing.

Now I might ask you, how thin does the neck of the drop get as it's dropping? It gets thinner and thinner and thinner, and eventually it totally breaks free. We might be tempted to conclude that the drop gets infinitely thin in the instant before it breaks free. But that's not right.

It gets as thin as like a molecule of water, but it's not infinitely thin. But now we've just jumped from fluid dynamics to a whole new description. We've now jumped to the molecular description of water. And so that resolves the singularity. That shows us that the molecules never hit this infinitely thin moment. But fluid dynamics does. And so that's a singularity.

You use the word singularity. That is the glitch. Yes. That's the moment either at the beginning of the universe or in the black hole where something that should be realistic and comprehensible actually breaks and goes to infinity, at least in theory. The idea is that in the real universe that we live in, if something goes to infinity...

That's an indication to us that something in our understanding of it is broken. Yes. We can never measure something infinitely large, infinitely small, infinitely dense, infinitely thin. It's a message from the math that our framework is breaking and that we need a new framework, a more realistic framework to give us those answers. So singularities. This is a term...

people might be familiar with from movies or a elementary understanding of black holes. How are we defining singularity in this context? This is following in the footsteps of Roger Penrose, who we might talk about later. But we're thinking about the singularity as effectively a point that we can't see past. And so if we go back to rewinding the universe, there's this big bang and we just can't see past that moment.

the black hole, a person's falling in, they hit the singularity, we don't know what happens to them next.

And, you know, people sometimes even talk about the technological singularity, how we'll all upload our brains into the cloud if we're into that kind of thing. And that's spiritually taking after this. It's a dramatic transformation in society that we really can't see what happens next. So I think that's kind of the colloquial definition. Yeah. But in our context, we're essentially describing it as the glitch. Yeah. So if we have a different theoretical framework...

that resolves singularities and prevents them from happening, that would suggest that we're closer to a theory of quantum gravity, a theory that reconciles the two theories. That's right. Whatever theory we have should give us answers to all the questions we're allowed to ask. Okay.

I'd like to track this line of thought back to its origin. If we're thinking about the singularity, when does that first come up in the study of physics? So the first person to write down a solution of general relativity that contained a singularity, although he wouldn't have used those words at the time, was Karl Schwarzschild. He was actually a German soldier fighting in the Russian front during World War I when he figured this out.

And Einstein had just published his field equations, which described how spacetime reacts to matter. And yet it took physicists kind of decades to tease out all the conclusions of the solution. But, you know, they found that it had these very strange features. It had this point of no return, a spherical boundary around the point where if you fell in, you couldn't get out. And it also had this singularity, this point which as you fell farther and further towards it, certain quantities like the curvature of spacetime seemed to become infinite.

And so that didn't make a lot of sense. And that's the first conception, although I don't think the term had come yet, of a black hole. Yeah, the term black hole became popular in the 50s or 60s much, much later. But yeah, he was the one who wrote down the solution and people started figuring out, man, this has some very strange properties. Yeah. It feels like as we run through your story that you wrote about this, a lot of the

leading lights of physics in the 20th century, their names come up. So people like Penrose, Oppenheimer, they've all kind of weighed in on this place where our theory breaks down. Yeah, I mean, it really captures the imagination. And I think for a while, physicists had the sense that maybe this shouldn't be possible in reality. It's a little bit too extreme to grasp. And so Robert Oppenheimer worked with this guy, Hartland Snyder, to see if nature would actually do this. Because maybe it's in the equations, but we don't know if this is a real thing or not.

And they took a spherical shell of matter and said, "What happens if it collapses?" Again, maintaining its perfect spherical nature. Mathematically, theoretically, they're following what would happen. Yeah. Okay. If it's a perfect circle, perfect sphere, collapsing without any kind of bumps or wiggles or anything. And found that, yeah, in fact, it does get dense enough and shrinks to a point in a way that would affect space-time like Schwarzschild.

had calculated. They ran into the singularity as well. So yeah, they raised the possibility that things like stars and space in our universe might actually do this. Okay. But even then, people weren't convinced.

People said, well, they had this crazy assumption that the star has to be perfectly spherical. And stars are pretty round, but they're not perfectly round. Right. So that's where Penrose comes in. And he really shuts this line of thinking down and says, we're going to put in two simple assumptions. We're going to assume that energy should be positive, which is a pretty reasonable assumption to make. Yeah. And that means that gravity is attractive and light rays should bend toward each other.

His second assumption was that we just have to have a shape of space-time that has a surface called a trapped surface. Okay. And the trapped surface has the feature where at any point a light ray fired out

will fall in to that surface. So it's kind of like the event horizon. Not exactly, but the same vibe. So something that resembles a black hole. Yeah. And so he showed that with these two assumptions in these three elegant, beautiful pages of math, this really incredible paper, that you had to get an end to spacetime.

And so, you know, the key feature here was that this trapped surface could be bumpy, could be misshapen. He got rid of that spherical assumption that Oppenheimer and Snyder had required. And this really drove home the point that black holes with singularities should exist in our universe. And Penrose won the Nobel Prize for this in 2020. Now, there's a number of more recent papers that physicists have been producing that are

trying to take the lineage of Schwarzschild to Oppenheimer and Snyder to Penrose and take it a step further by adding some of the quantum ideas, the quantum weirdness, let's be honest, it's strange, to the models to see if they can get the infinite glitch to disappear.

Yeah, that's right. These very closely follow in Penrose's footsteps. I think of it as kind of like a trilogy of theorems, a trilogy of proofs. And Penrose's is perfectly classical, and then each one will add just a little bit of quantumness and see what happens. One of the first people to work on this was a researcher at the University of Maryland at the time, Aaron Wall, and this is back in 2010 or so.

So he was building on Penrose's theorem. And again, we had those two assumptions, right? Energy is positive, trapped surface. Now, everyone kind of knows that the first assumption isn't quite right. So quantum mechanics, like you said, it's weird. Energy is not always positive. It's not always positive. Okay. This is actually, this is in the realm of normal weirdness in quantum mechanics. It's something that happens.

you might wonder if that invalidates Penrose's proof, and then you can just erase singularities. He showed that isn't the case. So he found a stronger assumption, that is that black holes obey the laws of thermodynamics. In particular, they have this property called entropy, which describes very loosely how mixed up a system is. And so a black hole and its surroundings should have this property of entropy, and it should increase over time. And this is true of almost every system we know in the universe.

So in the model that Wahl came up with that added some quantumness, a new set of assumptions, in that model, singularities are still happening. Yeah, that's right. You still can. So adding a little quantum did not resolve the glitch. Yeah, and this is a big deal, right? It was kind of a proof of concept that...

the glitch can withstand some contact with quantumness. You can almost think of it as putting like an infinitely thin smattering of quantum matter throughout the space-time. And it's so small that you can't even detect it's there. But we do this, and a universe like that still has...

Singularities. You mentioned a trilogy of theorems. First one was Penrose, and then Walls was the second. Yes. So one thing black holes do is they evaporate. They emit radiation. And we know that, observationally, that black holes are emitting radiation.

You can't observe it, but it's very well established theoretically. This is what kind of made Stephen Hawking famous in the 70s. He calculated the temperature of the black hole, the radiation it was emitting. So this is very certain that this is a property of black holes. And so Wall's assumptions let a black hole do this. It lets it radiate. So in Penrose's universe, it wouldn't radiate. In Wall's universe, it does radiate. But the radiation doesn't actually shrink the black hole.

because the space-time cannot feel this infinitely mild energy.

quantum effect of the matter, okay? So it's a step towards our universe, but it's not quite there. In our universe, we expect that black holes do evaporate, eventually shrinking into nothingness, but it takes trillions and trillions and trillions of years. In Wall's universe, it would take an infinite number of years. An infinite number of years is kind of like trillions and trillions and trillions of years, so it's a good model, but it's not a perfect model. What's the third paper in the trilogy?

Raphael Bousseau, very recently at the University of California in Berkeley, he revisited Wall's proof using some kind of upgraded mathematical machinery developed over the last 10 years by Wall and himself and others. And so he showed that in a universe where the black hole does evaporate in a finite amount of time, trillions and trillions of years, that yeah, the singularities still exist.

This would be kind of like a universe with a little more quantum matter than before. It's still like a very thin gas, but it's no longer infinitely thin. It's finitely thin. You just can't get away from them. Okay. So we've added a couple of layers of quantumness

to our models and singularities still glitch out. Yes. The hope was that developing a model in which the singularities no longer happen would point a direction toward a quantum theory of gravity. But we haven't gotten there because the singularities keep happening. The models keep glitching out.

And we also are still not at a quantum theory of gravity, to be clear. Yeah. Right? So that big asterisk now with Broussel's recent work is that the spacetime is still classical. It can feel the quantum particles and it reacts to the quantum particles, but it still always has one fixed configuration. And so there still is the hope that someday if you let the spacetime really become quantum, that all our questions will be answered. Does this also raise the possibility that singularities...

aren't just a mathematical glitch, but that there is actually a thing in the center of a black hole or at the beginning of the universe when space-time itself, not just the math, but space-time is glitching and there is a singularity, an actual real existing singularity. Is that possible?

I would say that is the trend in thinking in the community of theorists like Bousseau and Jeff Pennington, a quantum gravity researcher at Berkeley in California, and some of the other people I talk to. And, you know, it's tricky, right? Because these proofs all rely on the second law of thermodynamics, which in the case of black holes relies on the area of the black hole. The area gives you the entropy, which should increase. Okay.

And they expect that this whole line of thinking kind of falls apart if you let everything get very quantum and very super position-y because you then, if space-time is here and there and all over the place, what's the area? Area doesn't even mean anything anymore. If we try to think of space-time in the same fuzzy way that quantum mechanics makes us think of electrons, the whole idea of area kind of falls apart.

Yeah, so I want to be clear. This is speculative. This is not approved. This is a vibes level argument. Okay. We're in the realm of vibes. That's good. Okay, but that's exactly right. And so the second law of thermodynamics, entropy, all this is breaking down in a fully quantum universe where matter and space-time can fully interact in a quantum way.

In which case, what are you even talking about when you talk about time? What are you even talking when you talk about space? So when you get to the center of the black hole, when everything's kind of falling apart, right, it might no longer make sense to say a clock ticks. There might not be a second clock.

after the second at which you are approaching the singularity. That could be the last instant. So this very well may be an end to space and time, kind of in a way that Penrose might recognize in the spirit of his original proof. What would that mean if a singularity is real and there's a place where space and time just end?

That's the million-dollar question, and we basically have no idea. But a common guess of how this might work in general is that the end of spacetime could be something like more of a feature than a bug.

We've been hopping between these two definitions of spacetime today, the infinite answers, that's the glitch, and the end of spacetime, like Penrose defined it. Now, those aren't necessarily the same thing. What if taking the end of spacetime seriously is a way to resolve the glitch of the infinite answers? I mean, if you don't have spacetime, then you also don't have the infinite curvature of spacetime.

It's kind of like the water droplet. It's an infinitely thin neck. That was a sign that we needed to change our language, start talking about a handful of molecules instead of a continuous fluid.

And when we talk about the molecules, then we shouldn't be thinking about thinness. We should be thinking about the distance between molecules or the number of molecules. Those are better questions and they have more meaningful answers. So if space-time breaks down in some real sense, then that might mean something new, something very quantum perhaps, takes its place. And then we need a whole new language to talk about that thing. But whatever language we use, it should be glitch-free. Our questions will have finite answers.

We want to get to a place where all of our questions about reality, the universe, and everything have answers. But right now, because of singularities and glitches, we have a place, a weird place, where there are no answers. So that means we have to ask different questions. That's exactly right.

If you want to learn more about this topic and explore it in more depth, you can check out Charlie's story on quantummagazine.org, Singularities in Space Time Prove Hard to Kill. Thanks again, Charlie. Thanks, Samir. We like to ask all of our guests for a recommendation, something that's exciting your imagination this week. What are you into?

I've been reading this great book by the physicist David Merman at Cornell University called Why Quark Rhymes with Pork. And so putting aside singularities and space-time, this is all, he's a quantum guy and a condensed matter guy. It's this collection of really delightful columns he wrote for Physics Today in the 90s and 2000s. In one column, he coins the famous phrase, shut up and calculate, which is a now famous way of describing kind of a philosophy of quantum mechanics. And it's just way funnier than any physics book has had a right to be.

So also on quantummagazine.org this week, there's plenty of quantum-related things, including a new approach to quantum computing, which is a world of computing that ideally rests on some of the concept of quantum mechanics that we were talking about. And there's another physics story about using geometry to better understand quantum materials as well. So you should check those out in addition to Charlie's story on quantummagazine.org.

we're going to leave you today with the actual sound of an actual black hole well sort of this is the sonification of data from the black hole at the center of the perseus galaxy cluster which is 240 million light years away the black hole causes ripples in the gas that surrounds it which scientists picked up 20 odd years ago with the chandra x-ray observatory

This particular sound has been adjusted to the range of human hearing, which meant raising it something like 57 octaves. So enjoy the sound of the Perseus Galaxy Cluster. The Quanta Podcast is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. I'm Quanta's Editor-in-Chief, Samir Patel.

Funding decisions by the Simons Foundation have no influence on the selection of topics, guests, or other editorial decisions in this podcast or in Quanta Magazine. The Quanta Podcast is produced in partnership with PRX Productions. The production team is Ali Budner, Deborah J. Balthazar, Genevieve Sponsler, and Tommy Bazarian. The executive producer of PRX Productions is Jocelyn Gonzalez.

From Quanta Magazine, Simon France and myself provide editorial guidance with support from Matt Karlstrom, Samuel Velasco, Simone Barr, and Michael Kenyongolo. Our theme music is from APM Music. If you have any questions or comments for us, please email us at quanta at simonsfoundation.org. Thanks for listening. From PR.