The Joy of Why - Is Perpetual Motion Possible at the Quantum Level?

Episode Date: May 4, 2023

A new phase of matter called a “time crystal” plays with our expectations of thermodynamics. The physicist Vedika Khemani talks with Steven Strogatz about its surprising quantum behavior. The post Is Perpetual Motion Possible at the Quantum Level? first appeared on Quanta Magazine

Hello, I'm Brian Cox. I'm Robin Ince, and this is the Infinite Monkey Cage trailer for our brand new series. We've got mummies, we've got magic, we've got asteroids. Mummies, magic and asteroids. What's the link? That it was an asteroid that magically went over the world that led to Imhotep the mummy coming back to life? That's correct. I thought it would be weird, scientific as ever. But the most important thing to know is that we are going to deal with the biggest scientific question we finally ask. What is better, cats or dogs?

Listen wherever you get your podcasts. I'm Steve Strogatz and this is The Joy of Why. A podcast from Quantum Magazine that takes you into some of the biggest unanswered questions in math and science today. In this episode, we're going to be talking about time crystals. What are they? Well, have you ever heard of a perpetual motion machine? And have you heard that they're impossible? Yeah, well, they are impossible in the world that we live in because of friction. But in the quantum world, all bets are off. So is there any way to play with quantum phenomena to make a state of matter that will keep changing back and forth, back and forth forever?

Well, my guest today is a member of a team that theoretically discovered the time crystal and helped realize it experimentally on a quantum computer. Theoretical physicist Vedika Kamani is an assistant professor of physics at Stanford University. In 2021, she received the New Horizons in Physics Prize from the Breakthrough Prize Foundation for her work on non-equilibrium quantum matter, including time crystals. She joins me to explain what time crystals are, how they're expanding our understanding of what's possible in the quantum sandbox, and whether all of this is consistent with the second law of thermodynamics. Welcome, Professor Vedika Kamani.

Thank you, Steve. It's great to be here, and thank you for having me. You're very welcome. I'm super excited to be talking with you. I think your work is spectacular, and I'm really curious to be talking with you. I think your work is spectacular and I'm really curious to hear more about it. So, you know, mentioning perpetual motion machines, that's an invitation to disaster on any science show since there really are all kinds of reasons not to believe in them. So maybe before we start talking about their possibility or impossibility in the quantum regime, why don't we just start with crystals? You know, people may have seen crystals at some kind of a shop downtown or they think of,

well, you tell me, what is a crystal to a physicist? So, yes. So, you know, when you see a crystal in a shop, maybe you see some beautiful amethyst crystal, diamond or rock salt on your tabletop. But to a physicist, crystals are defined in terms of symmetries and their breaking. And this is really a fundamental idea in how we think about phases of matter. So a phase of matter, you know, you may be familiar with phases such as solids, liquids, and gases. A phase of matter is often described in terms of symmetries. So one of the fundamental symmetries of nature is that of translation symmetry in space. Okay, so this means that the laws of physics look the same, right? So if I do an experiment here at Stanford, and then repeat it

where you are at Cornell, we should get the same results, hopefully, right? I can translate by any amount and the laws of physics would be the same. On the other hand, if you look at how a crystal is arranged, it spontaneously breaks this translation symmetry because the crystal doesn't look the same everywhere. What you see instead is a periodic array of atoms separated by space, and then there's an atom, and then there's space, and then there's an atom, and this continues forever. Okay, so given that there is this separation between atom and space, this crystal has spontaneously broken the continuous translation symmetry and arranged itself in this manner.

As far as breaking symmetry in space, I was thinking the image that came to mind when you talked about space and then atoms was like on a more everyday level. If I'm walking up a staircase, there's space between the stairs. And then when I'm on the landing of a stair, I'm in a special place. And it's kind of equivalent to the next landing above, as opposed to walking up a ramp, where in a ramp, every point is more or less the same as every other point. So the difference between a ramp and a staircase feels to me like the difference between continuous symmetry, that's like the ramp, and discrete symmetry would be more like the staircase or a crystal, if I'm hearing you right.

Yes, that's exactly right. And, you know, crystal is usually a solid phase, you know, like ice. Ice is a crystal. On the other hand, a liquid or a gaseous phase, in those phases, they look the same everywhere. They don't break translation symmetry. everywhere. They don't break translation symmetry. In a statistical sense, you could look at a little volume of water, and no matter which volume you pick, it always looks the same. So we say that liquids and solids or water and ice are in two different phases of matter because one of them respects the translation symmetry of nature and the other doesn't. The other spontaneously breaks it. All right. So now that we understand better what a crystal is, then what's a time crystal?

So just like we talked about translation symmetry in space, equally fundamental is translation symmetry in time, which means that if you do an experiment today or tomorrow or the day after, you should get the same answer. But, you know, space and time aren't the same because you can easily go forwards and backwards in space, but you certainly can't go forwards and backwards in time. And that's the reason that, you know, because space and time are different and systems tend to evolve towards these entropy-maximizing equilibrium states, which by definition are in rest, that's the reason why, you know, it had been believed and proven that in equilibrium settings, you couldn't get time crystals, okay? So the recent kind of angle on this work has come from this very different corner of physics, where we've been thinking about quantum systems that are fundamentally out of equilibrium. And that's one of the things that's very exciting

to me about time crystals, that it's an instantiation of this out of equilibrium quantum phase. So a time crystal is a phase of matter that spontaneously breaks this translation symmetry in time to show you some kind of periodic pulsing forever. So to show you some kind of periodic time dependence forever. So it's like the emergence of a clock in a system. But importantly, this should happen spontaneously, which means without any feed of energy or without any drain of energy. Okay. Because, you know, battery operated clocks are all around us. You can buy one on Amazon.

Right. Okay, good. I'm glad you're bringing that up because I had been sort of wondering, you keep saying spontaneously. So let's hear it again. Spontaneously is as opposed to something that's being triggered or driven to do its thing because of some battery or other source of energy? Exactly, exactly. Okay. So in a time crystal, unlike a clock that needs a battery or it has to be plugged into the wall, the time crystal is going to be some kind of thing that goes back and forth or changes in a clock-like manner without a source of energy?

That's right, yeah. So there's no net input of energy in the system, and it should be able to spontaneously, off its own accord, show you this kind of periodic motion in time forever. It sounds like science fiction. Yeah. I mean, once you dig into it, it really is science and not science fiction, but it's pretty cool.

It's sort of hard to believe. You know, we're so used to thinking of, like, say, anyone who's had a grandfather clock, you know, which is based on a pendulum swinging back and forth. They do pretty well for a while, but if you go inside the pendulum clock on a grandfather clock, there are some weights that start to get lower and lower. And, like, after a week goes by, they're down at the bottom and you have to lift them back up again. Like that's putting source of energy into the, to keep the clock running. What's different about it? Like, how can a time crystal avoid that? Great question, Steve. So we indeed can use just a simple pendulum to understand why the second law of thermodynamics and the first law of thermodynamics would tell you that time crystals or perpetual motion machines are impossible. And indeed, this had been the

accepted wisdom for centuries. And the recent developments that have enabled us to see a time crystal have come from a corner of physics in which these laws of thermodynamics simply don't apply. So we'll get to that later, but let's come back to the pendulum. And, you know, for the pendulum, as you said, you know, it should need some source of energy, right? It should need something, it needs to be rewound. And one simple reason for that is friction. Okay, so your pendulum is swinging along, and there's friction in the ball bearings, and that causes some dissipation of energy. But, you know, let's be theoretical physicists for a moment and just live in an idealized world where we say that, you know, there is no friction, and we've stuck our pendulum in a perfect vacuum jar, which is frictionless.

So, you know, we can sidestep the first law of thermodynamics or this loss of energy due to friction by working in this ideal environment. But even then, we have to contend with the second law of thermodynamics, which says that systems relax to entropy-maximizing equilibrium states. lax to entropy-maximizing equilibrium states. So what this means for the pendulum is that if you think of the pendulum as just one single particle, if you could take one particle at the end of some string and have it moving, and you stuck that in a frictionless environment, indeed, that could go forever. But an actual pendulum bob is a many-body system with many, many atoms. And there's a center of mass mode for the pendulum that can swing forever.

But over time, the energy gets redistributed from the center of mass mode into all the other numerous internal modes of all the atoms making up the pendulum bob. other numerous internal modes of all the atoms making up the pendulum bob. And eventually, that motion, that redistribution causes the pendulum to come to rest in this entropy maximized equilibrium state. So if I get you, you're saying if I had a rod, like say made of steel, and then at the end of the rod, there's a heavy ball. That's my pendulum bob. Even if I had a perfect bearing at the top of the pendulum's arm so that I wasn't getting any friction from swinging on that bearing. If I hear you right, you're saying that over time, the swinging of the pendulum would cause the iron or the steel bar to sort of internally – it's made of atoms too. Its atoms would start jiggling. It would seem imperceptible to the naked eye, but there would be some kind of jiggling or heating up or something happening to that suspension rod that over time,

even with a perfect bearing, would cause the pendulum to damp out. Exactly. And even if you didn't have a suspension rod but had an invisible perfect string, the bob itself would have many, many atoms. Ah, the bob. Okay, man. It's really hard to get around this second law. Exactly. It's kind of silly, but I'm trying to imagine what the, you know, you've mentioned continuous symmetry in time or discrete symmetry in time. Is there a way you could sing them for us? Like what would continuous symmetry sound like? What would discrete symmetry sound like? Okay.

So continuous symmetry is just a constant hum, if you will. Whereas discrete symmetry would be beep, beep, beep, beep, beep. So a periodic repetition forever. Now a time crystal actually, the time crystals that we've realized, they actually don't break continuous translation symmetry, but they further break discrete translation symmetry. So that means that the system, the equations that we started with already had beep, beep, beep, beep, beep. And the time crystal then comes in and does beep, bop, beep, b is now repeating every two seconds. Okay. So it breaks that discrete symmetry further down to an even smaller discrete symmetry. Okay. And is there, I mean, it sounds like a kind of jazzy tune, but I'm wondering why to a physicist would that be notable? Like why is that a, Because it is kind of a big deal, you and your colleagues with the experimental realization of them.

What's exciting about this for you? So for me, what's really exciting about this is that time crystals are a new example of a non-equilibrium phase of matter. Okay, so I'm a many-body physicist. I study the emergent phenomena of systems with many, many particles. And this has been a very rich playground. You know, you can't talk about phases of matter for a single atom. It's impossible to say whether a single water molecule is in a liquid phase or a solid phase. But when you put together billions and billions of atoms, many, many particles, then you can get all sorts of novel emergent phenomena, ranging from the familiar solids, liquids, and gases to much more exotic things like semiconductors

and superconductors. And much of the last several decades of quantum physics has been spent inodynamics. And the reason for that is that it's really, really hard to describe systems of billions of particles. There's something in quantum mechanics, there's quantum states live in what's known as Hilbert space. And Hilbert space is exponentially large. If you think of the state of just one particle, that can maybe be, let's just simplify and say, and it could be one of two states, up or down, head or tails. But now let's look at two particles. You know, now there's four states. Look at three particles, there's eight. And this number quickly grows astronomically. So in describing systems of many, many particles,

it's hopeless to try to keep track of every individual particle. Instead, what we do is rely on some macroscopic statistical descriptions of these many particle systems. So you can talk about things like temperature, density, and you use these macroscopic variables to characterize your quantum state. And then in terms of that, and then you can take those equilibrium states defined in terms of a few macroscopic variables and talk about phases of matter. Okay. So this has been the program for the last several decades.

But, you know, equilibrium is just a tiny, tiny corner of everything that's possible. Right. If you think of the world around you, nothing is in equilibrium. Right. So thinking about equilibrium states is such a small corner of what's possible in the description of quantum mechanical systems. of what's possible in the description of quantum mechanical systems. And now for the first time, we actually have a window in both experimentally and theoretically, we have a handle on how to think about non-equilibrium states of quantum matter. And in these non-equilibrium settings, it's possible that the laws of thermodynamics that we relied on so extensively simply don't apply. I'm in equilibrium. I'm not moving. I'm balanced. But what do you mean when you say equilibrium? Because you keep talking about many particles or many body systems. So what's kind of in simple terms, what does it mean to be in equilibrium or what does it mean to be out of equilibrium?

By equilibrium, I mean that certain statistical macroscopic properties of the system don't change in time, even as microscopically the system could be all over the place and constantly changing. Okay. Like I'm sitting here in a studio where the air in my room is keeping, I didn't notice any sudden chill in the room. The temperature is staying the same, but the individual air molecules are zipping around in the room. the same. But the individual air molecules are zipping around in the room. Exactly. So imagine that you created a barrier. Suppose you painted all the air molecules pink, and you picked one molecule and you painted it black. And let's say that you start with a barrier so that all your molecules started in one half of the room, and then you lifted the barrier and you waited a little bit, okay? Then very quickly, the density of these molecules would look uniform statistically

everywhere. But if you try to take that one tracer molecule, which was black, that's still zipping around like crazy, right? So if you were trying to track that one molecule, that's never an equilibrium. But if you're trying to track something like the density of molecules in any one region of space, then that shows some initial transient and then settles down into a near equilibrium state, right? Yeah. And I think people know this from the days when smoking used to be allowed in public places, right? Like somebody over there is emitting a puff of smoke and then if you waited long enough and like you were stuck on a plane with them or something, that smoke would diffuse around the whole room and eventually, you know, let's suppose they've stopped smoking now. That like the whole room would be uniformly filled with these smoke particles and you wouldn't notice any plume or any structure. Yeah.

Okay. So things come to equilibrium sort of in these conditions if they're closed off and just no energy coming in or going out or, yeah. Okay. But so what's out of equilibrium look like? Out of equilibrium would shockingly be that suppose you started again with all your air in the right half of the room and you lifted the barrier and then you waited and you waited and you waited and you waited and you came back and you still found that most of your air was stuck

in the left half of the room, even though there wasn't any physical barrier preventing it from leaving. That is a weird image. Yeah. So that sounds crazy. But in an actual system of quantum atoms, in the quantum setting, this is a phenomena known as many-body localization. Localization just means things get stuck. So this experiment was actually done in the lab in an experimental group in Germany where they prepared an atomic trap where all the atoms were on the left half of the trap. And then they waited for a long time, as long as their experiment would allow. And then they came back and they preferentially the atoms preferentially remained in the left half of the trap. and the atoms preferentially remained in the left half of the trap. So in the quantum setting, we now know that this is the possibility.

And the reason that this completely gets around the second law of thermodynamics, I don't want to say it breaks it. It's just a setting in which the law of thermodynamics doesn't apply. And that's because the second law of thermodynamics tells you that systems reach entropy-maximizing equilibrium states. Okay, so by entropy-maximizing, it just means it's going to go everywhere it can go. Okay, so it just explores everything that's available to it. But in these settings that I was telling you about, if you start with atoms in the left half and they remain in the left half, then they're clearly not exploring all the space that's available to them because they're not leaking into the right half, right? So we're talking about quantum systems that can remain out of equilibrium,

which means that all of our usual notions of how to think about phases of matter constrained by the laws of equilibrium thermodynamics should be revisited. And what's really exciting is that the full universe of everything that we might be able to get in this new out-of-equilibrium quantum setting is just completely open. So time crystals are just the tip of the iceberg. And I think it's just one very striking example of some kind of new out of equilibrium phenomena. But really, what's exciting to me is what else is out there? You know, everything that we that we thought we knew we can now reimagine. These amazing possibilities that you're describing

of these quantum many-body systems that somehow manage to stay far from equilibrium, I don't know that I've ever seen one in my house. Is this something that occurs in the natural world? No, no.

So unlike diamond or rock salt, you know, you can't go mining for time crystals. So these are phenomena that exist in highly engineered quantum systems that remain out of equilibrium forever has been motivated in part due to experimental advances in building quantum coherent and controllable systems. It sounds like you're about to say quantum computing, that there's this race around the world in China, in the US, in Europe to build this thing that people have been talking about for decades now, the idea of using quantum mechanics in a new kind of computer. So that's the hardware it sounds like you're talking about. Yeah, that's right. And indeed, a lot of this effort has been motivated by the

quest to build a quantum computer. We're very, very far from there now. And whether or not we eventually get there, these new systems, these new platforms that labs around the world have built are already amazing as new types of experiments from any body physics. I want to just underline that. I don't want to cut you off, but I just think that's such a cool thing that you just said. I want to make sure our listeners heard that. Because people have heard all this hype about quantum computing and how it's going to break our cryptography on the internet or it's going to this or it's going to that. Okay, we'll see. That may turn out to be true or not. But as you say, we're far from that. But what we do have is what you just called these quantum platforms that may someday give

us quantum computers. But right now, they're giving us these new quantum playgrounds or sandboxes to do very interesting experiments and see weird new physical phenomena. Exactly. And these new experiments allow us to probe quantum matter in ways that are extremely different from the experiments that we had access to. You know, in the past, your experiments were designed to probe near equilibrium phenomena. You start with some sample, you connect some leads to it, maybe the leads are at slightly different temperatures, you see some current flowing through the sample, you know, so but these new types of quantum experiments are giving us access to completely novel new regimes of quantum systems, in particular, out of equilibrium regimes. And they're also allowing us new types of probes into these kinds of quantum platforms. So for me, what's really exciting is that we have new experiments that allow us to ask questions about new regimes in which quantum matter can exist. And so you collaborated with some people on this. I mean, you don't have the quantum platform that we're talking about in your lab.

No, no, I'm squarely in theory land. Okay, you're a theorist. All right. You don't even have a lab, it sounds like. Yes. But so who did you work with? What group? So we worked with the Google team. So Google has been one of the leaders in the effort to build these quantum devices. And in particular, they have a chip called their Sycamore chip. So we worked with their team to use their controllable quantum platform to realize this time crystal phase. Uh-huh. And so what are some of the ingredients then?

In your time crystal, you've mentioned the Sycamore chip from Google. Is that enough? Do you need any other components? So what does the Sycamore chip allow you to do? So right now, we're thinking of this quantum platform as a quantum simulator. Now, this chip, in trying to build a quantum computer, what it allows you to do is realize a system of qubits. Okay, so what are qubits first? You know that in a classical computer, you have bits, which are zeros and ones. And fundamentally, which are zeros and ones. And fundamentally, all computation is reduced to strings of zeros and ones and operations acting on those strings. Okay. You know, instead of a bit, we have a qubit or a quantum bit. And this qubit is going to be in a mixture or superposition, a coherent mixture of zero and one,

until you go in and make a measurement. And when you make a measurement, then you know whether it's zero or one. Okay. But now in your case, you're not going to be using the Sycamore chip or this quantum platform to compute anything. You're not trying to solve some difficult computational problem. But you are trying to use the quantum platform's ability to do amazing tricks in time. It sounds like. And you tried to get it to do, we were talking about beep, beep, and beep, bop, beep, bop.

Is that, can we, maybe we can tie it back to that now? What did you get your chip to do? Or, yeah. Yeah. So any computation is just a time evolution, okay? But if you wanted to factor integers, that's a very difficult, very specific type of calculation, which is very hard to do. But in the meanwhile, now that we have these gates, which make the qubits interact in certain ways, to get the beep, beep, beep, beep, beep part of it.

Let's say we have two types of gates, just to simplify this. Okay, we have a type of gate that causes the qubits to interact with each other. And then we have a type of gate that flips the state of the qubit. Okay. So what the quantum platform can do is apply a sequence of gates in a periodic fashion. So let's say I apply a layer of the interacting gates, a layer of the flip gates, a layer of the interacting gates, a layer of the flip gates. And then I can continue that in this periodic pattern. So that's the beep, beep, beep, beep, beep, beep.

I see. You're imposing that on the chip. I'm imposing that at the chip. But the chip doesn't respond with that same symmetry. Exactly. And then I go in and I measure my system after every beep, beep, beep, beep, beep. But I find that, oh, actually the state does beep, bop, beep, bop, beep, bop, and only comes back to itself every two periods and doesn't respect that symmetry. And what's important to call it a phase of matter is that all of this is stable. Okay, so then you can go in, and you can change the parameters of the interaction gates. You can change the

amount by which you flip it. Okay. And in some extended range of parameters, you continue to get this beep, bop, beep, bop, beep, bop response. I see. So it's not a very delicate, like super cherry picked kind of thing. It's pretty robust. Sounds like it's totally robust. Exactly. We called it absolutely stable in one of our works. And that's important. You know, you want to call it a phase of matter. This is really, this is really very, very robust. It's not a fine-tuned evolution in any way. Can you share with us your own feeling when you first realized that this idea that you had years earlier was working in real life? Like, did you jump around the room? Did you start singing?

What did you do? No, because it was a long path here, right? So we had this idea years ago, and sorry, I don't know, no sounds very negative. You could say whatever. Tell me the truth. What happened? Yeah. No, this wasn't really like a Eureka moment, but it was several years in the making. So, you know, we had this theoretical idea of a type of evolution, a type of system that would show this phenomena. you know, saw pieces of this and very quickly tried to realize some of this physics in lots of different platforms. And, you know, all of these precursor experiments saw certain aspects of the physics, but not the physics in its full glory. In its full glory, you know, the definition of this phase of matter is through something called eigenstate order, which extends across the entire spectrum of the system. It's quantum coherence at very, very hot temperatures, you know, that's not fully accurate, but at very high energies, okay? And no experiment had really seen that part of it, okay? So what we

did in the several years since the theoretical conception and the precursor experiments is really work to identify what would it take, you know, what are the types of programmable interactions we would be looking for in a quantum platform? And what are the types of capabilities for measurements we would be looking for in a platform to be able to do this type of experiment. And that required just a lot of detailed analysis of what different experiments had done, what they had achieved, what was missing. And then looking around, we were like, okay, the Google experiment in its current incarnation with the capabilities that they had is a good platform, checks all the boxes to be able to realize this physics. So then we approached the Google team

and it went from there. Now, this idea of using these quantum platforms, you know, as computers, it's actually a sort of an old idea, isn't it? Going back to Richard Feynman, the great Caltech physicist and joker, wisecracking, mischievous. Also a great teacher, problematic person in certain respects. But anyway, Feynman had this vision of quantum computation. I wonder what – maybe you could summarize for us. What did he think quantum computers could be used for? And what do you think he would have thought about what you did? Just to speculate. Actually, Feynman was the one who said,

if you're trying to simulate quantum matter, well, use a quantum computer, right? Because quantum matter lives in this exponentially large Hilbert space. So trying to simulate quantum systems on your classical computer, you're trying to fit a square peg in a round hole. It's just not designed for that. You know, I think Feynman really got us started on this path of thinking about these quantum systems as quantum simulators. And our experiment is really an example of a quantum simulation. Do physicists need quantum computers? Like, do you think that computers using either the Sycamore architecture or something else will actually help physicists continue to understand or even discover new exotic forms

of quantum matter? Yeah, and I think they already have, right? Because I think the ability to experimentally realize and study and probe quantum matter in all of these different non-equilibrium ways has forced us in theory land to really think about all the amazing things that quantum systems can do in regimes that are far from what we were used to thinking about. And this has already led to many amazing new kinds of phenomena that we have understood, like time crystals, on new possibilities for out-of-equilibrium quantum systems. And indeed, the hope is that at some point, you know,

this new theoretical understanding of what isolated quantum systems or quantum dynamics can do will then feed back into also pushing the envelope in building better quantum platforms. So I think that's a very productive cycle. Well, I'm sure some of our listeners are wondering about that, that do we expect to see applications coming, you know, outside of a physics laboratory? Well, say for time crystals or maybe the successors to time crystals, the even more exotic states of matter, could we ever have something like the way that the transistor was once an exciting quantum system that then now it's in every, you know, every radio, every computer?

Yeah, I think you answered the question, which is the reason I work on this is for the joy it gives me to understand what different quantum systems can do. But anytime you have a new stable phase of matter that can do unexpected things, you know, the possibility that down the line it could be used in some kind of application is always real, right? Like when Einstein was thinking about general relativity, he didn't foresee that it would make its way into your GPS on your phone, right? And like you said, when people were thinking about semiconductors, they surely couldn't have envisioned the semiconductor revolution that followed. Well, it's a very inspiring example of curiosity-driven research. I mean, I love the way you come out and say that you're doing it for the joy, just to probe

the strange and fascinating behavior that's possible in quantum systems. And we don't know yet where it will go, but we need people like you with curiosity doing it just for the excitement of it. So Vedika, Kamani, thank you very much for talking with us today. Thank you, Steve. It was a lot of fun. Stay up to date on the latest happenings in science and mathematics. Sign up for the Quantum Magazine newsletter. It's free, landing every Friday in your email inbox. Head to quantummagazine.org for more info on how to sign up. The Joy of Why is a podcast from Quantum Magazine, an editorially independent

publication supported by the Simons Foundation. 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 Joy of Why is produced by Susan Vallon and Polly Stryker. Our editors are John Rennie and Thomas Lin, with support by Matt Karlstrom, Annie Melchor, and Allison Partial. Our theme music was composed by Richie Johnson. Special thanks to Bert Odom-Reed at the Cornell Broadcast Studios. Our logo is by Jackie King.

I'm your host, Steve Strogatz. If you have any questions or comments for us, please email us at quanta at simonsfoundation.org. Thanks for listening.