321 | David Tong on Open Questions in Quantum Field Theory

0:00:00.5: Hello everyone. Welcome to the Mindscape Podcast. I'm your host, Sean Carroll. In the last AMA, the last Ask Me Anything episode, we touched on an issue that has talked about a lot in the set of online discourse involving people who care about physics and people who care about science, which is the rate of progress in physics. Are we making progress as fast as we should or in science more generally? Personally, I think that in science more generally, or even in physics, outside fundamental theoretical physics, the rate of progress is really, really good. And we have nothing to complain about, although people will complain just because they don't have their flying cars. There is something to be said about the rate of progress in modern fundamental physics. From the inside, it just makes perfect sense that the rate of progress is not as big now as it was in the 1920s, a hundred years ago, or even in the 1960s, because you have to deal with the hand nature deals you. You have to play with the hand nature deals you. You don't get to pick your cards. We don't have as much experimental input and puzzles to solve, and we have a really mature theory that works too well, et cetera, et cetera. There's a whole bunch of things to say about why we're not having earth shattering discoveries in particle physics and gravity as frequently now as we did a hundred years ago. There's a counter way of thinking about it, that it's all because of sociology and group think. And there are powerful personalities who are keeping good ideas down, which is, I mean, I want to say it's nonsense, but it's not 100% nonsense, it's like 98% nonsense. Physicists are people. Some of them do have strong personalities and strong opinions, and others will say like, yeah, if that person thinks it's a good idea, maybe it is a good idea.  

0:01:51.4: But it's really hard sometimes to explain what theoretical physicists are spending their time doing in this world where we have a pretty good theory already. So, today's podcast in part addresses that question. David Tong is a very distinguished theoretical physicist, quantum field theorist in particular, at Cambridge University. And we're actually talking about two separate things. One is that David has launched on an incredibly ambitious effort to write a series of textbooks that basically explains everything that a young theoretical physicist needs to learn. It's sort of the successor to the famous Landau and Lifshitz series of books from the 1950s. So David is starting with classical mechanics and then going through electromagnetism, quantum mechanics, statistical mechanics, fluid mechanics, all of the things you need to know. Hopefully eventually he'll get to general relativity and quantum field theory. So, why would you do that as a working theoretical physicist?  Why would you write so many books? What is the need for them? We'll talk about all that stuff. But then moving on specifically to quantum field theory, which is David's stock and trade. What's going on? What does it mean to do research in quantum field theory when you don't have an experiment to explain? Well, the answer is, there are little things going on in quantum field theory that remain mysterious to us. And how can you say that you don't have a good idea of where to go next if there are still things in the theory you don't completely understand? So, it's a little bit technical from point to point in the discussion. I thought we could indulge ourselves in this particular case, because I really wanted to give a feeling for all the exciting stuff. There's more than one topic that is going on in theoretical quantum field theory right now. If anything, I just hope that people can get a flavor for how the working physicist thinks about these things. And David is a wonderful, wonderful explainer of difficult ideas. So I think even if not every bit of jargon makes perfect sense, the spirit comes through very vividly, and hopefully we'll all enjoy it. Let's go.  

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0:04:13.3: David Tong, welcome to the Mindscape Podcast.  

0:04:15.0: Thank you very much. Pleasure to be here.

0:04:17.2: So obviously the immediate impulse for impetus, I suppose, for inviting you on the podcast is that you're publishing a billion books at the same time. And that's both scary and impressive that you're doing that. Tell us about the book series. I know that it's obviously textbooks, not trade books, but still of interest to the audience.

0:04:38.6: That's right. So there is a little less than a billion. There were four that came out two weeks ago. The plan is, do you know what? I put in a proposal to do 10. That was my original plan. I said to the publisher, I wanted to do 10 covering most of theoretical physics. I didn't quite have the heart to commit to that in the books. In the books, it says this is a series of N where N is much bigger than one. And we will decide in the future what N is. So the plan was an ambitious one. The plan was to write a series of textbooks covering, all of theoretical physics is a silly thing to say, there's no way I could cover all of theoretical physics, but to cover the parts of theoretical physics maybe that I understand or I would like to understand. And to just tell the story from really the beginning. F equals ma in Newton all the way through to our modern understanding of quantum field theory. That was the small goal that I set myself. And it's not quite as crazy as it sounds. So for 20 years, I guess, now I've been writing lecture notes. I do a slightly weird thing where I teach a new course every single year. I think that's a little unusual. But I just really enjoy learning physics. Best way to learn physics. Best way to learn physics is to do research on it. But I'm not that good. So the second best way to learn physics is to teach a course on it. So I teach a course, new course every single year. I've been writing up lecture notes for 20 years now. And the plan was to somehow bring those together and start filling in the gaps that are obviously there. Improve them and just formalize them a little bit.

0:06:28.3: I found that the best way, other than doing research, to learn physics is to write the book about it. Because in teaching, you can still kind of cheat sometimes. You can kind of leave things for the students to fill in or whatever. But in the book, you kind of got to get it exactly right.

0:06:45.1: I guess that's true. I like cheating. That's an important part of teaching. It's figuring out what details it's important to get right and which ones you can wishy-washy a little bit. It's why teaching physics is much easier than teaching mathematics. I have taught mathematics courses. When we teach general relativity in Cambridge, we do it properly. We do differential geometry. We do it very, very rigorously. It's very hard to hide when you're teaching mathematics. Very hard. Very hard to lie. Very hard to argue by force of personality alone. In physics, that's very easy.

0:07:27.0: Oh, yeah.

0:07:27.9: Just sort of push through. There's a bit of bombast. So I'm not afraid to do that when necessary.

0:07:34.2: Okay. So what are the books? What are the titles?

0:07:37.5: So, the first one is classical mechanics. Starts, at the beginning as I said, starts with Newton. Newton was in the college in Cambridge where I'm based, Trinity College. His presence looms very large. So starts with Newton but then moves through. The plan with all the books is that they start basic. Basic means first kind of course you're going to see at undergraduate level, but then they really move through to teach you what I would say you would need to know as a practicing physicist. They don't do all the details but really a working knowledge of theoretical physics and for classical mechanics that means topics such as Lagrangians and Hamiltonians. There was this interesting development where in the centuries after Newton other mathematicians/physicists reinterpreted what he did, and it's actually those reinterpretations, different ways of looking at things, focusing on things like energy rather than forces, which is the important way moving forward.

0:08:44.8: And book two?

0:08:47.0: Book two is electromagnetism. Basically the story of electricity, magnetism and light, how they all fit together. There is an amazing set of equations called the Maxwell equations that govern everything. I like the way this one works actually. The book starts with the Maxwell equations. I think page six or something has the Maxwell equations.

0:09:11.8: Wow. Okay. Because usually you move up toward that carefully because the notation is not necessarily familiar, right?

0:09:19.3: Good. So the last, there's appendices, there's 100 pages of appendices where I do all of vector calculus. So if you want to start, you start on page 300, not page one, and you learn vector calculus. But then for electromagnetism, it's not the way it's usually taught. Usually you end with the Maxwell equations, you build up how electric charges work, how magnetic charges work. I like doing it backwards. If you've got the maths, you write down the Maxwell equations, everything else is commentary. That's literally everything you need to know about everything to do with electricity and magnetism. So I like that way of doing things, of teaching physics, of having the fundamentals there and then working somehow, I don't want to say backwards, backwards compared to everybody else, but forwards in some sense.

0:10:07.4: Well, we're competitors because one of your books is quantum mechanics and I'm in the midst of writing my own quantum mechanics textbook.

0:10:16.2: I beat you to it.

0:10:17.1: You did. We'll spare the audience, but there's a tremendous amount of thinking that just goes into what order you present things in a quantum mechanics textbook, where the Schrodinger equation goes, where qubits go, all that stuff.

0:10:36.8: That precise one is, as you know, I'd be interested to know what you did, is a big one, because you've got these two different ways to approach it. One is mathematically more complicated, the Schrodinger equation, all sorts of horrible mathematical subtleties you have to either deal with or sweep under a rug. Right. But of course, it's much more in contact with things that you know already, with just ideas of how particles move. Other one is mathematically trivial, but you ask, this is to do with qubits? And you ask, why on earth are you doing that mathematics? Why is that the thing that connects to anything else that I've ever seen? So, which did you take?

0:11:16.9: Well, you tell me first, because yours is coming out first.

0:11:19.8: Okay. I greatly value the connection between different ideas in physics. It's why I'm writing the series, precisely so you can see how different ideas in physics connect to other ideas, some of it very obvious, some of it much less obvious. So for me, it had to be the Schrodinger equation. It had to be Schrodinger equation where you can see how it's really connected to volume one, classical mechanics, how one goes into the other. But then I felt guilty.

0:11:46.0: Of course. So, you mean, you feel guilty no matter what though, is the problem?

0:11:50.4: That is right. So then I jump and do the qubit very early, like chapter four or something.

0:11:54.2: Well, that's close to what I do, because in order to be a little bit different, there's qubit books out there, and there's Schrodinger equation books out there. And I figured just do both right away. I think that it makes sense to say the Schrodinger equation for a point particle. Because like you say, the students know what a point particle is classically, and now you're telling them what is quantum mechanically. That's something they can wrap their minds around. But oh my goodness, you have to hide so much math under the rug. So I very quickly say the states are vectors. They're in an infinite dimensional space. Maybe it'll be easier if we thought about the two dimensional case and really worked on that.

0:12:35.0: Yeah. That's right. That infinity right there, even for just a free particle that's got no force acting on it, just a free particle, like unbelievably complicated, really annoyingly complicated.

0:12:45.4: I'm trying to teach myself the algebraic approach to quantum mechanics and quantum field theory. Are you into that?

0:12:52.7: Quantum mechanics, yes. But quantum field theory, that's operator algebras, things like this?

0:12:58.0: Well, thinking of states as, this is going to be fun for the audience, as linear functionals on operators, namely the expectation value. You can express a state by saying what the expectation value of every possible operator is, and that gets you like algebraic quantum field theories where the mathematicians prove theorems.

0:13:16.3: I concede. I'm going to duck that. [laughter]

0:13:18.6: Yeah. Okay.

0:13:19.7: Duck that as much as I possibly can. Is this going in your book?

0:13:25.8: Oh, no. Certainly not. No, that's just for research purposes. But I've reached the point in my life where I'm like... I guess I've cycled back around to the graduate student phase of my life where I'm looking for new reasons to learn new things, and this is a great excuse.

0:13:43.3: Yeah. That I empathize with, which again is large part why I'm writing the books. It's entirely selfish endeavor, so I get to teach myself lots of wonderful physics.

0:13:51.7: Okay. So we've mentioned classical mechanics, E&M, quantum mechanics.

0:13:58.7: And the last one is interesting, at least for me, it's fluid mechanics.

0:14:02.6: Okay.

0:14:03.4: And I'll admit, I have sort of inappropriately grandiose plans for my fluid mechanics textbook, which of course will crash. I don't think fluid mechanics gets the respect it deserves in physics departments.

0:14:19.4: I'm on your side.

0:14:20.9: You are?

0:14:21.5: Yeah.

0:14:22.9: I don't think it's taught often in physics departments. I don't know about you, but I got shoved over to an engineering department to learn fluid mechanics. I thought, immediately, because I'm a little bit arrogant, I thought, well, these engineers can't possibly have anything to teach me. And somehow that sort of seeps through the whole subject. If you open any fluid mechanics textbook, it will tell you why is fluid mechanics important. It's because we can understand how planes fly, and we can understand how you push oil through pipes to minimize the energy loss, and we can understand how the climate works and how the climate manifests itself in weather and why pushing oil down pipes screwed up the climate so badly. And all of these things are true, but it's never been the kind of argument that really excites me as a physicist.

0:15:08.1: Theoretical Physicist. Yeah.

0:15:08.9: Exactly. And so I wanted to get across the theoretical physicist's perspective, which is very straightforward. It's that you take anything in the universe, it doesn't matter what it is, you throw a bunch of it in a box, you heat it up, and no matter what you started with, that stuff is described by the Navier-Stokes equation of fluid mechanics. And that's an amazing statement. There's billions of things in the universe, and we go to enormous lengths to try and study them, and yet somehow in a particular regime, if things are hot enough, all of those differences just literally evaporate. And what you're left with is essentially the same. And so I wanted to get across, why is that universality true? Where does that come from? That's sort of why fluids are interesting from a physics perspective. And of course, I do all the exciting things like why planes fly and why stuff goes turbulent when you push it fast enough down a pipe, because it's all beautiful as well. But the emphasis, I think, is a bit different from most fluids textbooks.

0:16:07.0: And for the audience, fluids in this case includes gases as well as liquids.

0:16:11.8: That's right. Even speaking now, having written the book, whenever you say fluids, you sort of think liquids in your head, of course.

0:16:19.9: Yeah. Exactly.

0:16:20.3: It's anything that flows. And so a gas or a liquid, and in many ways gases are the things we understand very well. When the particles are far separated, we've got all sorts of control over this. You can start with 10 to the 23 particles in a box and just derive the Navier-Stokes equations if they're far separated. It's a beautiful calculation, which is chapter something of the book. But you can't do that for a liquid. Liquids are much more complicated than gases.

0:16:49.4: Do you talk about the famous outstanding math problem? There's a millennium problem about proving the existence of solutions to these equations.

0:16:58.2: I talk a little bit about it. I certainly point out that it's there. The problem is in the full, what's called the Navier-Stokes equation. Navier-Stokes equation has one really annoying term, which is the viscosity term. It's the term that captures the friction between fluid as one bit rubs against the other. If you get rid of that, and then you have to add an ingredient. You have to allow the fluid to be more like a gas so that it's compressible. And in that context, you can show that shockwaves emerge. If you start with certain initial conditions, then you will find a singularity. That's exactly what we would like to prove or disprove in the Navier-Stokes equation. I talk quite a lot about shockwaves. I dug into a lot of the history of this. The paper that first discovered shockwaves is rather wonderful because the guy did the calculation and then didn't believe it and then checked it over and over again. He kept finding this infinity, this singularity. So he finally wrote a paper saying, "I know I've done something wrong. This can't be right, but I can't figure out my mistake. Hopefully somebody else can." So I go through that and then I talk about the singularity problem, the millennium problem, but also compare it to the issue in general relativity as well. In general relativity, there's also a question of when do singularities form? We know they do form, but there's a conjecture which seems even harder than the millennium prize problem of Navier-Stokes. The conjecture is that when singularities form, they appear inside black holes. They're shrouded by event horizons. And so you never get to see them. So the fact that the two preeminent equations of classical physics, Navier-Stokes and Einstein's equations of GR, both have very subtle things that after at least a century, mathematicians have still not got on top of strikes is curious. So that's sort of the take I make on that. I don't talk about all the details, but just the conceptual idea that singularities are important and poorly understood.

0:19:05.9: So these are the four books that are coming out or will be out. I don't know. By the time the episode gets released. How close are we to the rest of the 10?

0:19:15.7: Oh, I don't know. Volume five is statistical mechanics. Volume six is condensed matter. They're both about 400 pages each at the moment. They're probably going to get to 700. So, I'll be honest, I feel a bit knackered, I feel a bit tired after getting these through. You know better than me. Everybody tells you don't write a book. It's stupid. It takes up way too much time. I remember long ago when you had the blog. This is maybe 20 years ago. You had some very thoughtful, honest blog posts about how you felt about writing your great textbook, about writing popular books. And it's a lot of work. And the horrible thing is it's not the writing. You think you're done. You finally close down the lid of your laptop and say, yeah, I've finished. All that work. And at that point, I think you're less than halfway there. Because you send it off to the publisher and then there's all this copy editing. And they get these professional grammar Nazis, basically, who tell you you have to change this and you have to change that.

0:20:28.3: I don't want to call them Nazis. They were lovely people. They helped me greatly. But they all had very insistent opinions on where commas should go. And they all had completely different ideas of where commas should go. So, I was sort of fighting with this. In some sense, I've always thought a comma is a gauge choice. You don't get to put a comma anywhere you like. And this has reinforced that. But yeah. The work was pretty tremendous. So I'm trying to take some time off. It might be a couple of years until the next ones come out.

0:20:59.9: But surely at least quantum field theory and general relativity have to be books, right?

0:21:05.7: That's right. I think... Where was I? Five and six. Yeah. Volumes seven and eight are going to be QFT and standard model combination of those two. I'm going to do GR later, actually. Because it's a classical field theory. And logically, it could have come in volume three. Famously, Landau and Lifshitz, that amazing Russian collection of textbooks, has Maxwell's theory of electromagnetism and general relativity all thrown in together. Classical theory of fields. It's just one. But I sort of noticed there are some pretty good books on general relativity out there already.

0:21:43.8: It's a tough market.

0:21:45.3: Boy, that's right. I wasn't really sure I had too much to add if I just did a standard GR book. But I thought it would be nice to do GR plus quantum field theory, so that the latter part of the book would involve the wonderful discoveries of Hawking, for example, of what happens during expanding space-times. There's all sorts of amazing physics when those two get combined together. So for that reason, I thought I'd push it towards later in the series.

0:22:12.3: And for the non-physicists out there, maybe say a bit about the folks in whose shadows you are walking, namely Landau and Lifshitz. They're the other people who did this marvellous attempt to write down all of theoretical physics as it was understood at the time for students.

0:22:30.0: That's right. I'm reluctant to go there. It's the obvious comparison. Because no one else has been this stupid to try and write down all of theoretical physics. So in the 1950s, these two great Russian physicists, Landau is one of the giants of 20th century physics, just so much named after him. The story goes that he was imprisoned by Stalin at some point. And it was when he was in the prison cell that he envisaged writing down 10 volumes covering all of theoretical physics. And then the later story goes that he would just dictate, that he would stand in front of Lifshitz. And I don't know how true this is, but that he would dictate. And Lifshitz was apparently the perfect scribe because he couldn't write anything down that he didn't understand. So between the two of them, they would carve out this, what is an incredible achievement. It's fair to say it's not easy going.

0:23:29.2: Not easy going, no

0:23:31.6: If you understand the subject well, that's the place to go and look and hone your understanding. If you're a struggling student, that is not the place to go. So I don't have the ambition of Landau and Lifshitz. I don't go into as much detail as they do. I think it's fair to say the books are maybe more human than Landau and Lifshitz. They're more fun than Landau and Lifshitz. I'm excited about physics, and I want to convey that excitement, and I hope that comes across.

0:24:00.6: Well, I'm looking forward to the whole series being done. I'll tell you one selfish reason why. I often get people emailing me basically saying, what do I need to know to do theoretical physics? And I usually point them toward Gerard 't Hooft's webpage. Have you seen that? 't Hooft has this webpage called How to Be a Good Theoretical Physics, and he lists every subject you need to know, and he points to both textbooks and online resources. The problem is that to be a good theoretical physicist by 't Hooft's standards is just too high. It is just too much. He lists the foreign languages you need to know and all of the math, a crazy amount of stuff.

0:24:42.5: You have to read those papers in the original French from the 1920s?

0:24:47.0: I think you do. So when your books are all out, I'll just say, read David's series. That's what you need to know.

0:24:52.3: Perfect. Yeah.

0:24:54.1: And the quantum field theory book is interesting because, of course, that's another subject where there's a lot of textbooks on the market. They're all different. They're all remarkably different. If an alien came down and didn't know quantum field theory and was trying to learn it from these books, they'd be like, why are the books on the same subject so different? So do you have an angle on that?

0:25:16.8: I have, maybe not for the early part, but I have an angle for the later part. I think they just all stop way too early. I think they stop before you get to the really wonderful things about quantum field theory, the things we learned in the '70s, the things where quantum field theory links with ideas of topology in mathematics, the fact where or the point the point where the interactions between quantum fields become so strong that you can't use the techniques that you've been learning for the last 500 pages. You can't use Feynman diagrams anymore. So questions like confinement in QCD, the quarks in a proton are stuck in a proton. You can't get them out. They've been stuck there for 13 and a half billion years. That force is so strong, you can't get a quark out on it. So how is that possible? In some sense, it's another one of the Millennium Prize problems, but it's closely related to it. And we have ideas. We can't prove it, but we have ideas that have been extremely useful, ideas like putting the theory on a spatial lattice where you can do a large part of making space discrete, in other words, rather than continuous. It's useful for simulating on a computer, but it's also useful conceptually to address these problems. So, I think when I get there, when, it's going to be a more modern take on quantum field theory, where modern really only means '70s and '80s. It's not like it was yesterday, but very few, I don't think there's any real textbooks that cover that later material.

0:26:48.3: No. I think everyone uses Sidney Coleman's lectures in Aspects of Symmetry for a lot of that stuff, but it's not systematic in any way.

0:26:57.3: That's right. That's one place where it's done beautifully. He's one of the great pedagogues of our subject, one of the great explainers.

0:27:09.4: But this is a wonderful segue, because I did want to actually talk about what you're doing when you're not writing 100 books in all theoretical physics. You're still cranking out the research papers, and quantum field theory is your expertise. So, let's take a breath and step back. What is this quantum field theory thing that people need to know about? I mean, if they've heard about quantum mechanics, why are fields such a big deal?

0:27:34.3: All right. So this is the framework in which all the laws of physics are written, all the fundamental laws of physics are written. And the deep idea, which goes back 1930s, 1940s, soon after the discovery of quantum mechanics, is that what we call particles, lumps of energy that we call particles, are ripples of an underlying field, waves of some underlying field, that this field is a fluid-like substance that spread throughout all of space, a substance that permeates the universe, not something you can remove from space. And that field has a wave in it, a little ripple. And because of the laws of quantum mechanics, that ripple gets molded into a lump of energy. And those lumps of energy are what we call particles. And so there's one aspect of this that I think is more familiar than most. Everywhere in the universe, there are two fields called the electric field and the magnetic field. And so everywhere in the universe, there's a little, at every point, there's a little arrow that tells you the strength and direction of the electric field and another one for the magnetic field. Rather famously, when the electric and magnetic fields oscillate, when they ripple, you get what we call light.

0:28:58.7: And then it was realized after the discovery of quantum mechanics that if you look closely at those ripples of light, they're made of particles and we call those particles photons. So all of that, I think, is reasonably familiar to people who have an interest in science. The amazing story that I think is not told as much as it should be is that that same story holds for all other particles in the universe. So there is in our universe something called an electron field. And when the electron field ripples that they're the particles that we call electrons. There is a quark field and a neutrino field and a W boson field and a Higgs boson field. And all of the fundamental particles in the universe are not really the ultimate building blocks. It's the underlying fields which are the fundamental things from which we're made, that the laws of physics are built on.

0:29:49.3: As far as our current best understanding goes, at least.

0:29:53.7: That's right. Although it's also clear that I don't think we're going to get beyond that in our lifetimes. There's speculative things like string theory. Very, very hard to test them. So this idea that quantum fields is the fundamental. Fundamental is a time-dependent concept. Of course, we all know that. But it's not going away anytime soon. This is the framework that we have to work with for now.

0:30:19.7: So this is way out of sort of logical order, but I can't help but asking. Do you personally think, as a working theoretical physicist, that gravity will ultimately be described by some kind of quantum field theory? Or do you think that the fact that we have things like black hole entropy, the holographic principle, blah, blah, blah, is that evidence that we need to go beyond quantum field theory?

0:30:43.6: I think at the moment gravity is described by a quantum field theory. Space-time is the field in question. Einstein gave us the classical field theory. The idea that quantum gravity is this big mystery, that we've got no idea what's going on, that's totally oversold. The truth is you can quantize the gravitational field. You can quantize it and explain any experiment we've ever done. And it's true that we don't understand everything. It's true you run into difficulties, but those difficulties arise only in the most extreme situations in our universe. What happens in the center of a black hole? What happened in the Big Bang? Also, there are subtleties like the fact black holes have entropy, which... Often in physics, when a theory doesn't tell you... A theory will tell you when it's giving the wrong answer. A theory will give infinity in physics, and that's the way of the theory putting up its hands and saying, yeah, I don't know what's going on here. And occasionally there are things where the theory tries to lie to you and doesn't quite give you the right answer. So, it doesn't admit its own failings. So I would say that the entropy of a black hole is closer to that. All of which is to say that for everything we're going to do in our lifetimes, quantum field theory of gravity that we have is perfectly adequate. But you wanted more. You wanted to know what's going to happen after we die. What are people going to discover after we die?

0:32:12.7: The point you made is a very good one and one that I've made many, many times, that of course we understand quantum gravity in a certain regime as an effective field theory. It explains why apples fall from trees, why the earth goes around the sun.

0:32:25.0: There you go. All of those are quantum phenomena. It's quantum matter interacting.

0:32:29.7: 100% okay. But then, yeah, we do think that there is an ambition to get a full theory of quantum gravity that will account for black holes and the Big Bang. And I'm persuaded, at least we have to make these conjectures because, like you say, we might not be alive to hear them resolved. But I'm persuaded that gravity is the one reason we have to suspect that quantum field theory is not the be all and end all of the full theory of everything.

0:32:58.3: That might be true. I'll say two things, one of which I think agrees with you and one maybe differs. The thing that agrees with you is that, this was one reason, in fact, I spent so long learning fluid mechanics, that there is a sense in which Einstein's theory of general relativity, the Einstein equations, feel more like the Navier-Stokes equations of fluid mechanics. And the entropy is really the big clue there. And of course, Navier-Stokes equations aren't fundamental. You derive them from underlying atoms moving around. And so it similarly feels that the Einstein equations might not be fundamental for the same reason. So that I think is the big clue that maybe something more fundamental is going on. The other thing to say is that we do have one theory of quantum gravity that works. I don't know if it's the right theory, but string theory absolutely, but whatever you think about it, whatever the baggage it comes with, it's a theory that shows you that you get Einstein's theory of general relativity compatible with quantum mechanics, and you can absolutely see how the two fit together. And every way we know to understand string theory, it's actually just a quantum field theory. It's weirdly a quantum field theory that doesn't live in our three plus one dimensional world, three space at one time. It's one that lives in one plus one dimension. It's the theory that lives on a string. But all the techniques you use to solve string theory is quantum field theory. Maybe that's our limitation. Maybe it's something else. Everything looks like quantum field theory because that's the only thing we can do. But when you get to what the microscopic degrees of freedom are of quantum gravity, it was QFT.

0:34:43.8: You're just trying to convince us that your quantum field theory book is still going to be worth buying even once we quantize gravity. It's still going to be an important part of how we think about these things.

0:34:52.1: Yeah. That one and the fluids book.

0:34:53.8: And the fluids book. Good. Let's dig a little bit more deeply though into the working physicists' ideas about quantum field theory. There's this big idea called gauge invariance, gauge symmetry, gauge theories. It's famously sort of, I don't know, people struggle, people sort of on the street who are not physicists. It sounds spooky and a little bit intimidating. I don't think it's that hard, but maybe I'm oversimplifying it in my mind. So what is your way of explaining the person sitting next to you on the bus, what gauge theories are all about?

0:35:28.9: No one on a bus has ever asked that, but I will try. I think there's something deep and surprising here actually in gauge symmetry. So what's the essence of it? It's the fact that all the laws of physics that we currently have, Maxwell's theory of electromagnetism, Einstein's theory of general relativity, quantum mechanics, quantum field theory, every single one of them is built on objects that we could not measure even in principle. And that's the essence of what we call gauge symmetry. So the simplest example we learned about at school. When we were in school and taking those very early physics classes, we were told that voltage isn't important. Voltage differences are important. Touch two things of different voltages, that's bad if the voltage difference is big enough. But the overall voltage is not important at all. It's why birds can sit on these high voltage wires and not get fried. It's the difference in the voltage between the earth and the wire that's important. So all voltages could just be shifted by an overall, let's call everything thousand volts bigger, wouldn't change anything. So of all the things we learn in school, most of them sort of evaporate later in life.

0:36:49.1: You learn that force is important. Force is a very 17th century concept. It's not something that really survives as we learn later laws of physics. But that lesson, that lesson about the stupid birds on the wire and the fact that potential differences are important, that's the lesson that miraculously blossoms into this idea of gauge invariance, that there is a redundancy in the way we describe the laws of physics. So for example, you have to introduce voltage in the laws of physics, even though the overall value of the voltage is not important at all. You have to introduce in Einstein's theory of general relativity something called a metric. Can't possibly measure the value of the metric. It doesn't make any difference. If you pick Cartesian coordinates versus polar coordinates, it takes completely different values, but nonetheless you have to introduce that object. The wave function in quantum mechanics is importantly a complex number. It's the key feature of quantum mechanics. Complex numbers have a magnitude and a phase, so you should ask, what's the overall phase of the wave function? Got to be a complex number. Overall phase doesn't matter in the slightest. So, it's just weird.

0:37:54.8: You are obliged when you write down the laws of physics to introduce things that somehow are unphysical. That's the gauge principle. We elevate it to this fancy name. We call it gauge symmetry. It's a terrible name. It's gauge redundancy. It's a redundancy in our description of the laws of physics. I don't really understand why the laws of physics are like this. And I like that it is, because it's a beautiful thing. It allows loopholes to appear. There are things in the laws of physics that you might think were mutually incompatible, but with this gauge redundancy, you look at something one way and you see that one feature appears. In quantum field theory, for example, you want physics to be local. You want that if you do something here, it doesn't affect what's going on on the far side of the universe. And so there's one way of writing down the laws of physics where you make use of this redundancy, where you can see things are local, but then it doesn't appear that it's unitary. Unitary is the statement that all the probabilities in quantum mechanics have to add up to a number that's equal to one.

0:39:05.8: That's quite important as well. So there are these two crucial features of the laws of physics, and you can see one of them or you can see the other one, but somehow it's very hard to see both at the same time. And it's this redundancy that allows you to see both. So it's a very deep principle. It's what all of our laws of physics are based on. I think we don't really understand why it's the case. I've never heard anybody say, oh, it's got to be like this for some reason.

0:39:32.2: I have an anthropic argument.

0:39:35.3: I'm not sure I want to hear it.

0:39:37.1: So, if you think that living conscious creatures are complex systems made out of little tiny constituents, and there's sort of like a fitness landscape where a certain arrangement of things can survive and be complex and metabolize, et cetera, how do you find yourself at what we physicists would call the minimum of that landscape? How do you settle down into it? You need to give off energy. You need to dissipate energy to sort of lower your energy down to where it needs to be. So your stuff needs to be coupled to an essentially massless particle that interacts noticeably with you, because you need to be able to give off arbitrary amounts of energy. You need to be able to give it off pretty efficiently. And in quantum field theory, generically, if you have a massless particle, it's not going to couple to anything. The one exception are gauge bosons, and therefore gauge bosons are necessary for complex life to exist.

0:40:37.7: I'll go on to that, but that's a statement about why there are massless particles, and in particular, things like the photon in our universe. It's not quite answering the question of why our description of the photon requires us to introduce things that are unphysical, which really is what gauge invariance is about. Can I say equations or is that bad?

0:41:00.4: You can. Look, the audience is going to have to go along with the ride.

0:41:06.1: In the basic field of Maxwell's equation is called Aμ. It's A, and it's got a little index μ, which takes value zero, one, two, and three, where the zero is time and one, two, and three are space. So those things aren't physical. You can't describe electromagnetism without it, but you can never say what's A0. A0 actually is the voltage. It's the same thing, but none of those things are physical. So I agree that we need a massless spin-1 boson for anthropic reasons. It's not the same as saying why we need gauge symmetry. That's a choice of the way we've come up to describe the theory. I don't understand why we need to introduce that redundancy.

0:41:45.9: Fair enough. We could wonder about these things we don't know the answer to, but I think it's an important point you made that you think that even though we've been talking about it for 900 years, we don't fully understand this idea of gauge symmetry. My impression is, and this is beyond what I'm an expert in, physicists are still kind of thinking about new generalizations of symmetry and how that can play out in quantum field theory.

0:42:14.5: That's right. So, there's all sorts of new symmetries in the past few years that have sprung up. So to set the scene, I think it's about 100 years that we've understood symmetries. Emmy Noether's work really put that on firm footing. Emmy Noether told us that there is a close relationship between symmetries and conservation laws. And so anything in our universe that is conserved, electric charge, what's called baryon number, that basically means number of protons and neutrons, all of these things that are conserved are conserved because there's an underlying symmetry. Momentum and energy, another but very obvious example. So we've learned that symmetry is important. It's also the thing that allows us to make progress in finding patterns in nature. And so it's been important for the simple reason that it's allowed us to figure out what's going on with the laws of physics. And so symmetry has been unbelievably important. And then rather surprisingly in the last 10 years or so, quantum field theorists have realized that there's much more to symmetry than we appreciated before. I have to say, there's been a lot of work on this. The mathematics is lovely. It would be nice to have a real smoking gun.

0:43:42.6: This is something we could not have understood without these new developments. A lot of what's been going on is we've understood more deeply things that we knew already. Subtle things to do with nature. There's a fact that the pion decays to two photons, which has long been understood to be curious. The first thing is it shouldn't decay at all. The next thing is it should decay, but the decay rate should be faster. There's been all sorts of subtleties. It was figured out in the 1950s. I think we've understood that these new kind of symmetries give us an explanation for it. But at the end of the day, we did know in the 1950s that the pion decayed and why it decayed. So I'm not yet sure that we've... It feels good. It feels like it's progress. I'm not yet sure there's something we should be shouting about on a podcast, let me say, about it.

0:44:31.5: Well, I think it gives a little bit of an insight into what is going on in physics departments, theoretical physics departments. I mean, we have this, like you say, super successful framework of quantum field theory. And yet, despite all of its many successes, there's not a feeling that we get it perfectly, there's still a lot to learn. And maybe if you're a cynic, it's a fishing expedition. We're trying to learn more in hopes that it will pay off. But still, learning more is important.

0:45:04.9: I think that's right. And I think it doesn't have to be a cynic. It is a fishing expedition. There's lots we don't understand about quantum field theory. One way of saying this is you can teach a mathematician general relativity. And the mathematicians contribute enormously to our study of Einstein's theory of general relativity, because they're better at maths than we are. You can't teach a mathematician quantum field theory.

0:45:31.2: They don't like it.

0:45:32.9: Because it's not well defined. We're using mathematics that mathematicians haven't yet invented. And when they try to use it, I think they call it rigor, I would call it pedantry. But they struggle to get beyond the fact that the maths hasn't been invented yet. But I have to say, for decades, I thought, yeah, these stupid mathematicians, they should just get up to speed, we're clearly doing it right. My mindset has changed a little bit. If we can't tell mathematicians, and mathematicians are not stupid people, it's because there's things we're not understanding. And so there's various ways you proceed. One is that you try to make it more rigorous in a way that a mathematician would understand. I think it's important. It's not my style of doing physics, but I think it's important. Another is that you look in the places in quantum field theory where our understanding is limited. You can sort of tell there's something we're not quite getting, something not quite there, and you just push. And it might be that you push and you push, and okay, you understand a little bit, but there's nothing of great significance. The hope is that you push and you push, and suddenly it opens up new vistas. It opens up a new way of thinking about things and a new way to understand the world. But that's just research, I think. All research, to some extent, at least the kind that you and I do, where it's really pushing the laws of physics beyond what we know, it must have been like that for centuries.

0:47:08.4: And that's a very interesting discourse that you just went into because I see resonances, maybe you're not gonna agree here, with the foundations of quantum mechanics. Where we have something that works fine, we can make predictions with quantum mechanics, but there's little hints that we don't really understand what's going on, and then there's an ongoing debate, how much time should you spend trying to figure out what's really going on?

0:47:34.7: I'll agree to some extent. I'm not a fan of foundations of quantum mechanics. I bit the bullet in my quantum mechanics textbook. And had a discussion about how unsatisfactory Copenhagen interpretation was, you'd like that, and a discussion about how unsatisfactory many worlds interpretation was. You might like that less. And basically settle down on, shut up and calculate that. There is so many amazing things that you could discover if you just use quantum mechanics to understand the world and that's the right thing to do. I think I had a phrase that if you pause at the starting point, having deep thoughts and saying words like epistemic and ontological, that you are in danger of missing the quantum vistas that await just around the corner.  

0:48:18.5: Okay. But you could have said exactly the same thing about the mathematicians five minutes ago. I think it's very, very parallel.  

0:48:25.7: That's true. I think you might be right. And the point is none of us know what quite what the right question to ask is or what the right experiment. So we all have our own tastes. And I think that's important that people go in different directions.  

0:48:37.2: Well, speaking of the making it rigorous thing, quantum field theory in particular, it is in this weird world where it works. Sometimes we're just sort of happy that it works without fully understanding why. One of the techniques people use is to replace the smooth continuum of spacetime with some sort of discrete lattice. You mentioned this possibility before. This is something that has pros and cons, and you've been thinking about this. Like in some ways, yes, it helps you get some infinities to go away, and that's good. In other ways, it brings up new problems that weren't there before.

0:49:16.8: So, this is what I have been obsessed with for the past few years. Let me say that lots of people do this, huge communities of people that do this, and they do this for a very good reason, which is once you replace the continuum of space with a discrete set of points, and think about quantum field theory in that way, you're in place to start to simulate quantum field theory on a computer. And if you know one thing about quantum field theory, it's that quantum field theory is unbelievably hard. We're not very good at solving it. In particular, there are situations where interactions become very strong, things like interactions of quarks binding to form a proton. If we just sit there with pen and paper, we're simply not smart enough to understand how that happens. But we have these enormous computers, we can simulate quantum field theory on these computers, and it tells us what happens. And it agrees perfectly with experiments. So it's on a practical level, maybe practical is not quite the right word to use if we're talking about how quarks bind together to form protons, but a level of just doing physics, comparing to experiments, is extremely important.

0:50:30.5: However, there is a problem with discretizing. And I think it's one of the most underappreciated problems in theoretical physics. Long ago, when I was a postdoc, I went to a conference and a very famous theoretical physicist gave an after-dinner speech and said, here's my advice on how you choose a problem in theoretical physics. Firstly, you pick the problem and you try to put a value on how important that problem is. He didn't explain how you do that, but that was his first step. Then he said, you divide by the number of people that are already working on it. And so you shouldn't do it. Honestly, I think it's terrible advice for a graduate student. It's probably terrible advice for a postdoc. But once you're settled in a nice job like you and me, this is exactly the way that we should pick our problems. And so for me, I think the problem that scores highest by this ranking is the following. It is that it is not possible to simulate the laws of physics on a computer. It's certainly true that no one knows how to do it. But in addition, there is a mathematical theorem.

0:51:45.9: It's a theorem that was written down in the 1980s. It's called the Nielsen-Ninomiya theorem. And it says you simply cannot do it. And the problem is not with the strong nuclear force, the thing that binds quarks together into protons. If it was, we'd be screwed. We wouldn't be able to understand quarks. But it's with the weak nuclear force. And the weak nuclear force has a particular property that I'll tell you about shortly. But it means that it's not possible to write down a discrete version of the weak nuclear force, that you can't put it on a lattice, make space a discrete lattice. The theory, as we currently understand it, can only be formulated in the continuum. That's the problem.

0:52:28.9: Very quickly, the idea behind putting it on a lattice is not to say that space is discrete, but as a calculational tool, you imagine it's discrete and then you take the limit as the distance between the points gets smaller and smaller.

0:52:45.3: There's two ways to do it. If you want to simulate, you're exactly right. It's just a tool and just like you could simulate the weather, you do exactly the same thing. You think of the atmosphere as being many, many discrete points. The weak nuclear force, it's a slight quirk. We don't actually need to simulate on a computer. That's one we can just do with pen and paper. So that somehow, that practical impetus to try and put this on a lattice has not been there. And I think that's largely why this problem hasn't been addressed. But for me, I'm not someone that does simulations. I don't really know anything about computers, if I'm honest. But it's a bit weird that there's a theorem that says space time cannot be discreet. And I have no reason to think it is. But isn't it odd? I mean, it should be above our pay grade, we don't have access to that information. That's right. This should be something at the plank scale. Have to build a particle collider that's 15 orders of magnitude more powerful than the LHC before we get to answer that question. So how can there be a mathematical theorem that tells us this? And so I don't believe the conclusion of the mathematical theorem is right. I think there must be a way to evade it. Nice thing about theorems is they come with certain assumptions.

0:54:05.4: Sure.

0:54:06.2: These are famously, these no go theorems in physics have certain assumptions, and you find which one you're willing to discard, even though they all seem very reasonable, in order to make progress. So this is what I've been struggling with for the last three or four years, I would say. I also say I'm doing this because I was inspired by the results from the LHC. Results from the LHC count the Higgs boson, absolutely spectacular. And yet many in the community, and I was one of them, thought that when we found the Higgs boson, it would be a portal to the next layer of reality, if you like.

0:54:47.9: Me too.

0:54:49.4: That there would be accompanying the Higgs boson. You wrote a whole book on this. That there would be something else. And I didn't have any skin in the game, and I didn't know what the something else would be. But there was an argument called the naturalness argument or the hierarchy problem. It's an argument that I entirely subscribe to. I've spent 20 years thinking about quantum field theory. It seems right to me. And yet nature is telling us it's wrong. That Higgs is not natural. That the hierarchy problem does not have a solution. I'm shocked by this. I don't know what to do with it because the LHC is working beyond our wildest dreams as a machine and yet those particles are not there where we thought they would be. So what I decided to do was just go back to basics, go back to the standard model that we know is correct, and as we said before, find what you think is the weak point. Find the thing that just doesn't quite sit right with you and push and see if somehow we can make progress. So that's what I've been trying to do.

0:55:47.5: So you did promise to tell us what is it about the weak nuclear force that makes it harder to put on a lattice than the other forces.

0:55:55.3: Very good. The technical name is parity violation. The non-technical way of saying it is that nature has an astonishing property, which is that things can happen in the mirror that cannot happen in our world. That the laws of physics look different when viewed in a mirror compared to what's sitting in front of you. So, if you do see something in our world reflected in the mirror, I know the listeners can't see this, but I can see your books behind you. I can see that your books are the right way round because your general relativity textbook is sitting there prominently and I can read the words. And if this screen was flipped, actually for you it probably is flipped because we're doing this on Zoom and Zoom does that, you wouldn't be able to read it. So you can tell whether you're looking at the real world or looking at something in a mirror. That's true in our world because our world is complex and there's things like writing that we've developed. The astonishing fact that was discovered by Chen Sheng Wu in the 1950s is that the same is true on the most fundamental level.

0:57:10.4: There are interactions that happen on the most fundamental level where they look different if they're reflected in the mirror. And if you saw a movie of such an interaction, you could take a movie of such a small interaction, you would be able to tell whether you were looking at the original or you were looking at the reflection in a mirror. This is, I think, I might be stretching, it might be a bit too much to say. I think that this is the single most important experiment in particle physics of the 20th century. It's a bold claim. I might go back on it if you give me some other examples. But it was understanding this that basically lays the structure for the standard model, the theory that best describes our world. And the reason is because of very subtle mathematical properties. If you try to write down a law of physics where it's different when reflected in the mirror, these have a name. These are called chiral gauge theories, technical name that's given to them. Chances are that that theory will make no sense whatsoever. There are these very subtle mathematical consistency conditions that chiral gauge theories have to obey.

0:58:27.4: And it's the reason why the standard model is a thing of beauty. You know, you look at the standard model, it looks horribly complicated. There are quarks and there are leptons. And the leptons are electrons and neutrinos, and they have these weird charges and these weird interactions with the different forces. And it's only when you appreciate that there's a consistency condition that suddenly the whole thing just fits together like the most perfect, beautiful jigsaw, and it could not be any other way. And it really is stunning. Let me say this. I believe that theoretically inclined physicists like me would have stumbled upon the standard model and studied it, even if it was not the theory of our world, because it really is a thing of beauty. Moreover, it's... I don't know how you quantify simple in theoretical physics, but if you write down the simplest chiral gauge theories, the simplest theories that have this property that they're different when reflected in the mirror, I think standard model is number two, maybe number three. I'm not quite... So it's this stunning thing, and a large part of the structure of the standard model is forced upon you by this observation of Chen Sheng Wu

0:59:39.0: People might have heard the word chiral in the context of molecules before. There's certain biological molecules that look like right-handed screws versus left-handed screws, and that makes sense because the world of biology is messy. But the fact that we live in a world of particles that are all left-handed screws and none of them are right-handed screws is a little bit weird.

0:59:59.4: That's exactly the right analogy, that the electron has a left-handed part and a right-handed part, and the left-handed part knows about the weak force, and the right-handed part does not. Yeah, that's exactly the right analogy. So it's this very subtle property of the standard model that cannot be discretized. That's what the mathematical theorem says, that theories that were left and right-handed, where they look different when viewed in the mirror, cannot be cut on a spatial lattice. This feels odd to me. I can tell you, I can sort of try to give a sense of how deep this is. I wrote a paper a few years ago with my great student called Nakhirin Lohitsiri. We did the following. You take all the particles of the standard model, just what's called one generation. So that's an electron, an up quark, a down quark, and a neutrino. They all have different electric charges. If you go to the standard model, those different electric charges are actually replaced by something a bit more subtle called hypercharge, but it's not really relevant for the story.

1:01:08.1: What we did was the following. We said those electric charges or hypercharges can be anything you like, but they should be integers. They should be whole numbers. There's a slight subtlety because the quark is a third, but okay, multiply everything up by three or something. And then given that, what are the mathematical consistency conditions that these charges should obey in order for the theory to be consistent? That's the question we asked. There's some horrible change of variables. You get rid of these, some you add others. It was a bit complicated, but at the end of the day, we showed that in order for the theory to be consistent, you had to find three integers that obey the X, Y, and Z, that obey the following equation. X cubed plus Y cubed is equal to Z cubed. Now, that's rather famous. This is Fermat's last theorem. And Fermat's last theorem says that there is a solution to this. The solution is one cubed plus zero cubed equals one cubed. So you take the only solution that exists, of course, anything else instead of the one, but it's essentially the same solution. You take that, you plug it back into this horrible change of variables, and out come the electric charges of the particles of the standard model. So Fermat's last theorem is underlying the consistency of the standard model. This is amazing.

1:02:27.9: It is amazing.

1:02:29.0: So, there are these reasons that are pushing me in this direction. It just seems interesting to me.

1:02:37.8: And this is probably too wild, but we were just previously talking about hints from gravity and black holes that quantum field theory is not the right answer. I mean, those same hints might lead you to believe that you can't think of space as a lattice of points. Is there any relationship between these two ideas?

1:03:01.2: It's a great question. And first, the answer is I don't know. Some ideas. So what's really going on? One reason to replace a continuum space with these discrete points is precisely because, as you mentioned, it removes the infinities in quantum field theory. It's a nice thing to do for that reason. How does our world remove the infinities? Well, it removes it by quantum gravity, but the part of quantum gravity that we don't understand. The technical name is that there's some UV cutoff you should put in quantum field theory. You should not allow energies to get arbitrarily high. You should not allow distances to get arbitrarily small. And it must be that somehow gravity is smearing out what's going on on very, very small distances. There are many reasons to understand quantum gravity, but from my perspective, maybe the first one is it's the right way to think about quantum field theory. It is the right UV cutoff for quantum field theory. It preserves all the symmetries. Okay. So what does it have to do with this chirality?

1:04:16.8: As I said before, the only real quantum theory of gravity that we understand is string theory. And there's all sorts of wonderful stories that were understood back in the '90s about how you get these chiral nature out of string theory. And you need to do funky things. You need to make space go. String theory has these internal directions, Calabi-Yau manifolds or whatnot. They need to go pointy. They need to go singular in certain places. And that's how you get these chiral fermions. So everything is tied up. Quantum gravity doesn't strike me as the easiest way to approach this particular problem. So I've sort of tried to be ignoring it. But you're right. It's got to be the right way, ultimately.

1:05:00.4: But it's good. I mean, I love this discussion because it gives a hint of how, again, theoretical physicists are thinking in a world where we have a model, the standard model, that fits the data. But we are deeply unsatisfied with it as a theory of nature. And there's plenty of work to be done even without dramatic new experimental input. We would all love dramatic new experimental input. But it's not as if we are bereft of questions to ask.

1:05:25.6: That's absolutely right. And of course, there are the observational questions. What's dark matter? I've got no idea. What caused the universe to undergo this period of inflation, which there's overwhelming evidence for back in the day? Got no idea. So there's those. But there are also these more theoretical questions. Just got the theory. Know what it is. Don't understand it. Don't understand it as well as we would like.

1:05:50.8: I think we have time for one more example of exactly that, these phenomena that you get in quantum field theory that we don't fully understand, which are solitons. This idea that somehow fields can wrap in knots or something like that that can't be undone. I mean, maybe explain what that is, and is it really relevant to the physics of the real world?

1:06:14.4: It's absolutely relevant. I used to love solitons. I think I spent the first 10 years of my career working on solitons in quantum field. So what are they? Quantum field theories give rise to particles in two different ways. The first way is that the field has a little ripple, a little wave in it, and as I said before, quantum mechanics molds that ripple into a bundle of energy. The second way doesn't involve quantum mechanics at all. It's that, this might be hard to explain, but the field can sort of fold over on itself in a particular way, wrap around itself, and give rise to a lump of energy that doesn't disperse. That's the important thing. It doesn't disappear. It sits there in a stable way, even without invoking quantum mechanics. And that goes by the name of a soliton. There are some almost examples. There are some cheating examples that are easy to explain and some others that are genuine that are maybe less familiar. So, an example that isn't quite a soliton but is almost is a smoke ring. If you're into cigars, I don't know if that's allowed anymore, but if you're into cigars and you blow smoke rings, these are amazing objects. They persist for an extraordinarily long time and float around, slowly expanding. And if you're very good, I'm told, you can blow one smoke ring and then get another to go through it and backwards and forwards.

1:07:53.0: So they have amazing properties. They can link each other. But back in the 1800s, Kelvin famously had a theory of atoms, which was all to do with not quite smoke rings, but it was inspired by his love of cigars, that these knots that you could form from things like smoke rings were the underlying atoms. So that's something that's akin to a soliton. Another example is in a superconductor. So a superconductor is, as the name suggests, a material in which electricity passes with no resistance whatsoever. What happens in a superconductor is the electrons miraculously feel an attractive force, which is unusual because obviously the electrons both carry the same charge and they get repelled, but the lattice in the superconductor deforms in such a way that there's a compensating attractive force. Those pairs of electrons are called Cooper pairs. They do something funky and they give rise to this amazing superconducting behavior. But what happens in a superconductor is if you try to pass a magnetic field through the superconductor, it says no. It says no to start with. It's called the Meissner effect. In Japan, they managed to levitate trains using this. In my country, we're not technologically sophisticated enough to do that.

1:09:15.6: But you can levitate frogs.

1:09:19.7: We can levitate frogs. That's right. Guy in Manchester famously levitated a frog. Okay. So what happens if you insist? If you insist on pushing the magnetic field through, what happens is the superconductor relents, it has to at some point, but it relents in an interesting way. The Cooper pairs, these pairs of electrons, start to swirl around the magnetic field. And rather than the magnetic field just going everywhere through the superconductor, it forms what's called a vortex. And that vortex, it's a bit like the water leaving the plug in your bath. It's a swirling region, but the swirl is not water, it's these Cooper pairs. That's a genuine example of what's called a soliton. So it's something new in the system that happens because the field, in this case the Cooper pair field, is having some interesting behavior. So, these also exist in quantum field theory. And so it's quite interesting. There are these two different ways in which particles can exist in quantum field theory. Now, I should say that in the standard model that describes our world, there are no solitons, which is a little bit disappointing.

1:10:33.1: To theoretical physicist. Yeah.

1:10:37.4: For theoretical physicists. Actually, that's not quite true. There's a description of what's called pions. Pions are a state of quark-antiquark pairs. And the theory of pions has a soliton, which is the proton and the neutron. So you can actually think of the stuff we're made of as solitons if you view it in a particular way. You could also view it as made of three quarks. I think this touches on why solitons are interesting. There's often competing complementary ways to view the same system. You can either view a proton as made of quarks, or you can view it as a soliton of pions. But at a more fundamental level, I think it's true to say that any theory that goes beyond the standard model, certainly the majority of them, does have these solitons. My favorite kind of soliton, I think if I had a favorite particle, this is it, is a magnetic monopole. Magnetic monopole is the north pole of a magnet without a corresponding south pole. There is a law of physics that says they don't exist. It's one of the four Maxwell equations. And yet, I think anyone who's thought about this seriously is sure they exist somewhere in the universe. One reason is that if you have a grand unified theory where all the forces are unified into one, these magnetic monopoles arise as solitons. So I spend a lot of time, maybe less these days, but back in the day I would spent a lot of time thinking about these objects.

1:12:09.1: So for those of audience members who have not yet bought your book on electromagnetism and have not yet seen Maxwell's equations, there is this beautiful almost symmetry between electricity and magnetism. The only difference is that there are electrically charged particles and not magnetically charged particles. So, the magnetic monopoles would, if they existed, restore that symmetry, right?

1:12:34.8: They would, but they would kill gauge symmetry that we talked about earlier. That again, there are these almost mutually exclusive things in physics. When you pick one, you pick the other. So naively it looks as if having gauge symmetry, which is crucial, means that magnetic monopoles can't exist. But the great physicist Paul Dirac back in the 1930s figured out a loophole to that argument. So again, they sort of they stick just on the cusp of what seems to not be allowed. And yet just sneaks through. There's just a loophole that these things are allowed by the laws of physics.

1:13:17.1: And we're at the end of the podcast, so we can say provocative things and then not follow up on them. But that sounds like I could take electricity and magnetism and replace them with each other and take magnetic monopoles and electrons, replace them with each other, and I've invented a duality between two different ways of talking about E&M.

1:13:38.4: Wouldn't that be wonderful? It is something of a dream. And it's a dream that holds in other contexts. So if you go back to superconductors, you have these Cooper pairs, these electron pairs that are moving, and we think of these as fundamental, and we think of swirls of them as forming these vortices. But it's quite possible, and indeed often useful, to invert that. It's kind of a bit of a zen-like maneuver. You think of the vortices as being the fundamental objects that are moving around, and you think of a quantum field of vortices, and then the vortices themselves can start swirling. And when the vortices swirl, they give back the electrons. So there is this sort of complementary view, vortices versus electrons and superconductors, monopoles versus electrons in our universe. This is what quantum field theorists call duality. It's probably the most overused term in all of physics. I wish we had a better term for it. But the fact that there are two different ways of viewing the world, depending on whether you write the fundamental equations in terms of, let's say, electrons for us, or in terms of these admittedly speculative magnetic monopoles. So there might be an entirely different formulation of the laws of physics where the electrons aren't mentioned, they emerge as solitons coming out of the monopoles.

1:15:06.9: And these kinds of ideas were central toward the second superstring revolution and showing that all the string theories were the same because what was a soliton in one was elementary in the other, and it's all stuff we're still thinking about.

1:15:20.3: That's exactly right. It's beautiful stuff, and it feels like it's a little bit of a hiatus now. We understood a lot. It's not quite clear how it's useful for our universe. It has had lots of impact in condensed matter physics, the way materials work. That these ideas have been much more prominent. So it's clear that it's part of the story of quantum field theory. Be nice if it was part of the story of the fundamental laws of physics as well.

1:15:50.5: Well, since we are at the end, I'll close with, and you can be as loquacious or not as you like, what do you see the next 10, 20 years of thinking about quantum field theory bringing us? I mean, what is the best possible scenario? What are the breakthroughs we can get even if the LHC doesn't help us out with any clues?

1:16:11.9: Well, best possible scenarios experiment guides us. Maybe dark matter, axions, I don't know. If you study the history of physics, as I know you have, I think it's fair to say that everyone was confused at every single step of the way. And often the great breakthroughs happen by accident or they happen for the wrong motivations. And we do need experiments to guide us. We're not smart enough to do it on our own. So that's my dream, is that we find something, it's unsettling, and it pushes us in the right way. I know that wasn't the question you asked. So if experiment does not come to help us, one other thing I've been doing is looking more in condensed matter physics, partly because there is experiment. It's an amazing experiment.

1:17:07.2: It exists. Yeah.

1:17:08.0: And the ideas of quantum field theory that I learned about originally in string theory are extremely useful. And it's the right way to think about topological insulators or fractional quantum Hall effects or high energy superconductors or high temperature superconductors. Got my communities mixed up there. These are incredible quantum, many body entangled systems. They're described by quantum field theory and it's not fundamental physics, but it's important. It's important to understand them. They're also just as beautiful as anything in other parts of physics. From the high energy perspective, what I'd like to see, and I think this has started happening a little bit, is everybody just taking more of a chance on something. That if experiment isn't there to help us, what do you want? You want to just stand out probes in as many directions as you can. You want people just exploring crazy ideas. So I can see the community moving in that direction, certainly from 10 years ago when everyone was just gung ho on supersymmetry, string theory, whatever it is. We don't have such a strong guiding principle. I think that's healthy, actually, that people just start to explore different directions.

1:18:26.0: I mean, I'm very, very sympathetic to that. I completely agree. The empirical problem is you say, we should all strike out in different directions, and then people start striking out, and other people say, no, not those directions. That's not what we meant.

1:18:40.3: Neither direction.

1:18:41.0: It's a sticky situation, but I have faith that a bunch of people as smart as theoretical physicists are are going to keep trying new things and find out something new. And I hope that the audience has that belief also after listening to this wonderful conversation. So David Tong, thanks very much for being on the Mindscape podcast.

1:18:58.6: Thanks, Sean.

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