How did the famous Edward Witten go from being a history undergraduate to a physicist? How did you step by step into the field of mathematics, leading the revolution of superstring theory at the forefront of mathematical physics? Why, he was convinced, that the next possible upheaval in fundamental physics would come from "everything from qubits," from the relationship between geometry and entanglement? Check out popular science writer Graham Farmelo (GF)'s interview with Witten (EW).
The interviewer | Graham Farmelo
| interviewees Edward Witten
Translation | Lin Hai (Tsinghua University)
In the field of mathematical physics, if we're lucky, a brilliant mind like Edward Witten appears about once every 50 years. Since the late 1970s, Witten has emerged from a group of physicists trying to understand the fundamental laws of the universe or to discover the most fundamental equations of physics. Not only that, but Witten also had a significant influence on basic mathematics because of his study of the mathematical nature of nature—he was the only physicist to receive the Fields Medal. You know, the Fields Medal has almost the same status in mathematics as the Nobel Prize for physics.
Edward Witten was born in August 1951 and received his B.A. in History with a minor in Linguistics from Brandeis University in 1971. He received his Ph.D. from Princeton University in 1976. From 1976 to 1980, he worked at Harvard University. He then became a professor at Princeton University and the Princeton Institute for Advanced Study. Winner of the Fields Medal in 1990.| Image credit: Dan Komoda/IAS
I am the author of The Universe Speaks in Numbers. Witten is the central character in my book and has helped me a lot. He was hesitant to do so, so I was pleased when he agreed to talk to me about his career and the relationship between math and physics in August last year.
In the office of the Institute for Advanced Study in Princeton, Witten sat comfortably on the sofa in a tennis suit. As usual, he speaks quietly, so you have to listen carefully. And he also uses a lot of technical terms. If you're not familiar with them, I suggest you jump right over, and the key is to understand Witten's thinking about the whole image of nature.
How did he become interested in cutting-edge mathematics, but was always a physicist? He offers us some enlightening insights on this subject. First, I asked him if he had been interested in math and physics from the start.
Since the 1970s, experiments have led to fewer clues to physics, and many physicists have turned to modern mathematics for inspiration, while some have remained skeptical about this direction of physics. In The Universe Speaks in Numbers, author Graham Farmelo argues that physics has in fact continued its tradition since Newton. He interviewed scientists such as Witten, Atiyah, Michael Green, and others to explore the connections between mathematics and physics. ）
EW: When I was a kid, I was very interested in astronomy. It was the time of the space race, and everyone was interested in space. Then, when I was a little older, my father taught me calculus. For a while I was interested in math.
GF: You said for a while, so did that interest fade later?
EW: Yeah, it did fade after a few years, and I think the reason for the fading was that after I learned calculus when I was eleven, it actually took quite a while for me to see higher-order mathematics than that. So at the time I didn't really realize there was more interesting, higher-order mathematics. That may not be the only reason, but it is certainly one reason for the fading of my interest.
GF: Have you ever been interested in other disciplines? Because you started studying something like history, did you really have the same level of interest in history as you did in math and physics?
EW: I think for a while I envisioned doing journalism or history or something like that, but around the age of 21 or 22, I realized that I wasn't going to have a good future in that regard.
Interviewer narration
After studying modern linguistics, Witten ran for president with George McGovern and studied economics for a semester before moving on to physics.
He came to Princeton University to do phD research in theoretical physics. After he passed some junior exams, Princeton wisely accepted him. He learned quickly. A teacher in charge of teaching him in the lab once told me that within three weeks, Witten's questions about experiments had gone from basic to subtle, and finally even reached the level of Nobel Prize questions. As a postdoc at Harvard, Witten became acquainted with a number of pioneers in theoretical physics, including Steven Weinberg, Sheldon Glashow, Howard Georgi, and Sidney Coleman, who helped the young Witten become interested in the mathematics of these new theories.
EW: The physicists I studied the most in those years were Weinberg, Glashow, George, and Coleman. They are completely different. Glaxo and George built the image model, basically a model of weak interactions, with a more detailed description of the Standard Model. I found it fascinating, but it was a bit difficult to find the incision there. If the world had been different, my later career would probably have been doing what they did.
Wow. It was the first time I'd heard Witten say that he initially wanted to draw inspiration from real-world experiments, like most other theorists. I wondered what made him change direction and become so mathematical.
EW: Let me provide some background. In the 20 to 25 years until I was in graduate school, new discoveries continued to emerge in the field of elementary particle physics: exotic particles, μ, hadron resonance states, cosmic defects, CP (charge-cosmology) symmetry defects, scale invariance, deep inelastic scattering, cannica quarks, etc. That's enough to give you a rough impression. This period lasted more than 20 years, with many major discoveries, one every three years. At the time I thought that if the surprises and discoveries of experiments continued to emerge as they had been for the past 25 years, I would be involved in model building, as my colleagues like George and Glashow did. However, this period of constant surprise and turmoil came to an end at the right time during my PhD, so I had no clear direction later.
GF: Were you a little disappointed?
EW: Of course I'm disappointed, you're going to always be disappointed with one disappointment after another.
GF: Life is often tough and you're disappointed by setbacks.
Elementary particles in the Standard Model, including the fermions (quarks and leptons) that make up matter, and bosons that transmit the four fundamental interaction forces. | Image credit: Daniel Dominguez/CERN
EW: Since then there have been important experimental discoveries, but not exactly the same pace. While these later discoveries were important, the knowledge they taught us was more abstract and offered fewer opportunities to build only models than experimental discoveries in the 60s and 70s.
I want to tell you one or two things about my interactions with other physicists. The one I remember most clearly is Steven Weinberg. He was one of the pioneers in the field of current algebra, a direction that is an important part of understanding nuclear forces. But he thinks most other physicists don't understand it properly, and I'm one of them. Therefore, whenever "flow algebra" is mentioned in a lecture or seminar, he always gives a brief speech to explain his understanding of it. In my case, Steven's speech I've listened to probably eight or ten times.
Then there's Sidney Coleman. First, Coleman is the only one interested in the strongly coupled behavior of quantum field theory. When I was a graduate student, encouraged by my mentor David Gross, I became interested in strong coupling behavior. Maybe I should explain here that if you're a physics major, they'll teach you what to do when the quantum effects are small, but no one tells you what to do when the quantum effects are larger, and there's no general answer. For different problems, different methods need to be used to solve them. As a graduate student, I'm interested in it, but most of the time I run into a wall because the problems are usually tricky, and Coleman is the only one at Harvard who is interested in this kind of problem, and others think that strong coupling is a black box, so he is really the only person I can interact with.
In addition to interacting with him, he exposed me to mathematical topics that I didn't know before, which later became important to my work, and that most physicists didn't know about, and of course I didn't know at the time.
GF: Did you realize at the time that you were interested in higher-order pure mathematics?
EW: Absolutely not.
GF: No?
EW: No, not at all. I gradually entered the field of mathematics. Because the Standard Model has been discovered, the new problems in physics are not exactly the same as those of the past. The Standard Model introduces new problems. On the one hand, understanding the Standard Model requires a new mathematical approach. Just as I was almost finishing graduate school, Alexander Polyakov and others proposed the Yang-Mills instanton, which proved important for understanding physics, in addition to its many mathematical applications.
You can think of instantaneouss as transient events that occur in space-time on a subatomic scale. These events are predicted by the gauge theory of the subatomic world. The pivotal moment in this story is Witten's first meeting with mathematician Michael Atiyah at MIT. They will be among the leaders in using a more mathematical approach to understanding this trend in nature.
Mathematician Michael Atiyah (1929-2019). | Image credit: Cliff Moore/IAS
EW: After Polyakov and others discovered the Jan-Mills transient, Atiyah discovered an amazing mathematical method that could be used to solve the instantaneous equations. He said that when he went to Cambridge, I think it was in the spring of 1977 and I was very interested in it, so we talked a lot about it. I probably work harder to understand the math involved than most other physicists. This interaction undoubtedly enabled me to learn all kinds of mathematics that I had never heard of before, including complex manifolds and upper cohomology groups of layers.
GF: It was news for you at the time.
EW: Yes. So on a more basic level, it's fair to say that when I heard from Sidney Coleman a few months ago about the Atiyah-Singer index theorem, it was news to me.
The indicator theorem first demonstrated by Michael Atiya and his friend Isadore Singer links two seemingly unrelated branches of mathematics: on the one hand, calculus, the mathematics of variation, and on the other, topology, i.e., the properties of objects that do not change when stretched, distorted, or deformed. Topology is now essential for our understanding of fundamental physics.
EW: Like other physics graduate students of that period, I really didn't know anything about 20th-century mathematics. So it wasn't until Albert Schwarz pointed out that the indicator theorem was related to the understanding of instantaneouss that I heard about Atiyah and Singh, as well as the concept of the indicator theorem. Even then, that article did not cause an immediate shock. If Coleman hadn't pointed it out, I'm not sure how long it would take to realize its importance.
Then, Atiyah et al. made progress in understanding the instantaneous equations. The first person to actually make progress was Roger Penrose's phD student, Richard Ward. I'm interested in that, but in a sense, I'm interested in what this does for physics. I learned the math, or some of the math the teacher was using at the time. However, I have some doubts about whether these mathematicss apply to physics. As it turns out, I wasn't wrong, because the mathematical methods that Polyakov originally proposed didn't quite work. In fact, while mathematicians have clearly elucidated the details of the instantaneous equations, this doesn't help what physicists actually do. In the long run, the work of Atiyah and his colleagues taught me a lot of mathematical knowledge that I had never heard of before, which was important later, but in the beginning, its importance did not appear.
GF: When did you become convinced that math would really be fun?
EW: I think it happened gradually in the '80s. For example, back in 1981 or 1982, I tried to understand the nature of the so-called vacuum, the quantum ground state, in supersymmetric field theory, but in fact some of its behavior is difficult to explain with the ideas of standard physics. Because I didn't understand, I was always looking for simpler models, but they all had the same problem. In the end I found the seemingly simplest model that could explore this problem, but it was still puzzling.
One day, when I was at a swimming pool in Aspen, Colorado, I thought of Raoul Bott, who was actually a physicist in Calgarth a few years earlier, trying to explain something called Morse theory to us. I'm sure there are many other physicists like me who have never heard of Morse Theory and aren't familiar with any problem it can solve.
GF: Can you tell us what Morse's theory is?
EW: If there is a rubber ball moving in space, it will have a lowest point, that is, a minimum, and a maximum point, that is, rise to the highest, that is, there is a maximum point and a minimum point. If you have a more complex surface, such as a saddle face, its height function will have saddle points, maximal points, and minimum points. Morse theory relates the maximum, minimum, and saddle points of functions such as the height function to the topology of the surface or topological manifold that defines the function.
GF: Have you read Maxwell's 1870 speech "On Hills and Dales"?
EW: I haven't read it yet. Is he actually describing the two-dimensional situation of Morse's theory?
GF: I can't go into details, but historians of Morse Theory often refer to this speech.
EW: I heard that Maxwell's talk was related to the beginning of topology. Topology happened to be developing around that time.
GF: Is the revelation you gained at the Aspen Pool physically useful?
EW: Yes. For the vacuum state in supersymmetric quantum theory, it has a bit of a revelatory effect. I developed this further, which at first seemed special, but in the end these anomalies were too many to ignore completely.
GF: I don't know if that's true, in Michael Green and John Schwartz
It wasn't until John Schwarz developed string theory that these became popular, didn't they?
EW: Because of Greene and Schwartz's study of anomaly, what people call the first revolution in superstring theory arrived in 1984, when the mathematics that Atiyah and others used to study instantaneous equations suddenly became very useful. Because to understand string theory, all these interesting things, such as complex manifolds, the index theorem, the upper cohomology groups of layers, etc., are useful in constructing elementary particle models in string theory.
I should have given a better explanation. In physics, the forces of the elementary particles we see basically mean all forces except gravity. Gravity is so weak that we only see it on macroscopic masses like Earth or the Sun. We use Einstein's theory to describe gravity and quantum field theory to describe the rest of the forces. It is difficult to combine the two. Before 1984, we couldn't even build a partially reasonable model of elementary particle physics that contained gravity and all other forces. The progress made by Green and Schwartz through anomaly cancellation in 1984 made this possible.
But building such a model would require the use of many mathematical methods that physicists had not previously used, some of which were introduced by Atiyah and others when solving instantaneous equations. Physicists needed to use complex manifolds, the upper cohomology group of layers, and other mathematical tools that were completely unfamiliar to physics graduate students of the era. At a fundamental level, these things are useful for building an elementary particle model that includes gravity. And, if you want to understand it more deeply, you'll end up using more math. After string theory developed to be able to model particle physics in interesting ways, much of the previously unfamiliar mathematics became important.
What I mean by previously unfamiliar is, of course, in a broad sense, because obviously some people are familiar with it. First of all, mathematicians are familiar with this. Second, in some areas, such as Roger Penrose, used some of these mathematics in his Twister theory. But broadly speaking, most physicists are not familiar with these mathematics.
In 1984, Michael Green and John Schwarz published superstring theory based on a ten-dimensional space-time model, eliminating the divergence problems that had arisen after quantization of gravitational fields, thus triggering the first superstring theory revolution.
GF: So we actually got really good grades in physics, which is very important for mathematicians and physicists, who work side by side with each other. Looking back at Leibniz, he once talked about the harmony that was innately established between mathematics and physics. This is one of Einstein's favorite phrases. Do you think this is an objective fact that this thing can one day be explained, or can never be explained? Do you have any comments on the relationship between the two?
EW: The close connection between mathematics and physics seems to be an objective fact. I can't imagine explaining what it means. It may seem that the world is based on theories involving interesting mathematics, and that many interesting mathematics are at least partially inspired by their role in physics. Of course, not all.
GF: But when you look at some of the math that's very relevant to physics, does that inspire you? Or vice versa? Does this harmony between math and physics somehow motivate you to think you're on the right track?
EW: Yeah, when something looks beautiful, it does encourage you to believe you're on the right track.
GF: It's really the classic Dirac idea. Dirac regarded it as almost a religion. But I sense that you are more hesitant about this, and I don't know if hesitation is the right word.
EW: After discovering Dirac's equations, Dirac seemed entitled to say such things.
Dirac once said: "A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data." (A theory with mathematical beauty is more likely to be correct than an ugly theory that matches some experimental data.) Image source |: Wikipedia
Witten has long been a pioneer in the string theory framework, which sought to uniformly describe all the forces of nature based on quantum mechanics and relativity. The framework describes the fundamental entities of nature in tiny strings.
GF: Back to string theory. Do you think string theory is one of several candidate theories, or the most prominent of them? I mean, how do you see the framework's place in the field of mathematical physics.
EW: I think string theory/M-theory is the only really interesting direction we go beyond the established physical framework, which here refers to quantum field theory at the quantum level and classical general relativity at the macroscopic scale. We have made progress within the framework of string theory/M-theory, and we have found many interesting things there. I think there are a lot of interesting things we don't know at all.
GF: But you've never been drawn to other paths. Aren't the other options reasonable candidate theories?
EW: I'm not sure what other paths you're referring to.
GF: Like loop quantum gravity?
EW: Those are just empty words, and I don't think there's any other path.
GF: All right.
So we got to know Witten's point of view. An extra cautious Witten argues that if we want to discover a theory that unifies all fundamental forces, string theory is the only interesting path that has emerged at the moment.
In the 1990s, with the discovery of duality, a second revolution in superstring theory arrived. Witten proposed an eleven-dimensional M-theory that unified the five cases of string theory with supergravity. M-theory is often considered a prime candidate for the theory of everything. | Image credit: Olena Shmahalo/Quanta Magazine
GF: The stage we're at right now is a very unusual period because a lot of us expect the Large Hadron Collider to produce huge particle energies, looking for the Higgs boson and supersymmetry. We have obtained the Higgs particle as we expected. But there seems to be nothing really exciting about it. What are your thoughts on where we are now?
EW: My generation grew up with a very strong belief that was inspired by Steven Weinberg and others. We believe that when physics reaches an energy scale that can understand weak interactions, you will not only find the mechanism of electrically weak symmetry breaking, but also understand what determines its energy scale is lower than the energy scale of gravity. This eventually makes gravity so weak. Surprisingly, we reached the energy scale of detecting W and Z particles, and even Higgs particles, but didn't find the broader mechanism behind it. It was a very shocking development for my growing thoughts.
In those 40 years, another shocking thing has happened, that is, the discovery that the expansion of the universe is accelerating. For decades, physicists have believed that the expansion of the universe will slow down due to gravitational attraction between matter, and they have tried to measure it. And it turns out that the inflation is actually accelerating. While we're not sure yet, it seems likely that the effect of Einstein's cosmological constant seems small, but not zero.
These two things are very similar and very confusing. The cosmic constant is very small but not zero, and there are problems with the energy scale of weak interactions and the mass scale of elementary particles, which seems to be a lot of energy from a human perspective, but it is very small compared to other energies in physics.
Of these two conundrums, the first to be discovered about gravity may be the main motivation for discussing the vacuum cosmic landscape. This thought used to make me feel extremely uncomfortable and unhappy. I think this is due to the challenges these conundrums pose to our attempts to understand the universe and the detrimental effects that could be had on our descendants tens of billions of years ago. I was finally able to face this idea with ease, perhaps because I realized that the universe did not arise for our convenience.
GF: So you accepted it?
EW: I accepted the idea of landscape and stopped getting frustrated with it as I had for years.
GF: Really frustrated?
EW: I still wish there would be a different interpretation, but it no longer frustrates me as much as it used to.
GF: What do you think is the main challenge for all those who are concerned with fundamental physics?
EW: I think there's a good chance that new discoveries in astronomy or accelerators will bring new practical challenges. But, as far as we know it now, and to my personal preference, it's hard to avoid responding to new challenges about cosmology. I actually think that string theory/M-theory is on the right track and is moving towards a deeper explanation. But at the most essential level, our understanding of string theory is not very clear. We don't yet know what elements of string theory are missing, or where the missing concepts can be found. I don't know because in hindsight we had a very narrow view of what was missing in the '80s, and then in the '90s, instead of finding what we thought was missing, we expanded the image in unexpected directions. Because I went through that period, I felt like that could happen again.
If you ask me what is the most likely direction for another major theoretical upheaval similar to the '80s and '90s besides cosmology, I think that "everything comes from qubits," the relationship between geometry and entanglement, is one of the most interesting directions.
"It from bit" is a term coined by theoretical physicist John Wheeler, who speculates that "it," or natural matter, may ultimately be constructed from information bits. Perhaps information theory shows us the best way to develop fundamental physics. Witten is usually cautious about making forceful statements about the future of his discipline. So I was surprised by his interest in this research direction, which is now very popular.
EW: If there's another real upheaval in my career, I think that's going to be the most likely direction. In the early '80s and early '90s, I had a feeling that in the years leading up to the turmoil, I felt that the turmoil was most likely to come from those directions, and the results showed that the feeling was indeed correct twice. And then for a long time, I didn't know where another upheaval might come from. By the last few years, I've come to believe that it's likely to be "everything from qubits," though I'm not yet a pioneer in this area. I'm not the first to come to this conclusion or hold this doubt, but that's my point anyway.
GF: There's a famous book about nocturnal reflections on quantum physics. If a string theorist thinks at night, there is a wonderful theory that is developing, but knows that it cannot be verified. Will that bother you?
EW: Sure, it's going to bother us, but we have to live with our conditions. Let's go back 34 years, that was in the early '80s, and there were a lot of clues that something important would happen in the field of string theory, and when Green and Schwartz discovered anomalous cancellations, it became possible to unify the elementary particle physics model with gravity. Since then, I think the direction is clear. But some physicists reject it altogether, on the grounds that it may not be testable, or even think it will be too difficult to understand. My view at the time was that when we reached the energy scales of the W, Z, and Higgs particles, we would get all sorts of wonderful new clues.
I'm very surprised that some colleagues are so convinced that we won't be able to get important clues to new theories that may actually be fundamental to work. Now, if we analyze what's going on 34 years from now, I'd love to say that we're both a bit wrong. I think the energy scale that can be given clues from accelerators is not yet realized. In fact, the most important clue may be that we have confirmed the Standard Model, although we have not gotten the full expectations of the Standard Model. As I've said before, this could be a clue about the landscape.
I think the critics' conceptual flaw is that, while it is regrettable that the period of incredible upheaval, experimentation and discovery that existed until I first started graduate school did not continue, I think that physics has actually made much more progress since 1984 than if we had heeded our opponents and not developed string theory.
GF: And the development of mathematics has also benefited from it.
EW: Mathematics has also benefited, and now even other areas of physics, such as new ideas about the thermodynamics of black holes that have influenced condensed matter physics, and even the study of many other areas such as quantum phase transitions and quantum chaos.
GF: Hopefully all of us will be able to see some completely unanticipated wins, that would be the best thing.
Witten's precision in self-expression and avoidance of vague philosophical words always struck me. The close connection between fundamental physics and fundamental mathematics fascinated him. He was reluctant to say further that the relationship between physics and mathematics was an objective fact. However, no one can illustrate this relationship better than he does. Not only does mathematics unbelievably affect physics, physics also incredibly affects mathematics. Witten says it only makes sense if our modern theories are on the right path.
Surprisingly, Witten is sometimes underestimated by physicists, who describe him as a mathematician with only a momentary interest in physics. This is completely inaccurate. When I spoke to the great theoretical physicist Steven Weinberg, he told me that he was in awe of Witten's physical intuition, and on other occasions he had said that witten had an incredible amount of math in his head.
Graham Farmelo: Popular science writer, author of "The Universe Speaks in Numbers", "Quantum Monster: The Biography of Paul Dirac" and many other popular science books.
The transcript of the interview, translated from a software recording by Sabine Hossenfelder, a researcher at the Institute for Advanced Study in Frankfurt, Germany, was published on her blog in May 2019 with an authorized translation of "Back to Simplicity" with slight deletions.
Reprinted from the "Return to Simplicity" public account
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