Graham Farmelo’s interview of Edward Witten. Transcript.

[I’ve meant for some while to try an automatic transcription software, and Graham Farmelo’s interview of Edward Witten (mentioned by Peter Woit) seemed a good occasion. I used an app called “Trint” which seems to work okay. But both the software and I have trouble with Farmelo’s British accent and with Witten’s mumbling. I have marked the places that I didn’t understand with [xxx]. Please leave me a comment in case you can figure out what’s being said. Also notify me of any blunders that I might have missed. Thanks!]

GF [00:00:06] A mind of the brilliance of Edward Witten’s comes along in mathematical physics about once every 50 years if we’re lucky. Since the late 1970s he’s been preeminent among the physicists who are trying to understand the underlying order of the universe. Or, as you might say, trying to discover the most fundamental equations of physics. More than that, by studying the mathematical qualities of nature, Witten became remarkably influential in pure mathematics. The only physicist ever to have won the coveted Fields Medal which has much the same stature in mathematics as a Nobel Prize has in physics.

GF [00:00:46] My name is Graham Farmelo, author of  “The universe speaks in numbers.” Witten is a central figure in my book and he’s been helpful to me. Though he’s a reluctant interviewee so I was pleased when he agreed to talk with me last August about some aspects of his career and the relationship between mathematics and physics. He was in a relaxed mood sitting on a sofa in his office at the Institute for Advanced Study in Princeton wearing his tennis clothes. As usual, he speaks quietly so you’ll have to listen hard.

GF [00:01:20] He uses quite a few technical terms too. But if you’re not familiar with them I suggest that you just let them wash over you. The key thing is to get a sense of Witten’s thinking about the big picture. He is worth it.

GF [00:01:32] He gives us several illuminating insights into how he became interested in state-of-the-art mathematics while remaining a physicist to his fingertips. I began by asking him if he’d always been interested in mathematics and physics.

EW [00:01:47] When I was a kid I was very interested in astronomy. It was the period of the space race and everybody was interested in space. Then, when I was a little older, I was exposed to calculus by my father. And for a while I was very interested in math.

GF [00:02:02] You said for a while, so did that lapse?

EW [00:02:04] Yes, it did lapse for a few years, and the reason it lapsed, I think, was that after being exposed to calculus at the age of eleven it actually was quite a while before I was shown anything that was really more advanced. So I wasn't really aware that there was much more interesting more advanced math. Probably not the only reason, but certainly one reason that my interest lapsed.

GF [00:02:22] Yeah. Were you ever interested in any other subjects? I mean because you know you came on to study history and things like that. Did that really interest you comparably to math and physics?

EW [00:02:31] I guess there was a period when I imagined doing journalism or history or something but at about the age of 21 or 22 I realized that I wasn't going to work out well in my case.

GF [00:02:42] After studying modern languages he worked on George McGovern’s ill fated presidential campaign and even studied economics for one semester before he finally turned to physics.

GF [00:02:53] Apparently he showed up at Princeton University wanting to do a Ph.D. in theoretical physics and they wisely took him on after he made short work of some preliminary exams. Boy did he learn quickly. One of the instructors tasked with teaching him in the lab told me that within three weeks Witten’s questions on the experiments went from basic to brilliant to Nobel level. As a postdoc at Harvard, Witten became acquainted with several of the theorist pioneers of this model including Steven Weinberg, Shelly Glashow, Howard Georgi, and Sydney Coleman, who helped interest the young Witten in the mathematics of these new theories.

EW [00:03:33] The physicists I learned from most during those years were definitely Weinberg, Glashow, Georgi, and Coleman. And they were completely different. So Georgi and Glashow were doing model building, basically weak interaction model building, elaborations on the Standard Model. I found it fascinating but it was a little bit hard to find an entree there. If the world had been a little bit different, I might have made my career doing things like they were doing.

GF [00:04:01] Wow. This was the first time I’d heard Witten say that he was at first expecting to be like most other theorists and take his inspiration from the results of experiments building so-called models of the real world. What, I wondered, led him to change direction and become so mathematical.

EW [00:04:19] Let me provide a little background for listeners. Up to and including the time I was a graduate student, for 20, 25 years, there had been constant waves of new discoveries in elementary particle physics: strange particles, muons, hadronic resonances, parity violations, CP violation, scaling and deep inelastic scattering, the Charm particle, and I’m forgetting a whole bunch. But that’s enough to give you the idea. So that was over a period of over 20 years. So even after a lot of the big discoveries that was one every three years. Now, if experimental surprises and discoveries had continued like that, which at the time I think is what would have happened because it had been going on for a quarter century, then I would have expected to be involved in model building, or grappling with it, like colleagues such as Georgi and Glashow all were doing. Most notably, however, it turned out that this period of constant surprise and turmoil was ending just while I was a graduate and therefore later on I had no successful directions.

GF [00:05:20] Do you remember being disappointed by that in any sense?

EW [00:05:23] Of course I was, you never stop being disappointed.

GF [00:05:27] Oh dear, oh it’s a hard life.

GF [00:05:31] You were disappointed by the drawing up so to speak of the.

EW [00:05:33] There have been important experimental discoveries since then. But the pace has not been quite the same. Although they’ve been very important they’ve been a little bit more abstract in what they teach us and definitely they’ve offered fewer opportunities for model building than was the case in the 60s and 70s. I’d like to just tell you a word or two about my interaction with the other physicists. There was Steve Weinberg and what I remember best from Weinberg. He was one of the pioneers of a subject called current algebra which was an important part of understanding the nuclear force. But he obviously thought most other physicists didn't understand it properly and I was one of those. So whenever current algebra was mentioned at a seminar or a discussion meeting he would always give a short little speech explaining his understanding of it. In my case after hearing those speeches the eight to 10 times [laughter] what Steve was telling us.

EW [00:06:28] Then there was Sidney Coleman. First of all Sidney was the only one who was interested in strong coupling behavior of quantum field theories which is what I’d become interested in as a graduate student with encouragement from my advisor David Gross. So, he was really the only one I could interact with about that. Others regarded strong coupling as a black box. So, maybe for your listeners, I should explain that if you’re a student in physics they teach you what to do when quantum effects are small, but no one tells you what to do when quantum effects are big, there’s no general answer. It’s a smorgasbord of different methods that work for different problems and a lot of problems that are intractable. So, I'd become interested in that as a student but I was mostly beating my head against a brick wall because it is usually intractable, and Sydney was the only one of the professors at Harvard interested in such matters. So, apart from interacting with him about that, also he exposed me to a number of mathematical topics I wouldn’t have known about otherwise but that eventually were important in my work which most physicists didn’t know about. And certainly I didn’t know about.

GF [00:07:27] Yeah, can I ask were you consciously interested in advanced pure math at that time?

EW [00:07:32] Definitely not

GF [00:07:32] You were not?

EW [00:07:32] No, most definitely not. I got dragged into math gradually because you see the standard model had been discovered so the problems in physics were not exactly the same as they had been before. But there were new problems that were opened up by the standard model. For one thing there is new math that came into understanding the standard model. Just when I was finishing graduate school more or less Polyakov and others introduced the Yang-Mills instanton which has proved to be important in understanding physics. It’s also had a lot of mathematical applications.

GF [00:08:02] You can think of instantons as fleeting events that occur in space and time on the subatomic scale. These events are predicted by the theories of the subatomic world known as gauge theories. A key moment in this story is Witten’s first meeting with the great mathematician Michael Atiyah at the Massachusetts Institute of Technology. They will become the leaders of the trend towards a more mathematical approach to our understanding of the world.

EW [00:08:32] So Polyakov and others had discovered the Yang-Mills instanton and it was important in physics and proved to have many other applications. And then Atiyah was one of the mathematicians who discovered amazing mathematical methods that could be used to solve the instanton equations. So he was lecturing about that when he visited in Cambridge. I think in the spring of 1977, but I could be off by a few months, and I was extremely interested. And so we talked about it a lot. I probably made more of an effort to understand the math involved than most of the other physicists did. Anyway this interaction surely led to my learning all kinds of math I’d never heard of before, complex manifolds, sheaf cohomology groups.

GF [00:09:16] This was news to you at that time.

EW [00:09:18] Definitely. So I might tell you at an even more basic level the Atiyah-Singer index theorem had been news to me a few months earlier when I heard about it from Sidney Coleman.

GF [00:09:28] The index theorem first proved by Michael Atiyah and his friend Isidore Singer connects two branches of mathematics that had seemed unconnected. Calculus, that’s the mathematics of changing quantities, and topology about the properties of objects that don’t change when they’re stretched, twisted, or deformed in some way, topology is now central to our understanding of fundamental physics.

EW [00:09:51] Like other physics graduate students of the period, I had no inkling of any 20th century math, really. So, I’d never heard of the names Atiyah and Singer or of the concept of the index or if the index theorem until Albert Schwarz showed that it was relevant to understanding instantons. And even then that paper didn’t make an immediate splash. If Coleman hadn’t pointed it out, I’m not sure how long it would have been before I knew about it. And then there was progress in understanding instanton equations by Atiyah among others. The first actually was Richard Ward, Penrose’s doctoral student. So, I got interested in that but I was interested in a sense in a narrow way which is what good would it be in physics. And I learned the math or some of the math that the teacher was using. But I was a little skeptical about the applicability for physics and I wasn’t really wrong because the original program of Polyakov didn’t quite work out. The details of the Instanton equations that were beautifully elucidated by the mathematicians were not in practice that helpful for things you can actually do as a physicist. So, to sort of summarize what happened in the long run, Atiyah’s work and that of his colleagues made me learn a lot of math I’d never heard of before which turned out to be very important later but not per se for the original reasons.

GF [00:11:10] When did you start to become convinced that math was really going to be interesting?

EW [00:11:14] Well that gradually happend in the 1980s I guess. So, for example one early episode which was in 1981 or two I was trying to understand the properties of what's called the vacuum the quantum ground state in supersymmetric field theories and it really had some behavior that was hard to explain using standard physics ideas and since I couldn't understand it I kept looking at simpler and simpler models and they all had the same puzzle. So finally I got to what seemed like the simplest possible model which you could ask the question and it still had a puzzling behavior. But at a certain point, I think when I was in a swimming pool in Aspen Colorado, I remembered Raoul Bott and actually Atiyah also had given some lectures to physicists a couple of years earlier in Cargesse, and they had tried to explain something called Morse theory to us. I’m sure there are like me many other physicists that have never heard of Morse theory or are familiar with any of the questions it addresses or.

GF [00:12:11] Would you like to say what Morse theory is roughly speaking?

EW [00:12:14] Well if you’ve got a rubber ball floating in space it’s got a lowest point, where the elevation is lowest, it’s got a highest point where the elevation is highest. So it’s got a maximum and a minimum. If you have a more complicated surface like for example a rubber inner tube, it’ll have saddle points of height function as well as a maximum and minimum. And Morse theory relates the maxima and minima and the saddle points of a function such as height function to the topology of a surface or topological manifold on which the function is defined.

GF [00:12:48] You see that paper by Maxwell on that what he spoke about see in 1870.

EW [00:12:52] I’ve not read that.

GF [00:12:53] Oh I’ll show it to you later. It’s “On Hills and Dales,” gave it in Liverpool, very thinly attended talk, erm, anyway.

EW [00:13:01] So was he in fact describing the two dimensional version of Morse theory.

GF [00:13:04] I can’t go into detail but the historians of Morse theory, they often refer to that. At a public meeting incidentally in Liverpool. 

EW [00:13:13] Actually now you mentioned it, I heard the title of the Hills and Dales talk by Maxwell that had something to do with the beginnings of topology. And topology was just barely beginning in roughly that period.

GF [00:13:23] But this was useful in physics. Your Aspen swimming pool revelation...

EW [00:13:28] Well, it shed a little bit of light on the vacuum state in super symmetric quantum theories. So anyway I developed that further so you know at first that seemed exceptional but eventually there were too many of these exceptions to completely ignore.

GF [00:13:42] Am I right in saying, not to put into your mouth, but it was the advent of String Theory post Michael Greene and John Schwartz where these things started going front and center, is that fair?

EW [00:13:50] After... Following the first super string revolution as people call it which came to fruition in 1984 with the work of Greene and Schwarz on the anomalies after that the sort of math that Atiyah and others had used for the instaton equation was suddenly actually useful. Because to understand string theory, complex manifolds and index theory sheaf cohomology groups, all those funny things were actually useful in doing basic things like constructing models of the elementary particles in string theory. I should give a slightly better explanation. In physics there are the forces that we see for the elementary particles that means basically everything except gravity. Then there's gravity which is so weak that we only see it for macroscopic masses like the earth or the sun. Now we describe gravity by Einstein's theory and then we describe the rest of it by quantum field theory. It's difficult to combine the two together. Before 1984 you couldn't even make a halfway reasonable models for elementary particles that included all the forces together with gravity. The advance that Greene and Schwarz made with anomaly cancellation in 1984 made that possible. But to make such models you needed to use a lot of the math that physicists had not used previously but which was introduced by Atiyah and others when they solved the instanton equations and you had to use complex manifolds, sheaf cohomology groups and things that were totally alien to the education of a physics graduate student back in the days when I'd been a student. So those things were useful even at a basic level in making a model of the elementary particles with gravity. And if you wanted to understand it more deeply you ended up using still more maths. After string theory was developed enough that you could use it in an interesting way to make models of particle physics it was clear that a lot of previously unfamiliar math was important. I speak loosely when I say previously unfamiliar because obviously it was familiar to some people. First of all the to the mathematicians. Secondly in some areas like Penrose had used some of it in his Twister theory. But broadly speaking unfamiliar to most physicists.

GF [00:15:46] So we actually went very well in physics very very important for mathematicians in mathematics a very important physicist they're working harmoniously alongside each other. You go back to Leibnitz who used to talk about the pre established harmony between math and physics. That was one of Einstein's favorite phrases. Is there something you regard as a fact of life or is it something you would regard as possibly can be explained one day will never be explained. Do you have any comment at all on that relationship.

EW [00:16:09] Well, the intimate tie between math and physics seems to be a fact of life. I can't imagine what it would mean to explain it. The world only seems to be based on theories that involve interesting math and a lot of interesting math is at least partly inspired by the role that it plays in physics. Not all of course.

GF [00:16:25] But does it inspire you when you see a piece of math that's very relevant to physics and vice versa when you're helping mathematicians. Does that motivate you in some way to think you're on the right track.

EW [00:16:35] Well when something turns out to be beautiful that does encourage you believe that it's on the right track.

GF [00:16:39] Classic Dirac. But he took it as he put it to almost a religion. But I sense you are  a little bit more skeptical, if that's the right word or hard nosed about it I don't know.

EW [00:16:51] Having discovered the Dirac equation, Dirac was entitled to commit its use to extremes, to put it that way.

GF [00:16:58] Witten has long been a leading pioneer of the string framework which seeks to give a unified account of all the fundamental forces based on quantum mechanics and special relativity. It describes the basic entities of nature in terms of tiny pieces of string.

GF [00:17:14] Go back to string theory. Do you see that as one among several candidates or the preeminent candidate or what? I mean what do you see the status of that framework in the landscape of mathematical physics.

EW [00:17:24] Id say that string slash M theory is the only really interesting direction we have for going beyond the established framework of physics by which I mean quantum field theory at the quantum level and classical general relativity at the macroscopic scale. So where where we've made progress that's been in the string slash M theory framework where a lot of interesting things have been discovered. I'd say that there's a lot of interesting things we don't understand at all.

EW [00:17:48] But you’ve never been tempted down the other route. The other options are not.

EW [00:17:52] I’m not even sure what you would mean by other routes.

GF [00:17:54] Loop quantum gravity?

EW [00:17:56] Those are just words. There aren’t any other routes.

GF [00:17:58] Okay, all right, fair enough.

GF [00:18:01]  So there we have it. The preternaturally cautious Witten says that if we want to discover a unified theory of all the fundamental forces, string theory is the only interesting way forward that’s arisen.

GF [00:18:17] Where we are now strikes me as being quite an unusual time in particle physics because so many of us were looking forward to the Large Hadron Collider, huge energy available ,and finding the Higgs boson and maybe supersymmetry. And yet it seems that we have gotten the Higgs particle just as we were hoping and expecting. But nothing else that’s really stimulating. What are your views on where we are now?

EW [00:18:39] My generation grew up with a belief very very strong belief which by the way was drummed into us by Steven Weinberg and by others. That when physics reached the energy scale at which you can understand the weak interactions. You would not only discover the mechanism of electroweak symmetry breaking but you’d learn what fixes its energy scale as been relatively low compared to the scale of gravity. That’s what ultimately makes gravity so weak in ordinary terms. So, it came as a big surprise that we reached the energy scale to study the W and the Z and even the Higgs particle without finding a bigger mechanism behind it. That’s an extremely shocking development in the context of the thinking that I grew up with.

EW [00:19:22] There is another shock which also occurred during that 40 year period which possibly should be comparative. This is the discovery that the acceleration of the expansion of the universe. For decades physicists assumed that because of the gravitational attraction of matter the expansion of the universe with be slowing down and tried to measure it. It turned out that the expansion is actually speeding up. We don't know this for sure it seems quite likely that the results from the effects of Einstein's cosmological constant which is incredibly small but non-zero. The two things the very very small but non-zero cosmological constant and the scale of weak interactions the scale of elementary particle masses which in human terms can seem like a lot of energies. But it's very small compared to other energies in physics. The two puzzles are analogous and they're both extremely bothersome. These two puzzles although primarily the one about gravity which was discovered first are perhaps the main motivation for discussions of a cosmic landscape of vacua. Which is an idea that used to make me extremely uncomfortable and unhappy. I guess because of the challenge it poses to trying to understand the universe and the possibly unfortunate implications for our distant descendants tens of billions of years from now. I guess I ultimately made my peace with it recognizing that the universe hadn't been created for our convenience.

GF [00:20:43] So  you come to terms with it.

EW [00:20:45] I've come to terms with the landscape idea and the sense of not being upset about it. As I was for many years.

GF [00:20:49] Really upset?

EW [00:20:50] I still would prefer to have a different explanation but it doesn't upset me personally to the extent it used to.

GF [00:20:56] So just to conclude what would you say the principal challenge is all down to people looking at fundamental physics.

EW [00:21:01] I think it's quite possible that new observations either in astronomy or accelerators will turn up new and more down to earth challenges. But with what we have now and also with my own personal inclinations it's hard to avoid answering new terms of cosmic challenges. I actually believe that string slash M theory is on the right track toward a more deeper explanation. But at a very fundamental level it's not well understood. And I'm not even confident that we have a good concept of what sort of thing is missing or where to find it. The reason I'm not is that in hindsight it's clear that a view we might have given in the 1980s was what was missing was too narrow. Instead of discovering what we thought was missing instead we broadened the picture in the 90s in unexpected directions. And having lived through that I feel it might happen again.

EW [00:21:49] To give you a slightly less cosmic answer if you ask me where I think is the most likely direction for another major theoretical upheaval like happened in the 80s and then again in the 90s. I've come to believe that the whole it from qbit stuff, the relation between geometry and entanglement, is the most interesting direction.

GF [00:22:12] It from bit that was a phrase coined by the late American theoretician John Wheeler who guessed that the stuff of nature the "it" might ultimately be built from the bits of information. Perhaps the theory of information is showing us the best way forward in fundamental physics. Witten is usually wary of making strong pronouncements about the future of his subjects. So I was struck by his interest in this line of inquiry, now extremely popular.

EW [00:22:39] I feel that if in my active career there will be another real upheaval that's where it's most likely to be coming [xxx]

EW [00:22:47] I had a sense both in the early 80s and in the early 90s. I had a sense a couple of years in advance of the big upheavals where they were most likely to come from it and those two times did turn out to be right. Then for a long long time I had no idea where another upheaval might come from. By the last few years I've become convinced that it's most likely to be the it from qbit stuff of which I have not been a pioneer now. But I was not one of the first to reach the conclusion or a suspicion that I'm telling you right now. But anyway it's the view I've come to.

GF [00:23:20] There's a famous book about night thoughts of a quantum physics. are there night thoughts of a string theorists is where you have a wonderful theory that's developing you know unable to test it. Does that ever bother you.

EW [00:23:31] Of course it bothers us but we have to live with our existential condition. But let's backtrack 34 years. So in the early 80s there were a lot of hints that something important was happening in string theory but once Greene and Schwartz discovered the anomaly cancellation and it became possible to make models of elementary particle physics unified with gravity. From then I thought the direction was clear. But some senior physicists rejected it completely on the grounds that it would supposedly be untestable. Or even have cracked it would be too hard to understand. My view at the time was that when we reached the energies of the W, Z and the Higgs particle we'd get all kinds of fantastic new clues.

EW [00:24:11] So. I found it very very surprising that any colleagues would be so convinced that you wouldn't be able to get important clues that would shed light on the validity of a fundamental new theory that might in fact be valid. Now if you analyze that 34 years later I'm tempted to say we were both a little bit wrong. So the scale of clues that I thought would materialize from accelerators has not come. In fact the most important clue possibly is that we've confirmed the standard model without getting what we fully expected would come with him. And as I told you earlier that might be a clue concerning the landscape. I think the flaw in the thinking of the critics though is that while it's a shame that the period of incredible turmoil and constant experiment and discovery that existed until roughly when I started graduate school hasn't continued. I think that the progress which has been made in physics since 1984 is much greater than it would have been if the naysayers had been heeded and string theory hadn't been done in that period.

GF [00:25:11] And it's had this bonus of benefiting mathematics as well.

EW [00:25:14] Mathematics and by now even in other areas of physics because for example new ideas about black hole of thermodynamics have influenced areas of condensed metaphysics* even in the study of quantum phase transitions, quantum chaos and really other areas.

GF [00:25:31] Well let's hope we all live to see some revolutionary triumph that was completely unexpected that's the best one of all. Edward thank you very much indeed.

EW [00:25:38] Sure thing.

GF [00:25:43] I’m always struck by the precision with which Edward expresses himself and by his avoidance of fuzzy philosophical talk. He's plainly fascinated by the closeness of the relationship between fundamental physics and pure mathematics. He isn't prepared to go further to say that their relationship is a fact of life. Yet no one has done more to demonstrate that not only is mathematics unreasonably effective in physics physics is unreasonably effective in mathematics.

GF [00:26:15] This Witten said makes sense only if our modern theories are on the right track. One last point. Amazingly Witten is sometimes underestimated by physicists who characterize him as a mathematician, someone who has only a passing interest in physics. This is quite wrong. When I talk with a great theoretician Steven Weinberg he told me of his awe at Witten's physical intuition and elsewhere said that Witten's got more mathematical muscles in his head than I like to think about. You can find out more about Witten and his work in my book "The universe speaks in numbers.


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* Condensed matter physics. I am sure he says condensed matter physics. But really I think condensed metaphysics fits better.