# Magic, mystery or matrix?

## A conversation with string theorist Edward Witten

The ideas of U.S. physicist Edward Witten have had a significant influence on the development of theoretical physics in recent decades. He is one of the most cited researchers in his field and is convinced that membrane theory, an extension of string theory, could point the way to a world formula that describes all elementary particles and natural forces in a unified formalism. However, proof that this hope is justified has yet to be provided.

The interview was conducted by Ralf Krauter, physicist and science journalist.

**You were born in Baltimore, Maryland in 1951. Your father was also theoretical physicist and he was interested in gravitation and general relativity. How did he and his interests influence your career choices?**

I was exposed to math and physics from a young age. And when I was very young, I had a passion for astronomy. Those were the days of the space race. Everybody was interested in astronomy - but I really had a passion for astronomy. And I thought I would be an astronomer when I grew up. I remember being afraid that astronomers would have to live and work in space, which sounded dangerous. I've noticed, though, that 60 years later, space telescopes are very important, but the astronomers who operate them usually live on the ground. Then, after the age of 11 was exposed to calculus and got very interested in mathematics. But honestly, my life later took some zigzags and I wasn't sure what I wanted to do. It wasn't until the age of 22 that I really decided I was going to do theoretical physics. And finally, my father still is a theoretical physicist at the age of 102. And for his age he's in very good health.

*It took you while to discover that maths and physics is your cup of tea. After you finished high school, you first studied history and linguistics and then started writing articles for newspapers. So you were even thinking about going into journalism?*

I eventually had the sense to realize that my talent in some of these other areas was limited and that I'm better in math and physics.

*But it took you 2 or 3 years after school until you finally realized this?*

Sort of, yes. I don't recommend this trajectory for other people. I would recommend to other people to have fewer zigzags in their life than I did. Many people write to me and want me to tell them, that I think it was great to have all these zigzags, but I can't honestly say that. So I never do.

*You wrote your dissertation in 1976 at the University of Princeton under the supervision of David Gross, roughly three years after he made this interesting discovery on how to better describe how quarks interact, which later got him the Physics Nobel Prize in the year 2004. How inspiring was it to have such a prominent and renowed scientist as a mentor back then?*

It really was very exciting working with David Gross and also the graduate school environment at Princeton was very exciting. And a lot of things were happening in those days. As you just said: David's discovery of what's called asymptotic freedom was new and a lot of implications were still being worked out - including the mystery of how quarks are confined. Which became my passion at the time. It's still not fully satisfactory understood, today. I was preoccupied with that problem for several years and only very reluctantly accepted the fact that I had to work on things that were easier. We only can do things that we can do. And explaining quark confinement wasn't in that category at the time. Some aspects were understood in those years. But the kind of quantitative understanding that I dreamed of, still remains out of reach today.

*Was it during your PhD thesis when you got interested in quantum field theory and grand unified theories?*

Modern quantum theory, by which I mean quantum theory together with Einstein's special relativity, is what we call quantum field theory. And so the framework in which particle physics is understood is all quantum field theory. As for grand unified theories: They were getting started in those years. But they weren't yet having a big impact on Princeton, as far as I can remember. I can't exclude the possibility that some of my colleagues were excited about them, but I don't remember it very well. But then I graduated in 76 and went to Harvard. And there, there was a lot of excitement about grand unified. Some of the most important early work on great unification had been done by colleagues at Harvard. So once I was at Harvard grand unified was a very important part of the backgrounds. But the ones in those years who did have a useful idea about gravity were the ones who had never abandoned string theory. So as a theory of the strong interactions string theory had not turned out to be the best approach, although we still today believe it has some validity. Asymptotic freedom and quantum chromodynamics, where David Gross was one of the pionieers, was a much more effective approach. But some people, notably John Schwarz, Michael Green, Lars Brink and a few others, didn't give up on string theory. And in hindsight, those were the ones in those years who had a useful idea about gravity, though it didn't come very much to fruition until the early 80s.

*You're a very famous string theorist and you're also considered to be the father of M-theory. Can you try to briefly explain for laymen what M-theory is about and how it actually describes the universe and all the rest, as Douglas Adams would have put it?*

One thing I have to tell you is that the description of me as the father of M-theory is a big exaggeration. I made some contributions, but M-theory is still largely not understood - and a lot was understood before I was involved. So I'm torn between telling you that it hasn't been discovered yet or that it was discovered before me. Either of those positions is defensible. So 20th century physics had two primary achievements, which were quantum theory and Einstein's theory of gravity. Quantum theory describes atoms, molecules and subatomic particles. Einsteins theory of gravity describes stars, galaxies and the whole universe. Quantum theory was put in its fullest form as of today in the standard model of particle physics, which was finalized around 1973. Just when I was starting graduate school. A big mystery in physics has been that quantum theory and Einsteins theory of gravity appear to be incompatible. If you take quantum theory, as we have developed it in the standard model>: Einstein's highly nonlinear mathematics used in his theory of gravity is incompatible with requirements of quantum theory. This was first perceived perhaps in the 1930, but at the time the understanding of quantum theory was so limited that people thought that maybe the problem would go away if quantum theory was understood better. However, by the 1970s, with the rise of the standard model, quantum theory was sufficiently well understood that it was clear that the difficulty in incorporating gravity was serious. It's a big problem which no one on purpose had any real idea about how to solve. But physicists trying to understand the nuclear force, the strong interactions, what holds the protons and neutrons together in an atomic nucleus in the process of their approach discovered string theory, which actually does in a mysterious way that we still don't well understand not just allow us to include gravity with quantum theory, but it modifies quantum field theory in a way that forces us to include gravity. So gravity flips from being impossible to being unavoidable when you go from conventional quantum field theory, which is the modern framework of quantum theory, to string theory, which is a refinement of it. It turns out that gravity is forced upon you. So that was the big advance of the 70s and 80s, to say in a nutshell.

And by the mid 80s it was clear that in that framework you could make a theory that includes gravity and the other particle forces. There was a slight embarrassment that there were five possible string theories. If one of them describes our world, who lives in the other four worlds? In the 90s there were two big advances. The first of them involved understanding that, if you consider quantum effects to be weak, there are five string theories. But if you take quantum mechanics seriously, the five string theories are different limiting cases of one big theory. And that big theory is what we loosely call m-theory.

We don't understand it very well. When Einstein had developed his theory of gravity, he started with the ideas that it was based on. And then he threw a lot of hard work figuring out what the theory had to be. String theory is kind of the opposite. The earliest form of the theory was invented in the 1970s by people who had no idea that even it was supposed to describe gravity, let alone how it was supposed to modify and generalize Einstein's ideas. So string theory was invented basically by accident, by people who, had a good but not optimal idea about the nuclear force and had no idea about a new theory of gravity. And ever since then, we've been grappling with the fact that we know aspects of the theory, but we don't understand what it's really based on. So it's poles apart from once when Einstein started with the ideas and then dropped the theory, we stumbled into the theory and we don't fully understand the ideas. In fact, I'd say we only understand a small part. So we've been struggling with that ever since the 70s and 80s trying to understand the intellectual framework that it should have been placed in.

*There was a very famous conference in 1995. At this conference you were proposing how to unify these five string theories you were already mentioning. So wasn't that sort of the inception of of M-theory back then?*

Well, the story is sometimes told that way, but I would like to paint a more modest portrait. There were a lo t of threads around, that mostly other colleagues, in some cases me, had discovered, that could be interpreted in a certain direction. And I put them together at that conference - perhaps more convincingly than other people had done. So the story is sometimes told the way you did, but. I'm pleased with the contribution I made, but I'm torn between saying that M-theory had already been invented, and that it's still not hasn't been invented yet. Both points of view are defensible depending on your viewpoint.

*As a byproduct of your contributions to physics, you've also made a lot of important contributions to mathematics. Because you were applying concepts from physics and transferring them into mathematics, thus helping mathematicians to better understand problems they had to deal with. These contributions won you a very prestigious prize, the Fields Medal, which is considered to be the Nobel Prize for mathematicians. In which of the two disciplines - physics or mathematics - do you feel more at home?*

Well, it's got to be physics. Because I have the education of a physicist, I don't really have the education of a mathematician. I'm able to make some contributions to math for reasons that are mysterious but have been around since Isaac Newton invented calculus, which made mathematics vastly more powerful, because he was trying to understand the orbits of the planets. That's just one example. It has turned out that many important mathematical and physical ideas have common roots. I was trying to state that in a neutral way without giving primacy to either side. And now in modern times, quantum field theory is very difficult to understand mathematically, and string theory is even harder to understand. But they both contain a lot of mathematical secrets. And so as a quantum field theorist or a string theorists I was sometimes able to make mathematical suggestions that aren't so easy to come by for the mathematicians. And I believe it will remain so until string theory is better understood. I believe the fundamental reason that that's true. As I've told you before, the roots of M-theory are not that well understood. If they were understood, they would probably be possible to state it in a way mathematicians could understand, and physicists might then lose their advantage in making mathematical predictions from the theory. But as long as the roots are so murky, the ones grappling with it and trying to understand it are physicists. And that gives us a head start in coming up with a number of interesting mathematical ideas.

**If you look back 50 years: Would you say string theory and its successors have brought us much closer to understanding the true nature of the cosmos? Do we have a big picture of what the universe consists of?**

Well, we certainly don't fully understand it. I think we've taken important steps. But life doesn't come with guarantees. One of the reasons I think we're probably on the right track is that advances in string theory and m-theory have often given new insights about both established physical theories, especially quantum field theory and sometimes gravity and also mathematics. I feel that explorations of the theory wouldn't be giving us so much insight about existing physical theories and also purely mathematical theories if it wasn't on the right track. Because I find it implausible that physicists would discover a theory that is such a rich source of fruitful ideas about things that are definitely important in other fields by accident. And if we were not on the right track, I would say, it was a big accident. So my personal view is that it would be a cosmic conspiracy if string theory isn't on the right track. But as I said: Life doesn't come with guarantees.

*There is a growing number of critics who complain that string theory is very interesting, but hasn't really delivered. Because we still have no idea whether it's correct and we couldn't make any experiments, which tells us if this is the case. According to you: To what extent is that criticism justified?*

Well, not much, honestly. Where critics of string theory have had interesting ideas, they've tended to be absorbed as part of string theory. That's happened several times. Twistor theory, black hole thermodynamics and noncommutative geometry are three examples of interesting ideas. They were by some regarded as alternatives or competitors of string theory, but actually in practice were absorbed as part of the picture in string theory.

*In an interview you gave the german science magazine Spektrum der Wissenschaft in 1999 you've said: The Large Hadron Collider LHC at CERN in Geneva is the most probable place to discover supersymmetric particles, whose existence is one of the key predictions string theory and m-theory. But so far they haven't been found. How painful is that lack of direct evidence?*

Well, the results were disappointing, regardless of whether one is motivated by string theory or not. There's a major puzzle that's come from the LHC experiments and prior experiments, which had pointed in this direction. There's a mystery about the Higgs particle and the other elementary particles. Their masses are much less than the mass scale set by gravitation. That's an incredibly tiny factor of about ten to the -16. But in the laws of nature as we know them now, it looks like an accident. My generation of physicists grew up with the expectation that if we reach the energy at which we could directly probe the question, we could learn why that number is so small. We finally reached the relevant energies, but a resolution of the puzzle has not appeared. And in the meantime, a second similar puzzle was discovered, which has to do with the acceleration of the cosmic expansion. Einstein's cosmological constant, the energy of the vacuum, they're so tiny that my generation of physicists grew up assuming it was surely zero for some unknown reason. But cosmologists seemed to have discovered that it's slightly positive, not quite zero. So there are two rather similar mysteries, one coming from cosmology and one from the LHC and other particle physics experiments. Those two mysteries probably do change our understanding of the universe, but we don't fully understand how.

*The Hamburg Prize for Theoretical Physics comes with the obligation that you spend some time in Hamburg, in order to directly exchange ideas with the researchers and students there. Are you looking forward to that?*

Certainly, I always look forward to interacting with colleagues.

*If your hosts in Hamburg want to prepare perfectly well for your stay there, what should they do? I've read that providing a tennis court would probably be highly appreciated. Is that correct?*

Well, I do play tennis a little bit. That's true. For this upcoming visit in November for the symposium, I doubt there will be any time for tennis, but guess I'll be returning for a slightly more relaxed visit. We'll see then. I'm not a really good tennis player though. Just like to play.

*Are you a sportive player and run a lot? Or is it more like you're smart and try to stay in the middle?*

Well, my skills are limited, so I have to compensate for that by running. So I'm afraid I play in a very labor intensive way. Among people who play twice a week. I'm about average, I would say.

*What other leisure activities do you like?*

Just a few years ago, I started playing piano a little bit. Obviously, I started way too late in life to ever become very good at piano. But it's fun to try.

**You're married to the italian physicist Chiara Nappi who is a professor emeritus at Princeton University. How did you get to know each other?**

We were still students, it was in Les Houches in 1975, I think. During a physics summer school, near Chamonix, in the French Alps.

*You have three children together. Does any of them share your and your wife's passion for quantum fields, quantum gravitation and string theory?*

They're actually all in scientific or technical or computer science areas, but none of them is a physicist.

**Do you regret that?**

No, children should find their own way.