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Interview of Michael Green by David Zierler on March 22, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Interview with Michael Green, Lucasian Professor Emeritus at Cambridge University and visiting professor at Queen Mary University. He recounts his childhood in London as the child of secular Jewish parents who immigrated to London just before World War II. Green discusses his early interests in physics and the opportunities that led to his enrollment at Cambridge, and he conveys Geoff Chew’s influence with his ideas on S-matrix and bootstrap theory, which informed his thesis research on hadronic interactions. He narrates the founding ideas that led to string theory and how the work on dual models became transformed into string theory. Green describes his postdoctoral work at the Institute for Advanced Study and his interactions with Veneziano. He explains his decision to return to Cambridge and the importance of the CERN theory group for his research, and he narrates the origins of his collaborations with John Schwarz. Green connects string theory to the ideas that led to supergravity, and he explains why he does not like the term “revolution” in relation to advances in string theory to explain what was happening between 1981-1984. He explains the meaning of the pronoun “super” in relation to string theory, and he conveys his disappointment that supersymmetry has yet to be observed. Green describes the importance of AdS/CFT and his contributions to the origins of D-branes with Joe Polchinski. He discusses his increasing reliance on computers for understanding aspects of AdS/CFT correspondence. Green reflects on winning the Breakthrough Prize, and the supposed aspirational recognition on working to unify the forces which are not yet unified, and he discusses the generational de-coupling of string theory education from particle physics. He provides sociological perspective in response to the impatience that certain physicists have expressed regarding string theory. At the end of the interview, Green ponders the future relationship between string theory and quantum computing, and he describes the field as an intellectual adventure which makes it difficult to predict the significance of these changes.
Okay. This is David Zierler, Oral Historian for the American Institute of Physics. It is March 22nd, 2021. I'm delighted to be here with Professor Michael Green. Michael, it's great to see you. Thank you so much for joining me.
Thank you for inviting me.
To start, would you please tell me your title and institutional affiliation.
Well, officially, I've retired from my position in Cambridge. I was the Lucasian Professor until my retirement, from 2009, I think. For six years. And then, I had to retire from that, because in Cambridge, professors are required to retire at 67. But I stayed on in a different capacity for a few years. I'm now, officially, a visiting professor at Queen Mary University in London. Cambridge and Oxford are exceptional within the British system— they require people to retire at 67. Retirement has been abolished in most other UK universities.
And as a visiting professor, you're not bound by that. You can teach well beyond 67.
Yes, but my position at Queen Mary is very part time, which gives me a lot of time to do research.
Michael, the Lucasian Professor, it's such an august sounding title. Who is, or what is Lucasian?
Well, it originates with a man called Lucas, who funded it—it would have been in the mid 17th century. It was occupied by several very notable people, perhaps the most notable being Isaac Newton, of course. There's nothing particularly special about it, other than the fact that it's been occupied by such august people. In fact, several of the Lucasian Professors in history resigned their professorships in order to take up another Cambridge professorship that would pay a higher salary.
Well, Michael, a question we're all dealing with right now, how has your research been affected by the pandemic, not being able to see people in person, only communicating over Zoom? How have you fared over the past year?
Well, it's not a good situation. It is far, far better to be able to interact in some closer personal way. These interactions are very difficult to define, but in our subject collaborations arise spontaneously by meeting people. Personal interactions are important. But for me, personally, in some senses it’s been a good time in my research because I've been collaborating by Zoom with several very smart younger people, who have kept me on my toes. So, it's been productive and interesting. More generally, since my wife and I are academics, to some extent we are used to working from home, but the repeated lockdowns have been terribly disrupting for my daughter’s university life, as well as the lives of her young friends.
Of course, in your field, you don't need laboratories and big experiments. You just need a pen and paper, and you can continue on with your inquiry.
That's true. That's exactly right. And that's, of course, one of the reasons why it's possible to continue even during a lockdown. On the other hand, as I say, there's an undefinable quality to meeting people in person, and drinking coffee sitting at a table with them, and being able to show people things, or ask them questions, spontaneously. Zoom doesn't really work that way. It's much more impersonal.
Well, Michael, before we take it back and develop your personal narrative, I'd like to ask sort of an overall cultural question as it pertains to your field and your expertise, because, for our largely American readership, it will be very valuable to get your overall perspective from the British side of things. That is, the history of string theory, from its origins that you're, of course, a part of, all the way to today. It has a very unique ebb and flow to it in the United States: when it was popular, when it had a downturn, when it was something that most universities were very interested in hiring, and then there was a backlash to that. The overall question is, is your experience in Britain— more or less, do the attitudes in physics towards string theory and super string theory— would you say that it more or less mirrors, or is a similar trajectory to what we see in the United States, or do you see things differently from your side of the pond?
In many senses, it's a parallel trajectory. However, there is a difference in the way that American academic institutions seem to react to fashions in physics. So, I think the ups and downs have been much more extreme in the States than in Europe in general, but in particular, the United Kingdom. My impression is people have a somewhat different attitude to hiring faculty. I think in the periods in which there was a big boom in string theory, the boom was probably bigger in the States. On the other hand, the subject never really collapsed in the same way in the United Kingdom. So, I think that fashion seems to count much more in the States than it does here.
To take a specific example, when Shelly Glashow famously went on his campaign to make faculties “string free.” Were you paying attention to that? Did that have any particular import, and did it affect hiring practices in the UK at all?
Of course, I knew about it. My friends in the States were talking about it. The Americans seemed much, much more concerned than the Europeans in general, but I don't think that whatever Shelly Glashow thought had much impact at all in the United Kingdom. I think the way hiring is done here is not so much contingent on what other people say about the subject, but more about how good the candidate is. So, there's no question that my American colleagues were far more concerned about what Shelly Glashow and other people might have been saying about string theory.
Okay. That's useful. Well, Michael, let's take it all the way back to the beginning. Let's start first with your parents. Tell me a little bit about them and where they're from.
Well, my parents were immigrants into this country just before the war started, in 1939. They were both secular Jews of Central European/Eastern European origin. My father was born in what is now Israel. He was born in Tel Aviv. His parents and many brothers and sisters -- he was the youngest of seven -- came from Odessa, in the Ukraine, and they had been immigrants into Palestine in the earliest years of the 20th century, about 1905. So, my father grew up there, and he studied architecture there. My mother was Polish, and she emigrated to Palestine, as it then was, when she was a teenager. She was a member of a left-wing organization that was setting up a kibbutz in Israel. Her family then followed her from Poland. In the mid '20s she left the kibbutz and studied engineering. That's how she met my father.
So, my father and mother both studied in Haifa, in Israel, or Palestine at the time. And then they left to continue their studies in Paris. So, they left Palestine in the early '30s, and I suppose that at that time they would never have conceived that they wouldn't be able to get back to see their family, because of the Second World War. They were in Paris from about 1933 to 1939, to just before the war started. By sheer coincidence my father was offered an architecture job in London, and they left Paris. Of course, they would have had no idea that staying in Paris would have been a disaster for them. So, they ended up in London just before the war, and I was born a year after the war ended. I have a sister who is two years older than me, and who was born in the last year of the war. So, that's how they came to the UK. My father had a job at a very prominent architecture firm, and my mother in an even more prominent engineering firm.
Michael, what languages were spoken in your house when you were a young child? I could think of a least three possibilities.
Well, the amazing thing is how many languages my father, in particular, would have spoken. His parents only ever spoke Russian. They immigrated into Palestine, but they never learned any other language. So, he grew up learning Russian from his parents. When he was a very small kid, it was under the Ottoman Empire occupation. I don't suppose he spoke Turkish, but the Jewish community was speaking Hebrew by then, so he would have learned Hebrew. And they were very integrated with the Arab community, so he learned some Arabic. Then, the First World War came, and the Turks were displaced by the British. So, when he was a teenager, and a young student, he would have been under the British mandate. So, he learned English. And then they moved to France, and he learned French. So, he spoke at least five languages, and a bit of Yiddish as well, I guess. When I was a kid, if they wanted to say something that I didn't understand, they would say it in French. But I learned French at some point, so that didn't work for too long.
Michael, what neighborhood did you grow up in?
In London. North London.
What neighborhood in North London?
Hampstead. It's a very beautiful neighborhood, and it's now a very rich neighborhood. When my parents moved there, it wasn't quite such a high-class place. I'm living very close to it right now— sort of in the next neighborhood along.
Was this a place where there were a lot of Jewish émigrés, refugees from Europe?
There were a lot – mostly in a nearby area called Golders Green. So, yes, there were a lot of Jewish people. In my school, a very large fraction of my class was Jewish. Not all immigrants, but a lot of established British Jewry also live in that part of London.
What kind of schools did you go to as a boy?
I went to the local Church of England primary school. The school system in Britain starts with primary school from about 5 to 11, and I was sent to the local Church of England school, which was in retrospect very peculiar. My parents had no religious feelings at all, but that school was closest to where we lived. That was one reason. But I also suspect they really felt this was some way to integrate into being British. My parents had foreign accents, and in those days, and even now, that's not always totally acceptable in Britain. So, I think part of the reason for sending me to a Church of England school would have been to somehow fit in better. Church of England schools have close relationships with the local church, and the church curate, that's a sort of priest-like position, spent a lot of time in our school, and organized morning Christian services. I and another academically prominent Jewish boy were often chosen by the curate to play a prominent role on stage reading out the Christian morning prayers.
So, Michael, I take it, your parents' secular backgrounds filtered into your childhood as well.
Oh, absolutely. My parents had a secular background, and also their close family friends, were from very similar backgrounds to themselves. They were very un-British in many ways. Most of them had immigrated into Britain before the war, maybe shortly after the war, and I think they were basically a bunch of misfits. They certainly didn't fit in with the local Jewish community and furthermore, my parents wouldn't have understood the local Christian community. So, I think I grew up in an atmosphere which must be a bit like many children of immigrants today. They are born in this country, but actually, their culture is so influenced by their parents that they don't have a really close cultural connection with this country.
So, were you Jewishly connected at all growing up? Was your family a part of a synagogue? Were you bar mitzvahed? Was there a Passover seder? Any of that stuff?
The answer is no to all of those things. Not at all. My parents were secular and very politically involved on the left. They had been members of the Communist Party in the immediate post-war years, and probably pre-war years as well. All their friends were left-wing, secular Jews with foreign accents, because they all came from other countries. So, I didn't have a standard childhood like most other English people.
Was your family Zionistic at all? Was the '67 war a moment of pride?
No, not particularly. They were not Zionists. They were children of immigrants into Israel. My father was born in 1909, my mother in 1907, so they had grown up with the original people who eventually formed the state of Israel. But that community in Palestine were not really Zionists. Their community. I mean, the kibbutz communities where they grew up were founded on idealistic socialist principles, and had very little religion, if any. They were non-religious organizations. I think a lot has changed since then. The kibbutz movement is completely different now. So, there's this peculiar quality. I'm Jewish by culture. My parents were about as Jewish as you could get in terms of their backgrounds and their childhoods, but absolutely no religion at all. In fact, if anything, they were anti-religious.
Michael, what kind of high school did you go to? Specifically, did it have a strong curriculum in math and science?
I went to a school which is what we call a grammar school, which doesn't mean much to anyone who isn't British. It was a state school of a kind that was largely abolished in the ‘70s. When I was at school the British school system was very divisive and unequal. There was a state examination called the eleven-plus that everyone took at age 11. On the basis of that one exam, kids of 11 were streamed into either going into schools like the one I went to, called grammar schools, or going to other schools called secondary modern schools. If you didn't get into a grammar school at age 11, you would almost certainly not end up at university. You would go to a secondary modern school and end up leaving school at age 15 or 16.
Nowadays, there are still some grammar schools, but there are few, and they are very selective. The school I went to turned out to be one of the best grammar schools in North London, so I ended up at a very good school. And by complete chance, my physics teacher, a man called Michael Nelkon (I only discovered his first name after I left school), was quite inspirational. He was very well-known to almost anyone in England who studied school physics in my generation because he wrote several of the major school textbooks in physics. He was the author of the best-known physics textbooks aimed at the state exams called O-Levels that were taken at the age of 16, and A-Levels, that are taken at the age of 18. He was very good. But I eventually realized that he didn't know much physics beyond A-Level. What he knew, he knew incredibly well, but he didn't know anything beyond the school curriculum. The maths teaching was also very good. Yes, I went to an academically good school although I'm not so sure about other aspects of school life.
Now, as you well know, of course, many string theorists come to this field very talented in math. Was that your experience as well?
Right. I studied maths, of course, but I certainly didn't, and I still don't, view myself as a mathematician. I was much more interested in the physics. It’s very difficult to judge exactly what the influences were, but I was very taken by what seemed like very fundamental physics. In particular, I learned a smattering of quantum theory. It wasn't something that would have been taught in a school. I did have an interest from the age of about 14 in reading a lot about physics, and I also was interested in mathematics, almost as a recreational subject. I and a school friend used to read books, not on serious mathematics, but on the kind of mathematics which described conundrums that seemed to prove all sorts of nonsense. Tricks in mathematics, basically. But I would never have thought of myself as a mathematician.
When it came to studying at university, it never even occurred to me to study maths. I couldn't see the point of it. However, I now see much more clearly what the point is and how beautiful much of mathematics is, but I didn't at the time. I think it's also true that most people who ended up in string theory did not study maths as their main subject at university. The American system, of course, is different, but in the British university system, you make a very decisive choice about what subject you're going to study in your freshman year. So, you may study just physics for three years, or just maths for three years. So, most of my colleagues in Cambridge came through the physics side, not through the maths side, even though I'm in a mathematics department.
Michael, at Cambridge, I assume, as an undergraduate, particle physics, particle theory was the most exciting thing during your undergraduate years.
Yes, it seemed to be the most exciting subject, which is why I ended up wanting to do research in it. I was an undergraduate starting in '64. Undergraduates in Cambridge get assigned to a Director of Studies. That's a person who advises which courses to take within your major subject. My Director of Studies was a man called Tony Hewish, who shortly after I became a PhD student, discovered pulsars, together with his student Jocelyn Bell. He eventually got the Nobel Prize, and his student didn't, which is a scandal. Although astronomy in Cambridge was remarkable, I was never exposed to it, even though my Director of Studies was an astronomer.
Another major subject that was developing in Cambridge was molecular biology. Francis Crick was very much in evidence, for example. He had originally been a physicist, and while I was a student, he and his group were figuring out the genetic code. That also completely passed me by. Particle physics seemed to be glamorous and very interesting, as well as being very fundamental and very challenging. So, that's what I wanted to do, and that's what I ended up doing.
Did you have any idea about what was happening at Berkeley with S-matrix and bootstrap?
Well, we're now talking about a time after my undergraduate when I was a graduate student. Cambridge was perhaps the place in the world outside the US that was most influenced by what was happening in Berkeley. Geoffrey Chew had spent a sabbatical in Cambridge a couple of years before I became a graduate student and he left a huge mark on the group. He was the person I most I wanted to work with afterwards. It's difficult to imagine now, but at the time I was a student, Cambridge had been so influenced by Chew’s bootstrap idea that quantum field theory wasn't taken too seriously. This was a period when the beginnings of the Standard Model were being discovered by Steven Weinberg, and others. But in Cambridge quantum field theory was considered not to be as important as the S-matrix stuff that originated in Berkeley.
Michael, what kind of advice did you get about graduate programs? Did you think about leaving Cambridge? Did you get advice specifically to stay at Cambridge?
Cambridge was rather self-obsessed. My teachers suggested that it would be pointless to go anywhere else for a PhD program because nowhere else could possibly be as good. This is not a healthy attitude, and it's very different, I think, from what happens in the States, for example. It's probably a bit different now, but I feel there are aspects which are still the same. Undergraduates who do incredibly well in their undergraduate studies are very strongly encouraged to stay on to do PhDs in Cambridge rather than move somewhere else.
Did you know who your advisor would be going into graduate school?
Since I did very well as an undergraduate the people who were teaching me and who were in particle physics wanted to take me on as a PhD student. Cambridge has a very big physics department, but it has a rather small group of theoretical particle physicists. By a historical accident there is a large group of theoretical particle physicists and general relativists in a mathematics department called the Department of Applied Mathematics and Theoretical Physics. Following my undergraduate degree in physics rather than mathematics, I ended up as a graduate student in the physics department, where there wasn't much choice about who my advisor would be.
What was your thesis on?
Oh, it was on S-matrix stuff concerning hadronic interactions, which at that time was a really big deal. As I say, in Cambridge, just like in Berkeley, they were trying to get away from quantum field theory. Understanding the strong force seemed to be a really big challenge because it seemed as though you couldn't use quantum field theory for the strong interactions.
Why can you use S-matrix? What's the distinction?
Well, quantum field theory, as it was understood then, was only useful if the strength of the force is weak, as it is in quantum electrodynamics. Then you expand physical quantities in powers of the coupling, in the strength of the force. For example, if the strength of the force is weak, you could approximate the amplitudes that you're trying to calculate in terms of a perturbation expansion. This had worked beautifully for QED, the electromagnetic theory, but in those days, there was no other force that had been explained in terms of quantum field theory. There was this feeling around that quantum field theory was not going to work for the strong force. Or, for that matter, for the weak force, which had also not been understood when I became graduate student. Amazingly, within four years, the whole situation had been transformed and quantum field theory was triumphant.
But the interesting thing is that there were prominent groups where field theory had been virtually abandoned – most notably in Geoffrey Chew’s group in Berkeley. Although I ended up as a postdoc in Princeton, I did get to meet Geoffrey Chew, who was visiting Princeton on sabbatical. So, I got to meet him there and he invited me to Berkeley that summer. In the meantime, sadly, his had wife died whilst he was in Princeton. So, he was alone and he invited me to stay in his magnificent house in the Berkeley hills. He was admirable in many respects, although the way he thought about physics resembled religion as much as science.
What do you mean by that? How so?
Well, he felt deep convictions about what must be right without actually having much evidence, either from direct physics, or from theoretical derivations. He had written a book called The Analytic S-Matrix at the same time as my Cambridge mentors had written another book with exactly the same title! The difference between the books is that the one in Cambridge is fairly thick, and it's full of formulae, whilst Geoffrey Chew's book looks like a Bible. It had a gold rim cover, and was very thin, and was full of profound sounding statements.
Now, Michael, you said before, some of the theoretical limitations which were resolved four years later. What are you referring to? What was resolved four years later?
Well, first there was the paper by Steven Weinberg in 1967 that was virtually ignored after it was published.
“A Theory of Leptons.”
Yes. So, that essentially formulated the electroweak theory. It was, of course, highly influenced by other work that had come before, especially by the people such as Higgs, Englert and Brout and by Kibble, and earlier work by Salam and Ward and by Shelly Glashow. But even Weinberg probably didn't really believe that this was a very significant theory. At least, neither he, nor anyone else, developed it further between '67 and '71, when 't Hooft showed, essentially, that the theory made sense – more completely, ‘t Hooft and Veltman showed that it was a renormalizable quantum field theory. So, that's what I meant by saying within four years quantum field theory was triumphant. Suddenly the world was really set alight by the work of 't Hooft and Veltman, who showed that Steven Weinberg's theory made sense. Salam and Ward had also contributed and some of the initial ideas were contained in earlier papers by Glashow. In the end Glashow, Salam and Weinberg shared a Nobel prize and later ‘t Hooft and Veltman shared another.
Was your sense that this marginalized Chew?
Oh, it did – at least it certainly seemed to. Interestingly enough, of course, this was also the period in which the precursors of string theory were developing, although it wasn't called string theory. This was the dual model of hadrons, which emerged following some very clever phenomenological observations. Notably, in '67, Dolen, Horn and Schmid at Caltech, formulated finite-energy sum rules, based on experimental data on pion-proton collisions, which showed that the strong interactions exhibit a remarkable duality. These were independently formulated by Igi and Matsuda in Japan. According to these sum rules you could describe the amplitude for such collisions between strongly interacting particles in two ways. In one of these descriptions the amplitude is described in terms of the formation of resonances, which are unstable particles. More and more such resonances had been discovered in accelerator experiments since the early 1960s.
There was a whole zoology of resonances, and things were getting more and more complicated, as more and more of these resonances were discovered. Resonances tend to be seen at rather low energies as peaks in the cross section as you change the energy. But the experiments were also measuring very high energy collisions where the cross section follows a smooth curve as the energy changes. At very high energies the resonance peaks smooth out and give a smooth cross section, and the second description of the amplitude fits this smooth high energy behavior in terms of something called Regge theory.
The ’67 papers by Dolen, Horn and Schmid and by Igi and Matsuda made the connection between these two aspects of the pion-proton amplitude—resonances bumps in the cross section at low-ish energies, and a smooth cross section at high energy. They showed that the resonances and the Regge behavior fit together in a rather interesting way. I'm not sure that they used the word duality, but the word was coined very soon thereafter. Then, along came Veneziano in 1968, who had been collaborating with another group of young people in Israel, together with Fubini who a more senior and very brilliant Italian physicist. They generalized the finite-energy sum rules and extended the idea in a more theoretical way.
Shortly afterwards, Veneziano came up with his very famous paper in which he basically guessed what the amplitude for scattering mesons, could be, motivated directly by the experimental data built into finite energy sum rules. It was supposed to be an approximation to the amplitude, but it was a very, very striking approximation. That was in '68, and there's no question that that was the beginning of what became string theory. I think that's almost the only thing that everyone will agree on. If you go back in time, it's like our common biological ancestor. It’s the one paper from which everything else flows. That paper, of course, had emerged directly from consideration of experimental data following his collaboration with others. For me, that's always been the best answer to people who criticize string theory for not being connected to experiment. The original evolution of string theory was based on a very clever analysis of experimental hadronic data.
Michael, when is the first time you remember hearing the words string theory? In other words, people were talking about strings, but as a discrete discipline, when is the term string theory first used?
Before answering that let me say that for me, without question, the high point of my time as a graduate student was the '68 paper by Veneziano. To his credit, my advisor Richard Eden immediately saw that it was interesting and important, whereas many other people didn't. That point, in '68, was the moment I remember being captivated by the subject. At first the subject was known as Dual Resonance Theory, and it was not recognized as string theory until a few years later. The emergence of string theory followed from important early papers by Nambu and by Fubini and Veneziano. There was also important early work by Susskind, Fairlie and Nielsen and a few others that suggested a string-like interpretation. Many other initial developments took place in CERN in '70 to '72 where a number of young post-docs were doing great things.
In particular, there was a remarkable paper by four people, Goddard, Goldstone, Rebbi, and Thorn who first formalized the theory as a theory of strings in a way that was mathematically very compelling. Another person deeply involved in its origins was Stanley Mandelstam, who was in Berkeley and had been part of the S-matrix endeavor with Geoffrey Chew. Around this time there were other important developments in Princeton by Neveu, Scherk and Schwarz and at Yale by Ramond.
So, it's a bit murky exactly how the words dual models got transformed into string theory. And even when I first started working with John Schwarz, some years later, we didn't at first use the words string theory. In fact, we had cumbersome titles for our early papers - what eventually became called a superstring, we initially called a supersymmetric dual resonance model.
Why Princeton, Michael? Why did you choose to go to Princeton for your post-doctoral research?
Well, Princeton was one of the prime places in America, and furthermore, I had met various senior people from Princeton whilst I was a student in Cambridge. So, it seemed like a natural place to go. My memory is that I applied to Princeton early and accepted their offer of a position before hearing from other institutions. I was at the Institute for Advanced Study, and I had little contact with activities at the University Physics Department, by people such as Andre Neveu, Joel Scherk and John Schwarz, who were doing foundational work on string theory. I worked with a bunch of young postdocs at the Institute. The highlight of my time in Princeton was attending the extraordinary set of lectures by Ken Wilson, who was on sabbatical at the Institute and had just developed his revolutionary ideas on the renormalization group. The lectures were stunning and caused great excitement, as did their published form that appeared three years later in 1974.
Who, beyond the institute, did you interact with during these years? Anybody at Princeton University or beyond?
Well, I interacted with Gabriele Veneziano. At this point, he was an assistant professor at MIT. He took a term’s leave at the Institute for Advanced Study in my first year there. I started to work with him in Princeton, and then I went to visit him at MIT, where I met a large number of young people working in the same area. At that time, there were several leading young post-docs and assistant professors at MIT who were doing important work in the foundations of string theory. Sergio Fubini, was at that time a senior professor at MIT and he was the center of a lot of the activity. The other place where I spent time was Berkeley where I spent three months in both summers of my Princeton postdoc. I met a lot of smart people there, several of whom I collaborated with later on, including most notably Miguel Virasoro, Joel Shapiro, Marty Einhorn and Charles Thorn.
Did you like the experience culturally?
Yes and no. I'm ambivalent. I've gotten to know America a great deal more since then. Although I can see some very positive things about the USA, at heart I am European and I think I missed some very positive aspects of Europe.
You were also in the United States during a very politically fraught time.
I was, indeed. That's the time when Nixon was President, and the Vietnam War was still on. So, there were lots of demonstrations and things going on, and the Black Power Movement was very prominent.
But it seems like you were happy to go right back to your home, right back to Cambridge following Princeton.
I missed my friends and my family, and I've always felt, culturally, closer to Europe than America. But America is a place I've spent more time in than anywhere else, other than the UK. So, I have complicated feelings.
In what way did the department change at Cambridge since you had been gone?
Oh, very little in those two years. Cambridge doesn't change much on the scale of two years or 200 years!
But I'm thinking, in the world of theoretical physics, in the early 1970s, so many exciting things were happening. So, I'm curious if you felt just being absent for a few years if people at Cambridge were working on new things or there were different things to be excited about.
Well, Cambridge was slow to react to these changes, particularly the biggest change, which was the work of 't Hooft, and then other people who picked up on his work. He was a graduate student at the time that he wrote the stunning paper in 1971 I mentioned earlier, which galvanized the development of the Standard Model. Immediately, people like Steven Weinberg, for example, and many others in Harvard and elsewhere, went back to working on the electroweak theory. So, by '72, when I went back to the UK, there was a lot of work being done on the electroweak theory – none of it in Cambridge. However, there were a number of British people working on dual models, several of whom were post-docs or staff members in CERN. David Olive, for example, was one of the key people. He had been in Cambridge before, but he went to CERN on a six-year position.
Who were some of your American collaborators that you kept in touch with?
Whilst I was a post-doc in Princeton, I collaborated with Tony Zee who is at Santa Barbara now, and also with Bob Carlitz who later went to Chicago and then Pittsburgh. I lost contact with most of the other Princeton post-docs, but I had more in common with some of my Berkeley collaborators. After that I spent a number of summers visiting CERN and collaborated with other visitors there. In particular, in 1973 I interacted a lot with Pierre Ramond, although I didn't really work with him, I learned a lot from him about dual models. Of course, Pierre is an interesting person who I had already come across whilst I was at Princeton. He was at Yale at the time. One day in early 1971 he wandered into my office at the Institute. I had never seen him or heard of him, for that matter. He was looking for my office mate, who wasn't there, so he started talking to me about this equation he had discovered, which was in fact the work for which he later became very well-known. He had discovered how to put fermions into dual models, in a sense, generalizing the Dirac equation.
So, it was an amazingly interesting conversation. I got to know him much better at CERN in the Summer of ‘73. That summer I got to know a number of interesting people. This was when I wrote something which might count as my first string theory paper. I was at CERN for three months in a group with a bunch of very active young people working on dual models, or string theory as it was beginning to be called. David Olive and Daniele Amati were the central figures and they organized a small workshop, which was arguably the very first string theory workshop. John Schwarz came from Caltech and announced that he was organizing a workshop the next summer in Aspen in '74. So, the next summer I went to Aspen for the first time.
Michael, a question about the importance of CERN. Why is CERN such a key place intellectually? Of course, CERN, experimental particle physics is going on. So, why might this be a useful gathering point for string theorists?
Well, I've always wondered why you need to collect so many theorists in one place? It was probably the biggest theoretical particle physics group anywhere in the world. You certainly need to collect experimentalists there because the experiments are enormous and very costly, and you've got to put them somewhere. But why do you need to put so many European theorists together, far away from their home countries? The CERN theory group has a very large number of theorists, and a number of them were very important people in the subject. Because it is so large, it attracts a lot of visitors and so it is a stimulating place to spend the summer months. In addition, it’s also a great region for hiking and eating. In those days, it was one of the central places for string theory, and very soon afterwards, for supersymmetry.
Michael, what was it about your personalities, your intellectual sensibilities, your sense of partnership, where you realized that your first interactions with John Schwarz would ultimately become a long and formative collaboration? How did that develop for you, from your perspective?
First of all, you're asking a question that's incredibly difficult to answer in any definitive way, because collaborations somehow emerge from all sorts of reasons. As I said, we knew each other a bit, but not very well from previous interactions. We both found ourselves at CERN -- we're now talking about the summer of '79. My memory is that we started to chat over coffee in the cafeteria, which is a very common place to begin to talk to people in CERN, and we discovered that we were interested in the same sorts of things. It was the kind of thing that very few other people would have been working on at that time. By that time theoretical research at CERN was focused on supersymmetry and supergravity. That was a subject, which by '79 had been captivating people who had previously been working on string theory. A lot of people moved from working on string theory because amazing things were happening in quantum field theory.
So, the Standard Model, that combined QCD and the electroweak theory, had emerged by '73 following the discovery of asymptotic freedom. Supersymmetry emerged around about the same time, rapidly turning into supergravity, which was the great hope for quantizing gravity. Other properties of field theory also emerged, including topological ideas, such as monopoles and instantons. It was an amazingly fertile period for quantum field theory. These were really interesting topics which attracted the attention of many people, including those who had been working on string theory. So, there was a very sharp decline in people interested in string theory.
Did these other developments, in some ways -- I don't know what the right word is -- delegitimize string theory?
In a certain sense. I think that people work on what they're really interested in. I think people who had been working on string theory thought that what was happening in quantum field theory was now so interesting that they ought to be turning their attention to that. I don't think they necessarily thought the worse of string theory. I think people who had never worked on string theory must have felt some sort of sense of triumph. They had been right all along that quantum field theory was the way to go. A key person in much of what was happening was Joël Scherk, who very sadly died at a young age in 1981. But he had been one of the main proponents of string theory, and I don't think he ever lost his interest in string theory, but he was a key contributor to supergravity the years after '76. He wrote lots of papers on supergravity, which ultimately fused with string theory. I think '76 was perhaps the year that supergravity took off.
What were the developments that allowed supergravity to take off by this point?
I think that string theory was very influential in the formulation of supergravity but that’s not necessarily the way the key people saw it.
Again, these are as much sociological issues as they are scientific.
In a sense, yes. So, the key people in the West were Ferrara, Freedman and van Nieuwenhuizen, who did not have much of an interest in string theory – likewise, the Soviets who independently invented a version of supergravity were not involved in string theory.
So, we were saying that your sense is that string theory was really formative for the developments of supergravity in '75, '76.
Well, formative in a certain sense. One of the key aspects in supergravity, as opposed to gravity without the “super”, is the presence of the spin 3/2 particle called the gravitino. The presence of this massless spin 3/2 particle was rather obvious from the point of view of string theory by this time. The existence of that massless state in string theory meant that there was a very good chance that it would be there in supergravity. Yoneya in Japan, and Joël Scherk with John Schwarz, had worked on getting gravity out of string theory in '74. But before that, Joël had pioneered the idea that you could obtain field theory out of the string theory by taking a so-called low energy limit of string theory. In particular, he and André Neveu had discovered how to get Yang-Mills gauge theories out of string theory, as the low energy limit of string theory would be a gauge theory. So, this connection between string theory and field theory had been around, and in particular, was part of the argument for why supergravity should exist. But I doubt that was a direct motivation for the people who discovered supergravity.
What was your affiliation at this point? Were you on the faculty at Cambridge or were you still a post-doc?
No, no. I was a sort of glorified post-doc in Cambridge. I was there for a long time. After going back in '72, I was a post-doc there until '76. So, I was there for about four years. Then, after that, fed up with Cambridge, I went to Oxford on a more senior postdoc which was not very sensible. Because if you're fed up with Cambridge, you're going to be fed up with Oxford as well. Small university towns are not necessarily my favorite places. I spent less than two years in Oxford because I was offered tenure at Queen Mary College in London. In Britain, you get tenure when you get your first faculty position, which is very different from the US system. So, I got tenure in Queen Mary in London in '78, and I stayed there a long time.
We hear about the first string revolution. When do you place that?
Let me first say that I don't like the terminology of calling things revolutions. Something has to be extraordinarily important to be a revolution in a scientific subject – such as the Copernican revolution or the formulation of quantum mechanics. However, there's no doubt this was a huge transformation in our community, and there's no doubt about when it happened. It happened after the summer of '84. You can tell that just by looking at the statistics of people's research publications.
Why do you bristle at the term? Because it suggests that things were dormant before then?
Well, yes. I had been working with John Schwarz from '79, and we continued working up to '84, and a bit beyond. The time when things first looked really exciting and transformational, to me, was a couple of years into our collaboration when we proved something was true about string theory that wouldn't have seemed to be possible for any previous theory of quantized gravity. These have disastrous inconsistencies. For example, the Feynman diagrams that should describe the scattering of gravitating particles in any quantum field theory of gravity give infinite expressions – such theories are said to be non-renormalizable. This means that in conventional theories of gravity quantities are infinite that can't possibly be infinite, so quantum gravity seems to be inconsistent with the rules of quantum mechanics. In ‘81 we showed that the elastic scattering amplitude of two gravitons in superstring theory avoids such difficulties and is finite, at least to lowest non-trivial approximation. This uses an approximation procedure that is a string theory version of the Feynman diagram calculations that describe approximations to amplitudes in quantum field theory. This was amazing, because no previous theory of quantum gravity exhibited such consistency.
Michael, what was it about 1981? What might explain why this theory could not have been calculated earlier than that? What are the developments leading up to this breakthrough?
Good question. What John and I had been doing was reformulating the previous versions of string theory in a way that made supersymmetry manifest. Supersymmetry, as I'm sure you've heard, is a conjectured symmetry, which relates fermions and bosons, and it may or may not have relevance in the real world. Hopefully, it does, but in any case, it has a great deal of relevance to mathematical features of theoretical physics, and more generally to pure mathematics. Supersymmetry leads to mathematical structures that are amenable to calculation that would not be in the absence of supersymmetry.
Michael, on that point -- this is so important, because, if I may interject, as you protested earlier, string theory is born out of experimentation which so many of its critics don't recognize, or don't appreciate. So, if we can fast-forward to today when so many people in the field are frustrated that string theory is moving -- maybe this is a correct characterization, or not. I'm just merely voicing a criticism that so many people in string theory are moving farther away from nature, and more into theoretical abstractions. So, at this critical juncture of 1981, where you're discussing these things, do you see this as sort of string theory going more into a mathematical realm, or are you hoping, even from that early point, that these are things that actually will be borne out in the world of experimentation, ultimately?
This theory which had this wonderful property was certainly a model theory in the sense that it had lots of supersymmetry, which the real world doesn't have. So, it was not meant to be a prediction for real scattering of gravitating particles. But it showed that the theory has a structure which is able to accommodate sensible looking results. These were results that would be true in ten space-time dimensions. Since we know the world is not, in any manifest sense, ten-dimensional this was not meant to be an experimental prediction of any sort. However, it was meant to show that the theory had the kind of structure which is capable of avoiding the disasters associated with combining quantum mechanics and general relativity. It demonstrated that a string-like underlying structure is capable of giving consistency that is otherwise not there. All of string theory is somewhat mathematical, but then most of quantum field theory is as well.
Michael, are there computers that are entering the scene that are being useful for calculations that you might not have been able to do earlier, or is this still strictly pen and pad?
Are you talking about then, or now?
No, no. 1981.
Oh, 1981. That was pen and paper, absolutely. When you wrote papers, you wrote them out by hand, and a secretary typed them.
But there were computers in 1981. Physicists were using computers. Primitive as they were, they were around.
Yes, but at that time symbolic computing, or algebraic computing, was almost nonexistent. Nowadays you can perform the most extraordinarily complicated mathematical calculations, which couldn't possibly have been done by hand. These computations are not used to get numbers out, but to verify formulas, or to get formulas out. In particular, I use the software known as Mathematica a great deal.
Stephen Wolfram, right. He was at Caltech in the early ‘80s, a period in which I used to visit regularly. He and his collaborators were developing a program called SMP, Symbolic Manipulation Program, which was a precursor of Mathematica. But it wasn't yet in a state that could be used. I had done a bit of computing on mainframe computers, but it was not of use in the development of string theory.
Michael, so as we get to 1984, and you talk about just look at the publications, right? What's happening between '81 and '84 which, we won't use that term, but we recognize there's a lot of excitement that's bubbling up. What happens in the interim?
Well, in the interim, John and I were meeting regularly. Several times in Aspen in the summer, and several times I was at Caltech for three or four months. I was very well treated by Queen Mary who allowed me to have extended leave of absence on several occasions. And John spent a period in London. So, we met regularly for about four or five months a year, on average, including the summers. In between, we didn't do anything together. It was a very different mode of research from anything that followed. We knew that no one else was going to solve the problems we were interested in because almost no one was particularly interested.
So, we would work together and then decide what we were going to work on the next time we met, which would be six months later. And when we reconvened, we'd work on that. Very often in this kind of research things don't work, and ideas that you have often don't make sense in the end, or are too difficult to solve. However, rather gratifyingly, things worked out for us time and again. We had a program to formulate superstring theory and understand its properties, and we knew what we were going to do from one year to the next. As we went along, we became more and more excited by the fact that the theory was so consistent despite it looking as if it could have inconsistencies at every turn. It seemed to have a will of its own and the theory sort of guided us what to do next in order to sort out its possible inconsistencies.
I should point out that this is a very subjective view – there were crucial developments by others that we probably didn’t appreciate sufficiently at the time but have played a dominant role since. I am thinking, in particular, of two very important 1981 papers by Sasha Polyakov, one of the leaders in many earlier developments. This work formulated string theory in the language of two-dimensional quantum gravity in a manner that went on to transform the underpinning of the subject. Further insights in that period by Dan Friedan, Steve Shenker, Edward Witten and others proved to be of central importance to subsequent developments.
Returning to my collaboration with John Schwarz, by 1983 it was clear that there was a fundamental issue looming in the background, which was a problem to do with anomalies. These anomalies are potential problems in any quantum field theory that might be of relevance to real physics. They represent the possible breakdown of sacrosanct laws, conservation laws, such as the conservation of energy or conservation of electric charge. These are conservation laws which have their origins in the classical theory before quantum mechanics is brought into the game. But the quantum theory can lead to a violation of these laws. Such violations are called anomalies. They are a particular problem for theories in which there are chiral fermions.
Chirality is a handedness property that is seen in nature – for example, it is a property of the Standard Model. Since the kind of anomalies that are worrisome arise in familiar quantum field theories, we were led to believe that this was a potentially devastating problem in string theory. The anomalies would essentially make the theory inconsistent. We knew that was a potential problem, but I think we simply had blind faith that string theory is so beautiful that it would avoid such inconsistencies. In fact, that's what we proved in 1984. In '84, we met in Aspen, again. Luckily, that summer the Aspen Physics Center had a workshop in a very closely related field. It involved higher dimensional quantum field theory, and anomalies in quantum field theory. So, several of the world's experts were there, and we needed them to ask question of.
Like who, Michael? Who were some experts that spring to mind in your memory?
Well, let's think. Bill Bardeen and Tony Zee were among the experts on gravitational anomalies. Among the people working on high dimensional quantum field theory was Murray Gell-Mann and many others. In addition, Friedan and Shenker who I had met in ’79 at Cargese in Corsica, were there. There was a host of other very smart people who were experts in the things we needed to learn.
What's an example of something where, between you and John, you recognized: here's something that we can ask others about, and they know more about this than we do?
For example, anomalies in theories of gravity in quantum field theory had only been developed a couple of years before that. There was a seminal paper by Alvarez-Gaumé and Witten. There had been subsequent important papers by Bill Bardeen, Bruno Zumino, and Tony Zee, -- it was a newly developed subject, so the timing was very fortunate. We wanted to look at anomalies in string theory, but we needed some of the techniques that had been developed for looking at anomalies in quantum field theory.
In fact, an important reason why what we did was of so much interest to the non-string theory community was because anomalies, unlike other properties of string theory, are properties that don't depend on short distance physics. As is well known, string theory differs from quantum field theory, because the fundamental constituents in string theory are string-like objects, whereas in quantum field theory, they're point-like objects. But that's a distinction that sort of washes out when you talk about properties of the theory at large distances. The short distance properties of string theory are very sensitive to the fact that strings are not points but at large distances, much larger than the string length, a string is indistinguishable from a point and string theory looks like quantum field theory.
In fact, that's one of its selling features, that the large-distance, or low-energy, behavior of string theory matches that of quantum field theory. That means that string theory might be a useful description of nature. But that also suggests that if quantum field theory has problems with anomalies, and if string theory looks like quantum field theory, string theory would also have the same problem with anomalies. My only response to this line of reasoning before we did the calculation was faith that string theory is so beautiful that it is bound to get around these problems.
So, that's what was so wonderful about the calculation. Not only did it show that particular versions of string theory don’t have the problematic anomalies, but it could explain the resolution in the language of quantum field theory. The resolution was that in order to understand the absence of anomalies it was crucial to include the force of gravity along with the non-gravitational forces of the Standard Model. String theory does this, but conventional quantum field theories do not describe gravity consistently. This gave a way of explaining it to non-string theorists using the familiar language of quantum field theory.
Michael, another broad question that bridges the sociological and the scientific, to go back to the early-mid 1970s, to what we're talking about now, the early-mid 1980s. That is, to the extent that asymptotic freedom and QCD knocked the wind out of string theory to some degree, what had changed in that field that allowed for all of this excitement, all of these developments in string theories, a decade later?
Well, QCD had by then become incredibly well-established experimentally, and had developed theoretically to greater and greater accuracy. But what had changed was several important things had happened in gravity. One of the very notable developments took place in Cambridge, where Stephen Hawking produced his work on Hawking radiation in 1974. This changed the nature of the research community of Cambridge theoretical physicists. The researchers in the math department were historically divided into two groups. There were particle physics, and there were relativists, and these two groups rarely talked to each other when I was a graduate student.
Yes, the relativists had little interest in quantum theory, and the particle physicists thought gravity was such a weak force, that it was not relevant. You can't measure it in accelerator. Furthermore, although we might want to describe it quantum mechanically, we don't know how to. So, they were just living in two different universes. And then, Stephen Hawking’s work was very instrumental in bringing the two together. It's not clear, even today, exactly what the outcome will be. But he, more than anyone else, was trying to understand the union of quantum mechanics and relativity in the context of black hole physics, which is still a major line of inquiry. Furthermore, there had been a transformation in string theory, moving away from thinking of it as a theory of strong force, to a theory of all the forces, including gravity. Then, along came supergravity, which was an extension of Einstein relativity that has deep connections with particle theory.
When I was working with John Schwarz on superstring theory, the supergravity community was the community that was closest in interests. I would attend their conferences and workshops and listen, but I would never be asked to speak. I think I gave a short talk at one conference but there were no string theory conferences at that time. Supergravity was producing a lot of very interesting results, but it was clear that it was going to suffer from these terrible inconsistencies. In fact, this was implied in a seminal paper by Ed Witten, around '82.
When did you first meet Ed?
Well, he probably doesn't remember our first meeting, which was when I was a postdoc in Oxford and he came through to give a seminar. That was in '77, or '78 maybe. But in the period I was working with John I met him reasonably often. Edward had written a very important paper around ‘82, explaining why 11-dimensional supergravity could not explain the physics of the Standard Model. In a related paper, he explained why any high dimensional quantum field theory that might explain the physics of the Standard Model in four dimensions would suffer from anomalies, and therefore not be consistent. There was a strong feeling growing in the supergravity community that the anomaly issue was going to kill supergravity.
So, our discovery concerning the absence of anomalies in string theory was interesting to the supergravity people. We had discovered that the mechanism whereby string theory avoids such problems is one which is very natural in string theory but would not seem natural in general quantum field theory. It makes use of the astonishing connection between gauge theories and general relativity that is manifested in string theory. String theory provides a link between Yang-Mills theories that are the basis of the Standard Model and general relativity, which is Einstein’s theory of gravity. It's that relation between gravity and the gauge theory forces within string theory that leads to a cancellation of what would have been inconsistent anomalies in gauge theory and general relativity. So, the fact that string theory unifies gravity and gauge theories is responsible for the absence of the anomalies. That's what impressed people, I think. They could understand in their own language, in the language of quantum field theory, this mechanism which cancels the anomalies.
Michael, if you could explain the terminology. Of course, words are never adequate to convey these ideas, but what is the term superstring? Why superstring? What does it mean, and what does it convey?
Well, first note that a string has vibrational states, or normal modes, that are interpreted as massive particles. So, a state of excitation of a string behaves like a particle with a given mass. Those particle-like states, also have spin. Examples of spinning particles are the spin 1 photon in electrodynamics and spin 1 gauge particles in the Standard Model. The graviton has spin 2. In addition to these low mass states string theory has an infinite number of higher mass states with higher spins.
In the original string theory - the boson string theory – all these states have integer-valued spin, which means they are bosons. The Standard Model also describes spin-1/2 states, namely, quarks and leptons. Such ½-integer spin states arise as excitations of the superstring along with an infinite set of massive fermion states with higher half-integer spins. In particular, the signature of supersymmetry in both supergravity and superstring theory is the presence of a spin 3/2 fermion particle called the gravitino. Supersymmetry refers to a postulated symmetry that relates fermions to bosons. According to supersymmetry you can think of bosons and fermions as being different aspects of the same underlying structure.
It's very disappointing, of course, that supersymmetry has not yet been observed. I'm not convinced that it will be observed because it's always seemed a little clumsy. If it is a symmetry it implies that for every type of particle that we have seen so far, there has to be another type of particle that we haven't seen so far, which will have a different mass. We may not have detected these partner particles because they are too massive. But it doesn't seem very satisfactory to invent a symmetry which requires you to believe there's going to be a doubling of the number of the number of species of particles.
So, this is to say that you wouldn't be surprised, even if the SSC had been built, or there would be an ILC, or we would be able to have energies at high enough levels, you're not at all convinced that supersymmetry is out there waiting to be seen. It might simply not be out there.
I think it would be fantastic if it is out there. I'm very bad at predicting what's going to happen.
So, I wonder, Michael, if you can compare, then, how much confidence there was in the discovery of the Higgs in 2011-2012 before it was actually seen, and how that might relate to supersymmetry.
By then, the Standard Model had been incredibly well-tested in all sorts of ways. It would have been remarkable if they hadn't found the Higgs. There were, of course, things that were not known about how heavy it was. There were constraints on its mass, but it was still possible that it was too massive to be discovered at LHC energies. But I wasn't surprised that the Higgs was discovered because the Standard Model had been so well tested. But supersymmetry is not analogous. There's very little experimental indication that supersymmetry has to be a symmetry of nature. It is consistent with the attractive idea that the Standard Model forces get unified at a very high mass scale. But apart from that rather general statement, I don't think there's any experimental indication for supersymmetry. It makes certain things more natural than they would be without it, but it makes certain other things less natural. It would be fabulous if it was discovered experimentally. It would transform our understanding of the fundamental forces. But it seems to me that it's not necessarily correct— in a sense, it's the first attempt to relate fermions and bosons, but it's not necessarily the correct way of doing it.
Michael, as we get into the 1990s and the field is reaching maturity, there's of course a new generation, a younger generation of physicists entering the field. As you are a mentor, with graduate students, with your collaborators in the United States, what are some of the new questions that the up-and-coming generation is asking that is pushing the field into new directions?
Well, one of the strange things about the subject is that when I was in my 20s, the key people in the subject were in their late 20s and 30s, or people around my age, like Sasha Polyakov, or Ken Wilson who wasn't all that much older. And even Murray Gell-Mann wasn't all that much older. He was in his 40s, maybe. But by the time I was in my late 40s, all the key people giving major talks at international conferences were actually also in their late 40s. One of the striking things about the period that you're now talking about, the early 1990s, is that there weren't very many young leaders in the field, the way that the young people had been the leaders when I was young.
For example, in the middle of the 1990s there a radically new understanding developed about effects in non-perturbative string theory. That's when the word M-theory was coined. But that was the result of work by people who were not particularly young. These results unified a lot of understanding. It's the period where quantum field theory, supergravity, and string theory became really enmeshed with each other, and you could no longer really tell the difference between what was happening in supergravity and what was happening in string theory. So, there was this peculiar history where supergravity had come along when there was almost no work on string theory in the late '70s and early '80s.
And then, string theory suddenly exploded on the scene in '84. At that point, supergravity was almost blown away. People working in supergravity switched to string theory. Those who were working in supergravity and didn't switch to string theory were feeling a bit bitter about the fact that string theory had suddenly become the flavor of the month. And then, it all changed again in the '90s. It became understood that in order to answer many of the questions, the deepest question about the structure of string theory, you had to ask analogous questions in supergravity. The two were inseparable.
So, when people talk about M-theory, they're talking about an extension of string theory that actually includes supergravity in a very important way. There are questions about the structure of string theory that you can't answer without understanding more about supergravity. Those are the questions that were being asked and answered in the mid 1990s. A new understanding developed, based on duality. Theories that look very different from each other at some level are in fact different aspects of the same theory. This was based on understanding properties of string theory beyond perturbation theory. Perturbation theory involves expanding the theory in powers of a small parameter, such as the electric charge. In quantum field theory this gives Feynman diagrams, and analogous diagrams in string theory. The developments in the ‘90s involved understanding certain non-perturbative issues, which answered much more profound questions about the structure of the theory.
By getting away from perturbation theory, you're getting away from the idea that strings are fluctuating objects that move through spacetime, where spacetime is basically inert. You really want to find a theory in which spacetime itself is dynamical. In any theory of quantum gravity, it's not just the particle states that are fluctuating, but there are quantum fluctuations in the geometry of space. So, spacetime itself has to be replaced by something which is loosely called quantum spacetime. To do that, you have to get away from the perturbation approximation of the theory. That's what we're really trying to understand. The reformulation of string theory in which spacetime is itself quantized; there's some quantum notion of spacetime.
Michael, when did you first become aware of AdS/CFT correspondence?
Actually, the first hints of this were in a wonderful paper by ‘t Hooft in 1993 where he initiated the idea of a holographic relation between quantum gravity inside some volume and a quantum field theory on the boundary of that volume, which has one less dimension. This was a much more general idea of the correspondence between quantum gravity and quantum field theory than AdS/CFT, but it was also much less precisely formulated. Susskind then pointed out its relevance to string theory, but the first precise realization of this idea was in Maldacena’s work. I first became aware of Maldacena’s work on AdS/CFT in November '97.
Actually, Sasha Polyakov, who is one of the fathers of that subject as well, had given a rather obscure presentation at the annual string theory conference in Amsterdam in June ‘97. He's a bit difficult to understand sometimes. His talk was about QCD and it involved something like AdS5 space, although Sasha didn't have had anything that would have been immediately recognizable as AdS/CFT. I can't remember where I heard Maldacena whose paper emerged towards the end of ’97. Others were also thinking of similar things and very soon there were also important papers introducing AdS/CFT by Gubser, Klebanov and Polyakov and by Witten. I then visited Santa Barbara in early '98 and I started to work with Tom Banks on issues relating to AdS/CFT. Things picked up very quickly.
What was so important about AdS/CFT? How did it propel the field forward?
In many ways. First of all, it contains this general principal that there is a deep connection between gauge theory and string theory, and that by doing calculations more generally, in quantum field theory, in non-gravitational field theories, you can actually obtain results in quantum gravity, and in particular, in quantum string theory. So, there you have a handle on what you mean by string theory. You can define the theory to be the theory that arises via holography from quantum field theory. That's one way. In other words, you may understand things about quantum gravity by doing calculations in non-gravitational quantum field theory. And, of course, conversely, there are certain things that you may calculate in general relativity that you can then interpret as predictions for what might happen in non-gravitational theories.
So, since Maldacena and company's original ideas, that's been a very fruitful way of thinking about various systems. I'm not sure which way around the AdS/CFT correspondence has been used more, but it can be used in either direction. Either to think about ideas in quantum gravity based on non-gravitational quantum field theories, or vice versa, to think about ideas in non-gravitational quantum field theories, in terms of ideas in general relativity. So, there's a community of people doing condensed matter physics, for example. Non gravitational physics, where certain highly quantum regimes of condensed matter can be attacked by using ideas to do with black holes in one extra dimension, for example.
So, it's opened up a whole new way of thinking of things. But perhaps, at the most fundamental level, it's given ideas which are now very much the subject of current research of what you mean by quantum gravity in terms of information theory, basically. We understand a lot about quantum mechanics and field theory and the property of quantum entanglement. And that is now deeply involved in understanding aspects of quantum general relativity. So, it's got a very, very wide ranging influence. Of course, the aspects of AdS/CFT which have to do with condensed matter physics are very tentative in some ways -- I'm not sure what the condensed matter community think of it. But to the extent that it makes statements about condensed matter physics, it's making statements about condensed matter physics in a regime where it's very difficult to make any predictions in any other way, other than by using AdS/CFT.
Michael, when did you become involved in research that would lead to D-branes?
Ah. Very early, in a sense. It's a great sadness that I missed some profound things. Early on, in 1975 I realized that changing the boundary conditions at the ends of a string affected its properties very significantly. I worked on this with Joel Shapiro when we met at CERN in the summer of '75, and we wrote a paper which involved what we called Dirichlet boundary conditions. In a sense we were describing a primitive version of what is now called a “D-instanton”, which is a particular example of a D-brane. It was another 20 years before the full structure and import of D-branes was understood in beautiful work by Joe Polchinski. He understood D-branes, which are objects in string theory that are analogous to solitons in quantum field theory. They're massive solutions to the equations of string theory, rather like the more familiar black holes. They don't arise as fundamental objects in the theory, which are the strings, but they are solutions that come out of the theory. The way you can get a handle on them is by thinking about the string boundary conditions at the ends of the strings, if you like.
So, these are defined by open strings. In strings with endpoints, the endpoints may be fixed to these objects called D-branes. I didn't understand much of that in 1975, but I was interested in the way in which the boundary conditions of the ends of an open string would affect the behavior of the string, and the spectrum of the string theory. What I was really interested in was trying to modify the string theories that were around in the earliest days, in order to construct a string theory that described the states of hadrons, like mesons. In QCD mesons are superficially thought of as string-like objects.
QCD is the theory of quarks and gluons which hold the quarks together. The quark and the anti-quark inside a meson are confined – that is, they cannot be separated so you never see an individual quark. A quark and an anti-quark can never be pulled apart because they have a flux tube, which looks like a string between them. It's a bit like a magnet. If you cut it in the middle, you get two mesons, just like if you cut a magnet in the middle, you get two magnets. The earlier string theories had been invented as theories of mesons. Open ended strings were meant to be mesons, and you're supposed to think of a quark on one and an anti-quark on the other end. But there were all sorts of reasons why the earliest string theories were not adequate for describing the data on hadronic physics.
So, even though string theory had evolved by thinking about meson physics, the explicit string theories were not sensible as theories of mesons. In particular, they don't contain point-like structures – the quarks and gluons. Quarks and gluons, in some sense, behave like hard, point-like objects. Rather like the nucleus of an atom is a hard, point-like substructure inside the atom. Hadrons contain point-like substructure, and the original string theories didn't have any point-like structure at all. Therefore, some of their properties were completely at odds with experimental evidence.
So, in the mid-'70s, I was trying to modify the string theory, basically, to make it sensible as a string theory of hadrons. That's what I was interested in. And in doing that, I invoked this notion that you had to impose Dirichlet boundary conditions at the ends of the string. The word Dirichlet is where the D of D-branes comes from. So, I was interested in this point-like substructure, which I thought was exciting. I wasn't getting very far, and then I started working with John Schwarz on different things. But I always had this in the back of my mind. But in the meantime, I also met, and got on very well with Joe Polchinski.
I was going to ask if you worked with Joe. Of course.
Well, eventually we published one paper together. We didn't exactly work together, but we were interested in the same things. In fact, at some conference, he joked that he and I constituted the first international conference on point-like string theory. I didn't understand exactly what he was getting at in his first paper on D-branes. It was '89. And then, from '89 to '95, not much happened. After finishing the work with John Schwarz, I returned to my earlier interest in making a consistent theory with Dirichlet boundary conditions, which turned out to be related to the D-instanton. But then, in '95, Ed Witten gave a talk, which people call the beginning of the second string revolution. As I say, I'm not sure I approve of that word. In that talk Witten emphasized that there should be massive objects in string theories that are analogous to black holes.
In the middle of Witten’s talk Joe Polchinski crouched down next me and whispered in my ear, "Do you think Ed's talking about D-branes?" I must have replied something like, "I don't really know." I shouldn't have said that, because what I had forgotten was that in the intervening years between Joe Polchinski's first paper and '95, I had understood a lot more about what was going on, and my answer should have been, "Yes, he is talking about D-branes." It was sort of obvious that he was, but I said, "I don't know." After that, Joe Polchinski, very quickly, realized that Witten was talking about D-branes. And Joe Polchinski wrote a very complete and magnificent paper a couple of months later, the first paper that introduced D-branes that got attention. So, I missed that, which I very much regret.
Michael, what about, also, what was happening at this time, how brane theory was influencing cosmology? Specifically, with brane inflation, and what people like Henry Tye were working on. Were you involved in that at all?
I wasn't involved directly. Many people have been trying to get real physics, in this case cosmology, out of string theory. But in the end, it's difficult to judge. It's not a deductive subject since it's not tied down sufficiently accurately to know whether it's true, but it's nevertheless interesting. In fact, a lot of what's been happening in string theory has been incredibly interesting as models for how you might construct a theory of, say, cosmological inflation, or of elementary particle physics, for example. But you’d be hard pressed to believe any experimental number that might be predicted. I don't think there's very much which pins down string theory sufficiently to make very precise predictions, which is, of course, one of the things it's criticized for. In a sense, it's wrong to try to defend string theory from the point of view of predicting precise numbers.
I think it's a bit like quantum field theory. Quantum field theory isn't a specific theory. It's an overarching structure which is used as a tool in all sorts of branches of theoretical physics, far away from the original branch in which it was invented. But the structure of quantum field theory is very important in not only understanding aspects of particle physics, but also condensed matter physics, fluid dynamics and other areas. In a sense, string theory has evolved to have that kind of status. String theory is an extension of quantum field theory, and therefore, it contains the kind of physics that you want to use to describe many different aspects of theoretical physics.
As we were saying before, there are some aspects of condensed matter physics that might be described by AdS/CFT. Then, you've just mentioned cosmology, D-brane cosmology. There are other possible uses of string theory in fluid dynamics, for example, AdS/CFT. These ideas have not pinned down experimental numbers, but they have given general ideas of the structure, which may in the end be very useful. So, that's a rather longer answer to your question about D-brane inflation than you wanted!
Michael, I asked you earlier, which you laughed off, in the early 1980s, if you were using computers. Just to bring the narrative closer to the present, when, if at all, have you embraced computers for your research?
Oh, right now. I'm doing some very complicated calculations that would be inconceivable without the use of, for example, Wolfram’s Mathematica. And it's mostly not me, but my collaborators who use Mathematica much, much quicker than I can. I struggle to keep up, because otherwise I'd be humiliated.
It's a generational thing.
It's probably a generational thing, yes. And one aspect of that is I was rather late in coming to terms with it. You need a lot of practice, but it's become vital. It's not just me -- it's not just in string theory. It's all over the place. I'm collaborating right now with two young people who are wizards with Mathematica. It's used almost like an experimental tool. We look for mathematical patterns in very complicated looking solutions to rather simple equations. The patterns lead to simple ideas about the structure of these solutions. So, it's certainly not numerical computing, but it's being used to discover the equations. You try all sorts of intuitive procedures for modifying the equations until suddenly something clicks.
I recently wrote a paper with these collaborators, which I'm very pleased with— it looks like a beautiful result, but it would never have been arrived at without Mathematica. The other thing I've done a lot of in recent years is collaborating with pure mathematicians. These are real solid mathematicians, number theorists, in particular. Number theory is about as deeply into abstract mathematics as you can get. One of the things I've discovered is, firstly, how beautiful the mathematics is, and how relevant the mathematics is to the structure of the theory. And also, how some mathematicians, but not all that many, but some of the great mathematicians love to talk to physicists and get ideas from physics about what might be interesting.
I guess, this kind of physics is a very fertile ground for bringing to the notice of mathematicians certain things which they wouldn't have noticed otherwise. So, I have worked with a few astonishingly good mathematicians. And they are very versatile with computers. This is something in mathematics which would have been unheard of thirty years ago. There used to be controversies in math about whether you could really call a mathematical proof a proper proof if you've used a computer to get at it. About fifty years ago, there was a solution to a very famous mathematical problem -- the map coloring problem. The question is how many colors you need to color a map, and the answer is at least four. The way that was solved involved using a computer, and there was a vigorous controversy in the mathematics community about whether this was really a proof. Now, nobody would bat an eyelid. They would all be using computers. So, computers are crucial.
So, Michael, just to give a sense of your current work, what are some of the kinds of things that computers might help you do that continue to make string theory an exciting field to work in?
Well, I've been working recently on understanding aspects of the AdS/CFT correspondence— the correspondence that identifies gravity, or string theory, with a lower-dimensional gauge theory. I’ve been looking at details of the gauge theory. The most supersymmetric version of Yang-Mills highly gauge theory. This is a subject that very many people are working on for reasons we talked about earlier. But we've come across a set of equations which seem to be exact equations describing a regime of the gauge theory that you wouldn't normally have thought you could describe, which involves very intricate algebraic calculations, which I don't think you could conceivably have done without the computer.
So, in other words, you're using the computer to analyze, in this case, the gauge theory. But this is the gauge theory that's related by AdS/CFT, to string theory. So, this gives you more information. Once you have this exact expression in the gauge theory, then you can show that this maps into a statement about the string theory in AdS space. So, the AdS/CFT correspondence gives a correspondence between a very supersymmetric gauge theory in four dimensions and a certain string theory in a particular 10-dimensional spacetime, called anti-de Sitter space. So, we've learned a lot during the lockdown, about the string theory in anti-de Sitter space by understanding much more about the gauge theory.
That's a great explanation for what you're doing right up to present day. So, now that we've worked to this part of the narrative, for the last part of our talk, Michael, I'd like to ask some broadly retrospective questions about your career, and then we'll wrap up with some questions looking to the future. First, I certainly would not presume to burden you and ask you about all of the prizes and honors that you've been recognized with over the course of your career. But one, in particular, that I'm curios to get your reaction on, is with the Breakthrough Prize with John Schwarz. Part of that recognition was the research that you did to get us closer to an understanding of the unification of forces. The question there is, to what extent is that award aspirational, because obviously, the forces are not yet unified? How has your research clarified what remains to be done so that we get closer to, dare I say, a theory of everything, or at least integrating gravity into the Standard Model? What's your perspective on all of those things?
Well, firstly, let me say that one of the features of the Breakthrough Prize is that almost every theoretical prize winner has been working on a subject for which there's no experimental evidence at all, which is fine. The prize is not a prize for successfully predicting experimental data. Of course, there have been a number of great experimental prize winners, and those experiments are very, very concretely experimental results about the physical world. As I said before, I think string theory is much more interesting than simply a theory that unifies the fundamental forces. Of course, if one could show precisely how it unified the fundamental forces, that would, indeed, be extraordinary. It would also probably be very complicated because the physical world is not nearly as simple as the rather simplifying assumptions that are made in formulating string theory.
I think general principles are missing. For example, string theory was around for some time before the AdS/CFT correspondence was discovered. It grew out of string theory, but it's probably more general than the ideas in string theory which gave birth to it. There is some very deep connection between the ideas in quantum gravity and ideas to do with non-gravitational quantum field theory. But that was born out of string theory using the relatively simplified structure, or very special structure of the string theories that we have. So, I think that the best we can hope for, at least, for the foreseeable future, is general structural ideas. For example, people are struggling very hard at the moment to understand the resolution of the black hole information paradox that was brought up by Stephen Hawking many years ago. And in doing this, there have been some very impressive insights. Whether they will last the test of time, I don't know, but there have been some interesting insights which are largely based on using the AdS/CFT correspondence, and incorporate ideas of quantum entanglement and quantum information.
These are very general ideas. Very general, indeed, even though the specific way in which many of them emerged was via a specific string theory interpretation, via the AdS/CFT correspondence, which is implemented by string theory. So, I'm confident that in the future there will be deep insights which originate from our ideas in string theory. What I'm not confident in is that the precise details will emerge from understanding string theory in more detail. Arriving at general principles is more likely than particular details, if that makes sense. Another example might be the subject which has been a long-term interest -- how to describe hadronic physics in terms of strings. It's quite clear that QCD is a very precise quantum field theory of the strong force. But starting from QCD, it's almost impossible to do precise calculations of the extended string-like nature of hadrons. It is very likely that there is a complementary string theory description of hadrons, which is, in some sense, dual to the field theory description. What appears as fundamental particles, quarks and gluons, from one perspective, would emerge from the perspective of string theory, as point-like motions of the string. I can imagine some general principle like that emerging. Whether you'd ever be able to calculate detailed properties of the mesons is less clear.
Michael, in what ways have seen or do you see string theory exerting a positive influence on some of the major cosmological mysteries, such as dark matter or dark energy? These are problems that are very much an "all hands on deck" kind of situation for physics. We need everybody thinking about these things, so the question is how might string theory, in some novel way, help solve these mysteries?
The problem with answering the question is that string theory has a huge amount of flexibility if you want to apply it to any concrete physical problem. This is probably a symptom of the fact that we don't really understand the structure of the theory sufficiently. For example, within string theory there appear to be a humongous number of possibilities for particles that could be dark matter particles. The problem in having too much flexibility makes it very difficult to pin anything down. So, I don't think there's a direct answer that. And dark energy is similar. If you wanted to explain it by string theory the explanation would only make sense if you have a sensible model for the universe based on string theory. Dark energy is related to the cosmological constant, and there are zillions of different possible explanations. For example, there's possibly an anthropic explanation of the cosmological constant. I think the problem with trying to say string theory might answer such questions is that we don't yet really know what string theory is. The number one question about string theory is what is it? It is some sort of effective theory that somehow combines quantum mechanics and general relativity. It's leading us somewhere, but I think it's premature to even try and answer that question.
One question, it's another generational question, just in terms of the founders of string theory coming out of particle theory, as a matter of education, do you see the next generation of string theorists having that similar intellectual basis in particle theory, or is that no longer considered a necessary prerequisite to get into the field, as it were?
Oh, it's certainly not the same as it used to be. When I was a student PhD students would be asked questions in their vivas like, “what is the mass of a pion?” I don't think anyone would ask a student that now. There's been a huge cultural change which has taken down the barrier between general relativity and particle physics. The new thing that's replaced it is a much wider understanding of basic theoretical physics, I think, that bridges those two cultures and also encompasses related areas of condensed matter physics. More than that, the kind of mathematics that is now essential for understanding both particle physics and relativity is much more subtle and interesting than the mathematics that was being used when I was a student. Yang-Mills theories, in particular, that are the key ingredients of the Standard Model have topologically important structures in them, like instantons and monopoles. Those were all discovered in the mid to late '70s, and completely changed the way in which quantum field theory is viewed. There's just been this massive cultural change.
Another sociological question, coming right back to the beginning when we were talking about Shelly Glashow, the response to string theory, there's a spectrum. On the one extreme are going to be people like John Schwarz who say string theory has taught us amazing things already and you should remain excited about it in the future. And on the other extreme are people who have lost patience and say string theory doesn't really tell us anything about the natural world, and whatever excitement there was with this revolution, or that revolution, I've lost patience and I'm no longer interested. I'd like to ask you, from your perspective, in what ways has that second perspective been validated, or people in physics that say, "What does it tell us about the natural world?" To what extent has that been validated, and to what extent do you say, "Actually, here's where we can specifically refer to places where it has shown us things about the real world, and further, this is why you should be excited about what string theory could do in the future."
First of all, I think that people who don't think it's interesting because it hasn't taught us anything, should do their own thing. That's fine. It’s a matter of taste. That's absolutely fine. But I also think it's a matter of perspective. First of all, string theory grew out of experimental data. So, there is strong indication from the experimental data, there is something like string theory, at least in hadronic physics. So, those people must be talking about something else, a unified theory of all the forces, or something. We've already discussed, for example, AdS/CFT. AdS/CFT has taught us a great deal – for example, it's given us a lot of ideas about how certain regimes of condensed matter physics may be explained. Quantum critical behavior, for example. Regimes in which it's very difficult to do calculations using any other technique other than string theory.
Although, very precise predictions are not likely to emerge in the near future, it's certainly taught us qualitative things about all sorts of phenomena in condensed matter physics, and it's giving ideas, to do with cosmology, and to do with a possible way in which spacetime might emerge from quantum entanglement. All these things are possibilities. None have yet been brought to fruition. One major success of string theory is its remarkable symbiosis with mathematics. It is astonishing how many broad areas of mathematics have interacted with string theory. I hesitate to say that these areas have been transformed by string theory, because, in a sense, string theory has been transformed by them as well. There's been an interchange of cultures, which is probably the single most remarkable thing that's happened with the development of string theory. You're looking at this from the point of view of the American Physical Society, which is physics, I suppose. But I suspect that the American Mathematical Society would also be very impressed with the impact of string theory.
As I'm sure you've heard him say, John Schwarz loves to talk about how string theory is smarter than we are. What does that mean to you?
Oh, yes. I think of string theory as having a will of its own that will take us in directions that we can't predict -- that's why whenever I'm asked to predict something, I hesitate, because I know in the past, nobody's predicted what string theory would do. It was invented to be a theory of hadrons, and then it became a theory of gravity interacting with other forces. Then, it looked inconsistent in various ways, and it turned out to be consistent in ways that were not predicted. Understanding how we could avoid anomalies, that was sheer magic. Magic by string theory, not by us. We just simply went along for the ride. Just when it's beginning to look inconsistent, it turns out it's got a clever little trick.
So it's very difficult to predict what's going to happen because it's going to do something, which would explain things that we didn't even realize we'd have a chance of explaining. AdS/CFT was another such example. The idea that you could find such a profound connection between gauge theory and general relativity was amazing. String theory had been hinting at that for some time, because open strings contain gauge theories, and open strings can close, and closed strings contain general relativity. So, in some very general sense, it was noticed that you might get a connection between gauge theories and general relativity, but the whole way in which AdS/CFT emerged was quite remarkable. It emerged from D-branes, and D-branes themselves were sitting around for years without being discovered, even though they were obvious once they were discovered. That seems to be a hallmark of the theory.
Well, Michael, for the last part of our talk, I know you don't like to be involved in the prediction business, but I can't help myself, and I am going to ask you to make some predictions about the future, with the caveat, of course, that you work in a field that is not very friendly to predictions because as you say, we don't know where the theory is going to take us. What do you see is the potential impact of true quantum computing? When we talk about quantum information, and the information in black holes, and all of the excitement right now surrounding, first of all, the amazingly complex calculations that you're able to do with the current generation of computers, if and when true quantum computing is achievable, what might that mean for string theory, and what, in turn, might that mean for what string theory can do for physics more broadly?
I think anyone who makes predictions about computing is going to be off by many orders of magnitude. So, your question was what will quantum computing do for string theory, right?
What could quantum computing do for string theory, and what might string theory subsequently do, more broadly, for physics?
It's quite conceivable, in a way which I certainly can't predict, that quantum computing, and more generally, other aspects to quantum stuff, will be deeply connected to our understanding of quantum gravity. There's a whole enterprise going on involving quantum information and quantum entanglement, which turns out to have profound connections to quantum gravity. I obviously don't know exactly how that will interplay with quantum computing, but there's obviously a very deep logical connection between quantum computers and quantum spacetime. But this will not help understand string theory until we have a better idea about the structure of the subject. Sheer computer power is not what is missing at the moment.
Quantum computers would obviously have a major impact on big data-driven science, such as astrophysics, experimental particle physics and many aspects of biology. These are subjects that are clearly limited by computing power at the moment. But I don't think string theory is one of them. In string theory, we don't even know how to get a number to one decimal point. We need ideas rather than numbers. But I do think the structural aspects of quantum computing, its mathematical structure, may be a key ingredient in understanding the quantum structure of spacetime. Maybe we'll use black holes as quantum computers one day, at least in some fantasy universe.
Michael, for my last question, I'll make it a little easier. One that's a little less predictive, and that is more personal for you. You're active, you're working with younger students. What are you most excited about and optimistic about for your own contributions to the field for however long you want to remain active?
That's a very good question. A modest aim, although one that is very difficult is to make a contribution to understanding the resolution of the original aim of string theory, which is the nature of string theory for hadrons. Much of the current thinking is that this is something which would just be messy and complicated and not particularly interesting. But for me, it's still a very interesting topic to think about. I also want to pursue further the effort to understand string theory from the perspective of the AdS/CFT correspondence -- by understanding the implications of quantum field theory for the string theory dual. So, those are two things which I'd love to understand. My lifetime in this subject has been spent doing things which I find fascinating at the time, without really worrying too much about whether they're dramatically going to increase human knowledge.
It's been more of an adventure than an itinerary, is what you're saying.
It has. I'd like to see what string theory is going to tell us next. Right now there is a lot of excitement in trying to understand connections with quantum information theory. The possible emergence of spacetime from such systems, is probably the most interesting thing that's going on at the moment. Which is deeply connected to string theory in some sense, but it's also got an existence which is, in some sense, completely independent of string theory. It's connected with the fundamentals of quantum theory. Quantum theory is tacked onto string theory. String theory is consistent with quantum theory, because by assumption, quantum theory has been added onto it. It would be nice to have a formulation of string theory with quantum mechanics, which somehow naturally formed a consistent whole, and wasn't somehow artificially put together.
Well, Michael, maybe one easy prediction to make is that it will still be interesting, no matter what happens.
Right, absolutely -- I'm sure it will.
Michael, it's been a great pleasure spending this time with you. Thank you so much for doing this. I really appreciate it.
Very good. Thanks.