 So supersymmetry is the main contribution that string theory has made to predicting something new or generating something new that might be discovered in particle physics. There's at least a decent hope that we might discover supersymmetry at the Large Hadron Collider, the new accelerator that has started working at the CERN laboratory near Geneva rather recently. There are more exotic possibilities, large extra dimensions unlike where at large means large compared to what string theorists usually assume but actually small compared to the nuclear scale. But at least I would say the most compelling suggestion emerging from string theory for something new that might be found at accelerators is supersymmetry. Now if supersymmetry is right then regardless of what you think about string theory it's got to be combined with gravity and that led to the extraordinarily rich subject of supergravity which is what we get in making a supersymmetric theory that describes gravity. So supergravity is a kind of partial completion of Einstein's general relativity to include quantum variables in the structure of space and time. Supersymmetry is more or less the same thing for special relativity. So in developing special relativity and general relativity Einstein assumed that space and time was measured by numbers. It's three o'clock, we're at 40 degrees north latitude, 200 meters above sea level and so on. After Einstein's work quantum theory was developed and quantum variables became imaginable but they were not incorporated previously in the structure of space and time. Supersymmetry and supergravity begin the process of incorporating quantum variables into the structure of space and time and supersymmetry is the part of that that we might conceivably be able to explore directly experimentally. Supersymmetry and supergravity are actually the tip of a much bigger iceberg. String theory which has supergravity as a sort of semi-classical limit is somehow based on a new kind of geometry that we don't understand. So somehow this is a new kind of geometry that turns this kind of Feynman diagram into this kind and what that is we certainly don't know. We don't even have a conceptual world in which it's a sensible question. The question is kind of forced itself upon us without our having even in hindsight the ability to understand what it really means. That's why it was wisely said in the 70s, not originally by me, that string theory was part of 21st century physics that fell by chance into the 20th century. No one had the conception for it and to a large extent we still don't today. Somehow there is a new kind of geometry in which you aren't allowed to talk about points or lines in space-time, but you're allowed to talk about quantum minimal surfaces, namely world sheets of a string except you have to treat them quantum mechanically. But no one at the start foresaw anything like that and we're still having trouble understanding it. So again this is part of what I mean in saying that the theory is kept imposing its will upon us. Now these questions were there in more or less the form I've stated them by the early 80s, but they weren't very popular questions. In fact, living through the period at the time I was a bit puzzled at how neglected they were. I was, by the early 80s, familiar with the work that was being done by just a few physicists, Green Schwartz and Lars Brink and not many other people, in trying to keep string theory alive or revive it and develop it. But there was puzzlingly little interest until 1984 when a new method of anomaly cancellation found by Green and Schwartz and he had a new form of string theory found by Gross Harvey, Martiniak and Rom made it possible to derive from string theory a decent rough draft of the real world with the gauge forces and the quarks and leptons plus quantum gravity. So before 1984 the question existed. There was this new kind of theory based on a new kind of geometry we didn't understand. It made quantum gravity inevitable rather than impossible. It forced us to unify quantum gravity with the other forces, but the details of the elementary particles looked wrong. Most strikingly there was a problem in incorporating the parity violation between weak interactions. In 1984 there was a dramatic new theoretical insight and suddenly the models of particle physics that you could derive interacting with quantum gravity via string theory became vastly more realistic. So to me that was a sort of signal from heaven. A lot of miracles had gone into string theory up to this point. I've tried to convey this in the first part of my talk, but I think it's been hard to do justice to it. I've only given you a few hints. While a lot of miracles had already happened and probably many of them were as striking as the anomaly cancellation in their own way and at their own time, this was the first one that really happened while I was watching closely. So it had a big impact on me. And from this point on string theory and related matters have been my main scientific interest. I'd say in the few years before 1984 string theory and related interest just in the last few years before 84 were maybe a third of my time or something like that. But after the anomaly cancellation was discovered it's been my main interest. Now the prevailing view at the time was that string theory differs from pre-20th century physics because of the role of two parameters. One of them is Planck's constant h-bar and the other one is usually called alpha prime. Now every physicist knows about h-bar, that doesn't depend on string theory. Alpha prime is what's new in string theory. In string theory alpha prime is a fundamental unit of length below which ordinary ideas in geometry fail. So the concept of a space-time event makes sense if you don't look too closely but if you look within a precision of alpha prime you get trouble. Just like the concept of a point in classical phase space makes sense if you don't look too closely but if you look within an area h-bar you get into trouble. So alpha prime more or less does to space-time what h-bar does to classical phase space. So if string theory is right the two kinds of deformations are equally important and significant although they're very different. And Mohr's string theorists and for most part this includes me spent the decade after 84 studying the alpha prime deformation. The main tool was two-dimensional conformal field theory which describes propagation of the string. The world history of a string, that tube that I had about 15 minutes ago when I was comparing the Feynman diagram to the string diagram it's a two-dimensional surface that's described by two-dimensional conformal field theory it seemed like our main tool for studying alpha prime deformation. So typical results of this period were that you could make sense of processes which in conventional geometry you can't describe. I've drawn a picture but I won't have time to explain it that's meant to kind of symbolize the idea of a jump in the structure of space-time which you can't talk about in classical general relativity but you can talk about when you replace general relativity by string theory. So we had fun in that period discussing stuff like that. The prevailing paradigm was that string theory is based on a new kind of classical theory an alpha prime deform theory that's then supposed to be quantized more or less according to textbook recipes for quantizing classical theories. In other words the picture is that the classical theory is unusual but it gets quantized in a normal way. And as I think I told you a moment ago two-dimensional conformal field theory was seen as the best tool for studying this situation. So it seemed like the important branch of quantum field theory for string theorists. I remember this frustrated me a bit. I'd spent my formative years learning about more general varieties of quantum field theory. In fact the most basic case is the four-dimensional case that describes ordinary particle physics. And suddenly instead it seemed that we were supposed to study another special case wasting a lot of painfully acquired wisdom. But I don't think I ever channeled this frustration into trying to improve on the then prevailing paradigm. A few physicists and incidentally a lot of this work was done by British physicists both here and physicists out of the country especially Paul Townsend and Mike Doff among others but a few physicists did try to go beyond the prevailing paradigm. They started with a simple question why stop at strings why not membranes? So I've suppressed time here this is meant to be a point particle. Here is a string here I drew an open string stretched between two quarks and I'm not a good artist so this isn't a very good picture of a membrane. But we're trying to imagine that after going from point particles to strings we should then try membranes. So this question was asked. And if you take the question literally it actually has a good answer. So strings work better in a certain sense than membranes or other objects because of the unique properties of complex numbers. So a complex number is made from two real numbers and there's no way to combine any other number of real numbers to get anything with the magical properties of complex numbers. It's true that there are quaternions and you can do some stuff with quaternions but complex numbers are special. And in a sense if you interpret the question literally that's the answer. But it didn't prove to be the whole story. Eventually a more subtle version of the membrane idea emerged and now we know that the membranes and higher objects are actually part of string theory not an alternative theory but part of the same theory. Meanwhile there was another idea developing that also challenged eventually the established paradigm that was electric magnetic duality. Since the 19th century physicists have been fascinated by the symmetry of Maxwell's equations in vacuum between electric and magnetic fields. Now in a sense it seemed like an accident because for one thing in nature we see electric charges and no magnetic ones. And worse than that quantum mechanics seems to tell us that it's impossible to have a symmetry between electricity and magnetism because to write a Schrodinger equation we need to introduce a vector potential and the vector potential breaks the symmetry since we derived the magnetic field from a vector potential and the electric field from a scalar potential. So okay the symmetry seems impossible. But way way back Dirac showed that it's actually imaginable to have magnetic monopoles in quantum mechanics but if you want to do it you need Dirac's formula for quantization of magnetic charge which says that the product of electric and magnetic charge of any two objects is an integer in fundamental units that involve Planck's constant. But Dirac did not have a convincing theory that used this idea and such a theory didn't actually develop until the 70s. Again in the 70s as I actually told you before the modern theory of strong interactions emerged and it raised a lot of intractable problems of which the most obvious is that the strong interactions say a proton is made of quarks but we never actually managed to observe an individual quark. The quarks are confined or trapped into objects such as protons. So it was suggested by many of the leading physicists of the time that this could be explained in an alternative version of QCD using magnetic variables. It sounds good but none of these individuals told us how to do it. No one knew what the magnetic variables would be in the case of QCD and all of the people who made this suggestion went on then to work on other things leaving the rest of us to puzzle over it. There wasn't any real progress until the mid-90s when progress came in connection with the things I'm telling you about really with supersymmetry and string theory and even today we only have a partial understanding. The first relatively clear conjecture about how a non-dibillion gauge theory like we use for elementary particle physics could have symmetry between electricity and magnetism started to emerge in the 70s and emerged in a series of steps. But it took a long time until these ideas were developed in a way that most physicists found convincing and useful. That didn't really happen until the mid-90s. But by the 90s a number of clues were suggesting that electric magnetic duality in other words symmetry between electricity and magnetism is important in the general structure of string theory. There were a lot of clues for this but the most direct one is that such duality was known to be important in the structure of supergravity which as I've told you was a kind of semi-classical limit of string theory. Finally in the mid-90s some of the strands I've mentioned the membranes and electric magnetic symmetry and others that I don't really have time for were knitted together into a new and more comprehensive viewpoints. All I really be able to do today is to give a few hints about the new viewpoint that emerged. First of all, if a symmetry between electric and magnetic charge is important in the structure of a theory then that means because there's an H bar in Dirac's formula that the basic structure of the theory can only be understood quantum mechanically. So we have to give up on the idea of understanding string theory as a classical theory which then gets quantized. The idea of first understanding the alpha prime deformation and not the H bar deformation can't be correct we have to treat them together. That means that in some sense we're not just quantizing a classical theory in some sense if the theory is correct it must give a new interpretation of what quantum mechanics means. When we do treat alpha prime and H bar together we get a nice surprise. Instead of the five string theories of the 80s it turns out that there's only one string theory that is only one candidate for superunification of the laws of nature. So this can be neatly summarized in this picture which is oversimplified but still gives you a nice hint. It's a two-dimensional picture where, loosely speaking the two parameters are the two deformation parameters H bar and alpha prime but which is which depends on your viewpoints. There's one theory which has six interesting limits five of the limits are the five traditional string theories and the sixth limit is the famous, sorry, favorite theory of the supergravity practitioners which is 11-dimensional supergravity. This funny thing is an acronym for supergravity and the overarching, the overarching theory has five different limits plus sort of a sixth five different limits that can be interpreted as classical limits of one kind or another based on looking at a different parameter and calling it H bar. As for what the overarching theory is that has all these limits well, you can call it M theory as I've done and others have done but that's just to give a name to the unknown. It's better perhaps to indicate the overarching theory by a series of question marks. So if you try to think of a two-step process where you first find a new theory and then quantize then there are five string theories they don't seem to be related to 11-dimensional supergravity but if you treat alpha prime and H bar together you discover that there's only one string theory which is the candidate for super-unification of the laws of nature that has all five semi-classical limits plus another one. So the previous paradigm was that string theory is based on two-dimensional conformal field theory. The new paradigm, the new field, is that all quantum field theory in all dimensions everything Feynman did or didn't do and might have done using any variant of his ideas is grist for the mill, is part of the input for string theory. So for example, I mean, U n is a gauge group similar to what's used in the standard model except the standard model uses particular values of n. U n for any n in any dimension describes the behavior of n parallel brains where if you want to know what a brain is the name was coined by starting with the word membrane and then in going to an arbitrary number of dimensions people dropped the first syllable and just kept the syllable brain. So U n gauge theory in any dimension describes the behavior of brains in string theory in a particular situation. So that's an example of what I said here everything quantum field theorists do or don't do or might do using their methods have thought of or haven't thought of in the current view is part of the grist for the string theory mill. So the reinterpretation I should say the unification of the different string theories in a more comprehensive picture that uses not just two-dimensional conformal field theory but all conformal field theory has got all kinds of applications. I'm going to just mention two of them and the two I've picked I've picked because they involve areas where string theory is applied to better understand aspects of more conventional physical theories. The reason I want to stress this is that the reason I believe that string theory is on the right track is not only that it solves a problem of quantum gravity and gives a strikingly elegant way to unify quantum gravity with something a lot like the real world of particle physics or that it's generated a lot of new ideas in geometry that have often startled the mathematicians but it's also that string theory has often had success in shedding light on not well-understood questions that arise in better established physical theories. I don't think that would be happening by chance and I think it means that the string theory does involve a deeper level of understanding of the conventional physical theories which enables it to generate insights of which I'll give just very briefly a couple examples. Well, I will really not even be giving you examples I'll just be describing the strategy behind the examples. The strategy is the following thought experiment. If you want to understand the black holes you imagine building a black hole out of brains. In Einstein's theory black holes can be made out of tables and chairs which you want to make them out of but if you make a black hole like a collapsing cloud of tables and chairs you have a little bit of trouble in understanding it microscopically. You make a black hole out of something which is simpler which are brains in string theory and then you know the quantum laws that describe the brains. In fact it's what I told you, you engage the theory. So you get a situation where you understand the black hole quantum mechanically and you can use that understanding to compute the Beckenstein-Hawking entropy of the black hole by counting quantum states using methods of gauge theory. So Beckenstein and Hawking discovered in the 70s that a black hole must have an entropy. In the rest of physics the entropy is the logarithm of the number of quantum states but it traditionally was an unsolved problem to describe the states, quantum states of a black hole count them and show that the Beckenstein-Hawking entropy is the logarithm of the number of states. That's done here using the link between black holes and gauge theory that you get by forming a black hole out of brains. But you can also do this in reverse and understand gauge theory better. You map questions in gauge theory into questions about gravity. You had the UN gauge theory of the brains but the brains might form a black hole and although some questions about black holes are mysterious there are other questions about black holes that you can answer by solving Einstein's equations. So if you take a question about black holes that Einstein actually knew how to answer or Einstein and others who use his equations it might map into a question about gauge theory that you have trouble answering. So when you're lucky instead of using gauge theory to answer questions about black holes you can use black holes to answer questions about gauge theory. So this has had a lot of successes the part I've actually contributed to has to do with understanding confinement of quarks in terms of the formation of a horizon of a black hole but a more recent and perhaps more spectacular success I actually mentioned it near the beginning of the talk has been the modeling of the quark-gluon plasma produced at RIC in terms of string theory on black holes. RIC is the relativistic heavy ion collider on Long Island. So in sum, in the 1990s the prevailing view of what string theory means and how one has to try to understand it and what it can be applied to was greatly enlarged again and it would be fun to be able to tell you a little bit more about that but I want to try to look forward or at least more recently and to ask what's next what might be the next major change in perspective? Well, it's famously hard to make predictions especially about the future that's actually a remark that's attributed at least in my country to a famous baseball player but I realize that both the individual and possibly the remark might be less famous in this country than in my country certainly the sport is less familiar here although you've got your own local variants in form of cricket but this is a case where we have a little bit of trouble not just in foreseeing the future but in interpreting the recent past there has possibly already been another major change in perspective since the period I just told you about but it's hard to know for sure you kind of heard about this a year ago from a different point of view in the lecture of the last Newton-Metallist, Alan Guth since there's only one string theory it seems reasonable to hope that it might have only one quantum vacuum describing our universe and leading to definite predictions for the values of all the dimensionless natural constants like for example the ratio of the mass of the electron to its heavier cause in the muon but research and string theory has actually never supported this hope for example, back in the mid-1980s models of string compactification to four dimensions gave not one possibility but many that were at least roughly compatible with what we observe so as I told you the anomaly cancellation the generalized anomaly cancellation found in 1984 rather abruptly made it possible in a strikingly beautiful and elegant way to derive from string theory in other words from a unified theory of gravity and quantum theory a unified theory of gravity and something that was at least a good rough draft but the way of doing this wasn't unique there were many closely related constructions that were possible I always hoped that this would go away but later research always had the effect of generating more possibilities so I was one of the people working on these constructions and I'm tempted to say that the proliferation of possibilities was the embarrassment of my youth meanwhile developments in astronomy have made some of our most distinguished colleagues suggest that the real world might be based on just such a mega-verse of possibilities so one who's discussed this a lot is Martin Rees, the astronomer royal in this country it would be hopeless to try to explain all the contributions and all the distinguished people who have made them but certainly Alan Gooth is one who's explored such possibilities and I think described in last years Newton lecture and his point of view was not primarily motivated by string theory was mainly motivated by clues coming from cosmology the two most relevant developments have been the apparent observation of a tiny but not zero cosmological constant in other words the fact that the expansion of the universe is accelerating that was essentially first observed in around 1998 although it took a couple years for it to be really convincing at least to me and the second is the success of Gooth's theory of cosmic inflation in describing the fluctuations of the cosmic microwave radiation the way that when we look at different directions in the sky we see slightly different temperatures so the value of the cosmological constant makes the real world look like it actually might be unstable and might be a little bit of an accident and if the world were described by a megiverse of possibilities cosmic inflation gives a beautiful way of populating all of the megiverse of possibilities just starting with one, just starting with something simple so these clues and others have made some of our colleagues suspect that something like the multiplicity of string theory possibilities might be the way the real world is but if it's true we need more clues to make it convincing if the idea would be that the landscape of string theory vacuar again I'm not much of an artist I've tried to draw a mountain range with many valleys the idea would be that the early universe had many places it could have settled into and different regions of the universe might have settled into different valleys the inflationary universe of Alan Gooth actually gives away that just starting with one you'd end up tunneling to all the others if the landscape of string vacuar is the right concept it's another big shift in our interpretation of the theory but to my thinking we still need more clues to have a better picture of whether that is the right interpretation at any rate the process of learning what string theory means has a long way still to go one of the reasons that it is I think an exciting topic for today's students to work on is precisely that so much isn't understood it's sometimes framed as a criticism that string theories don't really understand their theory that's true but if we understood it it might be finished the fact that so little is understood and that such relatively small pieces are actually such big discoveries in their own right is part of what makes it exciting and there's a lot still more to do thank you very much half of the Institute of Physics it gives me great pleasure to present the Isaac Newton Medal the Institute's international medal to Professor Edward Whitten for your insight, your creativity your mathematical powers which have led to numerous and profound transforming contributions in areas of particle theory quantum field theory and general relativity are many congratulations to you thank you so much gentlemen