Duality, Spacetime and Quantum Mechanics (contd.)

0:00 Thank you. Bill, I want to press your introduction so that it makes it harder to get to talk. One bit of physics that most of you have seen in high school, if you've studied any physics at all, is the inverse square law of gravity and electricity, which was originally discovered by Newton by comparing the Earth's force on the Moon which causes the Moon to orbit the Earth to the Earth's force on an apple by which the apple falls to the ground and also by thinking about what kind of gravitational force would be needed to obtain Kepler's laws of planetary motion. And then a hundred years later it was appreciated that a quite similar force law holds for gravity, for electricity damage for the force between two electrically charged bodies. The N square law says that the force between two charges that are separated by distance r, or likewise between two masses separated by distance r, is the product of the two charges, E1, E2, or the product of the two masses, M1, M2, in that case with Newton's constant, divided by r squared, where r is the distance between them. Those are all the equations for tonight, by the way, just to urge you to relax, but I did want to let you put to good use your knowledge of whatever knowledge of physics you may have. So physics practically began, or physics in the modern sense practically began with Newton's discovery of the inverse square wall for gravity, and then one of the most fundamental advances of the next century was the similar law for electricity. And it has a lot of interesting properties, but one of its properties that caused the greatest attention in the last century but probably did not cause great headaches to Newton was the fact that according to this formula, the force between two masses is extremely large if the distance is extremely small. In fact, this quantity, 1 over r squared, would become nearly infinite if r is extremely small. That didn't really bother Newton because the moon was always at a safe distance from the Earth. And even with his apple falling downwards to the Earth, the r here is really the distance to the center of the Earth. And his apples were safely far from the center of the Earth.

2:30 And in fact, everything was fine with this for the first 200 years or so of the inverse glow law. The trouble really only began about a century ago was discovered. And shortly after that, the nucleus. Because it was very soon clear that atoms were at least roughly to be described, in terms of electrons orbiting around the nucleus, a little bit like the planets orbit the But if you think in those terms, you quickly run into trouble, into the singularity I mentioned, the bad behavior of the inverse square law when the distance r becomes nearly because a small calculation showed, for example, in the case of an atom, that if you treat the electron as a little charge orbiting around the nucleus, an atom should only last for about 10 to the minus 9 seconds before, drawn in by the extremely small force that it experiences when it's close to the nucleus, the electron will spiral into the nucleus. Well, a lot of physics in this century has to do with grappling with that predicament. So, first of all, in the case of electricity, at least if we ignore issues raised by relativity, the problem was solved in the first quarter, or first half of the century, to include some relativity, with the development of quantum mechanics. Well, how did quantum mechanics solve the problem of the electron spiraling into the nucleus? Not, for example, in a brutal way, wasn't correct if the distances involved were too small, which might be the most obvious thought that the question would suggest. The answer turned out to be a lot more subtle and is based on something called the uncertainty principle. The uncertainty principle says that everything is a little bit fuzzy if you try to express it in classical terms. So if you don't look too closely at a proton or an electron, classically, but if you try to look at, classically means, roughly speaking, on the basis of common sense. So your ordinary common sense notions, that a particle at a given time has a definite position and a definite velocity, and if you know what they are, you can figure out what will happen afterwards. Your ordinary common sense notions work fine if you don't look

5:00 too closely, but when you look very closely at an electron or a photon or any other subatomic you find that there's what's called a quantum uncertainty principle that makes everything fuzzy in a way that really can't be described properly on the basis of ordinary intuition. But mathematically, the effect of this fuzziness is that you don't really see what would happen at r equals 0 because long before you've really met the problem you have to deal with that quantum mechanical fuzziness. Can you hear in the back? It's on, as far as I can see. Okay. Well, I'll speak louder. Is that better in the back? Okay. A little bit? Okay, well, anyway, quantum mechanical uncertainty resolved the problem for electricity in the early part of this century, but perhaps rather surprisingly, was not powerful enough to solve the problem for gravity. There's a close analogy between the two forces, which seemed almost perfect before the 20th century. But in the 20th century, it became clear that the analogy between electricity and gravity, although very close, is not quite as close as the inverse square walls suggest. One learns early in the century, with Einstein's greatest discovery, really, Einstein's greatest discovery, which was completed in 1915, was that gravity has to do with the curvature of space and time caused by mass, and the motion, the distortion of the motion of other masses because of the curvature produced by a given mass.

7:30 So, in basing gravity on the curvature of space and time, Einstein introduced some very subtle non-linear mathematics in the description of gravity which left the inverse square law as a good approximation under ordinary conditions but if you look more closely it changed all the concepts drastically if you're planning to navigate in the solar system whether you need to know general relativity or you can make do with the inverse square law depends on how precise you want your calculations to be You'll make an error of a few kilometers per orbit if you just use the inverse ground law. If you want to be able to calculate and plan your trajectory more accurately than that, you should study general relativity and learn about the curvature of the solar system due primarily to the mass of the sun. Anyway, in general relativity, it was based on nonlinear mathematics, which changes physics in a lot of ways, is that quantum uncertainty alone cannot solve the problems of the inverse square law. Now, this problem is very much at the center of physics because the two theories that I've mentioned so far are really the main theories upon which our present understanding of physics is based. On the one hand, we have quantum mechanics, which was invented because of this problem of the inverse square law. understand atoms and molecules and subatomic particles and so on. And on the other hand, we have general relativity, which is Einstein's theory of gravity, his theory of the curvature of space and time and the large-scale behavior of the universe. One is applied to very small objects and the other is applied to very large objects, but they're in marked conflict. Because the non-linear mathematics relativity, makes it impossible to use quantum mechanics to tame the problems of the inverse square law. And in fact, the two theories just don't work together in any standard way. If you try to combine them, you run into a web of contradictions. Well, this conflict is really the contemporary version of earlier conflicts which shaped

10:00 many of the upheavals in 20th century physics. I mentioned one which was the role of the vs. Grela trouble in leading to quantum mechanics, but there were many others. Einstein invented special relativity because Newtonian mechanics was in conflict with the theory of electricity and light. And then he invented general relativity because Newton's laws of gravity were in conflict with his own theory of special relativity. And closer to our own times, an important part of the state of model, the weak interaction part, was invented essentially once again because of the contradiction involving the 1 over r squared fourth law for the weak interactions. So conflicts like this between different branches of physics have been one of the most fruitful starting points for progress in this century. And the most striking such conflict nowadays is surely the one I've mentioned between gravity and quantum mechanics. Well, I think it's a problem that has yielded little to direct assault. And had physicists not been lucky, I suspect it would be a problem that would not be under fruitful study in the 1990s. That physicists had the good luck to discover, essentially in the 70s, or starting in the late 60s, that this problem can be overcome in string theory. Well, what's string theory? Roughly speaking, in string theory, you reinterpret a non-entry particle not as a little point particle, but as a vibrating loop of string. Well, it's a very rough description because on both sides you have to remember quantum mechanics. So on each side you should include quantum mechanical uncertainty. So the particle is a fuzzy particle and the string is a fuzzy string. But nevertheless, you've got a little vibrating string, and try to think of that temporarily as your model for what an elementary particle is. Well, an important property of these strings is that, like a violin or a piano string, one of these strings has many different modes or harmonics of oscillation. The reason that a violin or a piano sound different, even if you play the same note, or for that matter, the reason that either of them sounds different from a tuning fork,

12:30 is that the violin or piano string have many different harmonics of oscillation. If you play middle C, you can also see it's higher harmonics. And you hear the different harmonics in different proportions depending on whether you play one instrument or another, which is the reason that music is played with symphony orchestras and not just on tuning forks, where the higher harmonics are avoided. So in the case of music, the richness and beauty depend almost completely harmonics. And in the case of string theory, the existence of many different harmonics, in this case the different harmonics are all interpreted as elementary particles, and the key to unification of the different particles is that the different particles, the photon, the electron, and so on, the quarks, the muons, the neutrinos, all the funny things that you've heard of or haven't heard of, they're interpreted as different states of oscillation of one basic string. The different harmonics are interpreted as different elementary particles. So, all at once, a single string describes a huge resourcement of different particles. Once you learn to correctly quantize the string, that means once you learn to study strings in the light of quantum mechanics, and calculate the spectrum, which means to understand harmonics, and what particles you get out of them, you find among quite a number of surprises what I think is one of the most great discoveries in the history of physics, and which incidentally I was also too young to participate in, which is that one of the harmonics of the string has just the right properties to be the graviton. or in other words the quantum of gravitational waves this is something that physicists were very reluctant to believe and perhaps literally hundreds, certainly dozens and perhaps hundreds of papers were written in an attempt to avoid this conclusion which Stringer is finally dragging and kicking ended up accepting and there's discovery about one of the vibrational modes of the string, was the beginning of the discovery that, in contrast to conventional quantum field theory, which makes gravity impossible, string theory requires gravity.

15:00 It's not just that the contradiction between quantum mechanics and gravity can possibly be solved if you adopt string theory as a new framework for physics. What initially became clear in the 70s was that in this new framework of physics, gravity of general relativity is not just possible, but necessary. It's forced to you. And as I've said, other modes of the string look a lot like the particles that we know, although we don't know how to make it work precisely. And so, with very simple assumptions, everything neatly, and at least more or less, fits into a string. the way it doesn't fit the details of what we see in nature, but which certainly, in a very attractively elegant fashion, describes the main points of elementary particle physics as we see it. Well, the stuff of going from point particles to strings sounds so naive that, at first sight, if it leads to anything deep. And I hope that was your reaction, since alternatively I would have to suspect that you weren't listening closely. For a simple explanation of why going from point particles to strings has faithful consequences, I'd like to begin by going back and telling you a little bit more about standard quantum theory. Well, according to Feynman, introduced one of his most well-remembered discoveries, a very intuitive way of calculating what will happen in different physical processes in standard quantum theory, in terms of what came to be called Feynman diagrams. So not in the fancy way that's usually presented in textbooks where they're telling you how to do technical calculations, but in the intuitive way that Feynman originally thought about it. A Feynman diagram is something like this. It's a space-time history. So I've parted time vertically and space goes horizontally. And this is a space-time history

17:30 in which some particles come in from the past and they go out to the future after being scattered. And the way the scattering happens is a succession of events in space and time. Particle A perhaps propagates to a space-time moment X, where it breaks up into two particles, one of which later joins with incoming particle B, It goes out, propagating to W, where after some further branching and joining, final particles go out, which I've labeled C and D in the drawing. I've sketched an example where two come in and two go out, but we could easily have, for instance, two going in and four going out, which is one of the characteristic properties of standard quantum filtering that the number of particles isn't constant. Matter can be created and annihilated in this illustration now. Two particles come in in the past and four go out in the future. So we've created matter. But anyway, whether matter is created or not, we compute such processes by summing or integrating over all of these space-time histories. So, as I've said, the lines in the Feynman diagram represent the free propagation of particles. Free just means that the particle is propagating with nothing happening to it. I'd use straight lines to make the previous picture easier to visualize but in quantum mechanics different trajectories are possible so here I've got a wiggly one but whatever it is as long as you just see a line a particle is propagating as a free particle nothing's happening to it but the vertices in the diagram where one line fork into two or two forks join into one those are the interaction events the interaction vertices as they're called technically, they're the interaction events where particles branch and rejoin. You should think of those as the space-time moments where something happens. So at this space-time event or at this space-time event, something happens. In this diagram, in the past, there was one particle, in the future there are two, and that's the very moment in space-time where it changed. there are lots of great things about quantum theory of which I mentioned one which was the fantastic and brilliantly vindicated prediction that matter gets created undemiolated

20:00 and equally important is the fact that the Feynman diagram technique led to fantastically accurate and precise calculations enabling one to verify standard quantum field theory with an incredible precision, to within one part in a billion or better in some cases. But at the same time, this description makes it possible to see some of the limitations of standard quantum theory. One of the most important limitations is that there are too many theories, because, first of all, you can be rather arbitrary about what particles are propagating in these lines. But even worse, there are many, many theories that differ by what kind of vertices one allows, which kind of special interaction events are permitted. In my drawings, to keep them simple, I only considered the case where one particle breaks up into two. But, well, nature shows us, and in elaborating the interesting theories we discover, that we need to allow more complicated vertices, two going to three or two going to two and so on, and to end up having many, many theories differing by what kind of special interaction events are found. The other thing is the infinities of quantum field theory, the mathematical troubles that you run into, which we call infinities, the fact that often when you do calculations you don't get sensible answers. The infinities, which ultimately make gravity impossible, arise because in this space-time history there were special moments, X, Y, Z, and W, taught us that you should integrate some of all possibilities. You should allow all possibilities for what X, Y, Z, and W were. And in particular, you could have a traffic jam where everything happens at the same space-time moment. And that leads to acute troubles, which ultimately make it impossible to have gravity in the light of quantum mechanics, which are the souped-up relativistic version of the old problem of the inverse square law. The inverse square law was the trouble that two particles could meet. And the relativistic version is that all these events could meet in space-time. Well, these are the limitations which you would like to circumvent, and you circumvent them in string theory in the following way. First of all, instead of a propagating point particle, you have a little propagating string.

22:30 So here I've drawn once again the space-time picture point particle. At each moment in time, the particle is somewhere in space. And as time unfolds, it travels at a later time than somewhere else. And I've indicated its trajectory in space-time by drawing a curve. For the string instead, at each moment in time, you have a string or a little closed loop somewhere in space. As time goes on, the string propagates in space and it sweeps out a little tube in space called the world tube just as the particle sweeps out a world line or curve so the Feynman diagram that I drew with tubes instead of lines. Now, lines can't very well meet smoothly. They have to branch and rejoin in the fashion of a standard plumber diagram. But tubes have the property that they can meet and rejoin in a perfectly smooth fashion, which I've drawn here, as if some plumber maybe has connected different tubes. So now, this picture will look a lot like this one which is more or less the intuitive idea for why strict theory can look like standard quantum theory if you aren't able to do sufficiently precise measurements. But if you look closely, it's completely different, and in particular, the vertices or distinguished space-time events of standard quantum theory have disappeared. Every sufficiently small piece of this picture is just a little smooth piece of a two-dimensional world tube, like any other small piece. In contrast to this picture, where if I draw a little circle around an interaction event, no matter how small that circle is, it really looks different from a little piece where nothing happens. One of them contains a fork and one didn't. But here, any sufficiently small piece has nothing happening in it. It just has free propagation, free motion.

25:00 and since the vertices led to all the troubles we might reasonably hope and we ultimately discover that the troubles go awry there are very few theories and the few theories that we have well they're finite they don't have the traditional mathematical contradictions and that means in particular that there's no problem with the inverse square law The statement that there are very few theories means, to be precise, that once you understand what you mean by a free string, once you understand what this picture means, that just describes free motion of a string with nothing happening, you automatically understand how the strings are going to interact, how they're going to behave, scatter each other and decay and so on. All the phenomena that will occur. Because, as I said already, these two pictures look locally the same. A small piece of one looks like a small piece of the other. So if you understand this one where nothing is happening, you understand this one where, in fact, something is happening. One string is breaking into two. This contrasts, as I've tried to stress, with field theory, with standard quantum theory, where after you understand the frame motion, you still must describe the interactions or vertices. so for this and other more or less related reasons there aren't many string theories and by the time the dust had cleared more than a decade ago it was clear that there were five possible relativistic string theories which differ by very general properties of what kind of strings you've got in type 1 these strings are electrical insulators and they can be either open or closed strings but if they're open strings they have electric charge at the ends of the strings. In the two type 2 theories the strings are electrical insulators with no charges with closed strings only. And in the two heterotic theories the strings are actually electrical superconductors which can carry gas, gas currents. They'd be extremely useful technologically

27:30 because of their huge current category and superconducting properties, except that, unfortunately, their large tension would make them a little bit hard to manage for industrial purposes. Well, the existence of five-string theories is a vast, vast improvement over the standard state of affairs in ordinary quantum theory, where there are infinitely many possible theories. But it still raised an obvious question. It's marvelous to learn that there is a rich new framework of physics where the traditional difficulties of quantum mechanics and gravity are overcome, and there only are five of them, but five is four too many, and if one of them describes our world, then who lives in the other four worlds? But in the mid-80s, that question was too difficult, so we'll leave it aside for a bit. Well, reducing in this way the number of theories has a faithful consequence for our general understanding of physics. I have trouble explaining this in completely non-mathematical terms. But in standard physics, when you talk about the free motion of a particle in space-time, you can describe it abstractly. I'll do a picture as if the particle space-timed. But you can really describe it abstractly. And as long as nothing is happening, you don't learn very much about space-time. But once interactions are occurring, once there's a distinguished space-time event at which something actually happens, then you've got some definite knowledge about space and time. The interactions depend on knowing exactly where you are. And in our diagrams, where we really talk about a definite space-time event, is where something happens. But in string theory, that last bit, which is where you really learn what space-time is, is absent. And as a result, you never really learn precisely what the space-time is. There's a certain kind of fuzziness that affects your notion of space-time, just as early in the century, a certain kind of quantum fuzziness came to affect many classical notions sense notions of the trajectory of a particle.

30:00 So you get a new source of fuzziness, a little bit like quantum fuzziness, but going beyond it. So quantum mechanical fuzziness is controlled by Planck's constant, and the stringy fuzziness is controlled by a new constant, called alpha prime, that controls the typical size of the smallest allowed strings. So, quantum mechanics put a limit or bounds on how precisely you can talk about some of your common sense notions, like a particle's position or velocity. And string theory puts a bounds on how precisely you can describe space-time. well once you attempt to reformulate physics in terms of string theory you're allowed to several very general predictions which I'll explain a little bit more in a moment especially the third of them but they are in brief gravity, gate symmetry and supersymmetry and apart from these general predictions if you manage to understand the vacuum which is where our understanding is severely limited you could aspire to learn a lot more to try to make a very rough analogy when standard quantum field theory was developed there was one very general prediction that was I think roughly analogous to these three which was that antimatter should exist that was certain that the idea is that every particle has a corresponding antiparticle and matter and antimatter can be created and annihilated turning into or being created from pure energy and radiation so this was a very striking prediction which was vindicated almost immediately so standard quantum field theory makes this general prediction and in addition, if you understand specific quantum field theories as we learned to in the decades following the invention of quantum theory in the 20s, you can make much more specific and detailed predictions So, in a similar spirit that this framework for physics made a very general prediction

32:30 string theory as a framework for physics makes several general predictions, something which By eliminating those interaction events and making the interactions things that are determined by the knowledge of the free motion, it greatly increases the predictive power and leads to three general predictions. And as I said, it leaves you with a tantalizing hope, which is really not fully realized, that if you could understand what the vacuum is, you could learn a lot more. That's analogous to saying, in this case, if you have a specific theory, you can learn a lot more. there are three predictions which I promise to tell you more about. Gravity, which I've really already mentioned. Gravity here means Einstein's theory of general relativity that describes gravity in terms of the curvature of space-time. And as I've already told you, it's automatic in string theory while impossible in standard quantum field theory. That surely is the single most important reason for the intense interest physicists have had in string theory. in the last generation. The second general prediction is what's called gauge symmetry. And I don't really have time tonight to tell you too much about gauge symmetry, but it's the bread and butter of the standard model of particle physics. It has its roots in the 19th century Maxwell theory of electricity, magnetism, and light. And the standard model was developed where when new kinds of gauge theories were understood and extended, and explored to describe first radioactivity, that is, the weak interactions, and then the nuclear forces or strong interactions. Well, these two general predictions, so to speak, of string theory are, in a sense, really post-dictions, because here on planet Earth, general relativity and gauge symmetry predate their appearance in string theory. It may well be different on other planets, and there may be planets, for example, where string theory was developed a little earlier, and physicists were a little bit more selfish with non-evilion gauge symmetry, and maybe where they consider gauge symmetry to be largely a consequence of string theory. But here on planet Earth, the two predictions that I've mentioned really predate string theory. And the third is therefore particularly exciting, because we in fact don't yet know if it's true.

35:00 it's a real prediction coming from string theory the third general prediction is supersymmetry which is a new kind of symmetry of elementary particles which physicists hope to discover in accelerators perhaps within the next decade or even earlier if we're quite lucky supersymmetry says roughly the following while we're accustomed to measuring by numbers. Space and time are classical concepts that require no special 20th century equipment to detect them. And right into that, we measure space and time by ordinary numbers, which are, again, classical concepts. It's now 3 o'clock or 200 meters above sea level and so on. And when Einstein developed special relativity, or even general relativity, quantum mechanics wasn't yet known. And space and time were conceived entirely in terms of ordinary it's practically the one area of physics that wasn't touched until the present by the development of quantum mechanics but according to supersymmetry supersymmetry is the beginning of a quantum structure in spacetime in addition to the ordinary variables the 3 o'clock and the 200 meters above sea level by which you measure space and time there would be no infinitesimal quantum variables or Fermi dimensions in spacetime which you really can't describe in terms of ordinary, familiar concepts. They're quantum mechanical in nature, just as an electron is quantum mechanical in nature. Whereas space and time, as traditionally described, are more classical variables like light waves that you can detect with pre-20th century equipment and measure by numbers. So, supersymmetry is a kind of new structure in space-time, but in down-to-earth terms, if it's correct, it predicts the existence of new elementary particles that involve oscillations of ordinary particles in the new fermionic dimensions, which we would see in accelerators as new elementary particles. As I've already stressed, in contrast to gravity and gauge invariants,

37:30 third general prediction of string theory is true. It's one of the main targets of accelerators, including the unfortunately defunct SSC, and including the LHC, which is the Large Hadron Collider, which is a somewhat lower energy version of the SSC, which will be operating in Geneva around 2005, and which the U.S. has recently committed itself to participating in. as well as in the lower energy accelerators that are operating currently. There are some experimental hints that supersymmetry is very near. One of the most striking ones is that a slight elaboration of the notion of supersymmetry called supersymmetric grand unification makes a detailed prediction about the values that you should see for the so-called coupling constants interactions that we know. And this prediction is very accurately tested in accelerator experiments, which gives a strong hint that supersymmetry may well be correct and very near in energy. If it were found, well, in many aspects it would be a very momentous discovery, the beginning of understanding the quantum structure in space and, among many other things, it would give a tremendous Bruce to Stringberry, which is where the concept originated. Well, so far I've given you a more or less unrelieved survey of good news, but at some point I have to be honest and tell you a bit of bad news, too. one bit of bad news, which I find particularly pressing, is that there's a basic problem in physics that has to do with quantum mechanics and gravity. which has to do with something that was called the cosmological constant, introduced by Einstein. It's the energy of the vacuum. And if it's not zero, it would show up in nature by the fact that when you measure the angles of a triangle, they won't add up to 180 degrees, as you learned they do in high school. But you'll get something a little bit different. The most accurate observation in nature is that the cosmological constant is either zero or else incredibly small. In its natural units, after the decimal point, the first 120 digits are zero, at least.

40:00 And astronomers are hard at work measuring the 121st digit. With some experimental evidence at the moment that it's not zero, but I think I'm one of those who suspect that we aren't lucky people We can just barely measure the 121st digit, which is the first one that isn't zero. So I think I would suspect it's zero. But whether it's zero or merely fantastically small, the cosmological constant is a mystery about quantum mechanics and gravity because the energy of the vacuum only matters when you've got gravity, general relativity. It produces a large-scale curvature in space-time, which is the reason that the angles don't add up to 180 degrees in a triangle. And it's quantum mechanics that makes it really difficult to explain why it's zero. And since string theory is the only theory of quantum gravity that makes any sense, string theory is the only framework where this is a well-defined problem. And therefore, it's incumbent upon string theorists to explain why it vanishes or is fantastically small, and they haven't. It's not just a big embarrassment, but I must say that my strong intuition is that not understanding this is the main roadblock to making models of particle physics derived from string theory more realistic. Well, that's one aspect of the bad news, but on a more cosmic scale, there's even worse news, which is that even after a generation of luck, we still don't understand what the theory is. I think that's really hard to explain, scientists, much less to the general public, because scientists don't ordinarily work for generational theory without knowing what it is. It has to do with the peculiar history, where the theory was discovered by accident in the course of physicists working on quite different problems, and they discovered formulas that were valuable and important, but not the most valuable and important formulas in the theory, and since then, for a generation, we've had no choice but to try to work gradually backwards, probing more deeply and understanding the more basic structures from which the amazing things that were discovered came. To try to very roughly describe

42:30 our predicaments, I could say that, well, physics can be described in terms of particles, which is actually the language I've used mostly because it's more intuitive. But at a deeper level, physics is described in quantum mechanics in terms of waves, which are then quantized to give particles. so both descriptions are important but the waves in many ways are more fundamental but string theory began historically by generalizing the less fundamental particle viewpoints and we've been having to cope with that lucky but nevertheless awkward start ever since a picture that those of cultural or popular talks on string theory have undoubtedly seen is this one. Here I've plotted the particle view of physics and here's the more fundamental wave view. And horizontally, I've drawn sort of old pre-string physics. And at the bottom is the new physics, which maybe if it hadn't been discovered until the 20th century, physicists would have discovered it when they were ready for it and they wouldn't have spent a generation studying it without knowing what it is. but our good luck as 20th century physicist of being able to study it at all by its lucky discovery at a premature time when we probably weren't ready to understand it has had the color that we've been grappling with it in this awkward way anyway that's what I've indicated as the new physics well the particle I've symbolized in all physics by a point particle that travels at the speed of light because the basic ones or all of them do that in some good approximation and the speed of light I've symbolized by a 45 degree angle to the horizontal in going to the new physics that simple straight line at a 45 degree angle is replaced by a vibrating world tube there's a lot of physics in this particle that travels at the speed of light but much deeper are the concepts of general relativity and the standard model of the gauge from which this is derived. And just like general relativity and gauge theory contain much greater truths than the straight line at a 45 degree angle to the horizontal, someone would believe that the synthesis down here

45:00 contains much greater truths than the vibrating world to fear. And trying to understand what really belongs in that box is the mystery of what is string theory, which physicists have grappled with a lot for a long time. Well, the problem, as I just posed it, is not new. It's been with us for many years. But the outlook has changed a lot, as David alluded to in his introduction. In the last few years, because of understanding of a new kind of symmetry called duality. very roughly duality is just a relation between different things that looked like they couldn't possibly be related but turned out to be if a new symmetry a new way of relating different things is sufficiently surprising then it gets dignified by the name of duality if it's too easy to understand it doesn't rate in its oldest form duality between electric and magnetic fields, which holds in vacuum. That means it holds in the absence of electric charges and currents. But it's spoiled in nature by the fact that we see electrons, but we don't see magnetic monopoles. A magnetic monopole would be a magnetic fourth pole without a south pole, or vice versa. We don't see those. We've got bar magnets, and as has been known since ancient times, if you try to separate the north and south pole magnet, by breaking it, you don't get separate magnets with only one pole. You just get little or bar magnets that have both north and south poles. So, for electricity, you can get a minus charge without a plus charge, or vice versa. But for magnetism, you never get a north pole without a south pole. although in some ways there's a very close symmetry between electricity and magnetism, it seems to be hopelessly spoiled in nature by the fact that there are electrons, but were monopoles. Well, in the early part of this