Duality, Spacetime and Quantum Mechanics

0:00 ...teamed to make a symmetry between electricity and mechanism impossible. Nevertheless, in the 70s, there was a remarkable insight about how you might get duality in quantum theory after all. yet for many years it seemed completely out of reach to determine if this attempt to resurrect the electric magnetic symmetry was it seemed out of reach because of one of the main limitations in our abilities in physics which is fairly drummed into us I might say in our graduate student days we're generally able to compute what happens only when the charge E you can think of E as being the charge of the electron the charge E is much less than 1 sometimes but only when you've got very special techniques you can calculate when that isn't true but basically you're limited in physics to computing what happens when E is much less than 1 the way that the idea of duality was rescued was by discovering that duality should exchange E with 1 over E but now the one mathematical fact I'll draw upon on your behalf on your part for the rest of this talk is that E and 1 over E cannot both be much less than 1 if E is very little then 1 over E is very big and so if you can calculate in terms of electricity speculate in terms of magnetism, and so you can't figure out if a conjectured symmetry between them is true, or so it seems. And so, for many years, visionaries who speculated about such symmetries were just visionaries. Well, as I stressed, to learn if these new symmetries are correct, you have to somehow get beyond the traditional limitation of small e, which is what's happened in the last few years with very broad implications, not just for string theory but even for our understanding of standard quantum theory. For standard quantum theory, we've gotten new insights about traditional problems of physics, such as quark confinement. Quark confinement is a very surprising phenomenon

2:30 that you can understand protons, neutrons, and the like much better by interpreting them as being made out of quarks, yet you never see an individual quark. We understand that to be that if you try to separate a quark from an antiquark, or if you try to separate likewise a quark from other quarks in a photon the energy grows until something else happens instead so we know well, experiments strongly indicate that this is true and computer tests have shown that it's true and there are a variety of theoretical arguments going back to the 70s but there's still a basic and important element in which it's much less understood than we'd like to understand such a fundamental phenomenon Well, the dualities have given some new insight about them because they relate this rather mysterious phenomenon of quark confinement to more standard physics, such as the behavior of a superconductor in a magnetic field, which we understand much better. For string theory, the implications have perhaps been reaching. For one thing, we've obtained the amazing insight that there's only one theory. You know, we thought there were, in the past, we thought there were five string theories. I listed them before and mentioned how they differed by whether the strings were conducting or insulating and so on. But we now understand that what we understood in the past of five different theories, raising the mystery, I stressed, of who lives in the other four worlds, were different aspects of one theory, which is even richer than we thought. And it's as if one group of physicists was studying the nose of the elephant, one group was studying the tail, another bunch was studying the ears, and two more bunches were studying the front legs and the hind legs, without suspecting that the five different phenomena that they were investigating were different aspects of one elephant. We now understand that the six theories, five theories because there were five theories that made sense, five-string theories. There was a cousin, which to most of us seemed like a near-miss, including me, but which some of our

5:00 colleagues always had faith would somehow be resurrected, which is called 11-dimensional supergravity. I won't quite have time to explain what it is. So in the quest for superunification of the laws of nature, in the last generation or so, physicists have really been studying six different theories. And we now understand via these new duality symmetries that these six different theories are limiting cases of one theory. To understand this, you've got to crack the small e barrier since for small e, the theories are really different. So I've tried to plot this schematically here. Well, in the center is the elephant, The mysterious theory, which we're still trying to understand. And then out in the periphery are six different things they can produce to in different limits where one or another parameter becomes small. This is a simplification, but you can imagine that the parameters I sketched are Planck's constant and the Stringy constant, which parameterize quantum and Stringy effects. And what combination of them is E, which causes all the trouble, depends on which theory you're eventually going to look at. So this two-parameter, this richer theory, can reduce inappropriate limits to any of the theories studied previously. And a type 2b string theorist, for example, since he was limited to small e, was only able to study just a little corner of reality. And if you asked him, well, what happens if e isn't small, his answer was, I don't know. As we learned in graduate school, you just can't calculate what happens when e isn't small under most conditions. And similarly, a heterotic E8 times E8 theorist was studying what we now understand as a corner of a richer world and similarly in the dark about what happens when E isn't small. What we've now understood is that if you get past the small E barrier in any one of these theories, you discover the other five theories. The six theories discovered in different ways and studied by physicists in the last generation and looking for superunification, are different limiting cases of this one-victure theory. In the process of learning that the traditional theories are different limits of one elephant's,

7:30 we've also obtained a rather different view of the basic ingredients of string theory. In a sense, strings are only the first among equals in string theory. They're the first among equals very important is that you can calculate systematically with strings in a way that you can't do with their cousins. But at a deeper level that we've now penetrated to, we see that if you look more closely, strings are just the first and one equals, and they share the stage, for example, with miniature black holes called d-brains that we've come to know about only very recently. So, in the process of understanding that the strings are only the first among equals, we've had to well, they've had to share the stage and the new objects they've shared the stage with are very interesting in their own right, because they are a kind of miniature black hole and understanding them has actually led us to a better understanding of quantum black holes. There are long-standing mysteries about physics raised by the existence of black holes because, for instance, according to Einstein's theory, a black hole is something that absorbs matter and can't emit matter. It's black. It looks like a hole in space. Nothing comes out. That notion actually contradicts the very ideas of quantum mechanics. Because quantum mechanics at a very deep level requires that if something can go in then something else can come out. So, physicists have long puzzled about this. It's a problem that, like the cosmological and only makes sense in the quantum theory of gravity, and therefore the problem only makes sense in string theory. And one of our endorsements until the last couple of years is that although we had a theory where we should address this question, we hadn't. But by learning about the d-brains, which are sort of elementary constituents or dutting blocks of a black hole, we've now been able to understand something about quantum black holes and to address at least some of the mysteries. So quantum black holes are one example, but you see, another, when I talk about combining quantum mechanics and gravity, you might want to ask, well, what question is that you might wonder about on a starry night while you're staring out into the clear skies?

10:00 It depends on combining quantum mechanics and gravity, and perhaps I'd like to leave you with the thought that such a problem is the very nature of the Big Bang. So, astronomers have observed that the universe is expanding. As far as we can see, that expansion began with an explosion, which we call the Big Bang. But the very mention of the Big Bang appears to raise paradoxes that you might puzzle out about with no particular scientific training at all. If there was a Big Bang, what was there before the Big Bang? How were the clocks started? And so on. These are really all questions about quantum gravity, because both quantum mechanics and gravity would have been important near the Big Bang. And I think most physicists believe that the answers have something to do with the fact that the notion of time is fuzzy and while the fuzziness won't keep you from looking at your watch and getting a measure of time that will be sufficiently good for your present-day purposes, that fuzziness about the notion of time is very important near the Big Bang. As you go closer to the Big Bang, the very notion of time breaks down and I think ultimately most physicists would guess questions like what there was before the Big Bang won't make any sense because the notion of before and after won't make any sense near the Big Bang whether that's true or not I can't guarantee because while we've learned enough to say a little bit about black holes although not as much as we'd like we haven't learned enough to address the Big Bang And the reason, incidentally, again, has to do with the small e-barrier. We've addressed the small e-barrier for questions where the time dependence isn't very important, but that isn't the case for the Big Bang. Looking ahead, the big question to me is whether or not, with our new understanding, we're finally well-placed to answer the big question of what is string theory. it's hard to know because we did discover string theory well almost 30 years ago at a time when the ideas needed to understand it were far from being in place and we've been peeling off layers of the onion ever since and it's really hard to know how many more there are we may be close to finally understanding what is string theory and it could equally well I think be another 30 years down the road

12:30 but I do feel that whether it's sooner or later If we would fully understand what is stringy, a lot of things I've mentioned to you this evening would become a lot clearer. Thank you. So I would be delighted to answer the question. My understanding is that Einstein invented the cosmological constant to keep the universe from collapsing, not knowing at that time the world was discovered in the world. Right. And then he said it was his greatest wonder. Now, why is this being brought back? Well, you see, Einstein carried out this discussion about quantum mechanics. and without quantum mechanics he could just say let the cosmological constant be zero but quantum mechanics doesn't allow you to just say let it be zero especially not in a theory like string theory which has no adjustable parameters I didn't stress that in the talk it's a unique theory which either has to agree with nature or not agree with nature so as a string theorist you've got to just calculate the cosmological constant you don't have Einstein's luxury of saying I think it should have been zero and we don't understand iteration would be zero to 120 decimal places. We do certainly understand why the first 70 decimal places would be zero, but we'll stop them the next 50. What is the string made out of it? You know, when Maxwell explained that electricity and magnetism, and especially light, I should better say light, when Maxwell explained that light was an oscillation of an electromagnetic field, businesses then spent decades worrying about what is a field and what is it oscillating in. And at the end of a long struggle, they learned that they shouldn't ask that question, because an oscillating field was simply the most deep thing they knew about, and they couldn't usefully explain it in terms of anything else. you know having learned our lesson the hard way we rest upon

15:00 the experience of our predecessors who learned such lessons the hard way so now I think I can tell you although we don't know for sure it's very likely that our best theories that we have now although we don't understand them very well yet we interpret matter in terms of strings I have to tell you as physicists eventually learned in the late 19th century the better part of the dollar is not to ask that kind of question. It must be in a position to go to a much deeper theory that would give a real answer. And isn't that a real parity change in the following sense? It seems to me that for years and years physicists and other scientists kept looking down inside, finding smaller and smaller objects that made up the larger and larger objects we saw. And now it seems to me you're telling me we are at the end of this search because you're not going to tell us what a string is. You would have been willing to tell us what a nucleus was or what a dwarf was made of a string, but you're now telling us you're going to stop. I'm telling you that if there isn't a better theory, then it's not useful to ask what a string is made of. What it would mean to give real answer to the question you asked. The question you asked is, what are strings made of? usefully would be to give a better theory. But I don't know whether there'll be a better theory, but I suspect it'll take at least another half century to understand this one in a sensible way. Is there any arbitrariness in the fact that you choose string because it gave some solution now you know what it is? And how distinct the string concept is? Well, a version of your question is why strings and not, for instance, membranes, which I can't draw as well. So, well, the math works with strings, and it doesn't work in the same way with membranes. There's a subtle sense in which we've now discovered with duality that there are membranes as well as strings, that the strings are the first among equals in the sense that the membranes aren't. You can systematically do with strings things that you can't do with the membranes. When I give colloquy to mathematicians or physicists, I like to give the analogy

17:30 but it's not really right in this audience that when Cauchy and his contemporaries replace the real numbers by the complex numbers a complex number is made of two real numbers and some must have asked well why two real numbers and not three for instance but there's nothing quite like this step. because the particle world line has one real number and the tube has got two, like the complex numbers. I think that the main reason I personally suspect, you ask what degree of uniqueness is there, for instance, in succeeding in making quantum mechanics and gravity. Well, one thing that convinces me it's unique, especially with the discovery that the different theories are different parts of one elephant, is that all the sensible ideas that physicists have had turned out to be different aspects of this theory. Now, of course, that doesn't exclude the possibility that this theory is a branch of thought that has nothing to do with nature. And there's a completely different branch of thought that we haven't fumbled upon at all. That's more of it. There are so many remarkable things, Oliver, that go into making this theory work and making it look as much like nature as it does that I would personally find out to be an amazing cosmic conspiracy. The question reminds me slightly of the fact that when the fossils were first studied historically, some interpreted them as records of life forms that existed in the past, and others thought that they had been placed in the rocks at the creation of the world to test our faith. Well, with that perhaps, we'll thank you again. Thank you.