Superstrings - towards a theory of nothing — Part 2

0:00 I suppose my way of interpreting this theory, I mean, I'm interested in, is this a quantum field theory where you've got a Hilbert space, where you have lots of algebras, but you don't, because you've thrown away the space by the points. I mean, what we can have, what we seem to have, is simply diagrams, so to sort of estimate this theory in a way. The way string theory has been formulated in terms of the space-time identification is entirely given in terms of the escalation, which is an unsatisfactory aspect of it, which is precisely one of the reasons we want to get away from. Description of the humanities is in terms of these two-dimensional surfaces that are all related to that two-dimensional surface. Well, the two-dimensional surface tends to be steeper. If I say that you're tipping, would that upset you? Well, I mean, I don't know how you would do a reconstruction theory. Well, I think if you, you know, how you would do an analytic continuation back to... I think it's not even on my diet. Well, as far as I know, it's no difficulty. But not if you've got a background in mathematics. If you've got a background in mathematics, you could write. Then, I mean, it may not be analytical. Sorry, in principle, a background in mathematics would not be difficult. In practice, if you want to... Are we talking about one principle or what is pragmatism? Well, I'm really talking about questions of pragmatism. I mean, I can't imagine at the moment what it would mean to have a set of writing axes, say. But what does it look like? What is it? You've raised the question yourself a moment ago.

2:30 What the fields are fields. If you try to formulate it any academic way, you'll get stuck at the first possible point. I mean, for example, you certainly do not expect that these fields... The trouble is, these fields create no other options. So the whole question about locality is actually a different question from... For example, let me take, let me consider... Well, you might have had a shot at writing axioms for just a few of my lectures quite a long time ago. I think it would be very, very surprising anyone would formulate string theory in any axiomatic sense because order by order of perturbation theory, the way I describe it, it would appear to violate any axiom of the sum. It has an infinite number of these states which are stable, order by order of perturbation theory, and that is inconsistent. The problem is that all we really know... It's an analogue of the quantum diagrams. And, you know, diagram by diagram, the final diagram is a violet. They themselves, sort of, perform the actions of quantum filtering. And here we're going to get something much worse. An illustration of how bad it will get is, imagine this picture I drew of two strings interacting to form a third string. Now that's something like a pi-q interaction in the state of a filter. However, they interact by touching at least two points. So if, for example, you think of the field, what we're tempted to do is write a field which is some sort of function of the string. That's sort of the obvious angle of the scalar field. It's obviously contained within it an infinite set of modes. I mean, fields one through each mode of the string. And if you were to be so foolish as to decompose this field into an infinite set of components of the scalar field, With many of these, of course, there's an infinite sum of interactions between the five of these fields, so they were all non-local, so that sort of decomposing a string field into ordinary fields makes the ordinary, in the magic of ordinary fields, everything will look tremendously non-local, and I don't know of any systematic way of approaching that, although maybe I'll be able to do it.

5:00 Certainly the viewpoint that people in the subject take is that we don't know what the fundamental facts in string theory should be, because we don't even know what, in a sense we don't really know what it is, but we have something which looks pretty magical in what it does to us, and we're really burping around, and we're discovering, these symmetries that we're discovering must be related somehow to one another. There are infinite numbers of gauge symmetries of a type which have no parallel in all of the filters that we know of. And somehow that infinite set of symmetries is the tip of some iceberg that's trying to tell us something about the spin that we just don't understand. You said you did not think these dimensions were physical dimensions. What do you think to that? Well, the way the theory works is that in some sense you can think of them as physical and enlarged. They appear to be solutions in which space-time is approximately 10 minutes long. And then there's ten dimensions in nanoproximations. However, when you curve up these six dimensions, then the consistent six-dimensional, you call it six-dimensional background, the consistent background, I mean, this is a theory which contains a lot of other things, general relativity, and so the solutions of the theory are generically curved. I mean, space-time is curved. In general, the solutions... I'm trying to remember. Isn't the science always based on the design of gravity and what it is, and it's just a set of formal rules? No, but I looked down a set of equations which, in some sense, at low energies, we could use Einstein's equations.

7:30 So in that sense, in the approximation it makes sense to try and make that series at the lowest terms, at low energies. Then there is, in that sense you can solve the equations. And there's also an enzyme that's been in this couple for a certain bunch of fields. So you can look for solutions. And the spaces I've called Calabi-Yau spaces before, which are six-dimensional manifolds, which are, I don't know if there's a technical definition of them, are exact solutions of string theory. In fact, all of them. Those equations have known solutions which are exact solutions, which are curved manifolds. Now, those curved manifolds have a scale which is not defined by a solution. There's a parameter, if you like. And when the scale is very large, then the curvature is small, and in that sense, they are probably a good approximation, I mean, thinking of them as classical dimensions is probably a good approximation, but when they're very small, it's probably a very bad approximation. Professor, would you like to offer the last question? I think we've been sticking it up on some previous discussions with Michael. Of course there are many questions but I think I want to ask this one really. My vague understanding is that the excitement of these new crop of symmetries is that they will of course reduce greatly the number of things and be clued to the underlying things. There is a way of thinking which I think is controversial, and I don't know whether you're actually doing it when you're saying that. I'm not saying it's wrong, I think it's controversial. In a simple-minded case, the way of thinking would be like this. Try and do it in some rough analogy with the Yang-Nil. Given a certain physical theory that gives a mathematical description to a certain distribution of electric charges, And it so happens to give the very same mathematical description to a completely different distribution of magnetic charges. Infer, because of the sameness of this mathematical description, that the underlying physical reality Isn't either the electric charges thus and so or the magnetic charges blah blah blah in another way, but rather something that is, like the mathematical description, unitary, i.e. regard the electric and the magnetic charges as hints about new quantities, which you can think of as electric in blah blah way, think of as magnetic in thus and so.

10:00 Is that the kind of thing? You're moving towards the invariant, right? R and R' are to be regarded as just perspectives on an underlying reality, which is pointed to by the very fact of the symmetry on the future. In a certain sense, that's right. Which precisely embodies this in a very simple way. And that's this two-dimensional example, where we know that there's a theory of fermions in the pyramid model, and there's a theory of bosons called the sine-Morgan theorem, which looks utterly different. We've got the theory of bosons, which has fundamental objects in a robotic field. It has an extended, solitonic-like solution, if you like, which is a kink, one-dimensional. The field changes in a limited space. The localized energy density. That kink is known to behave as a thermion, as a high mass, if you look in the perturbation expansion around the bosonic theory. However, it is known that the bosonic theory, as a quantum field theory, is identical in every respect. So the cloning model, which is a model of a thermion, where if you just think of the phonemes, the phonemes are the fundamental expectations of the cloning model, they play the role that kinks play. In other words, these two theories are actually identical quantum field theories that they can be solved in that way. The picture in which you think of the kinks as being extended solutions is a perturbative, I mean, you have to set one of the fucking constants with small values in the bosonic theory, and then you get this picture where you have kink minus quantum. Setting it to another value gives you a picture where the fundamental education is component and you can see explicitly what were the kinks to come.

12:30 So that embodies, I think, more or less precisely what I'm trying to say. Saying that you have a certain spectrum of fundamental education and extended solid arms, it's our way of being doing it because we don't have the right. It's important to think of one as being more fundamental than the other, since we know that there's an exact, an identity, you could even know that strongly, that there is a symmetry which tells you that you need to change the laws and truths and treat the magnetic as being fundamental instead of the electric. So neither would really be fundamental. Does that fit in with what you're saying? Yeah, it helps, it helps, yeah. I think, I would only more quickly say that it looks as if, given that example, It wouldn't be perhaps scientific good practice but it would be at least metaphysically possible to say that starting from the fermionic I can, roughly speaking, define myself into the bosonic theory by definition, setting certain parameters. Similarly, vice versa. But, who knows, maybe there's a fact of the matter. Imagine that the world was far more simple and that there was only this quantum field theory, which you call the same theory. One could take the view, well, the best way to interpret this theory is that actually there's only one quantum field theory. Oh, is there going to be? We know the exact solution. No, it would be, that would be arbitrary. To say that, but it would be logically coherent, and then some other people could come and say, well, I have the other interpretation. And they would be empirically equivalent. Because the only real property of the theorem is its exact solution, which we haven't known in that case. And we know what the final perspective is. And it doesn't matter whether you start with the momentum or the burden of the picture. You get the same exact solution and all the experimentally knowable properties are identifiable. And so it's not necessary to say that one is more fundamental than the other. It may be pragmatically important, and certainly in the context of string theory, the hope would be that one of these theories, in perturbation and approximation, is approximately good enough to make contact with physics, because we'd like to make contact with physics, and we have probably enough hope to solve these theories exactly anyway, so that it's better to be true in perturbation. A perturbative approximation which, by its very nature, says that one particular kind of expectation is fundamental.

15:00 That may be a good approximation of what I'm going to do, but it doesn't mean in an intrinsic way that it's really important. That's fascinating. I think it's good for you to come back in a month's time, maybe a year's time. Thank you very much indeed.