It is difficult to find another instance of one physicist dominating a branch of theoretical physics so comprehensively as Edward Witten dominates the study of string theory. A Professor at the Institute of Advanced Study, Princeton, Witten's own work, prior to 1984, on the internal consistency of the various models of the unification of fundamental forces then current, laid the foundation for the paper by Professors Michael Green and John Schwarz that brought string theory centre stage in theor etical high-energy physics. Subsequently he has been at the forefront of the string theory revolution, a one-man powerhouse of ideas and insights in the great revival of string theory in the second half of the 1980s. One of his hallmarks is his ability t o interpret and enormously extend the results or even breakthroughs of other string theorists and place them in the correct overall perspective.
In 1995, Witten's path-breaking paper that drew on the scattered insights of other physicists including India's Ashoke Sen, on the so-called duality symmetries of string theory, signalled the beginning of a new phase in the development of string theory, setting themes and directions that still dominate the discipline. At the Strings 2001 conference in Mumbai, Witten was the same picture of concentration during the lectures as was familiar to those who had attended previous meetings in the series. Despit e his perceptible tiredness at the end of a long working day at the conference, Witten spoke to T. Jayaraman about the successes and future prospects of string theory. Excerpts:
Prof. Witten, you have described string theory as "a piece of 21st century physics that happened to fall into the 20th century". What did you mean by that?
First, I want to tell you that I wasn't the one who said that originally. I always say "it's been said that string theory is a piece of 21st century physics that happenned to fall into the 20th century". I heard the remark from Paolo Di Vecchia (an Itali an theoretical physicist) who attributed it to one of the Italian string theorists from the early 1970s. But I thought that it was a very wise remark so I always used to quote it. What I meant was that string theory was discovered way ahead of its time. It wasn't discovered because anyone had the idea behind string theory.
Nobody understood that in this new framework we could go beyond Riemannian geometry and make a new theory improving over Einstein's theory. Rather by a lucky process of tinkering, physicists who were trying to understand the nuclear force stumbled into s tring theory, which then provided a framework, as it turns out, for understanding quantum gravity and unifying the fundamental forces. But nobody had the concept behind it and I think it was discovered long before the concept would have developed.
If it hadn't been discovered by a lucky accident around 1970, string theory would probably have been eventually discovered sometime in the mid-21st century after the necessary ideas would have emerged. But as it was, physicists discovered string theory and started working on it way before they really had any idea of what maybe makes it work, what theories exist, what is the new kind of geometry that generalises what Einstein used. And so, we've been playing with this theory for 30 years.
Doing our best to learn what's behind it but without fully understanding it to the present day.
As various people have pointed out, we don't even have a fundamental principle behind string theory, an analogue, for instance, of the equivalence principle in general relativity. Despite all the difficulties and the ups and downs of string theory, w hat still makes string theory so compelling to work on? Why pursue string theory?
Well, one thing I can tell you is that if the bits and pieces that we've discovered so far are so beautiful, imagine what it would look like if we actually discovered the basic ideas like the analogues of the principle of equivalence. There are a lot of things that to me make it look like string theory is on the right track. The most basic of course is that string theory forces quantum gravity upon us while the conventional quantum field theory framework for physics makes it impossible to have quantum g ravity. We know that we've got quantum mechanics and gravity so we need a theory of quantum gravity. And string theory is the only real idea.
A hundred years down the road from the discovery of the quantum, do you think that string theory has something new to say about quantum mechanics or is it going to be that quantum mechanics is going to teach us something new about other aspects of our universe?
Well, I still first of all think we don't know how things are going to turn out. But if I had to guess, I would guess that the generalities of quantum mechanics aren't going to change, but that we will understand quantum mechanics better because it will be more fully integrated into our base. In previous theories before string theories, like for example in quantum electrodynamics, the theory of the electromagnetic force, there is a classical theory which you could study classically (so it has a classica l limit) and you can also quantise it.
But you don't feel from that that you've really understood why it had to be quantised. But string theory, although we don't really understand it yet, is I think a theory where the proper understanding is only at the quantum level.
Do we understand why string theory is to be understood properly only at the quantum level? Why is that necessary?
I don't think we understand this properly, but we are seeing the evidence. One bit of evidence is in the duality symmetries which really only exist quantum mechanically. And since they play a very important role in the theory, when you have all these imp ortant symmetries that only exist quantum mechanically then it appears to me that the theory really has to be studied quantum mechanically. If you try to look at it classically, it seems that there are five different string theories plus eleven-dimension al supergravity which are all different theories but quantum mechanically they are all one theory, different limiting cases of one theory.
What progress has string theory made in understanding black holes? What are the challenges that remain?
Where there has been some success is in understanding microscopically what the quantum states of black holes are, in some simple situations where the black holes carry some electrical charges that make things easier. One thing we would like to do is to d o that more generally, more or less with astronomical black holes. But even more fundamental is that we'd like to understand how quantum mechanics works in the full formation and evaporation of a black hole. And that's far from being understood. I would say in general that in string theory we don't understand how to calculate when the fields are strong and the time dependence is big. And that includes the big bang and also black holes.
You have often remarked that when we try to understand string theory properly, we may need to revise radically our notions of space and time. What direction is such a radical revision likely to take?
I don't know of course what the answer is but we see bits and pieces in string theory. For example, even in perturbative string theory, that is when the quantum effects are weak, the notions of space and time become fuzzy because of the way the string is spread out. And that leads to important phenomenon like mirror symmetry, in which two different space-times are equivalent in string theory which you can't have classically. And indeed in quantum dualities, the effects are even more striking.
One of the areas in which you have contributed is the link between the techniques of theoretical high-energy physics and its application to questions in mathematics. You were yourself a recipient in 1990 of the Fields Medal of the International Mathem atical Union, the equivalent of the Nobel Prize in mathematics, probably the only physicist to have received this award. Is there something new that we are seeing in the interaction between physics and mathematics? There has always been some feedback bet ween physics and mathematics but are we, in the development of string theory, seeing a new level of interaction?
I think there is some change. If you went back to the 19th century or earlier, mathematicians and physicists tended to be the same people. But in the 20th century, mathematics became much broader and in many ways much more abstract. What has happened in the last 20 years or so is that some areas of mathematics that seemed to be so abstract that they were no longer connected with physics instead turn out to be related to the new quantum physics, the quantum gauge theories, and especially the supersymmetr ic theories and string theories that physicists are developing now.
At first it seemed that there were just isolated cases when you could link up some bit of theoretical physics with more modern geometry than physicists had known. But then it turned out that it was more than that. And for a number of years it was my main interest really. That is a litte bit less true now, simply because of the fact that in the last five years with these string dualities string theory became so exciting and less directly related sometimes to the mathematics.
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