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Among the brilliant theorists cloistered in the quiet Woodside campus of the Institute for Advanced Study in Princeton, New Jersey, Edward Witten stands out as a kind of high priest. The only physicist who has won the Fields Medal, first prize in mathematics, Witten is also known for discovering the M theory, the main candidate for a unified "whole theory of all" physics. The genius of a genius, Witten is tall and rectangular, with hazy eyes and an air of being only a quarter attuned to reality until someone moves him away from more abstract thoughts.

During a visit this fall, I saw Witten on the central turf of the Institute and requested an interview; in his quick and loud voice, he said he could not promise that he could answer my questions, but that he would try. Later, when I crossed him on the stone paths, he often did not seem to see me.

Luminaries of physics since Albert Einstein, who lived his days in the same intellectual refuge, has sought to unify gravity with the other forces of nature by finding a more fundamental quantum theory to replace the approximate Einstein image of gravity as curves in the geometry of spacetime. The M theory, which Witten proposed in 1995, could offer this deeper description, but only some aspects of the theory are known. The M theory incorporates into a single mathematical structure the five versions of string theory, which turns the elements of nature into tiny vibrating strings. These five string theories are connected to each other through "dualities" or mathematical equivalences. Over the past 30 years, Witten and others have learned that string theories are also mathematically dual to quantum field theories: descriptions of particles that move through electromagnetic fields and others that serve as the language of the "Standard Model" that reigns particle physics While best known as a string theorist, Witten has discovered many new quantum field theories and explored how all these different descriptions are connected. His physical perceptions have led again and again to deep mathematical discoveries.

Researchers carefully study their work and expect to be interested in them. But despite all its academic influence, Witten, who is 66 years old, often does not disseminate his views on the implications of modern theoretical discoveries. Even his close colleagues enthusiastically suggested questions they wanted him to ask.

When I arrived at his office at the appointed time on a summer summer last month, Witten was not there. His door was ajar. The papers covered his coffee table and his desk, not piles, but floods: text oriented in all directions, some pages near spilling on the floor. (The research papers get lost in the maelstrom when it ends with them, he explained later, and from time to time throws the piles away.) Two girls smiled from a framed photo on a shelf; Children's artwork decorated the walls, one celebrating grandparents' day. When Witten arrived minutes later, we talked for an hour and a half about the meaning of the dualities in physics and mathematics, the current perspectives of the M theory, what he is reading, what he is looking for and the nature of reality. The interview has been condensed and edited for clarity.

** Physicists are talking more than ever about dualities, but they have been studying them for decades. Why is the topic interesting? **

People continue to find new facets of dualities. Dualities are interesting because they often answer questions that would otherwise be out of reach. For example, you may have spent years analyzing a quantum theory and understanding what happens when quantum effects are small, but textbooks do not tell you what you do if the quantum effects are large; You're generally in trouble if you want to know that. Frequently the dualities respond to such questions. They give you another description, and the questions you can answer in a description are different from the questions you can answer in a different description.

** What are some of these newly discovered facets of dualities? **

It is open because there are many different types of dualities. There are dualities between a gauge theory [a theory, such as a quantum field theory, that respects certain symmetries] and another gauge theory, or between a string theory for weak coupling [describing strings that move almost independently from one another] and a string theory for strong coupling. Then there is the AdS / CFT duality, between a gauge theory and a gravitational description. That duality was discovered 20 years ago, and it is surprising to what extent it is still fruitful. And that's largely because about 10 years ago, new ideas were introduced that rejuvenated him. People had new ideas about entropy in quantum field theory: the whole story about "qubit."

The AdS / CFT dualityconnects a theory of gravity in a space-time region called anti-de Sitter space (which curves differently than our universe) to an equivalent quantum field theory that describes the gravity-free limit of that region. Everything there is to know about the AdS space, often called "bulk" since it is the region of greatest dimension, is encoded, as in a hologram, in quantum interactions between particles in the lower dimension boundary. Therefore, AdS / CFT gives physicists a "holographic" understanding of the quantum nature of gravity.

** That is the idea that spacetime and everything that appears emerges as a hologram of information stored in the tangled quantum states of particles. **

Yes. Then there are dualities in mathematics, which can sometimes be interpreted physically as consequences of dualities between two quantum field theories. There are so many ways in which these things are interconnected that any simple statement that I try to make on the fly, as soon as I say it I realize that it did not capture the whole reality. You have to imagine a network of different relationships, where the same physics has different descriptions, revealing different properties. In the simplest case, there are only two important descriptions, and that might be enough. If you ask me about a more complicated example, there could be many, many different ones.

** Given this network of relationships and the question of how difficult it is to characterize the whole duality, do you think that this reflects a lack of understanding of the structure, or is it that we are seeing the structure, only that it is very complicated? **

I'm not sure what we should expect. Traditionally, quantum field theory was constructed starting with the classical image [of a smooth field] and then quantifying it. Now we have learned that there are many things that happen that that description does not do justice. And the same quantum theory can come from different classical theories. Now, Nati Seiberg [a theoretical physicist who works down the hall] will possibly tell you that he has faith that there is a better formulation of the quantum theory of fields that we do not know and that would clarify everything. I'm not sure how much you should expect it to exist. That would be a dream, but it could be too much to wait; I really do not know.

There is another curious fact that you may want to consider, which is that quantum field theory is very central to physics, and in fact it is also clearly very important for mathematics. But it is extremely difficult for mathematicians to study; the way physicists define it is very difficult for mathematicians to follow with a rigorous theory. That is extremely strange, that the world is based so much on a mathematical structure that is so difficult.

** What do you see as the relationship between mathematics and physics? **

I prefer not to give you a cosmic answer, but to comment where we are now. Physics in quantum field theory and string theory somehow has many mathematical secrets, which we do not know how to extract systematically. Physicists can invent things that amaze mathematicians. Because it is difficult to describe mathematically in the known formulation, the things you learn about quantum field theory have to be learned from physics.

I can hardly believe that there is a new formulation that is universal. I think it's too much to wait. I could point to theories where the standard approach really seems inadequate, so at least for those kinds of quantum field theories, one might expect a new formulation. But I really can not imagine what it would be like.

** Can not you imagine it at all? **

No, I can not. Traditionally it was thought that the theory of the interacting quantum field could not exist above four dimensions, and there was the interesting fact that this is the dimension in which we live. But one of the offshoots of the string dualities of the 1990s was that it was discovered that field theories actually exist in five and six dimensions. And it is amazing how much is known about their properties.

** I've heard about the mysterious theory (2.0), a quantum field theory that describes particles in six dimensions, which is dual to the M theory that describes chains and gravity in AdS space of seven dimensions. Does this (2.0) theory play an important role in the network of dualities? **

Yes, that is the pinnacle. In terms of conventional quantum field theory without gravity, there is nothing like it above six dimensions. From the (2.0) existence of the theory and the main properties, one can deduce an incredible amount of what happens in the lower dimensions. A huge amount of important dualities in four dimensions and less are followed by this six-dimensional theory and its properties. However, while what we know about quantum field theory usually comes from the quantification of a classical field theory, there is no reasonable classical starting point for the theory (2.0). Theory (2.0) has properties [such as combinations of symmetries] that seem impossible when you first hear about them. Then you can ask why there are dualities, but you can also ask why there is a 6-D theory with such and such properties. This seems to me a more fundamental reformulation.

** Dualities sometimes make it difficult to maintain a sense of what is real in the world, since there are radically different ways of describing a single system. How would you describe what is real or fundamental? **

What aspect of what really interests you? What does it mean that we exist? Or how do we fit into our mathematical descriptions?

** The last one. **

Well, one thing I'll tell you is that, in general, when you have dualities, things that are easy to see in a description can be hard to see in the other description. So, you and I, for example, are quite simple to describe in the usual approach to physics developed by Newton and his successors. But if there is a radically different dual description of the real world, perhaps some things that physicists worry about would be clearer, but the double description could be one in which everyday life would be difficult to describe.

** What would you say? about the possibility of an even more optimistic idea that there could be a single description of quantum gravity that will really help you in all cases in the real world? **

Well, unfortunately, even if it's correct, I can not guarantee that that can help. Part of what hinders aid is that the description we have now, even though it is not complete, explains a lot. And so it's a bit difficult to say, even if you had a really better description or a more complete description, if it would help in practice.

** Are you talking about the M theory? **

The M theory is the candidate for the best description.

** You proposed the M theory 22 years ago. What are your prospects today? **

Personally, I thought it was extremely clear that it existed 22 years ago, but the level of trust has to be much higher today because AdS / CFT has given us precise definitions, at least in the AdS space-time geometries . I think our understanding of what it is, however, is still very confusing. AdS / CFT and what comes from there is the new main perspective compared to 22 years ago, but I think it is perfectly possible that AdS / CFT is just one side of a multifaceted story. There may be other equally important facets.

** What is an example of something else we might need? **

Perhaps a massive description of the quantum properties of spacetime itself, rather than a description of the holographic boundary. There has not been much progress in a long time to get a better overview. And I think that could be due to the fact that the answer is of a different kind to the one we're used to. That would be my guess.

** Are you willing to speculate on how it would be different? **

I really doubt you can say anything useful. I suppose I suspect there is an extra layer of abstraction compared to what we are used to. I tend to think that there is no precise quantum description of spacetime, except in the types of situations where we know there are, as in the AdS space. I tend to think, otherwise, things are a little darker than an exact quantum description. But I can not say anything useful.

The other night I was reading an old essay by 20th century Princeton physicist John Wheeler. He was a visionary, no doubt. If you literally take what he says, it is hopelessly vague. And, therefore, if I had read this essay 30 years ago, which I could have done, I would have rejected it for being so vague that I could not work on it, even if I was on the right track.

** You mean Information, Physics, Quantum Wheeler's 1989 essay that proposes the idea that the physical universe arises from information, which he called "bit". Why were you reading? is? **

I'm trying to learn about what people are trying to say with the phrase "qubit". Wheeler spoke about "it from bit", but you must remember that this essay was probably written before the term "qubit" was coined and certainly before it was widely circulated. When I read it, I really think I was talking about qubits, not bits, so "it from qubit" is really just a modern translation.

Do not expect that I can tell you something useful about it, about whether it was correct. When he was a beginner graduate student, they had a series of lectures by professors about new students on theoretical research, and one of the people who gave a lecture was Wheeler. He drew an image on the blackboard of the universe visualized as an eye looking at itself. I had no idea what he was talking about. In retrospect, it is obvious that he was explaining what it meant to speak of quantum mechanics when the observer is part of the quantum system. I imagine there is something we do not understand about that.

** Observing a quantum system changes it irreversibly, creating a distinction between the past and the future. So, the problem of the observer seems to be related to the question of time, which we do not understand either. With the duality AdS / CFT, we have learned that the new spatial dimensions can appear as a hologram from quantum information in the limit. Do you think that time is also emergent, which arises from a complete timeless description? **

I tend to assume that spacetime and everything in it are in some sense emerging. By the way, you will surely find that that is what Wheeler expected in his essay. As you will read, he thought that the continuum was incorrect in both physics and mathematics. I did not believe that the microscopic description of a person's space-time used a continuum of any kind, neither a continuum of space nor a continuum of time, nor even a continuum of real numbers. In space and time, I sympathize with that. As for real numbers, I must plead ignorance or agnosticism. It's something I wonder about, but I tried to imagine what it could mean not to use the continuum of real numbers, and the only logical one I tried to discuss with did not help.

** consider Wheeler a hero? **

I would not call him a hero, necessarily, no. I really just noticed what he meant by "it from bit" and what he was saying. She definitely had visionary ideas, but they were too far ahead of her time. I think I was more patient when I read a vague but inspiring essay of what could have been 20 years ago. He also got about 100 references that sound interesting in that essay. If you decide to read them all, you would have to spend weeks doing it. I could decide to see some of them.

** Why do you have more patience now? **

I think that when I was younger I always thought that the next thing I did could be the best thing in my life. But in this moment of life I am less persuaded of that. If I lose a little time reading someone's essay, it does not seem so bad.

** Do you ever forget about physics and mathematics? **

My favorite pastime is tennis. I am a very average but enthusiastic tennis player.

** Unlike Wheeler, it seems that his work style is reaching perceptions through calculations, rather than pursuing a vague vision. **

In my career, I've only been able to make small jumps. Relatively small jumps What Wheeler was talking about was a huge leap. And he does say at the beginning of the essay that he has no idea if this will take 10, 100 or 1,000 years.

** And I was talking about explaining how the physics of information arises. **

Yes. The way he expresses it is broader: he wants to explain the meaning of existence. That was actually the reason why I thought you were asking me if I wanted to explain the meaning of existence.

** I see. Do you have any hypothesis? **

No. Just talk about things you should not do and things you should do to try to get to a more fundamental description of physics.

** Do you have any idea about the meaning of existence? **

No. [Laughs.]

* Correction: This article was updated on November 29, 2017, to clarify that the M theory is the main candidate for a unified theory of everything. Other ideas have been proposed that also claim to unify the fundamental forces. *

* Original story reprinted with permission from Quanta Magazine, an independent editorial publication of the Simons Foundation whose mission is to improve public understanding of science by covering research developments and trends in mathematics and physical sciences and of the life. *

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