Filming the Nova Series Musser: My questions fall into a few categories. There’s future-of-string- theory questions, there’s sociological questions about popularization of science, and then I have a few questions about string theory. One thing that I wanted to ask you about—this is the sociological side of things—is that whenever we do an article in physics generally, certainly fundamental physics or cosmology, we run into an intimidation that readers have when they hear the word “string theory” or the word “cosmology,” and they throw up their hands and say: “I’ll never understand it.” Have you dealt with that kind of roadblock that people have in their mind? Greene: Well, I’ve definitely encountered a certain amount of intimidation at the outset when it comes to ideas like string theory or with the features of cosmology. But what I have found is that the basic interest is so widespread, and so deep in most people that I’ve spoken with, that there is a willingness to go a little bit further than you might with other subjects that are more easily taken in. And that fed right into The Elegant Universe. A decision I had to make was, How close to the science am I going to be? There are two kinds of books out there; both serve a great purpose. One is just very general, but gives you a flavor of the subject. The other tries to take you into the subject, again leaving out the math but really tries to give a pretty accurate portrayal of what’s really going on, and I decided to take the latter route, and I found that many people, through the questions that they’ve asked, appreciated that. Musser: I think people said the same thing of Steve Weinberg’s book. Greene: The First Three Minutes? Musser: Yes, The First Three Minutes—that it really took the latter approach. Greene: Oh definitely. Steve’s book is an absolute classic, and I think it’s really been a model for many of us. Musser: So what kind of particular decisions did that bring up for you as you were writing? Did you structure the book differently? Greene: Totally. I structured the book in a way where it was very much like a detective story, where you’re taking clues and ideas at every point on the way in the scientific journey and then subsequently using them for the next step of exploration. I tried to make it so that the diligent reader would have a self- contained account. Basically, every time I introduced a new idea, I would really think through, What does it require to understand this, and have I set up the appropriate scaffolding for that to happen? Whereas, by doing it more generally you know you can always say, “As it turns out” or “People have found,” and you throw it into that vague place. I really tried to do that as sparingly as possible. Musser: I noticed you did have the rough idea and the detailed idea at several points broken out. Greene: Exactly. I found that to be a useful way of going about it, especially in the harder parts. It gives a rough idea and gives the reader permission: If this is the level at which you want to take it in, that’s great, and feel free to skip this next stuff; and if not, go for it. Musser: How do you find things have changed in TV? Or have they? Greene: You mean in terms of trying to get these ideas across in a television context? Well, it is very different, in some ways, because a book can assume that the diligent reader will turn back a few pages to fill in something they may not have gotten the first time around when they recognize they need it later. But TV goes by once. So, there’s a real sense that it has to be something absorbable on the spot, on the fly. And that changes what you could do. It definitely means that the story you can tell is at a somewhat less detailed level, but at the same time it gives us the opportunity to be more entertaining. So, there’s a trade-off, and I think that was part of what the challenge of the whole series was—to find the appropriate balance between entertainment and science and a level at which science could be presented and so absorbed. Musser: Did your thinking on that evolve as the series took shape and as you talked with the producers? Greene: Yeah, definitely. I was fairly diligent all the way through; even small scientific bends of the facts, I examined really carefully to see whether I was going to stay with them. But I would say by the end of the program, or the end of the constructing of the script of the program, the balance was much more clear to me about what you could do on television. Part of it came from looking at small rough cuts and realizing, You know what, I just had too many words in that description and it’s too much. You just can’t take it in. And the shorter, punchier one, which I thought perhaps would be too quick, in television, it was actually more than enough to get the idea, because you are not just dealing with the words. You’re dealing with images, you’re dealing with sounds, you’re dealing with a continuous story that you’ve been watching and that does allow you to take in things more quickly. And I didn’t really realize that until getting my hands dirty with the process. Musser: So you would redo scenes? Greene: We would often do scenes a couple of different ways. The director would say, “Here’s what I think would work,” and I’d be like, “No, I think it needs a little more than that,” and we would do it both ways, and always he was right. Musser: That’s their job, I guess. I think at one point, in one of our discussions some months ago, you mentioned that TV is a lot different from being on stage or in front of a classroom. What are some of the differences in the way you had to present yourself? Greene: You know, when I give a lecture, part of the enjoyment and part of the energy comes from a kind of interaction with the audience. Not a direct one—I rarely do back-and-forth exchanges until question-and-answer period, but you just feel the audience’s reaction, the energy in the room. Whereas when you’re filming for television, there’s just you and the director and the camera. You’ve got to generate the energy from a different place. And I guess everybody has their way of doing that. After working on the program intensively for a few days, a couple of weeks, I began to find my own ways as well. But it was definitely a different experience to stare into the blank eye of a camera, as opposed to the life of an audience. Musser: Was that also something you had to iterate through? Greene: Yeah, I found that after we had done a bunch of shooting, the early stuff, in the first few days, I didn’t like. I had yet to find a rhythm, and so we redid it. And that’s something you can also do that you can’t do in a live situation. So in that way, it’s forgiving. I like to say things more than one way. Sometimes people have said that makes me wordier than them, but I feel that with a hard idea, you want to say it like this, and you want to say it like that, and you want to tell it like that, and after you hear it three different ways, the fourth way really solidifies it. That does not work on TV. On TV you’ve really just got to say it right the first time and just find the right way to do it, and that’s it.

Seeing Things From Different Perspectives Musser: When you’re teaching, do you try to say it in various ways? Greene: Constantly. I just think that when it comes to abstract ideas, you just need many roads into them and if you stick with one road from the scientific point of view, I think you really compromise your ability to make breakthroughs. I think that’s really what breakthroughs are about. Everybody’s looking at it one way and you come from the back. You’re getting to the same idea, you’re just getting there differently, and that different way of getting there somehow reveals things that the other approach didn’t. Musser: What are some examples you’ve encountered of that take-a-back- door approach? Greene: Well, probably, the biggest ones are Ed Witten’s breakthroughs, and that’s his style. Just to tell you an example, in the second superstring revolution, the idea of branes was out there for a long time. A bunch of guys were pushing it, and nobody was listening. Ed came along and he put things together. He just walked up the mountain and looked down, and saw the connections that nobody else saw, and that way united the five string theories that previously were thought to be completely distinct. It was all out there; he just took a different perspective, and bang, it all came together. And that’s genius. Musser: In your own learning, as you puzzle through different fields over the course of your career, do you also find that you need those different entrances to a subject? Greene: Yeah. In just about every significant breakthrough that I’ve been fortunate to be involved with, I’d say it was a matter of putting together things that were already there, and just seeing them differently. For instance, on the stuff I’ve done on topology change a while ago, it was in the air. People had thought about various pieces of the story, and in retrospect, you can say to yourself, I wonder why so-and-so didn’t get there first, because they were so close. And it really is that if you don’t think about it the right way, you miss a significant connection. In fact, I remember, as we were writing that particular paper, Andy Strominger, Dave Morrison, and myself, we were like, My God, we’ve got to get this out tomorrow because there’s so many others who are so close to this idea and they just haven’t quite made that final link. Musser: That worry about someone else getting there first happened with Einstein and David Hilbert, too. Greene: That was a somewhat complicated story, because they’d interacted and communicated various aspects, and Hilbert then went off and did various things. But yeah, once something is in the air, I think there are a lot of people who can snag it and turn it into a great piece of work. To me that suggests what a fundamental discovery is. The universe in a sense guides us toward truths, because those truths are the things that govern what we see. If we’re all being governed by what we see, we’re all being steered in the same direction. Therefore the difference between making a breakthrough and not often can be just a small element of perception, either true perception or mathematical perception, that puts things together in a different way. Musser: Do you think that a lot of these discoveries would have been made without the intervention of genius? Greene: Well, it’s tough to say. In the case of string theory, I think so, because the pieces of the puzzle were really becoming clearer and clearer. It may have been five or 10 years later, but I suspect it would have happened. When you go to something like relativity—well, special relativity was really in the air. In fact, people like Lorentz and Poincaré essentially had the equations of special relativity. They were just interpreting them in what we believe today to be the wrong way. It was Einstein’s genius to see them in a way that nobody else had—as an effect of space and time, as opposed to being some kind of mechanical effect on measuring equipment. So, I think at some point somebody would have gotten that idea. But general relativity, I don’t know. General relativity is such a leap, such a monumental rethinking of space, time, and gravity, that it’s not obvious to me how and when that would have happened without Einstein.

The Guiding Principles of String Theory Musser: Are there examples in string theory that you think are analogous to that huge leap, or are we still waiting for that leap? Greene: I think we’re still waiting for a leap of that magnitude. It’s a very different subject, string theory, in that it has not sprung forth out of some miraculously new thought that has steered us in a completely new direction and resulted in string theory. Instead, string theory has been built up of a lot of smaller ideas that a lot of people have contributed and they’ve been slowly stitching together into an ever more impressive theoretical edifice. But what idea sits at the top of that edifice, we still don’t really know. When we do have that idea, I believe that it will illuminate the edifice; it will be like a beacon shining down, it will illuminate the edifice in a way that we have previously been unable to do, and it will also, I believe, give answers to critical questions that remain unresolved. Musser: That brings up a question I wanted to get into, so it segues nicely. In the case of relativity, you had the equivalence principle, general covariance, in that beacon role. In the Standard Model, it’s gauge invariance. I think in the book you suggested the holographic principle could be that principle for string theory. What’s your thinking on that now, or what other principles might fill that role? Greene: Well, the last few years have only seen the holographic principle rise to a yet greater prominence and believability. Back in the mid-’90s, shortly after the holographic ideas were suggested by t’Hooft and Susskind, the supporting ideas were rather abstract and vague, all based upon features of black holes. Black-hole entropy resides on the surface; therefore maybe the degrees of freedom reside on the surface; therefore maybe that’s true of all regions that have a horizon; maybe it’s true of cosmological horizons; maybe we’re living within a cosmological region which has its true degrees of freedom far away. Wonderfully strange ideas, but the supporting evidence was meager. But with the work of Maldacena, where he found an explicit example within string theory, where quite literally in that hypothetical world, physics in the bulk—that is, in the arena that we consider to be real—would be exactly mirrored by physics taking place on a bounding surface. There’d be no difference in terms of the ability of either description to truly describe what’s going on, yet in detail the descriptions would be vastly different. One would be in five dimensions, the other in four. So, even the number of dimensions seems not to be something which you can count on, because there can be alternative descriptions in different numbers of dimensions would accurately reflect the physics you’re observing. So, to my mind that makes the abstract ideas now concrete; it makes you believe the abstract ideas. And even if the details of string theory change, I think that, as many others do—not everyone though—I suspect that the holographic idea will persist and will guide us. Whether it truly is the idea, I don’t know. I don’t think so. But I think that it could well be one of the key stepping stones towards finding the essential ideas of the theory. Musser: Do any other principles in the works have the ring of a true idea or a proto-true-idea? Greene: I’d say the holographic principle is the closest, again because it’s an idea that steps outside the details of the theory and just says, Here’s a very general feature of a world that has quantum mechanics and gravity. That’s the kind of idea you want. Now, Einstein stepped outside. His idea, that gravity and acceleration are equivalent—it’s a very general idea, independent of details of what’s creating the acceleration, what’s creating the gravity—it’s just a very general principle, and from that, whoa, look at what follows: the general theory of relativity. So you need something, I think, which is very big and very much independent of details, and that’s the kind of principle that the holographic principle is.

String Theory and Quantum Mechanics Musser: What do you think that guiding principle is for quantum mechanics? Or is there one? Greene: Well, I guess you could say the uncertainty principle. It basically says that things that you thought constituted reality—the position and the velocity of particles—is not truly what reality is. Reality is half of that. Reality is half of those features that you previously thought to truly constitute the universe at a given moment in time. Or, even more generally, you could say the principle of complementarity—that the things that a classical person would have in mind as constituting reality are far beyond what the universe actually can attain. You have complementary features, half of which are in that list, and the other half of which are in that list as well, but you can’t have both of them at the same time. That’s the new idea; that’s the break between quantum and classical physics. Musser: Now, those are incorporated into string theory, by virtue of it being a quantum theory. Greene: Yeah, string theory basically takes quantum theory on board without change, and that’s good and bad. It means the successes of quantum theory are part of string theory, but it also means that the mysterious elements of quantum theory are not resolved by string theory. Now, again, these are not errors. There’s nothing wrong with quantum theory. But there are features of the theory which are so mind-bogglingly weird that you wish you had a better intuitive grasp on them, or you wish you had a new way of looking at them that would make you a little more comfortable with how strange these features are. String theory doesn’t do that. Musser: What particular features of quantum physics really stand out? Is there a number-one mystery? Greene: So-called quantum entanglement—this idea that widely separated particles or objects can have features that are somehow correlated with one another. A way of describing it I like to use is: If you had a pair of magical dice, where if you throw one die in Nevada and the other in New York, each picks out the number that it lands on randomly and independently, but yet according to quantum mechanics they pick out the same number—somehow, even though they’re both operating ostensibly independently of one another. That’s a very strange idea, but it’s borne out by experiments. Is there a way of thinking about that that makes it a little less mind-bogglingly odd? I don’t know. It’d be nice if string theory could shed light, but it hasn’t. Musser: You think there’s a potential that it will? Greene: Well, there is a chance that string theory could help us understand the mysteries of quantum mechanics, because, again, it’s what we were talking about before—having different ways of looking at one and the same thing can shed light on previous unresolved mysteries. In this particular case, string theory does admit so-called dualities, where one and the same physical system can be described by many different mathematical frameworks. You have five string theories. Each can describe one and the same physics from five different angles, five different windows. It turns out that for certain descriptions which are highly dependent upon quantum physics, there are dual, mirror, alternative descriptions where quantum physics doesn’t play a substantial role. So that at least gives you the chance of taking one physical situation, which seems to manifest the weirdness of quantum physics, from one point of view, and maybe translate it into another description where the weirdness of quantum mechanics is not playing a significant role. Musser: It would be more of a classical system, like Newtonian mechanics? Greene: In principle. This idea really hasn’t been realized in any particularly concrete or interesting ways as yet, as far as shedding light on quantum mechanics goes, but it might.

String Theory and Relativity Musser: A related topic that has interested me is the precise relationship between string theory and general relativity. We hear that GR falls out of string theory, but is the general covariance still there? Are the basic ideas of relativity in there, or how are they modified? Greene: Right. General relativity does fall out of string theory, and the way it does is particularly interesting, and it’s really the way the theory was discovered to be a theory of quantum gravity. Namely, people were studying string theory, John Schwarz and Joël Scherk and others, and they found that one of the string vibrational patterns was a massless particle that had spin 2. At first, everyone was like, Oh, that’s unfortunate, because that’s not part of the so-called strong interaction that they’d hoped string theory would describe. But then there was a brainstorm, where it was thought, Well, there is another massless spin-2 particle that comes out of attempts to quantize gravity, to quantize general relativity. The graviton has just those properties. Then it was thought, Well, maybe this is not just a theory of the strong force, maybe this is a theory of gravity, because one of the vibrational patterns has those properties. When you then study the equations further, you find that that particle, that vibration of strings, is described by none other than Einstein’s equations. You find Einstein’s equations within string theory when you study the physics of this particular vibrational mode. And indeed, you do have general covariance; you do have the basic equations of general relativity. However, string theory modifies them, because now general relativity is sitting inside a larger theoretical framework—string theory—and you find that Einstein’s equations are the lowest-order approximation to the string version of the physics of this vibrational mode, and there are additional terms. You can write down those additional terms. So you have Einstein’s equations plus new stuff. And that’s what comes out of string theory. In fact, I had a student—a high-school student who was writing one of these Intel science-research projects—and I had her use those additional terms to calculate how the bending of starlight by the sun would change. Of course, I knew that it would be minuscule, even smaller than other kinds of quantum effects which would actually dominate if were actually looking for this stuff. You can do this calculation, and the answer is tiny—maybe a one part in 1090 deviation. But the point is, string theory does change general relativity. General relativity does get changed when it is incorporated in this quantum-mechanical version. Musser: One thing that is confusing about this, though, is that the Einstein’s equations are the equations for generally covariant gravity. So what do those additional terms represent physically? Where are they coming from? Greene: They’re coming from the fact that a string is not a point. A string is an extended object. General relativity is based on Riemannian geometry, developed in the 19th century, and a key thing in Riemannian geometry is that you have space being described as a so-called manifold. It’s described as a geometrical space, in looser language, which itself is composed of little points. So the fundamental entity, if you will, of general relativity is the point. String theory says: Forget points. This theory does not have the physical realization of that mathematical idea of points. It has these little loops. And because of this little change from points to loops, the equations suffer a little change—roughly speaking, proportional to the size of the loops. If the loop size goes to zero, the additional terms get dropped out perfectly. And mathematically, Einstein’s equations are based on curvature, and these new terms involve curvature squared, or curvature to the fourth. Musser: If you were to forget string theory and reformulate relativity in terms of noninfinitesimal points, would you arrive at a similar set of corrections? Greene: In principle, you could. I think ultimately, though, you’d just be reinventing string theory. That would be my guess. It’d be hard to really know what the rules of the game would be unless you were also thinking quantum mechanically, and then that would lead you to strings. So I suspect there are many roads to the same theory, but ultimately you’d be reconstructing string theory.

String Theory and Other Theories of Quantum Gravity Musser: Actually, maybe this is a good point to talk a little bit about loop quantum gravity and some of the other approaches to quantum gravity. Greene: A subject which I know something about, but certainly many people are much more expert than I am. Musser: You’ve always described string theory as the only game in town when it comes to quantum gravity. Do you still feel that way? Greene: Well, I think it’s the most fun game in town when it comes to quantum gravity, but to be fair, the loop-quantum-gravity community has made tremendous progress. Wonderful progress. There are still many very basic questions which I don’t feel that they’ve answered, not to my satisfaction. But it’s a viable approach, and it’s great there are such a large number of extremely talented people working on it. My hope—and it has been one that Lee Smolin has championed—my hope is that ultimately we’re again developing the same theory from different angles. So maybe that’s the theme of what we’re talking about here. It’s far from impossible that we’re going down our route to quantum gravity, they’re going down their route to quantum gravity, and we’re going to meet someplace. Because it turns out that many of their strengths are our weaknesses. Many of our strengths are their weaknesses. Musser: For example? Greene: Well, for instance, one weakness of string theory is that it’s so-called background-dependent. We need to assume an existing spacetime within which the strings move. You’d hope, though, that a true quantum theory of gravity would have spacetime emerge from its fundamental equations. They, however, do have a background-independent formulation in their approach, where spacetime does emerge more fundamentally from the theory itself. On the other hand, we are able to make very direct contact with Einstein’s general relativity on large scales. We see it in our equations; at the same, we see the deviations. They get larger and larger when you look smaller and smaller. They have some difficulty making contact with ordinary gravity as described by general relativity on large scales. So, naturally you’d think maybe one could put together the strengths of each, and that’s where progress could be made. And then that may be the answer. Musser: Has that effort been made? Greene: Slowly. There are very few people who are really well versed in both theories. And these are both two huge subjects, and you can spend your whole life, every moment of your working day, just in your own subject, and you still won’t know everything that’s going on. So there’s a certain kind of hesitancy to then try to take on yet another subject, although many people are heading down that path and starting to think along those lines, and there have been some joint meetings where you have people from both communities talk about these ideas. So I think that you’ll see more interaction as time goes by. Musser: What about some of the other, more dark-horse candidates for quantum gravity? Like twistors. Greene: Twistors historically have played a significant role in some of the loop-quantum-gravity ideas, so I don’t know that an independent approach based solely on those ideas is one that is being pursued by a great number of people. But the ideas are wonderful. I guess there are some of these other, more condensed-matter approaches. I can’t say that I’ve looked at them too closely. On a cursory glance, it looks interesting but needs a significant amount of development before I would be convinced that it really had the potential to reach the goals that it has set for itself. Musser: You mention the background-dependence of the theory. Is that also true of some of the nonperturbative approaches that people have gone after? Greene: Yeah. One way or another, it seems that the background-dependence is still there. People are working hard to try to extract the essence of the theory and formulate it in a way that would not have this shortcoming, but I say it’s fair to say that it really hasn’t been done. We’re tethered to an approach which may in its very nature obscure the true underlying essence of the theory. In essence, it makes the mathematics very specific—specific to a particular spacetime, whichever one that you’re working around. And if we could remove that specificity, that may allow us to take that step back, remove the details like we were talking about earlier, and just see the ideas in their pristine form.

String Theory and the Nature of Space and Time Musser: If you have this background-dependence, what hope is there to really understand, in a deep sense, what space and time are? Greene: Well, you can chip away at the problem. For instance, even with background-dependence, we’ve learned things like mirror symmetry—there can be two spacetimes, one physics. We’ve learned topology change—that space can evolve in ways that we wouldn’t have thought possible before. We’ve learned that the microworld might be governed by noncommutative geometry, where the coordinates, unlike real numbers, depend upon the order in which you multiply them. So you can get hints. You can get isolated glimpses of what’s truly going on down there. But I think without the background-independent formalism, it’s going to be hard to put the pieces together on their own. A background-independent formalism will set the frame within all this stuff sits and without that frame it’s really tough to put the pieces together. Musser: Maybe we can march down some of those ideas, though, and here you can shed some like about what they’re specifically telling us about in terms of the fundamental nature of space and time. Greene: Well, it’s hard for me to go beyond the actual results themselves. The way I like to think of it is, Newton gave us the first idea, or one of the first ideas, of what space and time were: absolute, unchangeable structures. They are, period. They exist. Einstein comes along and says, Well, that picture needs to be modified. Here’s what space can do: it can warp and wiggle. Here’s what time can do: it can change the rate at which it ticks away. Strange and wonderful new ideas. The old ideas of Newton are now morphed into the more sophisticated and refined ideas of Einstein. String theory then comes along and says, Well, those ideas of Einstein are wonderful when you’re looking at big scales, but on smaller scales, things seem to be a bit different. What are the differences? Well, we’ve come upon some of them. Ideas of mirror symmetry: Einstein said, The geometry of space is tightly tied to physics. If the geometry is different, physics is different. Now we say, Well, actually, the geometry can be like this and like that, in different ways, and physics can be identical. Hmm, that’s weird, but it seems to emerge from the microscopic modifications to general relativity that string theory provides. Einstein says, Well, space can stretch and morph, but it’s really hard to rip; the equations seem to break down. String theory says, Whoops, when the rip is really small, the equations of string theory modify the physics so that it can rip in such a way that makes perfectly good sense. So it’s as if we have a painting of space and time. Newton’s was a blank canvas; Einstein lets the canvas warp and wiggle. String theory comes along and now lets the structure of the canvas have a much richer repertoire of behaviors compared to what you think they’d have from examining space on large scales. So you ask me, OK, now tell me what the true theme of that painting is. I don’t know. I can make an accounting of the new ways in which it can behave, but I don’t know what they add up to. What do they add up to? I don’t know. Musser: The mirror symmetry, unless I’m misunderstanding, is incredibly profound, because it divorces the geometry from physics, and that was always the Einsteinian and John Wheeler-type of program. Greene: That’s right. Now, it doesn’t divorce it completely. It simply says that you’re missing half of the story. Geometry is tightly tied to physics, but it’s a two-to-one map. It’s not physics and geometry. It’s physics and geometry- geometry, and which one you want to pick is up to you. Sometimes using one geometry gives you more insight than the other. Again, different ways of looking at one and same physical system. Two different geometries, and one physics. And people have found there are these mathematical questions about certain physical and geometrical systems that people couldn’t answer using the one geometry. Bring in the mirror geometry that had previously gone unrealized and, all of a sudden, profoundly difficult questions, when translated, were mind- bogglingly simple. Amazing. Musser: Another example of this back-door approach. Greene: Yeah, exactly. You know, for the mathematicians, it was quite a shock. I remember, in the ’90s, when we had this wonderful meeting at Berkeley—I wrote about this in the book, The Elegant Universe—where you know mathematicians and physicists got together, because the physicists were claiming that they could solve mathematical problems of the counting of the spheres. And mathematicians just couldn’t do it. Physicists were saying, not only can we do it, we can count variations on the spheres that you wouldn’t even dare to think about mathematically. And we can do it with the push of a button on a computer using the mirror symmetry of string theory. And it turns out that the physics was right. A total back-door approach. Musser: How much of these kinds of shifts in thinking that topology can change come from this idea that space is not a set of infinitesimal points—that there is some finite dimension to those basic entities? Greene: Well, it is basically that. But the way I would say it is: To change topology from a classical geometrical point of view would require punching a hole in the space, ripping it apart, and then regluing it together. String theory basically says that even though mathematically punching a hole seems to be very difficult to make sense of—the equations break down—string theory smears out the hole. It takes the points and says, Well, actually, there aren’t really points. It broadens it out, it smears the edges in a way, and it softens the potentially disastrous mathematics in that way. So overall, it’s very much tied to the fact that there are extended objects in the theory. Without the extended objects, it’s hard to see how it would be possible that this would apply. Musser: Coming from the Wheelerian and Einsteinian perspective, I’d always thought that if we were to have some kind of theory out of which space and time emerge, some kind of timeless, spaceless formulation, it would have to somehow be geometric. But does the mirror symmetry cast doubt on that idea? Greene: No, I don’t think so at all. Mirror symmetry says that geometry is more rich in its ability to describe physics than we previously had thought. We previously thought that there was this lockstep relationship, but in fact the geometry is somewhat more fluid, giving you more freedom in the way you describe things geometrically. But nor do I think that mirror symmetry has yet given us any insight into what the spaceless, timeless formulation would be. I don’t think anything’s really given a clue as to what that would be. I don’t even think we have the language yet to really say, from string theory’s point of view, what that would be. It’s really hard to know. I think we do need a radical new idea, which would have no glimmers of space and time within it, yet would be sufficiently robust that it could be a starting point for a unified theory of this sort. I can’t even explain it. I want to say, “As the theory evolves,” but you have to have time for something to evolve—so it’s even hard to phrase what I’m talking about in the English language. But space and time would be one particular way that that theory could manifest itself. It would be one particular kind of solution to the theory’s equations. But there’d be other solutions where there’d be no space and time in those solutions. Now, maybe those would be abstract solutions with no bearing to the world, or maybe there’d be other universes where space and time just don’t exist. What would that universe be like? I don’t know. I have trouble even thinking about it. I don’t know how to think about it—something without a space and time. I can say the words and I sort of know what I mean, but I don’t have a picture.

Noncommutative Geometry Musser: You had mentioned noncommutative geometry a little bit earlier during our conversation. Can you describe that a little bit? Greene: Well, basically, since the time of Descartes, we’ve found it very powerful to label points, either on Earth by their latitude and longitude—by their coordinates—or points in three-space by their three Cartesian coordinates, x, y, and z, that you learn in high school. And we’ve always imagined that those numbers are like ordinary numbers: 3, 2.7, 5.9. Numbers which have the property that, when you multiply them together—which is often an operation you need to do in physics—the answer doesn’t depend on the order of operation: three times five is five times three; two times seven, seven times two. What we seem to be finding when we study the physics of string theory is that when you coordinatize space on very small scales, the numbers involved are not like threes and fives, which don’t depend upon the order in which they’re multiplied. There’s actually a new class of numbers, if you will, that do depend on the order of multiplication. They’re actually not that new, because for a long time we have known of an entity called the matrix. A matrix is a collection of mathematical numbers with a well-defined notion of how you multiply two matrices together. But, sure as shooting, matrix multiplication depends upon the order of multiplication. A times B does not equal B times A if A and B are these matrices. String theory seems to indicate that points described by single numbers are replaced by geometrical objects described by matrices. And noncommutative geometry would describe the geometry of these entities. Now, you say to yourself, Well, how do I recover ordinary geometry on big scales? Well, wonderfully. On big scales, it turns out that these matrices become more and more diagonal, and diagonal matrices do have the property that they commute when you multiply. It doesn’t matter how you multiply A times B if they’re diagonal matrices. So, the proposal is that everything that we know about is a large-scale manifestation of noncommutative geometry, in which things approximately, to a high degree of accuracy, commute. But then if you venture into the microworld, the off-diagonal entries in the matrices get bigger and bigger and bigger until way down in the depths, every one is roughly the same magnitude, and then geometry has to be noncommutative. These off-diagonal pieces are there and playing a significant part. That’s the basic idea. Musser: How does that change the function of geometry on those scales? Greene: Noncommutative geometry is a whole new field of geometry that some people have been developing for years without necessarily an application of physics in mind, although some applications have been thought of. The French mathematician Alain Connes has this big thick book called Noncommutative Geometry, and he’s developed the whole theory. Euclid and Gauss and Riemann and all those wonderful geometers were working in the context of commutative geometry, and now Connes and others are taking off and developing the newer structure of noncommutative geometry. Now, in that big thick book that he has, it’s not obvious to me which elements are truly relevant to string theory. Some seem to be, and some, it’s not so clear. So how much of this structure will string theory truly make use of, I’m not sure. But it seems quite plausible that noncommutative geometry will be the right language for describing very small things. Musser: It is baffling to me—maybe it should be baffling—that you would have to label points with a matrix or some non-number, some non-pure number. What does that mean? Greene: I wouldn’t quite think about it that way. I think the way to think about it is: There is no notion of a point. A point is an approximation. If there is a point, you should label it by a number. But the claim is that, on sufficiently small scales, that language of points becomes such a poor approximation that it just isn’t relevant. And so you say, How does this all comes about? It turns out that the massless particles of string theory and M-theory are really the correct substitute for the idea of points. When we talk about points in geometry, we really talk about how something can move through points. It’s the motion of objects that ultimately is what’s relevant. Their motion, it turns out, can be more complicated than just sliding back and forth. Sometimes they can move apart relative to each other and so forth and all those motions are captured by a matrix. So, rather than labeling an object by what point it’s passing through, you need to label its motion by this matrix of degrees of freedom. Now, on very large scales, the matrix becomes diagonal and the only motion that matters is the familiar motion through points. Musser: By large scales, do you mean large amounts of motion? Greene: I mean large scales relative to, say, the Planck scale. So when you’re not analyzing with such an incredibly fine microscope—you’re just looking at objects through a more broad picture where you can’t see anything smaller than, say, the Planck length—then points matter, the matrices become diagonal, and the diagonal entries are the coordinates. But on very small scales, the kind of motion is far richer than just what you would know about on large scales, and you need a matrix to describe what’s really going on. Musser: So instead of just going to point A to point B, you take some complicated path. Greene: Yeah. And then if you go there, these guys move slightly relative to each other, and so forth. Musser: Are these ideas of noncommutative geometry informing string theory as it’s being practiced today? Greene: To some extent, yeah. It’s a highly mathematical subject, so not everybody has been able to take it in yet, but a certain branch of the subject is definitely being driven by these ideas. Whether that branch is going to be the one that ultimately sits on top of the edifice, or whether it’s the spotlight illuminating one stairway up to the top, it’s really hard to say. Musser: Have any particular new results come out that stick in your mind from this union of math and physics? Greene: It turns out that people talk about things like the fuzzy sphere. The fuzzy sphere, in some sense, has got the ordinary sphere you’re familiar with from elementary school. But then when you express what that looks like in the context of noncommutative geometry, noncommutativity fuzzes it out in some well-defined mathematical sense. So it does give a whole new way of thinking about familiar ideas in a new context, but I can’t say yet for sure that it’s entered truly fundamental questions in string theory. Maybe it will. Musser: Is it another case where physicists and mathematicians have to stay up until 11 o’clock at night, tutoring each other, as you discuss in The Elegant Universe? Greene: It’s not quite as bad, I think, as some of the algebraic geometry that we needed back in those particular problems. But yeah, it’s a big, intimidating subject of mathematics that you need to inhale if you’re going to pursue these kind of ideas.

Life on a Brane Musser: So what are some of the ideas of space and time you’re developing in the new book? Greene: Well, when I was writing The Elegant Universe, the main theme was the search for the unified theory. But there were these two noisy characters that kept trying to get all the attention, and they were space and time. And they did a lot of attention, because the search for unification involves extra dimensions. It involves strange ways in which space can evolve—dualities, R-goes-to-1/R dualities and weird things like that. But space and time really didn’t get their due, and in this book, they’re the main characters. And the book really asks more fundamental questions about them, like: Is space a real thing? Is time a real thing? Where did the features that we experience intuitively about space and time—in particular, the flow of time, second following second following second; the arrow of time, the fact that time seems to go one direction and not the other—where did these experiential features of space and time come from? Can we find them in the laws of physics? And in searching for them in the laws of physics, what do we learn about the universe? Then when you try to search for the answers, as I develop in the book, it takes you very naturally to the field of cosmology. In trying to seek the origins of space and time, you wind up seeking the origin of the universe, and when you try to seek the origin of the universe, you’ve got to talk about inflation and the wonderful things in big-bang cosmology, but ultimately you get stuck because of the conflict between general relativity and quantum. It takes you back to string theory, back to M-theory, and now the cutting ideas in M-theory are suggesting new kinds of cosmology: braneworld cosmology, which is a fantastically interesting idea. Space really becomes a something in the braneworld. It’s an entity in the theory, the brane on which this is all taking place. So, basically, this new book traces space and time from Newton through ideas of Mach, who had his own impact on Einstein in terms of whether space was a real object or just an abstract idea, through Einstein’s developments, through the impact of cosmology on ideas of space and time, through the impact of unified theories like string theory and M-theory on space and time, and finally to fun stuff like teleportation through space and travel through time, and then I end by giving a more detailed description of the holographic principle as perhaps really the next step in the spacetime story. Musser: There’s a lot there to talk about. A lot of the physics you talk about in your first book is the physics of the compactified spaces, the geometry of Calabi- Yau spaces. How is that whole approach modified by the idea that maybe we’re stuck on a brane? Greene: Well, it’s modified in a couple of ways. First, certain aspects of the physics you see on a brane are governed by properties of the brane itself. So, for instance, if you have a bunch of branes on top of each other, then physics is different than if you have one brane separately. So, for instance, one of the things that I describe in The Elegant Universe is how the extra dimensions, by affecting the vibrational patterns of strings, can dictate the kinds of particles that you might observe. In the braneworld scenario, the number of branes that are stacked on top of each other can affect the number of massive particles. Roughly speaking, if you have an open string stretching from one brane to another, when the branes go on top of each other, the string is very small and its mass goes down. So, the more branes you stack, the more varied light [that is, lightweight] particles you’d expect. If you have branes that are intersecting each other, and you have strings going from one to the other, the angle between the branes can affect the kinds of particles that you’d see. So, in a nutshell, the branes themselves play a very important role in the kinds of low-energy particles that you might see. Now, the extra dimensions can still play a powerful role as well, because these branes still exist in a universe of 10 or 11 spacetime dimensions, depending on how you’re thinking about things, and you have to say something about those extra dimensions. Now, in some formalisms, the extra dimensions play less of a role, because you imagine that the branes are fairly insensitive to the space around them, because everything is stuck to the brane, so they don’t probe the extra dimensions so much. But there are other approaches in which you still imagine that the extra dimensions are curled up into a small space, one of these Calabi-Yau spaces, and then the physics you observe on the brane is partly dictated, much as it was in the older times, by the shape of the extra dimensions. So, I’d say that it now fits into a broader framework in which low-energy physics is dictated by geometry more broadly defined—the geometry of the extra dimensions and the geometry of the brane configuration. Musser: Are we still thinking of those extra dimensions as being compactified, or could they be infinite? Greene: In some formulations, they can be infinite. But they need to be curved in a very specific manner, so it becomes somewhat of a choice of language as to whether you want to think of them as being truly infinite or not, because if something curves steeply, just one region of that space is at all relevant. But in terms of the mathematics, yes, you can imagine that these extra dimensions are not compactified. Musser: Do you still get the R-to-1/R duality, the winding mode/vibrational mode trade-off? Greene: It’s definitely there. It, in fact, drives part of the subject. Part of the reason why people were led to branes was a puzzle having to do with R-goes-to- 1/R symmetry. If you think about it, R-goes-to-1/R symmetry works well for closed strings, because on a circle, they can either be little loops on the circle or wrap around the circle, and the duality between R-goes-to-1/R winds up exchanging the strings that wrapped around the circle and the ones that didn’t. What if you have an open string? It can’t wrap around a circle; it’s got no ends. So, if you have a theory that has both open and closed strings, and you take a circular dimension and you make it very small, the closed strings will still see it, because by R-goes-to-1/R, when you make it really small, it’s the same as making it really big. But the open strings won’t see it, because they don’t have this R-goes-to-1/R symmetry, so if you make it really small, it kind of disappears; they’re insensitive to it. Does that mean you have open strings living in one dimension less than the dimension of the closed strings? What do you do? And the answer is the branes—the idea that the open strings have end points that are stuck in certain regions, the brane. So in a sense they can live in a higher- dimensional space but not see the other dimensions. The closed strings see all the dimensions, but the open strings might not, because their ends are stuck. They’re not able to explore the totality of the space, and that’s the way in which they live in a lower-dimensional space even though the closed strings live in a higher- dimensional space. And that’s the resolution to how R-goes-to-1/R persists in this more complicated realm. Musser: Now, what does the braneworld view of space and time tell us about the big questions you were bringing up about space and time—is it a substance, is it a thing? Greene: Well, from a real concrete point of view, if you’d go back to Newton’s time, people were worrying, Does space exist? Newton says yes. Leibniz says no. Within string theory, if the braneworld scenario is right, the three dimensions of space that we know about would be a three-brane—a real honest-to-God physical entity within the theory. No ifs, ands, or buts—it’s really a thing. And the four-dimensional spacetime that that brane sweeps out would be the world volume of this brane; it would be a real thing. Of course, you could then say, But what about the larger spacetime within which that entity lives? Is that a real thing? No real answer to that, but it feels that that question is now one step removed, because if we’re truly living on a brane, we can hardly probe off of it, so it doesn’t bake your noodle quite as much. Because the thing that you experience would be real, and this other thing that you don’t experience, well, you wouldn’t be able to say much about it. The thing that is puzzling about Newton is: You experience space. We see it around us; we move within it. So it seems like it’s a something, but then you scratch your head and say, But what is it? You can’t seem to get your hands around. But within string theory, at least, the theory would tell you, Well, here’s what it is. It’s a thing, and there are others of them in the theory, too. There are other branes here, there are other branes here, and they’re part of the ingredients of the theory. Musser: So what is this brane, at some level? Can you enumerate the properties? Greene: It’s a thing that has energy. It’s a thing that can respond to an impact; if a string smashes into it, it can respond. And it’s truly a location in space that is the substrate for a certain class of physical phenomena—namely, it’s where these open strings end, and these open strings can correspond to the particles that we know about; it can correspond to the world as we see it. It’s tough to go further, beyond enumerating its properties. For example, what if I say, What’s this glass? Well, it’s this thing, a well-defined location in space. It can respond when I kick it; it’s where certain phenomena happen. I pour water in, it stays in there. It’s that kind of a description. Musser: Is the brane a fundamental object, an elementary object, in the way that a string would be? Greene: It’s tough to know that right now. I don’t think anybody really knows. There’s a chance that everything is made up of, maybe, D-zero branes—even smaller entities within string theory. There’s a chance that maybe they’re fundamental. In fact, I think likely the answer is: It depends how you look at it. In this formulation, they look fundamental; in that formulation, well, they look composite. So, the questions that we thought that had unique answers may not have unique answers in this theory. It may be: from this point of view, yes; from this point of view, no. Musser: What about all the philosophical conundrums that Leibniz and Mach and all those others came up with? How does that impact the braneworld view, or vice versa? Greene: The biggest conundrum, I guess, that was asked was: Is space, devoid of everything, an entity? Does it still exist if you take everything out of it? And there was definitely reason to argue that no. Space is that which provides a vocabulary for relations between objects’ location. You got no objects, you got no relations, you got no space. The braneworld scenario would answer a little differently, at least as far as life on the brane goes. Again, if you’re in the big ambient space, and you say, remove all the branes, then you’re back in a similar situation. But as far as the three dimensions that we know about, the brane is a brane is brane; it’s an entity, and that’s all there is to it. So there is potentially a different slant on the three- dimensional question. But presumably, Mach or Newton or somebody, if they believed these ideas, would simply shift their conundrum to the higher- dimensional space, in which case it’d be tough to say much. People even argue about what general relativity says on these questions, even before string theory. Now, my—and many others’—reading of general relativity is that it pretty much does say that spacetime is a thing, is an entity, largely because in general relativity, the curvature of space is gravity. Gravity is a field, the gravitational field, so spacetime from the get-go embodies gravity, and therefore is ultimately a thing. We feel gravity. We can respond to gravity; we can affect gravity; we can affect spacetime. There are others even today who disagree vehemently with that point of view. Musser: Some of the branes—ours included—are three-dimensional or four- dimensional, however we count it. Could others be higher-dimensional, up to the limit of the theory? Greene: Sure, definitely. So there could a society of people living on a seven- brane in an eight-dimensional spacetime slice in a higher-dimensional space. Definitely. The world, the universe, is a rich place in the theory.

The Arrow of Time Musser: You said there are a whole complex of other issues you deal with in the book, like the flow of time and the arrow of time. What’s your thinking on the arrow of time? What kind of ideas do you develop? Greene: Well, I spend some time explaining the problem, because I think it’s one of those slippery problems where, at one and the same level, it can seem both deep and trivial. And unless you see the problem fully, you don’t really appreciate the depth of the puzzle that it presents you with. And the puzzle, I’m sure you’re familiar with, is that the laws of physics seem to not show any preference for one direction of time or the other. The laws of physics govern everything we know about, so why is it that everything we know about seems by and large to have this manifest orientation to time? And the natural answer that some people have is entropy: The second law of thermodynamics is the answer, because there’s a time-asymmetric law if you’ve ever heard one. Entropy increases in one direction, and that’s what causes the forward-in-time direction. But then as people, even Boltzmann, knew a long time ago, over a hundred years ago, the second law of thermodynamics is not a law in the inviolable sense. It’s a statistical law, and in fact when you study it in detail, you realize that what it really says is that from any given moment in time, entropy increases toward the future of that moment and toward the past of that moment—a completely time- symmetric statement. And I explain how that’s disturbing, because we’re all happy to use it, the second law of thermodynamics, in the forward time direction. Eggs splatter, water spills, glasses break, entropy increases. We’re all happy with that. But we’re not too happy to use it the other direction. So where do we get off chopping the second law of thermodynamics in half and just using it toward the future? Because toward the past it says that eggs should break toward the past, which says that in the forward time direction, eggs start splattered and, ooosh, come back together into a pristine egg. It says that glasses should spill water in the backward time direction, which means that water, chhhhhhh, would go back in its own container. And we don’t like any of those, because we don’t ever see them. So that’s a puzzle. Where do we get off? And that takes us to, actually, cosmology, because, as people have known for many years—really even going back to Boltzmann, but Roger Penrose played a big role in this, and other people who have thought about it—the basic issue is: Can you give an explanation for why entropy would go down toward the past, as opposed to go up toward the past? And so ultimately it comes down to a question of cosmology. Can you in any way, shape, or form give a compelling reason why, just after the big bang, the universe would have very low entropy, setting us up for a future when entropy got ever higher. In other words, you need more than physics to answer this question of the arrow of time. You need history. And is there some way you can give some formal explanation of this historical fact that seems to be the case—that the universe had very low entropy; it was very highly ordered in the past? Musser: Do you think that it’s purely contingent, or is there some physics that leads you to that history? Greene: Well, I think inflationary cosmology does not necessarily lead you to that state of affairs, but it does give you some explanation for how that state of affairs might have arisen, because inflation, almost independent—and that’s where the catch is—almost independent of the conditions early on, when inflation happened, it stretched the universe by such a colossal factor that all details, all manner of bumps, wiggles, warts, were stretched out smooth,. And then when matter was created, as the so-called inflaton field rolled down its potential and gave back matter, described in detail in the book, it gave a uniform bath of particles, matter and radiation—which, in the context of gravity, is a very low-entropy, highly ordered configuration. And that’s the kind of thing that you want in order to explain a low-entropy past. So, in a sense, inflation gives you want. But then you have to say, Why did inflation happen? And then when you study that, it’s a little hard to give an airtight reason why inflation happened. But surprisingly, the ultimate answer which I feel most comfortable with, goes back to an idea of Boltzmann. And Boltzmann had this crazy idea. When he realized that entropy goes both ways, he said, Well, maybe everything that we now see right now got here by just a chance fluctuation from disorder. Maybe everything you see just got here, or maybe got here some years ago. We just had an eternal era of disorder, and every so often, bloop, the universe had a fluctuation to some order, and that’s what we are. Musser: And we were born with all those memories? Greene: Yeah, exactly. Now, of course, that has its own problem, because, if we’re born with those memories, and we can’t trust our memories, how do we trust the laws of physics? Because they are based on experiments that we remember. And we saw the results in a book. If you can’t trust records and memories, we seem to be caught in a bit of quagmire. So, that’s why you want to look for a better explanation than that, because that one’s not particularly satisfying. But imagine that in the very early universe, there was total disorder, and then there was a fluctuation, not to what we see today, but to a state of order in a tiny little nugget—it would only have to be about 10–27 centimeters across—of inflaton field, the thing that drives inflation. If its value took on the right uniform value inside this tiny nugget, that would ignite inflation, create a huge universe, highly ordered at the beginning, from which everything we know about could follow in the ordinary way. So, basically taking Boltzmann’s idea, but not applying it today. Apply it to the early universe, and getting this little tiny nugget of ordinary space, from which everything we know emerged from inflationary expansion. That, to my mind, is the most satisfying solution so far to how the arrow of time could have been imprinted on the world as we know it. And that I go through in some detail in the book. Musser: Of course, one of the problems with inflation has always been, Where does inflation come from? Where does it fit into particle physics? Has string theory shed any light on that? Greene: Well, the key ingredient in inflation is the so-called scalar field, and string theory has a preponderance of scalar fields. So, it feels like it has the potential to mess with inflation, but in detail, I don’t think anybody’s really done it. There are other cosmological theories separate from inflation that have emerged from string theory that you’ve probably covered—this cyclic model of Steinhardt and Turok, and so forth. It has its own approach to time. That’s a model in which time might be eternal, in which case it might just repeat cyclically through the banging of these branes. That’s again something I go through in the book as one of the other avenues that string theory is putting up in the search to unravel the mysteries of the early universe. Musser: But that has an inflationary epoch, too. Greene: I agree. I absolutely agree. It’s a slower one, but inflation absolutely plays a key role.

String Theory and Cosmology Musser: Actually, while we are taking about cosmology, there are a few cosmological questions I wanted to ask you. One was about dark energy and whether you see any conflicts with string theory. Greene: Well, dark energy is a fantastically interesting and apparently genuine fact of life, unless future experiments undo what seems like a very compelling and unexpected story. There was talk at one point that string theory would be unable to cope with this kind of situation, that it couldn’t deal with so- called de Sitter space, the solutions that are compatible with dark energy. Musser: What was the problem? Greene: There were a couple of problems. One of a fairly technical nature is that string theory is formulated in a manner that is most happy with spaces which, at least in the far past or far future, are flat and unchanging. That makes the formulation of the theory most mathematically rigorous, and that’s the way it’s really been developed. And if the universe was perpetually expanding at an accelerated rate, it wouldn’t really fit into that framework. But that to me is much more a technical issue than some fundamental issue. A fundamental issue, though, was it seemed very hard to find solutions to the equations of string theory that had a so-called positive cosmological constant. You could find a negative cosmological constant—anti-de-Sitter space, which is what Maldacena uses in his work. But finding the reverse of that just seemed very difficult, and there are even some reasons why you wouldn’t be able to find solutions with a certain amount of supersymmetry—again, a technical feature of the theory. But since people have been able to jury-rig the theory and attract solutions which do have this feature, mimicking a positive cosmological constant, so I don’t think it’s a real serious issue. But really understanding whether those theories can match in detail the observations, that’s a huge issue and that’s the real one. How close can string theory come to truly matching what experimental physics and observers actually find? And that is a very open question. Musser: Has there been progress in that area? Greene: No. I’d say that we’ve made progress in understanding the structure of the theory, the ways in which the theory can be formulated, braneworld models, all sorts of interesting new twists and turns, but nobody’s really made a substantial bridge to observation yet. There are opportunities—for instance, at the LHC, the possibility that we might see extra dimensions, maybe even at Fermilab if they’re big enough. We may see them through missing energy experiments. There’s a possibility we might see the production of microscopic black holes. If some of the braneworld ideas are true, that may be possible. You would see it through a specific signature of decay products. I don’t know exactly what that would be off the top of my head, but people have worked this out. So, um, if it does happen, it will be obvious. So, if it does happen it would be strong evidence that some of these ideas are pointing us in the right direction. Supersymmetry—finding supersymmetric particles—is another possibility. Finding microscopic black hole through cosmic- ray experiments, too. Friends of mine, Al Shapere and Jonathan Feng, are working on this. Cosmic rays slam into the atmosphere, and if the braneworld scenario is right and if gravity is stronger than we previously thought, those collisions, which are very high energy, could produce microscopic black holes, which, again through their decay products, shower down into an array of detectors on the ground, would indicate those black holes have been produced. Musser: Like a poor man’s LHC. Greene: Yeah. Not even that poor, because the energy levels are actually higher. The difference is that you don’t have control over what’s slamming into what, and therefore your ability to run certain kinds of experiments is highly qualified, highly limited. Black holes are largely insensitive to what creates them. Get enough energy in a small enough small space, then you will create a black hole. Therefore it’s quite possible, if these ideas are right, that you may produce black holes that way. I mean, they’re safe. People get worried a little bit about black holes, but it’s perfectly safe; it’s just another species of particles, in a sense, which itself would decay in a manner that would betray its existence. Musser: What other kinds of cosmological signatures? You’ve talked before about CMBR. Greene: Yeah. CMB, you know. There are some people who have discussed the possibility of certain kinds of defects that you’d see in the microwave background, but it’d be a different kind of signature if some of these braneworlds are correct. There have, as you’re familiar, been these ideas of quantum-mechanical dispersion of light by distant sources. There are a bunch of things on the table, all of them fascinating. It’s unclear whether any of them will really work. But that’s what we need to put vigorous research effort into, because we only need one to work to find a signature of these fantastically interesting ideas. And the only way you find out is by trying. Work out the math and see whether you can’t get some plausible signature that you can look for. Musser: Or conversely, looking for experimental signatures you can’t explain in the Standard Model. Greene: Exactly. Yeah, that’s the other approach. Yeah.

String Theory and the Multiverse Musser: One of the other issues I wanted to bring up was your current thinking on anthropic and multiverse-type ideas. You talked about it in The Elegant Universe, especially in the context of whether there is some limit to the explanatory power of string theory. Greene: Well, you know, I and many others have never been too happy with any of these anthropic ideas, largely because it just seems to me that at any point in the history of science, you can say, OK, we’re done. We can’t go any further and the final answer to every currently unsolved question is: Things are the way they are because had they not been this way, we wouldn’t have been here to ask the question. So it sort of feels like a small cop-out. Maybe that’s the wrong word. Not necessarily like a cop-out; it feels a little dangerous to me, because maybe you just needed five more years of hard work and you would have answered those unresolved questions, rather than just chalking them up to, That’s just how it is; no fundamental explanation. So, that’s my concern: that one doesn’t stop looking by virtue of this fallback position. But you know, it’s definitely the case that the anthropic ideas have become more developed than simply “things are the way they are because if they weren’t there wouldn’t be.” They’ve become more developed. They’re now real proposals whereby you would have many universes, and those many universes could all have different properties, and it very could be that we’re simply in this one because the properties are right for us to be here, and we’re not in those others because we couldn’t survive there. It’s perhaps less of just a mental exercise, when there’re actually well-defined theories that suggest that these worlds really could be there. So it’s a little less disturbing as an abstract idea when it can be grounded in things that we do have some faith in. But as an explanation, it does feel unsatisfying. Musser: String theory, and modern physics generally, on the one hand, seems to be approaching that point of view you discussed in the book a little bit—of a single logical structure that had to be the way it is; the theory is the way it is because there’s no other way it could be. On the one hand, that would argue against an anthropic direction. But on the other hand, there’s this flexibility in the theory that leads you to an anthropic direction. Greene: Yeah, that’s right. Again, the flexibility may or may not truly be there. That really could be an artifact of our lack of full understanding. But were I to go by what we understand today, there does seem to be not freedom in the theory but freedom in the solutions to the theory. The theory seems to be able to give rise to many different worlds, of which ours seems to be potentially one but not even necessarily a very special one. And if you take that at face value—which I’m not advocating—but if you take that at face value, then it might suggest that these other worlds are out there and that this is the world we’re in because this is the one in which beings like ourselves can exist in, and maybe there are other beings in those other worlds. Maybe not. So, yes, there is a tension between the goal of absolute, rigid inflexibility in the theory, so that the world in some sense exists because logic dictates it, and the world as we know it not existing would be logically, logical nonsense—that would be wonderful. We’re here because we could not not be here, because that’s self-contradictory. That would be beautiful. That’s a wonderful goal, but there doesn’t seem to be a shred of evidence in our current understanding which feels that it’s the situation. Musser: Are there other directions to these very deep issues, like Nielsen’s—like a law-from-lawlessness approach—that you’ve given thought to? Greene: Nothing that I’ve ever found particularly compelling. If you think about it, it’s quite a challenge. No matter what you come up with, one can say you needed to invoke a certain set of words to describe to me your ideas. Why those sets of words? Why those ingredients? Why that reasoning? Unless uniqueness dictates those words and those ingredients, you’re always going to face the question of, How did you start? Why’s that the right starting point? Musser: If you had another grad student waiting in the wings, what would you steer them to? Greene: Well, the big questions are, I think, the ones that we’ve discussed. Can we understand where space and time comes from? Can we figure out the fundamental ideas of string theory or M-theory? Can we show that this fundamental idea yields a unique theory with the unique solution, which happens to be the world as we know it? Is it possible to test these ideas through astronomical observations or through accelerator-based experiment, of mini black holes or CMB fluctuations? Those are the big ones. I guess the side issues are—not really even side issues—can we even take a step further back and understand why quantum mechanics had to be part and parcel of the world as we know it? Can we extract a way? I guess the basic question would be: How many of the things that we rely on at a very deep level in any physical theory that has a chance of being right—such as space, time, quantum mechanics—how many of those things are truly essential and how many of them can be relaxed and potentially still yield the world that appears close to ours? For instance, is it possible that in 1900 through 1930, another generation of different physicists, not the ones that we know and love, could have come up with another idea that would have been adequate to explain the strange properties of radiation and the strange properties of atoms? Could physics have taken a different path that would have been experimentally as successful but completely different? I don’t know. But I think it’s a real interesting question to ask. How much of what we believe is truly fundamentally driven in a unique way by data and mathematical consistency, and how much of it could have gone one way or another, and we just happened to go down one path because that’s what we happened to discover? Could beings on another planet have completely different sets of laws that somehow work just as well as ours? Musser: This goes back to the whole question of uniqueness, of logical consistency. Of course, there probably were people in that time period, 1900 to 1930, that were developing other ideas, and historically we have forgotten about them. Greene: They got steamrolled.

Comments on How Science Is Done Musser: The question is always, of course, when you’re making a decision in research, of what to do. You’ve only got 24 hours a day. Greene: Less. Musser: Well, you seem to have even more than most people. You have to make a decision where you’re putting your time and your energy. Greene: Yeah. Those are the toughest decisions to make. You know, when you’ve engaged yourself in a project, you could be setting yourself down a path of months and sometimes years of thought. Is it the right direction? Is it a fruitful direction? Is it the one that’s really going to bear the deep insights that you’re searching for? I remember when I was a graduate student, I didn’t care. I just wanted to do physics. So any problem that came along that hadn’t yet been solved, no matter how small or trivial it might have been, I would just eat it up. The thrill of learning and discovery, that’s what all that it was. Later on, you begin to say, time is finite. There are just so many papers I’m going to write on this earth before I’m gone. There’re just so many things I’m going to think about, so you begin to be much more discerning. Where is the breakthrough going to be? And to tell you the truth, sometimes breakthroughs can’t be planned. Often they can’t be planned. Often they come from the most unexpected thing. You’re working on a particular project and, my God, it yields something that was totally unexpected. And I do think that as you get older, your willingness to blindly go down a path in the hope that there’s going to be some breakthrough around the bend probably diminishes a little bit. So I think it changes the way you go about your own work. Musser: Do you try to leave some room for serendipities, some fraction of your day that you spend on strange things? Greene: Ideally, yes. But in practice, I have a hesitancy to get involved in a project if I don’t have a gut feel that this is going to be interesting. I think that most people are the same way. And the bottom line is, some breakthroughs will come from directions that you might not have had a good gut feel about, and you’re going to miss them. Some young grad student who is just eager and energetic and says, I just want to do something, is going to find it. And that’s great. That’s how it keeps going. Musser: A decade ago, when I was planning what to do with my career, the whole job market in physics and astronomy weighed on me. Greene: Oh definitely. Very tough times. Musser: Do you think it’s better these days for students? Greene: Mmm, maybe. I think it’s better. Do I think it’s great? No. String theorists, I think, have done much better in these years. I remember there was a time when I got a job and a couple of other people got a job, back in the late ’80s/early ’90s, and there was talk that we may have gotten the last string-theory jobs. And that was totally wrong. Because string theory had its renaissance, and string theorists have dominated the job market. But who could predict that? Who could predict where the real interesting stuff will be in the next few years? And it is tough for students, because ideally you do this and you get to continue doing it if you like it. But for many, it’s not going to be the case, unfortunately. Musser: It seems so stochastic. Greene: Yeah. Even discovery is that way. As I was saying, great discoveries tend to be made by the greatest students, or by the second-greatest students, or by the third-greatest students. In a sense, that’s what’s so wonderful about it all. Musser: I can’t wait to see your new book. You’re wrapping it up now, or you’ve turned your manuscript in? Greene: Well, I turned it in, and it’s in the copy-edited phase, but I can’t leave it alone. I’m sure it’s the same when you write anything. And they’re going to kill me! I wasn’t supposed to touch the manuscript, I guess, but I’ve done it. To me, this is where the book happens—in the last two percent. You’re 98 percent done, and you realize, Oh, if I say it that way, that’s better, but then I’ve got to change that, and you’ve got to do it. To tell you the truth, on The Elegant Universe, I made changes when you’re not supposed to make changes anymore. They charged like five thousand dollars for the changes. I didn’t care. It’s not about money; it’s about making the book. Whatever. So, I’m sure I’ll be doing that in this book, too. Musser: Did you find that explaining it to a popular audience helped you grasp it better yourself? Greene: Definitely, definitely, definitely. I’ve learned a lot from both these books. In the first book, it wasn’t so much that I learned a lot about string theory. No. But I did learn. I did organize my own thoughts about what I considered important in string theory, and it led me to this cosmology stuff, because it really became clear to me, My God, why are we doing this? We’re doing this, at some level, to understand the big bang, because that’s where the known laws break down. So, if that’s what we’re trying to do, why is nobody thinking about the big bang? And I started thinking that way, and other people did, too. In this other book, there are many foundational questions that my own thinking was not clear on, wasn’t as refined as it might be, and I feel like I’ve gotten to a much deeper place on a lot of these questions. Musser: You must be thinking of your third book already, then. Greene: I don’t think so. Musser: It takes times away from all the other things? Greene: Yeah. For this book, I was pretty good about not letting it intrude, until the last few months. But then you know what happened to me in the last few months. I’m looking forward to not having anything. Nova will be done, the book will be done. I’m looking forward to being able to change focus. No deadlines. Musser: Do you feel you have a backlog of ideas you want to work through? Greene: A handful, but what I find is the ideas are generated by the ideas. So, when you stop thinking about things, there’s a double-whammy, because not only are you not doing the thing that you wanted to be doing, but you’re not generating ideas at the rate that you used to, because you’re not engaged in that way. So yes, you get it from both sides. That’s why I really ready to get back more completely. You know, I’ve been involved in these cosmology projects. In a way, I find them a little bit easier to research these projects because they rely on more standard mathematical and physical methods. That’s why, for instance, graduate students can jump right into string cosmology, and not have to spend years and years to learn this whole hierarchy of material that we have developed in the past. So, there’s ways in which I’m thankful for that feature, because now that that’s what my focus has been the last few, it’s somewhat easier to be involved in the research without being all-consuming. Musser: In terms of thinking about the geometry? Greene: Yeah, yeah. To keep all the math of Calabi-Yau spaces in your head, and to keep all the physics that interplays with those is tough. And for me, I found that to make progress, I had to be immersed 18 hours a day, and not really think about anything else. And this cosmology stuff, while physically as challenging, is not as mathematically challenging. So it frees up your mind to think about it almost more pictorially, as opposed to really rigorous mathematics. That’s why it’s been somewhat easier in this book than in the last book to keep some research going. But I’m definitely ready to put these projects aside. Musser: In Santa Barbara, do you think you’re going to go back to work on the old geometry, mathematics? Greene: No, I don’t think so. I’ll tell you why. I’m tired of that approach. It’s not that it’s bad or wrong. It just began to feel like mathematics to me. I mean, there’s definitely a lot of physics in this Calabi-Yau work—we spoke this whole day about all the physics. But I need to do something where the word “data” plays a bigger role. Just from a personal stance as a physicist, I just feel like I need that. And that’s a lot of what drove me to this particular focus. And I may get back to the other at some point, but no, there is a difference between being a physicist and a mathematician, and I think the mathematical physics side of string theory veers a little bit more to the math side—which is fine, for a while, for me. But I need to go back to my roots. Physics is a data-driven, experimental science, and if you aren’t using the data, ever, it starts to feel a little empty.