222 | Andrew Strominger on Quantum Gravity and the Real World

0:00:00.8 Sean Carroll: Hello everyone, welcome to the Mindscape Podcast. I'm your host, Sean Carroll. Quantum gravity is a topic that we've returned to again and again, in part because I think it's really interesting, it's part of what I do and my research career, but also because it's a great example of science in action, or at least theoretical physics in action. Theoretical physics might not be representative as a science, but it's an example of a science. And we know there's quantum mechanics, those are the fundamental ways that the world works, we know there's gravity, it exists, so somehow they need to be reconciled, and we're not sure how. If you've read The Big Picture, you've heard me talk about the laws of physics underlying everyday life, you know that we have enough idea of how quantum gravity works to explain simple conditions like the solar system, why apples fall from trees, but when things get extreme in black holes or the Big Bang, we don't have the full theory, so we don't know exactly what to say. We do have a set of rules for taking a classical theory, like Einstein's general relativity, and quantizing it, but those rules don't work for gravity, or at least not in any ordinary straightforward way.

0:01:08.6 SC: So by following progress in quantum gravity, you can kind of see how science works when we don't know the answer, and also for that matter when there's not a lot of detailed experimental evidence. There is experimental evidence, namely all of the experiments that say that gravity is real and all the experiments that say the quantum mechanics is how the world works, but that's not a lot of guidance when it comes to reconciling them. And of course we know that there's different strategies for doing this, loop quantum gravity is something that is still popular. The very second episode we ever did of Mindscape was Carlo Rovelli, who talked a little bit about that. But string theory is by far the most popular approach to quantum gravity for many decades now.

0:01:51.0 SC: And so today's guest, Andrew Strominger, is one of the world's leading theoretical physicists of any sort but string theorist in particular, and I think it's a really great overview, a really great interview, because we both get into some details about specific questions in string theory and quantum gravity, but also you get to see a little bit of the development of the field. Andrew was there at the beginning of string theory, not the very, very beginning, the ideas behind string theory stretch back to the '60s and '70s, but what is called the First Super String Revolution was in 1984, when Andrew Strominger was a young scientist and he helped develop the idea of compactifying 10-dimensional space-time down to our four-dimensional world in ways that make it look like the physics we observe, the standard model of particle physics, look like vaguely, because we still don't know how to get exactly the correct complete theory of the standard model from string theory, but the first huge step was taken by Andrew and his collaborators, and since then he's still been at the forefront of many different ideas.

0:03:01.4 SC: We'll talk a lot in this podcast about the work that he did with Cumrun Vafa, who's also at Harvard, on figuring out why black holes have the entropy they do in terms of the microscopic states that you combine to make a black hole in the context of string theory. That was an extremely influential paper, thousands of citations. But also the theme that I want to tease out, which is maybe not obvious to someone who just reads Andrew's CV and looks at his papers, where he has many, many very influential papers, is that he does keep his eyes on the prize. He wants to connect quantum gravity to the real world. So you might know that... Well, let's just back up and put it in context a little bit. In the '60s and '70s, when people were doing string theory, they were scattering strings, kind of like particle physics. In the '80s this idea of compactifying and looking at different ways of getting string theory connected to four-dimensional physics became popular. In the '90s there was the Second Super String Revolution, where you realized that there were higher dimensional D-brains as well as strings, and of course the famous AdS/CFT correspondence that we talked about several times here on the podcast, most recently with Raphael Boussaut.

0:04:14.5 SC: And in the AdS/CFT correspondence you have a duality that relates quantum gravity, string theory in particular, in 10-dimensional space-time compactified in a certain way, to Quantum Field Theory in four-dimensional space-time. So the point of me running through this history is to point out that the boundaries between doing string theory and just doing Quantum Field Theory or theoretical physics more generally have become increasingly blurry. That's why every time we have the string theorists on the podcast, they are slightly reluctant to call themselves a string theorist because sometimes they're just doing Quantum Field Theory or just gravity theory or whatever. That's where we are now. But AdS/CFT is still consuming a lot of oxygen in the quantum gravity world, and Andrew has been one of the best people in pushing beyond AdS/CFT to think about de Sitter space, not just anti-de Sitter space, a universe with a positive vacuum energy like our real world has, and also to think about the duality or the holographic description of black holes in our universe.

0:05:20.0 SC: And Andrew is part of the Black Hole Initiative at Harvard where they combine people who do theoretical physics, like Andrew does, with philosophers and also experimentalists and observers who are actually looking at black holes with the Event Horizon Telescope and elsewhere. They're trying to figure out how we can get data from black holes that either just help us understand classical gravity and black holes or maybe string theory and quantum gravity. So that's why it's an exciting time. It takes a long time to make progress in these areas when you don't have guidance from data, but we're gonna get a master class here from one of the people who is really on the inside moving this field forward about how to make progress in quantum gravity and connect it to the real world. So let's go.

[music]

0:06:12.2 SC: Andrew Strominger, welcome to the Mindscape Podcast.

0:06:25.1 Andrew Strominger: Glad to be here.

0:06:26.6 SC: It's great to have you on because I was thinking about it. We have done quantum gravity string theory and things like that before, but we've had Leonard Susskind who was there at the very prehistory of it all.

0:06:37.6 AS: Yes.

0:06:38.9 SC: And we've had the younger generation, you know, Raphael Boussaut, O'Neda Engelhardt, Clifford Johnson, but you were sort of perfectly timed, right? I mean your physics career was just starting when super strings hit the scene. So maybe tell us...

0:06:54.1 AS: That's right. I hit the Beatles when I was an adolescent.

[laughter]

0:06:58.6 AS: And then I hit Super Strings when I was...

0:07:00.2 SC: Born at the right time. Very, very anthropically chosen.

0:07:04.8 AS: Born at the right time, yes.

[laughter]

0:07:05.4 SC: I mean, maybe we could just start by giving your view, be as personal as you want, about how quantum gravity research has evolved over your own research career.

0:07:17.5 AS: Yeah. Well, that's a really interesting question. So I started graduate school near the end of a really strong heyday of particle physics when new results were coming out of accelerators practically every week and there was all kinds of excitement, the strong interactions as... The QCD as a theory of strong interactions was not even fully accepted when I was a graduate student. I had to defend it in my thesis against...

[laughter]

0:08:03.0 SC: Wow.

0:08:03.1 AS: An experimentalists. Yeah, it's kind of surprising to think about now. And there were two of the really big problems that a really ambitious graduate student was expected to try to tackle were, you know, solving the strong interactions in some way, finding an analytic method to compute the mass of the proton, a problem which still remains unsolved, though basically progress continues with, very recently. And the other one was finding the grand unified theory, that was before people had become discouraged by the absence of a proton decay. And other things too, but those were two of the big ones.

0:09:01.1 SC: But just to help the audience, as a term of art, Grand Unified Theory does not include gravity. It's not a theory of everything.

0:09:10.9 AS: Gravity was so off of people's radar screen.

0:09:15.7 SC: Right.

0:09:16.8 AS: That the term Grand Unified was unification of the weak... The electroweak and the strong forces in one hole and people didn't... Oh gravity, who cares about that? It's very strange, very strange. But there was a small group of people, and by small, in the world, I mean dozens, and who were interested in, not so much unifying gravity with the other forces, but just having a theory of it.

0:10:08.6 SC: Right.

0:10:08.7 AS: There was a theory of the strong and the electroweak interactions that Nobel Prizes were about to appear for, but there was no theory of gravity that was consistent with quantum mechanics. And the fact that there was a problem, these are arguably two of the greatest achievements in the 20th century physics, the discovery of quantum mechanics and the uncertainty principle, and Einstein's theory of general relativity, and these two pillars of physics were at that time completely incompatible.

0:10:56.0 SC: Yeah.

0:10:56.5 AS: No way of writing them, having them both on the same piece of paper. No self-consistent way of having them both on the same piece of paper existed and the number of people interested in that problem was in the dozens. And in Cambridge at that time, I was a grad student at Berkeley and then I moved to MIT... In Cambridge in that time there were two or three people discussing it and it was, it's fair to say that it was heavily discouraged and looked down on.

0:11:40.7 SC: Yeah.

0:11:42.9 AS: My thesis advisor, who I can quote because he quoted myself, told me not to work on it, I would never get a job, and then several decades later when I was giving a colloquium at MIT, he said he told me that and then he added, "Good thing he didn't listen to me."

[laughter]

0:12:05.8 AS: And he wasn't the only one, many people. Basically all the influential leading figures in the field were, in the field of theoretical physics, felt it was a problem that, first of all, not very interesting and secondly premature, that we didn't have any ways to address it, and also that it was very far from having any possible contact with experiment.

0:12:47.1 SC: I don't know if you know the story but Hugh Everett, when he invented the many worlds interpretation of quantum mechanics, he was a grad student at Princeton and John Wheeler was his advisor and the thesis project he was given was quantized gravity, but he couldn't figure out how to do that but he realized that if you had the whole universe as your quantum system there were no outside observers and that led him to invent many worlds. So there was a good thing that came out of it anyway. [laughter]

0:13:11.6 AS: Yeah, yeah, yeah. Well, John Wheeler was certainly one of the early champions of the importance of quantum gravity. Though he has many... A mythic figure in 20th century physics with many great achievements, not least of [0:13:35.6] ____ which is coining the word black hole.

[laughter]

0:13:41.6 AS: And he worked on quantum gravity, but like many people who had worked on it in the preceding 20-30 years didn't have too much to show for it.

0:13:51.7 SC: Right. So I actually, I'll confess, I did research for this podcast. I went on to Inspire and went through your publication list because I was gonna guess that you would have been like many people in that era where you were working on Quantum Field Theory or QCD or unification and then string theory came along and you jumped on it, but you were already doing quantum gravity so you were coming at it from a different direction a little bit.

0:14:19.3 AS: I was doing quantum gravity and I wanted to... That was my main interest throughout my thesis, I had my day job which was QCD and so on. It was interesting, you know, those interesting problems but it wasn't where my real passion lied. And I guess somewhere sometime around 1983, yeah, 1983 it would have been, I realized that string theory was, that string theorists, of which there were really in practice only two at that time who were really...

[laughter]

0:15:14.2 AS: Green and Schwarz that were running around talking about it, I mean, other people had worked on it but they were the... That they were claiming to have a mathematical resolution of the problem of quantum mechanics and general relativity. In other words they were claiming... Well, let me back up. They were claiming to have solved the infinity problem.

0:15:48.5 SC: Right.

0:15:49.7 AS: Which is the one that Wolfgang Pauli first noticed in the 1950s, that you can't just take out your cookbook and dress up gravity with quantum mechanics in the way that we did so incredibly successfully for the electroweak and the strong interactions that somehow gravity wasn't gonna play by those rules. That was what Pauli noticed. And then there's also of course Hawking's problem of black hole entropy and information loss and so on which I imagine we'll come to later, I don't know.

[laughter]

0:16:35.6 AS: Conversation could go anywhere.

0:16:35.6 SC: Who knows.

0:16:38.4 AS: But... So Green and Schwarz were claiming to have solved the first problem in just an existence proof of a theory which could reduce to Einstein's theory of general relativity in one limit and Heisenberg Schrodinger quantum mechanics in another. And that was no mean feat.

0:17:03.0 SC: Yeah.

0:17:04.8 AS: They were very clear however about the fact that their theory could not be the real world because it didn't have quarks and leptons and parity violation and all those good things that we have observed and love. And so, but they came from both of them a particle physics background and the theory was presented in a very particle physics-like language. And I remember saying, just at the time I was trying to learn [0:17:49.9] ____... So I felt I had to learn it because somebody claimed to have solved the problem that I was working on and so I should understand what they were saying.

0:18:05.4 SC: Fair enough.

0:18:06.6 AS: Even if I was predisposed I was predisposed not to like it.

[laughter]

0:18:12.3 AS: Because you see my thought was that it was a very deep and, which I still believe it's correct, that it's a very deep problem and it had resisted solution for decades and we really needed some new conceptual input like the equivalence principle or the uncertainty principle or some really fundamentally way, different way of...

0:18:38.0 AS: And there the main hypothesis of string theory that particles are in fact little strings in my then eyes fell short of the deep, you know, it seemed a little just kind of trivial and mathematical and it fell short of what I was looking for. So I didn't really like it, but I felt obligated to learn it. And I remember just coincidentally around that time I was at the Institute for Viet study then and Mike Green visited for a week and they put him in my office and I had some conversations with him and I said to him, I remember saying to him... You know, so I begin to accept that it technically solved the problem, but I still didn't like it and I was trying to find something wrong with it. And I remember saying to him, "Mike, but isn't it just really ugly?" And Mike got these kind of stars in his eyes and he went on, something which I saw a lot about later, you know, about how beautiful it was. And it's one of those things that you really, but now of course we have far more elegant, they had the most clumsy possible way of describing it and presenting it.

0:20:15.3 SC: Brute force kind of...

0:20:16.6 AS: Brute force. It just looked like pages of technical complicated formulas and you get to the end and you find that the infinities go away and you feel kind of swindled. Like if something so simple is happening, why can't we understand it? If something so profound is happening, why do we need all these pages and pages of equations? I had slaved through their monographs on the light code formulation of string theory and I didn't like it. Of course, you know, obviously I turned around on it and in due course I began to see, it often happens in physics that people who get really totally a thousand percent immersed in a subject begin to see a kind of beauty and inner harmony in a set of equations that other people from the outside can't see, and it's easy to be critical of those people thinking they're just lost in their equations. But I think it's... Well, I have a great respect for these people who just calculated... Though it takes all kinds to do physics...

0:21:38.3 SC: It takes all kinds, absolutely.

0:21:39.9 AS: But we need those people that dive in, calculate and just to sort of feel, really get to the bones of something. And Mike and John had been doing that for 10 years and they saw something that really nobody else did. And... Yeah.

0:22:00.8 SC: And when you did dive into it...

0:22:00.9 AS: Well, I think there's some other people too.

0:22:02.1 SC: There's other people, we know. But when you did dive in, one of the first things you did was to help explain how it might be related to the real world. We don't want to leave that thing that you said hanging, that it's, it can't be the real world, we know better now.

0:22:15.4 AS: That's right. And so I had been, right, I had been trying to understand how, Kaluza-Klein Theory, of course, which Einstein was his, spent the last half of his life on trying to unify the forces using extra dimensions. That was very beautiful and compelling. And so, and Green and Schwarz didn't put geometry in, it was all scattering of gravitons with other particles. So we put the geometry back in and we found, as you just alluded to, we found that if you look very carefully at the equations of string theory and 10 dimensions and consistent ways to get rid of the 10 dimensions and get down to four, that just the simplest thing, which involved actually, it was the simplest thing, but it did involve a lot of very deep mathematics, the Calabi conjecture. Yeah, it was proof of the Calabi conjecture, some ideas in algebraic geometry, but nevertheless it sort of popped out of a hat that when you look through this carefully and you look at exactly how string theory allows the extra dimensions to curl up so that we can't see them, it very naturally results not only in a parity violating structure like the one in our world with plenty of room for all the leptons and quarks and all of that but the natural unified gauge groups were sort of the only thing that you could get.

0:24:23.6 AS: So when we did that, I had, it was a feeling like sort of throwing a basketball from the far end of the court and having it bing into the hoop. And the world resonated with that. I mean, within a few months after our paper, the number of people working on string theory went from dozens to a thousand or something like that. I haven't seen anything else like that in my career and it was sure fun to be right at the center of that.

0:25:07.0 SC: And I get the impression as someone who is string theory positive but not involved with it myself, that these days most of the people in the field are more on the geometry side than the particle physics side, like the questions that are involving our minds, or maybe they're just the questions I'm paying attention to, do have a lot to do with gravity as gravity, less so with particle physics as particle physics.

0:25:31.9 AS: Absolutely, absolutely. But that took... The thousand people who, oddly, the thousand people who started working on it after we showed this were the people, were mostly the particle physics people who had been trying to understand unification and they were... String theory was, in my view, wrongly viewed as kind of the final capstone in the reductionist program of physics and that was what got them excited. There was a less of a reaction from the general relativity community where most of the people who had been working on the problem of quantum gravity circulated. So the people who had been working on that problem oddly didn't embrace string theory as a solution, though at that time, though everything shakes itself out in the fullness of time, but, yeah.

0:27:00.1 SC: And at this point, just to jump right up to the present day, while we're still thinking very, very broadly here, give me your impression of how you think about string theory. You've already hinted by tone of voice that maybe it is not the completion of the reductionist program of everything. Is it something that teaches us things and a useful thing to think about for the moment, or are you really conceptualizing it as an 80% chance of being just the final answer to physics?

0:27:29.3 AS: Okay. So yeah. So after having thrown the ball across the court and got into the hoop, if we did that once more, that would be it. But we didn't do it once more and nothing that exciting in the goal to make direct kind of experimental contact with reality I don't think happened again. And I would rather quickly, I mean, the problem was that there were many ways to curl up the extra dimensions, and that led to a sort of proliferation of it's sort of, there's a sense in which string theory is unique, but as I would put it, there are so many phases of it that there's no real predictive power there. And I and many other people who the press was less interested in quoting took the point of view that string theory was not going to make an experimental prediction. I wrote that already in 1986, a year after my paper on that, and it was not this kind of the next step in the reductionist program. And so, you know, it's disappointing, of course, that we haven't been able to make contact with experiment. There's a basic problem that the basic scale and size of the phenomena that we're looking at, where quantum mechanics and gravity are both important, is 10 to the minus 33 centimeters, which is unimaginably small.

0:29:44.3 AS: And we're really, you know, it could happen that some these experimentalists are blowing our minds and our socks off every week. It could happen that they come up with something amazing, but this would be even more amazing, you know. So I'm not expecting that, and that's disappointing. But I think what has happened is more wonderful and more exciting than anything we imagined in 1984, 1985, in the sense that we've gotten ideas about how space and time might emerge from, the holographic principle and so on. Maybe we'll get into that later, maybe we won't. But what has happened is, you know, teasers and inklings of how different the universe might be than what we imagine and what our senses, tell us. It's like the analogy I like to use. So if you ask me about percentages, I would say the chance... People often ask the question, is string theory right or is it wrong in the sense of describing the real world. It's not a yes or no question. And I think the chances of it being 100% right, in other words, that we find the right Calabi-Yau space and that we, nothing needs to be added to what we said in 1985 except finding the right Calabi-Yau space and finding out how do the condensates work and whatever, I think the chances of that, of it really in the end being the solution of the reductionist paradigm as, was momentarily hoped in the '80s, are, I don't know, one in a million, one in a billion, zero essentially.

0:32:12.9 SC: Yes, yeah. Okay.

0:32:14.7 AS: But I think that the chances of it being completely wrong and irrelevant, that 100 years from now historians of science will look at this as an amazing prolonged detour on our path to the truth of about nature are even smaller. An analogy I would like to use is Yang-Mills Theory. Okay. So Yang-Mills Theory is a very famous theory discovered by Yang and Mills in the '50s. Everybody, every physicist knows about it. They invented it to describe the relationship between the proton and the neutron, that turned out to be completely wrong, but it had a kind of inner consistency in a structure and it kept bouncing back and appearing everywhere. And now we realize, well, it doesn't describe the proton and the neutron, it describes everything else at a more fundamental level except gravity. So I think that string theory, we tend to be too arrogant about how complete our current knowledge is.

0:33:36.4 AS: I think there are going to be fundamental new ideas and ways of looking at things, and we've already seen that happen within string theory many times and I think it will continue to happen. And then somehow string theory will find its place but not in the simple way that we imagined. And it may, how much it will look, string theory today is such a different theory than the one Green and Schwarz presented to us in the '80s, and it will grow and accrete other things and be connected to other things in many ways before it finds its home in some kind of home in physical reality. That's my guess.

0:34:31.3 SC: I think that makes perfect sense. And one of the things that we have learned by doing string theory is, of course, holography that you already mentioned, the AdS/CFT correspondence. We've talked about AdS/CFT a couple of times on the podcast with Raphael, with Neda Engelhardt, but I wanted to ask if you could explain it in your words and then move on to, you've been one of the leaders trying to bring it closer to the real world because we do not have an anti-de Sitter background in which we live. We don't have a negative cosmological constant. Maybe we could connect it to something with a more realistic positive cosmological constant.

0:35:09.2 AS: Yeah, I would frame it this way. I would go back to Bekenstein and Hawking and the holographic principle. So Bekenstein and Hawking showed using a stunningly simple and elegant argument that the number of gigabytes in a black hole, the number of gigabytes of information that a black hole can store is proportional to its area. And that is very, very strange because the number of gigabytes you could put on your phone and on your hard drive is proportional to the volume in your phone. You know, you stack the chips up in there and there's a fixed amount of volume for each one. So it's very, very strange that the number of gigabytes should go like the area. So now we have these giant black holes that we see in the sky and it suggests that you can only store the information or it's sufficient to store the information by putting the chips just on the surface, the horizon of the black hole. Now, you can't really do that because they would just fall in, nothing would keep them there and there's no, it's very hard to see exactly how that'll happen, but that is what happens in a hologram. In a holographic plate you can store all the information on the surface of the region you're trying to describe.

0:36:53.9 AS: So I would call this the first, the word, holographic principle, didn't exist then, but this was the first version of it. And then [0:37:09.8] ____ and Susskind recognized how, what an important idea this was. They talked about it, they had some important discussions of it, but nothing really took hold or became precise. And then what happened in string theory, again, in string theory we found, and this is what Vafa and I did, we literally, using a crazy complicated... It often happens in physics that you have some really complicated argument to derive something and then over time it gets simpler and simpler and simpler and you realize you didn't need all that complicated stuff. But we found a very complicated construction within string theory of special kinds of stringy black holes that do have event horizons and they are subject to the Bekenstein-Hawking analysis, which says that their gigabyte capacity should be proportional to their area. And Vafa and I actually constructed the hologram in complete detail.

0:38:42.0 AS: And it involved the kitchen sink. We had all kinds of mathematics, it was completely correct and we hit the answer on the nose, but it was very complicated. But it was an existence proof of the holographic principle. We realized how a region of space time, a black hole, the black hole being the hologram, could be realized by a holographic plate. This was then generalized to whole universes, which were really near horizon regions of the black hole, negatively curved universes. And Maldacena formulated a very precise conjecture, which applied to these negatively curved universes in specific examples that occur within string theory up to, I guess, seven dimensions, and showed, again, concrete realizations within the framework of string theory of the holographic principle.

0:40:31.0 AS: And again, these constructions have a lot of precise mathematics in them. And as you know, there have been thousands or maybe tens of thousands of papers working out details of this, generalizations of this. Enormous amounts have been learned about mathematics, pure mathematics, also properties of physical systems. It's been a great source of kind of inspiration of how quantum systems might be related to one another, but it's not the real world. And the real world in one approximation, in a very good approximation, is flat, it's not negatively curved like these space times, and if you're a little more careful, at least in the far future, it's expected that it's positively curved, just the opposite, de Sitter space rather than anti-de Sitter space. So of the three possibilities, negative curvature, zero curvature and positive curvature, the one that we've understood is the furthest from observable physical reality. So it's been surprisingly difficult to generalize this to those contexts.

0:42:13.8 SC: And is there a way, at this level of discussion, or maybe we need to fill in some more details, but is there a way to explain why it's so difficult? Shouldn't the real world be the easier one to explain, given our great experience with it, than the fake negatively curved world?

0:42:37.1 AS: Yeah, that's a really deep question, Sean. Well, I kinda suspect that when we... Sometimes you don't always understand the simplest things first. There's still hope. It could well be that when we do understand the right way to think about the kind of geometries, the holographic principle in the real world, that we'll kick ourselves and it will seem much simpler than whatever we were doing in anti-de Sitter space. That could easily happen, but also the real world is a very, very complicated place, a lot of stuff happens. And now complexity, of course, can arise out of simplicity, and often does, but to see through, we're looking at the end product, to see through this very, very complicated end product to some simple structure is... Well, it's super fun, but it's not easy and we haven't succeeded yet. Whenever we find some kind of... Every single physicist, where they can, make some kind of simplifying assumptions. Newton just talked about planets moving in empty space and treated the sun like a point like mass, and he didn't take into account all the magnetic fields. Of course, he didn't know about them. So we always make simplifying assumptions and sometimes we study theories with simpler systems, like an age old trick.

0:45:05.2 AS: Already I was using it in my PhD thesis to study quantum chromodynamics. If you can't do it in four dimensions, four space-time dimensions, go down to two. So that's a way to simplify things. There's another way to simplify things, which is to have more symmetries. And there's a very powerful symmetry known as supersymmetry, that people use to simplify things and gives you ways of calculating things that you couldn't otherwise.

0:45:48.6 SC: Let me run something by you. I'm going to invoke my privilege as the podcast host to be a little bit technical, hoping that the audience will stay with us and then we can back up a little bit.

0:45:58.1 AS: Awesome, awesome. Let's hope I can stay with you. Yeah.

0:46:03.4 SC: AdS/CFT, anti-de Sitter space conformal field theory, theory with gravity, theory without gravity in one lower dimension. One of the reasons why it works so well is because the non-gravitational side is a field theory, a quantum field theory. It lives in a space-time, it has an infinite number of degrees of freedom, Hilbert space, etc. One of the ways in which de Sitter space, which you mentioned, the more realistic, cosmology is different is that its boundary is not to the left or right but in the future or in the past, and that's a little weird. But the other way is that within a de Sitter horizon there's a finite number of degrees of freedom. There's a finite dimensional Hilbert space that characterizes it. So is maybe one of the things that is...

[overlapping conversation]

0:46:49.1 AS: Well, maybe.

0:46:52.1 SC: Maybe. I think so. This is why I said I'm going to conjecture.

0:46:52.4 AS: I agree with you. Most people would agree with you but we don't have a...

0:46:56.4 SC: We don't know for sure, absolutely.

0:47:00.8 AS: We don't have a solid calculation to back that up, yeah.

0:47:01.4 SC: But is there a potential idea that just we're better at quantum field theory than we are at finite dimensional models and therefore the thing that might be the dual description of de Sitter space is not in our toolkit already, and that's slowing us down?

0:47:21.5 AS: It could be. You don't solve it until you... It's not over till the fat lady sinks. We don't know what the final thing is going to look like but I think the basic problem that people have wrestled with... The problem you say is that, that is a very vexing one, but it's not the only vexing one.

0:47:56.5 SC: Fair enough, yes.

0:47:58.1 AS: And there's another vexing one, which is that the whole basic idea of a hologram is something which sits at a boundary. It's a boundary of the black hole and anti-de Sitter space, very conveniently, if you go out to the large radius, has a boundary. I often describe it as like a can of soup. You've got the soup in the inside, and then you've got the can and the can is the holographic plate and tells you what the ingredients are, and the soup is the space time that we live in. Now, de Sitter space, if you fix a moment of time and start moving off in space, eventually you'll come back right to where you are.

0:48:55.9 AS: It doesn't have a boundary in space. It has a boundary in time at the infinite future. So if you try to invoke the holographic principle that the holographic plate lives at the boundary, the boundary has no time. The boundary is at the infinite future of time and so this is like the ultimate sort of brain teaser. We don't have a boundary in space, we want to have a holographic plate. The holographic plate is supposed to have all the same information as the hologram, the image, but the image has time in it, the boundary doesn't. How do we put all these things... We haven't solved it, but it is just such a beautiful conceptual problem and it's really wonderful in this subject to be able to go back and forth between things like the anti-de Sitter, the AdS/CFT correspondence, where you can write out all the equations till you're blue in the face and then try to mesh that with these deep conceptual re-framings that we're clearly going to need, if we're going to take the lessons that we've learned from anti-de Sitter space, separate the general features of the AdS/CFT correspondence from the specific ones that are associated with string theory.

0:50:57.4 SC: Exactly, yeah.

0:51:00.1 AS: It's kind of sort of take the meat off the bones and import it and use those insights to say things about the real world that we can say without ever invoking string theory. Even if we got trained by string theory on how to understand these systems, in the end we don't want to invoke it. And that's true for de Sitter space, it's also true for flat space. It's boundary also doesn't have a simple time that you can identify with... Flat space, actually, of all of them has the funniest boundaries.

0:51:50.0 SC: You can buy my book. You can buy Space, Time and Geometry if you want to read more about that.

0:51:51.7 AS: We can buy your book. It's a great book. I use it when I teach the course on general relativity.

0:51:58.0 SC: Oh, good. Thank you. So, okay, I just want to get the footnote on the record that... My guess is that the finite dimensionality of Hilbert space is going to play a bigger role once we do understand this than a lot of people suspect.

0:52:08.8 AS: Absolutely, yeah.

0:52:12.6 SC: But all these things that you mentioned do lead very naturally to the next thing I wanted to ask you about, which is the Kerr/CFT correspondence, the idea that rather than looking at a whole cosmology, we can think about individual black holes and relate them to a dual quantum field theory. And I think I've just reached the limits of my knowledge there, but maybe you can fill in what the story is.

0:52:42.9 AS: Well, okay. So that was sort of an early attempt, which is still looking very promising, of trying to take lessons from string theory and apply it to the real world. So in this work with Vafa, where I said we use the kitchen sink and algebraic geometry textbook and everything to construct the holographic plate for these black holes in string theory, as time went by, we found simpler and simpler ways of doing the calculation until finally we realized that there was only one thing that mattered, and the thing that mattered was what we call an emergent symmetry. And that is, sometimes there can be regions of spacetime in which, or even emergent symmetries occur all over the place.

0:54:05.5 AS: For example, if you take, I guess the first example of it was measured, or one of the first measured examples was sort of at the end of the 19th century, the so-called critical opalescence in the liquid to gas phase transition in carbon. In other words, if we take carbon at just the right pressure and temperature, it goes from being a liquid to being a gas, all of a sudden it becomes opaque right at that moment. Very noticeable thing, and that's because at that point, it suddenly gets extra symmetries, so-called conformal symmetries, and that enables, produces excitations which can absorb the light and you can't see through it anymore.

0:55:00.8 AS: So there are many examples of this. This kind of critical phenomena in emergent symmetries is really the organizing principle of much of modern physics, from condensed matter to particle physics to everything and there are also examples of it in astronomy. They are fewer and further in between, but I think as time goes on we'll be seeing more of them. But of course, a well-known one is the theory of inflation, where the spectrum of the CMB fluctuations suggests, and various other evidence suggests, that the very early universe, there were emergent de Sitter symmetries and there's even experimental evidence for that. Now, so part of what Vafa and I did was to show that very near the horizon of a black hole, you got an emergent symmetry, and not just a few of them but an infinite number of them, emergent conformal symmetries. And there are other examples in physics where this has been experimented, like in the quantum hall effect you have emergent... Many examples, actually, of infinitely many emergent conformal symmetries.

0:56:29.3 AS: And when you have these infinitely many, you have a lot of control over the dynamics of the system. And in fact, there are universal formulas that you can derive for systems with these infinite numbers of symmetries that tell you how many gigabytes of information they can store at some excitation level. So weirdly, this infinite conformal symmetry was exactly what the doctor ordered for answering this question implicitly posed by Bekenstein and Hawking back in the '70s. How do we explain the gigabytes in a black, the area law for the gigabytes in a black hole. When we look up at the sky at GRS 1915 or M87 or Sag A star, these are not very like the black holes that Vafa and I considered. However, it turns out that black holes, in some cases, the ones we see in the black hole, up in the sky, particularly the very rapidly rotating ones, black holes can spin around. They're called Kerr black hole and every black hole we see is spinning to a greater or lesser degree, they don't stay still.

0:58:24.4 SC: Yeah.

0:58:27.0 AS: And a surprising number of them are spinning very rapidly. They like to spin rapidly. If you throw something at them, if they interact with stuff, they tend to spin up. Okay? However, there's a speed limit on black holes and the speed limit is that the surface of the black hole, the so called event horizon, is not allowed to spin around faster than the speed of light. That's basically Einstein's speed limit. And when they get very near the speed limit, as they like to do, they get exactly the same conformal symmetry that Vafa and I used to construct the hologram for the stringy black holes. And indeed, you know, Cygnus X-1, I think is 98, 99, within 1% of the speed limit. JRS 1915, maybe 2%. There's a lot of them that are really, really whizzing around up there. So these are black holes that you could apply some... You could take some of the extracted wisdom from our stringy adventures and use the same kind of reasoning to understand and explain their structure. And... So that's an example of... That's what we're calling the Kerr/CFT Correspondence, and the C there is conformal, field theory.

1:00:18.7 AS: So the conformal is the conformal symmetry and the Kerr is the Kerr black hole. Kerr is the person who found the spinning black hole solution. And yeah, this symmetry also, like the fluctuations in the CMB and so on, the scale dependence of the CMB fluctuations, the symmetry also has predictions which we've made for the structure of emissions from and signals from, you know, astrophysical black holes. I think it'll be some time before we get to the level of precision that any of these predictions could be verified. But we're getting closer than Vafa and I were.

1:01:13.4 SC: That was an extremely excellent explanation. There's just two little things I want to fill in. The word conformal we've been throwing around a lot. Is it good enough to think about that as a scaling symmetry? Like you zoom in twice as much and the system looks the same as it did at your original zoom?

1:01:32.7 AS: Exactly. Yeah.

1:01:33.8 SC: Okay, good. So that's all conformal means, it's not as scary as it sounds.

1:01:37.6 AS: Things look the same on all different length scales. You know, maybe the example people would be most familiar with would be like a fractal pattern. You look at it, you zoom in on your screen, it looks the same. Yeah.

1:01:55.2 SC: And the other thing... I think it's maybe worth just teasing out a little bit more of your work with Vafa and its relationship here. I mean, there, you did... Like you said, you did a lot of kitchen sink stuff, but the ultimate system was investigateable because you had so much symmetry. Just like there's a speed limit to the black hole rotating, there's also a certain amount of charge you can put in a black hole, and am I right to say that you looked at that limit in a certain number of dimensions with supersymmetry and everything?

1:02:28.4 AS: That's right. That's right. We looked at the limit... Right. I mean, when Vafa and I started the project, we didn't have the idea that we were going to find this conformal symmetry and we just kept, at some point, you know, we had learned so much, particular from developments in the mid '90s and so on, but we could calculate so much in string theory that we thought this calculation just has to be doable. And we just kind of in the stupidest possible way, sat down looking at every action. It was over a period of years discussing with many different people, but we tried all kinds of things and eventually we got something. And at first, it was a puzzle why we didn't understand that the conformal symmetry was enabling us to calculate things. If you pick the wrong example, it won't have the conformal symmetry, and you'll just get stuck. And so what happened was, in this case, we didn't get stuck and it was only retroactively that we understood that it was because of the conformal symmetry that we didn't get stuck. Yeah.

1:03:57.8 SC: Good. And that, even though it wasn't what you had in mind, that ended up helping you when you wanted to think about more realistic black holes in the universe, because even though they're not electrically charged, they're spinning so fast that something almost as good happens.

1:04:12.1 AS: Yeah. And... I don't know if you know this, so that we've sort of talked now about things from the mid '90s, from things from late 2000s, and so on. So very recently, the last few years, you know, some conformal symmetry keeps popping up. And it's our friend, we're always happy when we see it because you know... So it has popped up again but this time in a way that is of interest both to observational astronomers and to... Observational astronomers trying to focus in on what they can learn and see with particular... Well, both the Event Horizon Telescope and to a lesser degree LIGO, what you can learn about black holes by measuring them, both to those people and to theoretical physicists trying to understand the whole graphic principle and the mysteries of quantum black holes. And that's this business of the photon ring.

1:05:32.2 SC: Secretly, this is what we've been building up to intentionally the whole conversation, so you reached exactly where we want to go.

1:05:38.1 AS: Okay, okay, okay. I jumped the gun. I jumped the gun. I jumped the gun.

1:05:39.8 SC: But I mean, you made the provocative statement, like this is relevant to observation. So like in the '80s we might have guessed that the way string theory would connect to observation was it would predict the mass of all the particles that we see at our accelerators. And now we know that's going to be harder than we thought, but maybe, maybe in retrospect this should have been investigated earlier, but maybe the gravitational lessons of string theory are going to be helpful to observers.

1:06:10.9 AS: Yes. And already I think that this discovery of the beautiful and observable properties of the photon ring came out of... The discovery of those properties, although they all follow from general relativity, came out, the way of looking at it came out of string theory and things we were thinking about in string theory, and they are definitely having a profound influence on the astronomers and it is one of the, if not the main goals of the future development of the Event Horizon Telescope, of which I'm now a member.

1:07:06.5 SC: Oh my goodness.

1:07:10.5 AS: Yeah. To measure them. And so it's interesting from many different points of view.

1:07:18.9 SC: So what is the photon ring? We haven't told the audience that yet.

1:07:22.2 AS: Yeah, we haven't told... Okay. So it turns out that a black hole, if you look at it, is like a hall of mirrors. So if you shine a light on your face, it bounce off of your face, the photon can go off, head towards the black hole, it goes straight to the black hole or it'll just fall in, but if it just misses it, it'll boomerang around the back and come back to you and you'll see yourself reflected around the side of the... You'll literally see an image of yourself on the side of the black hole. But other things can happen. It can go and boomerang and wrap around the black hole once and then come. So you'll actually see an infinite number of images of yourself if you had perfect resolution while looking at a black hole. So it's like the hall of mirrors, it's like if you go in an apartment store with the three frames of a mirror, trying on some clothes and you can see infinite number of copies of yourself. A black hole is like that. But all the images converge on one place.

1:08:44.3 AS: And it turns out that a photon, if you aim it perfectly, will start to wrap around the black hole and will just keep wrapping around forever, it'll just orbit the black hole forever and never come back if it's perfectly aimed. That's the photon ring. And that photon ring is... If you look at the image of a black... So we haven't seen it yet. We've seen in that famous donut picture, which most of your listeners have undoubtedly seen, that is not the photon ring. That is light directly coming from hot matter swirling around the black hole directly to the telescope. But there are going to be finer images where the photons from that hot swirling disk have wound around the black hole and the whole series of images, and that is what we hope to observe, these finer and finer images. Now, this is extremely interesting for understanding and measuring the laws of physics because we don't know much about what that swirling disk is made of and we don't know what kind of magnetic fields are in there, we don't know how fast it's going, and as we measure the image better and better, we'll mostly be learning more about the makeup of the matter swirling around the black hole. But what we really want to learn about is the black hole itself.

1:10:44.9 SC: Well, we... You and I do.

1:10:48.0 AS: Well, I think... You and I do. Many things are interesting, but certainly the members of the Event Horizon Telescope are very keen to learn, to see properties of curved spacetime. We've inferred the existence of highly curved spacetime and black holes and so on, but our ways of directly probing it are a precious few. And seeing something like a photon that is wrapped around the black hole at the speed of light, that is really a qualitatively new observation. Now, what you're seeing... So the black hole is the mirror here. And if you go to the department store and you look at the direct image, you might learn about whether or not you want to buy the clothes you're trying on, but you won't learn much about the structure of the mirrors. But if you look at the relationship between the direct image of the mirror and the once reflected, you can from that totally... It doesn't matter what you're wearing, you'll get the same information about the arrangement of the mirrors. So it factors out the relative images, it factors out all the uninteresting information about the clothes you're wearing.

1:12:24.3 SC: You and your fashion sense, yeah.

1:12:27.6 AS: And you get all the information about the mirrors. So that's what we want to do with the black hole. And now... And it turns out that this is all possible because of a conformal symmetry that appears at the photon ring. And in this context the conformal symmetry relates photons which wind once to those that wind twice and so on. And in fact, if you dial this back to a black hole that's rotating at the speed limit, it's kind of the same conformal symmetry. So they're not very far apart. So we have some ideas of how to apply to, the holographic principle, to black holes spinning at the speed limit. So this photon ring has been interesting both to, as I said, to observers and to theorists and there's nothing like looking at an image to make you think about things differently. It's been amazing.

1:14:00.9 SC: It's very true. Yeah.

1:14:02.3 AS: Looking at an image makes you think differently. Another thing that makes you think differently is trying to explain something to observers or to answer their questions. Because basically, a little bit of a side, but basically, and you know this, Sean, theoretical physicists are by and large all really stupid, and what we all do is we rewrite with a few different words the paper we wrote last week, which is a rewriting of somebody. And basically, if you can just think about things a little bit differently, that's huge. Just a little bit different perspective is enormous. And observers are great for asking you a question that makes you think about things differently. So we were looking at this, and I invite you to look at that last few seconds of the beautiful numeric. I invite all your listeners to look at the numerical simulation with the stars in the background of the first LIGO merger. Look at the last few seconds and then ask yourself, where is the holographic plate?

1:15:24.6 AS: Well, there's a little circle around those black holes that seems to... When you look at it, that circle is saying, I am the holographic plate.

1:15:37.2 SC: I will look that up.

1:15:38.3 AS: Now, there's no mathematics here. There's no mathematics here. We're trying to get the mathematics. But the hypothesis is on the table, that the photon ring is actually the holographic plate and the best evidence for that hypothesis is just looking at the image. So I invite all your listeners to go dig up that video, it's beautiful.

1:16:09.9 SC: But that's fascinating because I think that most people, even physicists, would have guessed that all the holography is going on at the event horizon of the black hole.

1:16:19.5 AS: Exactly.

1:16:19.8 SC: And the photon ring is quite a bit separate from that.

1:16:24.1 AS: That's right. That's right. Though in AdS/CFT it will at the boundary.

1:16:29.5 SC: Yeah, yeah. Okay.

1:16:33.2 AS: But, you know, I would have said what you just said, but there's no sort of proof of that and it... Go look at it, Sean.

1:16:46.0 SC: Okay, yeah, I'll look at it then.

1:16:48.7 AS: Send me an email. Tell me when you're convinced. You may have to read our papers pontificating on that, about it. Just look at the picture.

1:16:57.1 SC: I will, I absolutely will. But I do want to ask, just again for clarity, we're not saying here that string theory is making a different prediction than classical general relativity would for these phenomena, we're using string theory to analyze a prediction that is the same as we would ordinarily expect. Is that right?

1:17:15.9 AS: Yeah. We're not even using string theory. So it's like this. So before my construction with Vafa, nobody even had the foggiest idea how it could possibly be that you would have that number of gigabytes in a black hole. There was just no way to... And it seemed like really irreconcilable points of view, the general relativity point of view and the particle physics point of view seemed irreconcilable. And the argument, however, the argument that they're irreconcilable had a series of loopholes which string theory brilliantly snaked its way through. So now we know that there's a route through that seeming paradox and it would be... Nobody thought of the route before the stupid brute force calculation revealed where it lied, and now it would be surprising if there's another route. In any case, it's worthwhile seeing if we can show, just starting with assuming quantum mechanics, general relativity and many other things that we've come to understand about... That we've come to show without assuming string theory or anything else about the nature of quantum systems involving gravity that a similar route is followed by the real world, but even a sketching of that route for black holes that are way below the spinning speed limit has been missing.

1:19:17.6 AS: We don't even have that. And we'd like to sketch how that route could work and looks to be like the photon ring is a step on that route. Okay. I haven't shown anything, but I'm excited about trying to understand this.

1:19:41.9 SC: Do you think there is any hope for finding anywhere in the universe a deviation from classical general relativity because of string theory, whether it's black holes or the microwave background or something weirder?

1:19:58.1 AS: There's certainly hope. But there's things that have happened. Like for example, there was a moment when it looked like there was a string up in the sky that was lensing stars and that might've been some kind of evidence for string theory. Now that disappeared, that signal disappeared but that's a nice existence proof bicep too. That was a wrong experiment, but it looked like we were measuring quantum gravitational effects. So it's not logically impossible, and I'm glad that there's a lot of people out there who are vigorously shaking the trees, trying to find some way of making the measurements, but my guess is, it's very important that those people are doing that, my guess is they won't succeed until... I mean, Science changes, they won't succeed... We can't say what... We have no idea what science will look like in say 20, 30 years, but I don't think anybody will succeed in the next 20, 30 years. After that all bets are off.

1:21:33.2 SC: But we hope we're wrong. Right?

1:21:34.1 AS: What?

1:21:35.5 SC: We hope we are wrong.

1:21:37.8 AS: We hope we are wrong. Of course, I hope I'm wrong and I don't want to be discouraging to those people who are trying to do it because I'd like them to continue, but every scientist has to bet science is not a science, it's an art and a gamble or whatever on what things are likely to pan out. And also what things each scientist feels they are good at. And so I think that this kind of understanding... You know, I spent the first 15 years of my career as a theoretical physicist, most of it on top down, assuming what can we...

1:22:30.3 AS: We had one example of a theory that is consistent with general relativity and quantum mechanics. What are the details of this? What is its structure? But for the last... That's top down physics. You start with some assumptions about microphysics and you try to push them down. But there's a lot to do. We're not short of ideas on bottom up. There's a lot to do. And the top down approach has given us ideas on how to proceed, how to organize the bottom up approach and we need to do everything. I'm sure that we won't get to the... I don't think we'll ever get to the final truth of nature, but I don't think we'll even get to the big next step without doing everything, using every approach, turning over every stone. That's our job.

1:23:31.5 SC: You know, that would be the perfect place to end, but I wanted to end with an anecdote. I mean, that's a very inspirational last place to go, but you probably don't remember, but this might have been the first time we ever met. You came to MIT to give a seminar back when I was either a grad student or postdoc there. We went out to dinner afterward with a bunch of people, including Roman [1:23:53.1] ____ Chakiv, who was a co-author on my first ever paper, as well as your thesis advisor. And we were just chit chatting and there were no string theorists there except you, because MIT didn't really do string theory at the time. And at some point you mentioned, you said, you know, obviously each of us thinks that whatever we're working on right now is the most important thing to be working on in all of physics and the rest of the table sort of looked uncomfortable and then you said, well, I think that anyway. So do you still stand by that statement? And do you think that's good advice?

[laughter]

1:24:33.2 AS: I stand by it. Yeah.

1:24:36.5 SC: It's a high bar. It's... You know, it's easy to do things in physics because we can do them, not necessarily because they're the most important thing to be done.

1:24:45.2 AS: Oh, no, but come on. But it's part of the statement, right? I mean, I wasn't trying to... You know, it's a knife edge. There are things that are, you can do, but they're not interesting and then there's things that are interesting but you can't do. And things which you can do and are interesting, that's a knife edge. And the art of being a good physicist is not falling off the knife edge, and most of the time we're all on one side of it or another. So the most interesting things, they're not as maybe the most interesting questions, you know, and we're not even addressing like the meaning of life. You know, I'd rather know what the meaning of life is than what's inside a black hole.

1:25:33.0 SC: Fair enough.

1:25:35.1 AS: Well, that would be... Yeah, okay. There's lots of questions we don't address. The most interesting ones are the ones that... Or the most important ones, what I meant by that were the ones that are both interesting and doable. Yeah.

1:25:56.9 SC: I think that's pretty good. Good. I'm glad that we stick by the advice. So Andrew Strominger, thanks so much for being on The Mindscape Podcast.

1:26:04.1 AS: Okay. Super fun, Sean.

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