218 | Raphael Bousso on Black Holes and the Holographic Universe

0:00:00.8 Sean Carroll: Hello everyone, welcome to the Mindscape Podcast. I'm your host, Sean Carroll. We talked a lot about physics on this show, and if you asked people on the street what physics studies, you might hear something about matter and energy moving through space and time, or space-time if they had been introduced to relativity just a little bit. Modern quantum mechanics and gravity are coming together to suggest that this space-time idea is not as fundamental as we thought. The reason why you think it's so fundamental, there's many reasons, but one is that things interact with each other when they bump into each other at the same point in space. This is basically locality. That's a crude way of putting it, but the same thing is true for a field theory like a quantum field theory, like the Standard Model of particle physics. If you poke the quantum fields, the field reacts at that point in space and immediately nearby. It doesn't react instantly very very far away.

0:00:58.4 SC: There can be interactions that ripple out that the speed of light or slower, but that's within space. That's where locality comes from. Now you make a black hole. You quantize the quantum fields around that black hole. Stephen Hawking says the black hole radiates, and we get the black hole information loss puzzle. If you throw a book or some other piece of information into a black hole, how does it get out in the radiation? Still don't know the answer to that. We've had some ideas. We had a podcast about it with Netta Engelhardt not too long ago, but along the way, we've learned some very interesting things. Like if you think the information does get out, which you have very good reason to think, then there's something non-local going on about the black hole. There is something as if the information of the black hole is distributed around its horizon, its boundary, its two-dimensional surface, rather than distributed within the three-dimensional volume of the black hole. And this idea was eventually developed in what we call the holographic principle by Gerard 't Hooft and Leonard Susskind, among others.

0:02:04.7 SC: Leonard Susskind, of course, being a previous Mindscape guest. We are still struggling to understand what the holographic principle precisely says and how to precisely formulate it, as well as what it implies for a new generation of physics where locality is not central. So today's guest is Raphael Bousso, who is a physicist at UC Berkeley, and one of the big names in holography and black hole information. I remember when I was a postdoc, we had the first intimations of holography within the context of black holes, but Leonard Susskind and Willy Fischler actually wrote a paper where they tried to generalize it to more general circumstances. And I instantly recognized that there were flaws in their ways of doing it. They sort of assumed some things that weren't always true, etc. And I thought to myself, you know, someone should do this right. Maybe I should do it right, but I was doing other things, didn't pay attention to it. And then very soon thereafter came a paper by Raphael that I read, and I remember thinking, I'm glad I didn't try to do this, because this is much better job [chuckle] than I would have done at this.

0:03:09.5 SC: And Raphael became a star after that, and has been since then still pushing our understanding forward on black holes, the nature of space-time, the multiverse, the holography, black hole complementarity, all these different kinds of things. And he's a very articulate explainer of these ideas. The whole field is still very much moving. We don't have the final answers yet, so I think you'll get some of the impression of that in this conversation. There's great ideas coming out here. We don't yet know how they all fit together. So like I always like to do for the young people out there, this is important stuff that you could think about and make a contribution to. We're still learning. That's the exciting fun place to be. So occasional reminder that we have a Patreon for the Mindscape podcast. Go to patreon.com/seanmcarroll, if you want to get signed up for some number of dollars, including one, for each podcast episode, you get an ad-free version and you get the right to ask questions for the monthly Ask Me Anything episodes. And it's fun. You get a sense of accomplishment and community, things like that. So with that, let's go.

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0:04:30.7 SC: Raphael Bousso, welcome to the Mindscape podcast.

0:04:32.9 Raphael Bousso: Thanks for having me, Sean.

0:04:34.8 SC: I thought that we would start because a lot of people I bet in the audience, like they've certainly heard about quantum gravity. I've talked about it. They certainly heard about string theory. We had a couple string theorists on. They've even heard about loop quantum gravity. But maybe there's some stage setting to be done about like how do you personally think about the relationship of gravity, general relativity, quantum gravity as a field, string theory as some sort of specific version of that?

0:05:01.9 RB: Oh, good. I guess I started out going into physics just sort of vaguely wanting to know about fundamental stuff. I was fascinated by what I'd learned, glimpsed in high school maybe about quantum mechanics and special relativity and about the fact that nature behaves in ways that are so hard for us to guess because they're so far away from our everyday experience. And that at the same time, you're sort of forced to these conclusions. And it just seemed like this was something I wanted to learn more about. And so then of course, I learned fairly soon that it's sort of those two big developments of the early 20th century that we haven't managed to fit together yet. There was this one track of Einstein discovering special and general relativity, which is the theory of how space and time are structured on large scales. And it tells you things like that you can't go faster than the speed of light.

0:06:12.5 RB: It tells you that gravity is really the response of space and time to the presence of matter, bending it in some ways and things trying to go as straight as they can in that warped world. And in itself, that was a huge success. It's very well-tested. It describes how the planets move and how the universe expands. But then there was a second track where people began to understand the atomic and subatomic world through this idea of quantum mechanics. And if you thought that warped space-time was crazy, that stuff is really crazy. I don't think quantum mechanics could have ever been discovered the way that Einstein did discover his stuff, by just kind of thinking abstractly about some contradictions between theories that he knew about and trying to resolve them. Quantum mechanics is so crazy that it had to be discovered by experiments, atomic spectra, the fact that matter when it's warm doesn't emit an infinite amount of energy turns out to be a surprising thing.

0:07:13.0 RB: Stuff like that, you had to have experimental data dragging you kicking and screaming to this crazy theory, which says that systems can be in two states at once. You can add a dead and a live cat together and crazy stuff like that. So those were both huge successes because also quantum mechanics explained how atoms work. It eventually led to our theory of elementary particles. All the known subatomic forces are very well explained by it. And yet we don't know how to fit those two strands together. And that's what quantum gravity is about. And when you think about how exciting the conceptual advances were that came with discovering that the universe is expanding, that space and time are warped, or with discovering these crazy aspects of quantum mechanics, you can only wonder how much more dramatic it must be to understand how those two things fit together. I think that'll be another huge step and it'll allow us to think about the universe in completely new ways. But as always in physics, it's important those are not random ways. Those are going to be ways which are dictated by consistency with all the experiments that have been done. And I can't wait to find out what they are.

0:08:37.3 SC: Do you think we're close? Do you think quantum gravity is in our lifetime, let's say? As young, vigorous people, that could be a long time, I understand, but.

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0:08:46.0 RB: Yeah, I wonder. There's a pessimist view where, we'll never quite get there. Whenever we discover a new theory, it's going to be richer, it's going to explain more things with fewer ingredients. But it's not quite... It's going to pose new questions that are going to lead us to the next frontier. I don't know if... Maybe that's actually not pessimistic, because that'll keep all generations happy and busy. But I think that's a possibility, but I think there are also reasonable arguments that could be made, that this might be it, that if you figure out how to put together gravity with quantum mechanics, then at least on the... Well, on that front of trying to understand nature fundamentally, you would be done. There would still be a lot of other things to do, like understand the consequences of such a theory. And I don't think we'll ever be able to describe the behaviour of a zebra using fundamental physics. So there's also other beautiful sciences. But it might be the end. Now, whether we'll get there in my lifetime, I have absolutely no idea, because I could be run over by a truck tomorrow. [chuckle] But I think we'll learn many interesting things in the decades to come. And I'm particularly excited about the time that we're in right now, actually.

0:10:21.9 SC: And do you think of String theory as the leading current candidate to be quantum gravity?

0:10:29.1 RB: String theory, I think, has given us from my perspective, as far as I can tell, the only consistent candidates for theories of quantum gravity that are in any sense complete. In particular, it has led to the discovery of the AdS/CFT correspondence. That is a lot of letters. But what it means is that there's a certain class of universes, unfortunately, not including the one that we seem to be living in, but still a very rich set of space times worlds that you can imagine, for which we have a complete quantum theory of gravity. Or at least it could be wrong. We haven't tested it experimentally. But it's a very significant statement that you have a theory which is complete in itself, it's not missing anything. You could put it on a computer and run it, you can calculate things with it. And so that I would say is, from the physics perspective, the number one thing that has come out of String theory, there's a lot of beautiful mathematical results, and many other applications that the theory has had.

0:11:41.2 RB: Another important consequence of String theory is that you would expect that the kind of world that we see around us, the kind of particles and forces that we see are no more unique than the kind of atoms that there are, or molecules. There's water, there's air, there's different things you can build out of the fundamental ingredients. And string theory suggests to us that the so called fundamental particles that we see might actually really be things that were put together from even more fundamental ingredients that exist in string theory, and that could have been put together in different ways, and probably in some far away parts of the universe that we can't see yet are put together in different ways. And that helps us explain a few things, or gives us a chance to explain a few things that are puzzling about our universe. For example, how it got to be so old and large.

0:12:43.0 RB: So string theory certainly had a huge number of successes. What we haven't done yet is get to it from... String theory fell into our laps. It was a theoretical structure that just seems to be very rigid, very rich. You can't dial a whole lot of things about it. And we don't have a whole lot of other very explicit ways of doing quantum mechanics and gravity at the same time. It was not discovered in the way that we usually make discoveries in Physics, either by some experimental data or by some... How did Einstein make his discoveries? He understood that there was a conflict between otherwise successful theories of Physics, Newtonian mechanics, let's say, and Maxwell's theory of electricity and magnetism. They were very successful, but at some sort of fundamental level, they were completely in conflict with each other.

0:13:43.2 RB: And so he thought about it for a while, and he decided, here are the fundamental principles that need to underlie unification of this. The space time structure has to be that of electromagnetism, he decided, and then he adapted Newtonian mechanics to fit that. And this way where you start with what you already know, and you identify some guiding principle, and then try to construct a new, bigger, better theory from that, that's not how we discovered string theory. But that's something that we're also trying to do when we do quantum gravity. So there's two ends from which we're trying to bore the tunnel, if you will. So that second end, we think about what could be guiding principles that tell us how to put together a theory that allows both of these structures to live under one roof, and to emerge from a more unified picture. And that's actually what I'm mostly busy doing right now. That's an area of physics where there's a lot of progress right now.

0:14:49.7 SC: But I guess I would say, or at least, I'll let you put it into your own words. But what I want to get across to the audience is the idea that people like you, I would say, work on quantum gravity in a way that is string theory-adjacent, string theory-compatible, but you're not calculating a lot of string loop diagrams, or maybe even really being beholden to the specific structures that string theory hands down to you. There's still quantum gravity as a field, in addition to string theory as a field, even though there's a lot of overlap between them. Is that how you would think of it?

0:15:25.4 RB: No, I would not. I think as much as... So I want to say this without diminishing string theory in any way. But the kind of progress that we're making right now could have, in principle happened entirely without knowing anything about string theory.

0:15:43.4 SC: Right. I think that's what I was trying to say. Sorry, maybe I didn't say it eloquently. I'm trying to say that you and your friends are doing quantum gravity in a way that is not in opposition to string theory, but is also not built upon string theory.

0:15:57.3 RB: Yeah. Now, for historical reasons, string theory does exist, and it's given us very powerful tools. And those tools have played, in practice, a huge role in allowing the kind of progress that I'm excited about in recent years to happen. So in particular, this AdS/CFT correspondence that I mentioned earlier, has in convoluted ways to some extent, led us to understand something about how gravity itself knows a lot more about quantum mechanics than we're giving it credit for. This is something that's not true for any other classical theory. Electromagnetism, Maxwell's Classical theory, doesn't know in any reasonable sense, anything about the additional features that quantum electrodynamics, that it's so called quantization, brings to the table. There's no way you could have extracted that from the Classical theory. But gravity, Einstein's theory, bizarrely, knows something about its own quantum states, and actually the quantum states of all the matter fields and forces that exist in nature.

0:17:08.0 RB: And that's a really fascinating and bizarre property, which we've sort of seen glimpses of over the last four or five decades in a bunch of places, for example, when Bekenstein-Hawking discovered how many quantum states a black hole has. That's something that you should have no right to figure out until you have an actual quantum theory that tells you what the individual states are. It's like asking how many states does a block of metal have, and you don't have any idea that it's made out of atoms. There's no way that you could know the answer to that. But gravity has tricky backdoor ways of letting you figure that out if you ask nicely. And we've recently understood how to ask a lot of new questions, a lot of more sophisticated questions nicely, and getting gravity to answer them for us. And in practice, the way that this was discovered had a lot to do with earlier breakthroughs in string theory. But as a matter of principle, the properties that gravity has that allow you to do this are independent. And maybe in some other planet they're discovering that before they discovered string theory, I don't know.

0:18:20.3 SC: This is very, very good. I like this perspective. I've heard it before, but I think you articulated it very clearly. Is it too much to say that this is a culmination of Einstein's insights into the principle of equivalence? When he says that gravity is like the other forces in some ways, but it's also different in some ways, it's more universal, there's not different electrical charges to go different directions. Gravity touches everything the same way, therefore, it's the curvature of space time. Is it too crazy to say gravity is even smarter than Einstein thought, it even knows something about quantum mechanics, which he never would have guessed?

0:19:00.0 RB: Oh, yeah, I think that gravity is much smarter than anybody would have thought. It's really an astonishing property for classical theory to know something about how many quantum states there are. Not only in it, of its own things like black holes belong to gravity. And so you can figure out how many quantum states those have. But gravity also leads to something called the Holographic principle, which tells you how many quantum states, other things can have. And so now it doesn't tell you in detail, at least so far, we don't know how to do that. It doesn't tell you in detail, how the quantum mechanics of various forces actually works, we figured that out in other ways. But the fact that it tells us anything at all about the quantum properties of matter and of gravity itself is a total shocker. That's a really remarkable property. And I think we haven't taken advantage of it enough. And right now we're going through a period where we're figuring out how to really get a lot of mileage out of that insight.

0:20:13.8 SC: Well, this is worth digging into a little bit more. So let's rewind to the provocative statement you made about Bekenstein and Hawking telling us how many quantum states a black hole had. I bet that went over the heads of some of our audience members. So what exactly do Bekenstein-Hawking do and what in the world does it have to do with a number of quantum states?

0:20:33.2 RB: Good. I think maybe we should talk a little bit about what quantum states are in the first place.

0:20:39.1 SC: That would help.

0:20:40.4 RB: So one way to think about it is that to go back to the origins of quantum mechanics, people were trying to understand what's called atomic spectra. That's if you have a certain kind of atoms and you shine light at them, then the light that comes out on the other side is missing some spectral lines. You know how you can break up light using a prism and the white light becomes this sort of rainbow spectrum of colours? And so you can send white light through a bunch of atoms and depending on what kind of atoms you use, what will happen is that these atoms are going to be very picky. They're going to choose some part of that rainbow spectrum. They're going to say, I like this one, I like yellow. And they're going to use this yellow to jump up to an excited state. That means that one of the electrons in the atom is going to go to a different quantum state that has more energy. And then what comes out at the end is the light that you send in minus the yellow, let's say.

0:21:40.0 RB: So you can use this prism to split it up and you're going to see a black line where that was supposed to be yellow. So that's how people first discovered this notion of quantum states that it's basically, there are different discrete things that electrons in an atom can do. And you can start listing them all and those are the quantum states of the atom. And you can imagine that the combinations of what electrons and atoms can do become this... There's a lot of different things you can do once you have more than one atom. If you have a block of iron, there's some insane number of atoms in there and an insane number of electrons and nuclei correspondingly. And those electrons can be in a lot of different quantum states. And now you're talking about these astronomically large numbers that have to do with how many particles you've got in there. But if you ask this question, how many quantum states does a block of metal have? It's not enough for me to say that block is a meter by a meter by a meter, and it's not enough for me to tell you how much it weighs.

0:22:43.1 RB: I need to tell you exactly what that stuff is made of. More precisely, I need to tell you what the atoms are that are in it, how they're arranged, what the electrons are able to do. I need to talk about that sort of fundamental tiny ingredient stuff that is responsible for these quantum states. And if I don't know what that is, because I've not looked through a good enough microscope or I haven't been able to, I can indirectly measure. I can try to measure how many quantum states the block of metal has. I could go that route. I could try to heat it up a little bit. And depending on how many quantum states it has, that's going to take more or less energy. So I can figure it out that way. But what Bekenstein and Hawking were able to do, now replace that block of metal by a black hole, by the kind of thing that you get when you collapse matter under gravity so strongly that it just bends space-time in this kind of hole shape. You can think of that as an object and you can ask how many quantum states it has.

0:23:42.6 RB: But nobody knows what the analogue of atoms are for that, or electrons. And nobody's taken one of these guys and try to heat it up a little bit to see how many quantum states it has by checking how much energy does this take? Nobody's been able to do that. And yet, Bekenstein and Hawking were able to calculate how many quantum states it has. And so that's really analogous to, being able to figure out how many quantum states a block of metal has without me telling you which metal it is, what the atoms are, and without me giving one to you so you can experiment on it. And nevertheless, you somehow figured it out. It's like, "Whoa." So that's what they were able to do. And the reason that they were able to do it has a lot to do with the fact that gravity, unlike any other theory that we know, is a theory about the dynamics of space and time. It's a geometric theory. And it's the fact that the geometry can do interesting things when black holes are present that effectively allows them to figure this out.

0:24:52.3 SC: And I think I'm betting that a lot of listeners are... Their minds are spinning right now in productive ways, because they've heard me talk about entropy. And they know that entropy is a way of measuring how many different microscopic states correspond to a kind of macroscopic configuration. And some of them will have heard that what Bekenstein-Hawking did is calculate the entropy of a black hole, and hopefully they're going, "Aha, that's just what Raphael just said." Is that right?

0:25:20.1 RB: Thanks for making that connection. I should have said the word entropy, but we were going with [0:25:24.4] ____. Those are basically the same thing up to exponentiation. So the larger the entropy, the more quantum states you're dealing with.

0:25:33.3 SC: But I think this is... I mean, the way that you put it is really wonderful, because, again, most people on the street, if they've heard of the word of entropy, they're thinking of cream and coffee mixing into each other, right? Or shuffling cards or something like that. And what you're pointing out, in the quantum world, it's really a way of counting how many quantum states go into something. And so that really is a incredibly profound thing to know about black holes, which we've never done any experiments on directly.

0:26:01.9 RB: Yeah, that's right. Now, what Bekenstein-Hawking were able to do was to calculate what is called the coarse-grained entropy of a black hole. It's basically saying, if you know nothing else about this black hole, except for the fact that it is a black hole, [chuckle] and it has this and that mass and maybe some spinning at some rate, but you just know these sort of very coarse features, then you can calculate how many states correspond to that. That's what they were able to do. More recently, we figured out a way to calculate how many quantum states a black hole has when I know a lot more about it. For example, I might have formed this black hole by collapsing matter in a very specific quantum state. Then I know that initially, it actually doesn't have a whole lot of different quantum states it could be in. It can only be in that one quantum state. Now, as the black hole starts evaporating, that's another great thing that Stephen Hawking discovered, and which I suspect your listeners will have heard about from you or others.

0:27:09.8 RB: So the black hole isn't just going to sit there. It's going to start emitting radiation, and it gets smaller and smaller and smaller, and in exchange, you get this growing cloud of radiation that's going off to far away regions and so the black hole basically converts itself slowly into this radiation. Now, if you know that the black hole is actually in one specific state, that means that later on, the black hole and the radiation together, whatever they became, also has to be in only one possible quantum state. And that in turn constrains the entropy that the black hole has to have by itself. The black hole is now not in one specific quantum state. If you have a quantum system containing two parts, in this case, the black hole and the radiation, and you're only asking about one part, then even if they're in one definite state together, that one part will be in an indefinite state consisting of a list of possibilities. This is something related to the word entanglement. So since we're throwing out words that your listeners might have heard...

0:28:11.7 SC: We'd heard that word.

0:28:12.9 RB: They're entangled, and if you look at one of them, they're going to be in what's called a mixed state, lots of different possibilities. And you can then use basic principles of quantum mechanics to say, well, the black hole should have a certain amount of entropy. Depending on how much of it has evaporated, that entropy goes first up and then back down as the black hole has fully evaporated. This curve is called the Page Curve after Don Page, who first derived it. And recently, my colleague Jeff Pennington and a group of people on the East Coast, well, actually East and West, a group of four other physicists, simultaneously and independently discovered a way to derive this Page curve using just gravity. So that was a huge breakthrough, because among other things, it tells you that the entropy or the number of possible states at the end, when everything is just radiation, the black hole is gone, is one. There's only one possible state.

0:29:10.3 RB: That alone is incredibly important because it speaks to this long debate that we've had for almost 50 years about whether or not black holes return information. When you make a black hole from a definite state, Hawking initially calculated it radiates into radiation, which is in a mixed state, lots of different possibilities and so you've lost the information about what that initial state was. You always get the same garbage out, no matter what you put in. What this calculation did was to ask gravity in a nice enough way that you could actually trust the answer and also do the calculation. [chuckle] And gravity said, no, no, no, the information is coming back out. And so this is the first time that we've had a direct gravity calculation check of the fact that, in fact, information is not lost in black holes. And it's more detailed than that because it tells you exactly how much entropy the black hole and the radiation have along the way. Not just in the beginning and at the end, but during every stage of this evaporation process. And you get the answer that's expected from information comes out on the [0:30:19.0] ____ nose.

0:30:19.8 SC: And I think, let's be very, very... I'm going to try to be as careful as I can right now, just so everyone gets this exactly right. Because this is very subtle stuff that is at the cutting edge of modern research and it's easy to simplify it just a bit too much. So we had Netta Engelhardt on the podcast. So she talked about her work a little bit. She was one of the four other physicists.

0:30:42.4 RB: Exactly.

0:30:44.8 SC: And I guess the way that I think, if I understand it correctly, I would say it is quantum mechanics says that the information should ultimately be preserved somewhere. We've been having trouble seeing how that is compatible with the evaporation of black holes. They haven't told us precisely how the information gets out in some sense, but they have provided more evidence that it does in a way that doesn't require too much specific craziness from string theory or extra dimensions or anything like that.

0:31:14.5 RB: Yeah, it has absolutely nothing to do with string theory. So that calculation is a calculation where you just ask gravity. Now, here's why it makes sense for them to have been able to confirm that information gets out, but not tell us how. Because initially that sounds weird. Like, how does that make sense? How can you confirm the information comes out? [chuckle] But not... Okay. So nobody is saying that gravity Einstein's theory, as we know it, is the final answer, or that some simplistic way of combining gravity with quantum mechanics by doing what's called a path integral, it's a favourite tool in quantum mechanics, that that's the final answer and knows everything. But it is a much more powerful approximation scheme than might have been initially realized. It allows you to ask... So it initially allowed Hawking and Bekenstein to derive the coarse-grained entropy of a black hole.

0:32:17.6 RB: That's already pretty sensational. But notice that the entropy or number of states, that's one number. It's one number. You're asking just about that one number. And gravity was smart enough to give you that one number. Again, already surprising, but it's just one number. Okay. Now, when you ask, how does the information get out? That's a complicated process. When you ask, what is the state that the black hole produces? What exactly state is that radiation going to be in? Well, having to choose out of some exorbitant number of possibilities, that's a very, very complicated question that there's good reason to think this approximation scheme that we're seeing is quite powerful. It's not powerful enough to do that. What Jeff Pennington and Netta Engelhardt and her collaborators discovered is that it is powerful enough to ask and answer the question, what is the entropy of the Hawking radiation as a function of time when it's emitted by a black hole that's initially in a definite state?

0:33:25.3 RB: It's again, just one number. It's a more sophisticated question than the one that Hawking and Bekenstein asked. But gravity is smart enough to answer the question. You sort of have to help it along a little bit. You have to use multiple copies of the space-time in which the black hole is formed and evaporate. You sew them together in clever ways and that gives a turbo boost to the smartness of gravity and it's able to spit out that answer. But the difficulty of explaining how the information gets out and in which precise state the radiation actually is, that looks like it's a significantly more complex question. It's not clear that we can ever make gravity by itself smart enough to answer that question. It's not like we're done. We still need to discover a quantum gravity theory.

0:34:11.6 SC: Plenty of work for future generations of students. That's always the message that we have here.

0:34:16.4 RB: Yes. Yeah.

0:34:17.7 SC: Young people listening. We're not done yet. [chuckle]

0:34:20.2 RB: Apply for grad school now.

0:34:20.2 SC: Exactly. And to be even a little bit more specific, but again, we're going to go back and forth from the 70s to 50 years later, I think. It's not just that Bekenstein and Hawking calculated the entropy of black holes and therefore the number of quantum states. They found that it was proportional to the area of the event horizon of the black hole. And this is again, just one little fact that maybe, okay, the lesser minds might say, "Eh, that's fine." But we've been beating our heads against this fact for a long time and it's led to ideas like holography and more. And you played a major role in clarifying what holography is really all about. How do you think about, how would you tell the person on the street what physicists mean by the word holographic or holographic principle, the phrase?

0:35:13.8 RB: Yeah. So what it means, and this really goes back to what I was saying in the very beginning about gravity knowing not only about its own quantum states, but also about the quantum states of matter. So just now we were discussing how gravity knows about how many quantum states a black hole has, that's its own stuff. Now let's talk about matter. Well, if I could take a bunch of matter and compress it and convert it into a black hole of a certain area, the only way that that's consistent with the principles of quantum mechanics, which say that information can't be lost, is if the black hole through that list of quantum states that it could be in, can store the information about which state the matter was in.

0:36:02.1 RB: I could reverse this. I could figure it out by looking somehow carefully enough at what state the black hole is in. Ah, it was made from matter in this particular quantum state. The cat was dead and not alive or whatever. In order for that to work, the black hole area in the appropriate units that Bekenstein and Hawking figured out, so the number of black hole quantum states has to be bigger than the number of quantum states the matter could have had to start with. It's like if I have a list of 1000 entries on some piece of paper and I give you a form with only 10 entries, you can't transfer them all. They're going to be too squeezed. So if I give you a longer list, there's no problem. I mean a longer form. But if it's any shorter than 1000 entries, you can't transfer it. You can't transfer the information.

0:36:49.3 SC: Entropy has to go up. So there has to be enough room in the black hole.

0:36:52.6 RB: Yeah, exactly. There has to be enough room in the black hole. And now what's interesting about this thought experiment that we just did is that all I said was, well, suppose I converted this matter into a black hole of a certain area. I didn't tell you anything else about what that matter was. I didn't even have to know what the elementary particles are that the world is made out of. I could be totally ignorant of that. It would still have to be true. So you can glimpse maybe from this argument that we can leverage this knowledge about how many states a black hole has, to make very universal statements about how much information there is in matter that fits into a certain region. If it doesn't fit in that region, you probably couldn't make a black hole out of it. You had to be able to compress it to make a black hole. Now this sounds very vague, but my contribution to this subject was to turn that into a very precise statement. I can start with any surface in any space time, and I can look at its area, and I can use that to constrain how many quantum states, how complicated the world can be in a very precisely defined neighbourhood of that surface.

0:38:05.0 RB: Roughly, it's inside. It's not always the inside in the way that you might think about it, but it's roughly that. It has to do with what light rays we see that come out of that surface. And so an example of that is, I could ask about the information content of the universe right now, by which I mean the part of the universe that we can see which is only as far as... The universe is 13 or 14 billion years old, and light's only had so much time to reach us. So there's a certain part of the universe that we can see. And what my prescription tells you is how much information there could possibly be in that part of the universe. And it tells you that in terms of the largest area on what's called our past light cone. So if you ask what is the surface that the light rays traced out that are reaching us just now and that started out the Big Bang, that has a largest sphere somewhere along the way. And its area tells you that the universe has an entropy that's no more than 10 to the 120 or something like that.

0:39:07.9 RB: So that's an example of a holographic principle at work. And it's surprising. It's surprising not only because it's, again, weird that gravity knows something about the quantum states of matter. It's completely universal, it doesn't matter that matter is made out of electrons or protons or maybe fundamentally it's strings. The statement is just true. But also it's surprising because you would have thought that the amount of information you can have in a region should grow like the volume, not like the area. If I make a... If I have a heap of computer chips that each store a gigabyte of data or something, then the volume of the heap tells me how much information is stored not the area of its surface or something. So that's another surprising feature, and that's why it's called the holographic principle. It's a bit like the information is stored on the boundary or on some surfaces.

0:40:05.5 SC: And also just a very simple fact that it's a finite number. There's a finite number of bits of information which you would not have guessed from any non-gravitational quantum field theory. Gravity is again being special.

0:40:20.6 RB: Yeah, that's right. And that's really one way of... A very nice way of thinking about it is to just start by forgetting gravity completely. Then as you say, our most fundamental theories tell us that there's just no limit at all on how much information you can store in any region of space-time because you can always go to smaller distances in principle, not in practice right now. But there's no wall you hit. There's nothing that tells you that it's not in principle possible. When you turn on gravity, the first naive guess you might have is that the maximum information content should grow like the volume. You might think that gravity gives you a sort of shortest distance scale that it makes sense to think about. And so you can divide your region up into tiny little cubes of that size and count them.

0:41:05.4 SC: The Planck length.

0:41:05.5 RB: Yeah, the Planck length. And then you'd think, okay, if I double the volume, I've doubled the amount of information I can store. But that would still be wrong. And the reason that it's wrong is that it's too easy to change the shape of space-time dramatically before you even have a chance to make use of these tiny distances. It's too easy to, for example, make a black hole. I know it's in practice pretty hard to make a black hole for us in the lab. We don't know how to do it. But compared to accessing all these would-be tiny regions in which we can store information, it's actually much easier to make a black hole. And that's what happens first. And so you're thwarted in your attempt to store a volume's worth of information in your region. And you just ended up making a black hole and that information content is now set by its surface area.

0:41:56.5 SC: And this leads to something that is a little bit both provocative and vague. And maybe those two things are helping each other out, but it's a kind of non-locality that is special to gravity. Quantum field theory of the standard model of particle physics or whatever is a quintessentially local theory. There's a wave, a field value at every point in space classically, and then you quantize it. And of course there's entanglement, but still particles bump into each other at the same point in space. But the holographic bound or the earlier Bekenstein bound and whatever, how much energy or information you can fit in a region, that's not a statement about what happens at a point. It's a statement about what happens in a region. And that's a different kind of physics in some deep way.

0:42:40.0 RB: That's right. Gravity is telling us that the world is in some deep way non-local. So, an important principle of physics, ironically, it's encoded in what Einstein first discovered when he formulated special relativity, is this idea of locality. That if I have something going on at the Andromeda... Let's say that some star explodes in the Andromeda galaxy right now. Well, I can't find out about that faster than the amount of time that it takes light to travel from Andromeda to here. I'm gonna have to wait. I can't learn about this instantaneously. In fact, that notion isn't even very well defined. So that's been a very important principle in physics. And yet the holographic principle tells us that at some level it has to be wrong. If I can store all of the information about some space-time region on its boundary, well, that means that in some sense I should be able to look at this boundary and read off information about what's going on instantaneously some distance away from it in the interior. And in fact, that is literally what we're able to do when we apply this AdS/CFT correspondence.

0:44:01.5 RB: The AdS/CFT correspondence that I mentioned, this explicit quantum theory of gravity that we have for some class of space-times, realises this notion of the holographic principle in a totally explicit way. Again, you can put it on a computer and do calculations. And you have the ability on the boundary of the space-time to act with what's called a quantum mechanical operator, like a thing that changes stuff in such a way that instantaneously in some sense it changes the state from, let's say, the universe is empty to the universe has an elephant in the centre. And now the reason that that's not a complete contradiction with what Einstein established 100 years earlier is that, in fact it is still inconsistent for an elephant to suddenly appear in the centre of the space-time. That's not the correct interpretation of what we're doing when we're acting with that elephant creation operator. There is in fact no consistent way of thinking about this as space and time and the way we like to classically think about it for a while. What is really happening is that, we've destroyed the universe and we've recreated it with an elephant in it. And I think we're beginning to see glimpses again thanks to this recent progress of how this kind of thing might play out more generally.

0:45:24.3 RB: So I was complaining over and over that this AdS/CFT correspondence is about universes that are not like ours. As wonderful as it is, it's not like our universe. What we wanna do is be able to describe our own universe. And in fact, Jeff Pennington and I just had a paper out in which we're trying to take a step towards being able to do that. We're trying to say that if you have access to a particular part of space-time, you don't have to literally be all the way on the boundary. It's not even clear what that means in the real world. In the real world, we're part of the space-time. So we wanna be able to say... To ask what can we do that's in some sense non-local that's analogous to this elephant creation operator, if we control some part of the space-time but maybe not all of it. There's some part that's far away where we want to make the elephant. And we were able to give a rule for not exactly how that should work, but for how far away you can make an elephant if you have control over a certain region of your universe. And hopefully, by studying that pattern, we can learn more about how quantum gravity actually works in more realistic situations like our own universe.

0:46:34.8 SC: And this is... Sorry, I should ask. Is that work that you just talked about with Jeff Pennington in the context of AdS/CFT?

0:46:42.5 RB: Well, no. It's motivated by some things that we learned thanks to AdS/CFT and thanks to string theory. But it is logically independent of that. What's a nice check is that, when you apply our more general rule to this AdS setting, where we already knew how things work, it gives us back those things that we knew how they worked. It doesn't contradict what we had before. But the whole point here is to allow it to be applied in a universe like our own or really any universe you can dream up.

0:47:17.6 SC: You've told us correctly that AdS, which stands for anti-de Sitter space, is not our universe. But we haven't actually told the audience what it is. So maybe we can take a breath here and try to explain what AdS is and why it is an implementation of the holographic principle in such a nice way.

0:47:39.0 RB: Ah, yes. Well, I'm sure your highly educated listeners will have heard this before. So I hope I'm not gonna create too much overlap. But our universe is more and more rapidly expanding. It has something called a positive cosmological constant. The thing I said earlier about string theory being a cool theory is that it can explain why it's so small. That's actually a mystery. But one fun fact about it is that it is positive. If it were negative, we'd be a little closer to something called anti-de Sitter space. We'd still not be an anti-de Sitter space because it looks like we have a sort of infinite amount of matter distributed all over the place as far as we can see. So that would still not quite get us there. But if you removed most of that matter and you had this negative version of this cosmological constant, then you'd be an anti-de Sitter space.

0:48:33.2 RB: And anti-de Sitter space is a funny place. If you were sitting in it and you throw your friend away from you because you don't like him anymore, your friend is gonna come flying back to you a little while later. How long? That depends on how large this negative cosmological constant is. And it's just gonna oscillate back and forth like this the whole time and you'll never get rid of him. De Sitter, where we live, it's the opposite. If I'm tired of my friend and I just put him out in space to float away from me, he's gonna fly faster and faster away from me and eventually will be gone and that'll... This is why I have no friends.

0:49:09.2 SC: [laughter] You [0:49:09.5] ____ are a little extremist a little bit. Making elephants, throwing away your friends. Come on.

0:49:15.2 RB: Yeah. But what this effectively means is that, anti-de Sitter space is kinda like a box. You're closed in a box. It's a little bit weird because it is spatially infinite. But no matter how hard you throw away your ex-friend, they're gonna come back to you. So you'll always have friends in anti-de Sitter space. And it being a box helps with this holographic stuff. Yeah, sorry.

0:49:40.0 SC: Just to say it again so I think we're on the same page. You're throwing away your friends. Some of us would have just chosen baseballs, but okay, you're throwing away your friends. The harder you throw them, the further away they get because space is infinitely big, but they will still always come back. That's the point.

0:49:57.0 RB: Yeah. And in fact, the time that it takes for them to come back won't depend on how far away I throw them. [laughter] They get turned around. It's a bit like a pendulum. You know how the frequency of a pendulum doesn't depend on the amplitude, which is why Galileo used them as clocks. It's a very useful analogy, I think. It's just like that, except it actually works even better than for a pendulum. If you move a pendulum too far out, then actually you start seeing that it's no longer true. But in anti-de Sitter space, this is just exactly true. Your friend is like a pendulum with a fixed frequency. Anyway, friends aside, anti-de Sitter is kinda like a box and you can think of the hologram as being on the boundary of the box. The hologram is our quantum gravity theory, which in some non-local way encodes what's going on in the interior of the box. And that theory, which is just a standard, completely well understood theory called conformal field theory, that's the CFT in the name, AdS/CFT correspondence, that theory is our complete quantum gravity theory for that type of boxy universe.

0:51:12.8 SC: And it's sort of the inside out version almost of the black hole where we're standing outside. And is it accurate in the black hole case? How accurate is it to say from the holographic point of view, that the information about the black hole literally is there on the horizon versus just equal in amount to the area of the horizon?

0:51:39.0 RB: That's a loaded question, to which I think it's also not a settled question. The reason that it's a loaded question is that, first of all, it's certainly from the viewpoint of somebody who sees the black hole form stays far away, comfortable, safe, and the black hole starts evaporating, this radiation is coming out. It is perfectly consistent with any experiment that they can do to say that the black hole is literally a membrane that stores an amount of information equal to its surface area. And they'll never have to think about what's going on inside the black hole. It never matters for anything that they wanna explain because they're not going there. And everything that they can observe can be completely explained by this picture where the world basically ends on the horizon of the black hole. The horizon of a black hole is a surface, in the simplest case, spherical that you had better not cross if you ever wanna get back out to distant regions. It's the one that if you cross, you're gonna get crunched eventually and hit some kind of singularity.

0:52:49.9 RB: Now, suppose you are that person who's gonna fly, you're the adventurous type, who's gonna fly across the horizon and find out what the interior looks like. Well, there's a real contradiction between what I just said the outside observer can do. Think about the black hole as an object, the world ending on that membrane, and you're trying to fly right through the horizon and see nothing special there and enter the interior. Einstein's theory tells you that there is nothing special there. Einstein's theory, general relativity, our theory of gravity, very well tested, is absolutely insistent that crossing the horizon of black hole is like empty space everywhere, like any other kind of empty space. There's not a sign saying, here's the horizon. There's not a slap you get when you... It's not even like hitting a fly on the freeway, splattering on your windshield. It should be nothing. You should not be able to notice it. We should be able to cross the horizon of a very large black hole right now without knowing about it. And those two principles are in a serious conflict with one another. I suspect you may have discussed this before. It's called the... In its old form, it's called the black hole information paradox. What I said earlier about the outside observer is predicated on the idea that information comes out of the black hole.

0:54:09.8 RB: In that case, it seems necessary to say that that information, while the black hole is still there, is stored on its horizon. And so it is what you want to be true if you care a lot about quantum mechanics. And then the other perspective where you fall in, you wanna see nothing special at the horizon, that's what you wanna be true if you care about gravity, if you care about Einstein. And real physicists care about both. And so they're like, "Oh my God, what am I gonna do now?" Because these two things don't fit together at all. And the modern incarnation of that is called the firewall paradox. It's just really a sharper, strengthened version of the argument that led Hawking to conclude that black holes don't return information. So Hawking came down on the side of the infalling observer of the gravity guy. And today, I think the evidence is overwhelming that the information does come out. So you are likely to take the point of view of the outside observer who sees information coming out, but then you seem to be forced to say that there's some kind of structure at the horizon in conflict with gravity, some kind of firewall or whatever you wanna call it. So we're still grappling with that.

0:55:18.4 SC: Well, we did have Lenny Susskind on the podcast. We talked a little bit about complementarity. And wouldn't he, if he were here, say both perspectives are correct to the infalling observer you see nothing and the outside one it looks like a membrane at the horizon?

0:55:33.1 RB: Yeah, I would say... Well, Lenny certainly is an advocate of a particular approach to resolving this problem, which I also tried initially after this firewall paper appeared. And I think we both would probably agree that it's worth exploring approaches of this type. I think we would have different levels of confidence that they solve the problem. In particular, my sense is that right now, there is no resolution of this paradox that fully preserves both of these fundamental principles, that doesn't in some way violate important aspects of quantum mechanics and or of gravity. The approaches that I like the least are the ones that violate both. Because I think one thing we learned from Einstein and some of his predecessors in the history of physics is, when you have two deep principles that turn out to be in conflict with each other, that's definitely a huge opportunity for progress.

0:56:50.0 RB: In physics, we like crises because it sharpens things and then tells us, okay, here's where we have to dig. But you wanna come down on one or the other side. You don't wanna violate both because that's really ugly. It doesn't seem likely to me that quantum mechanics is a little bit wrong and gravity is a little bit wrong. I'd rather have one of them be really wrong and understand how to move forward and preserve the other. So my feeling is that a lot of the approaches that we're seeing today kind of break both a little bit. I think, for example, Lenny would concede that black holes, in fact, can have firewalls. He's just trying to save us from having firewalls when the black hole has maybe freshly formed and it's not yet insanely old. And to me, that's like, who cares? Like, once you can have firewalls, it's just a terrible affront to general relativity.

0:57:43.1 SC: Right.

0:57:43.2 RB: And I don't really... To me, it makes very little difference when that happens. To me, it seems like either we get rid of them or if we can, then let's try to understand the problem in a different way. Let's try to understand where they come from, which we don't. I mean, if firewalls form, we have absolutely no idea what the dynamics of that is. So, I'm not saying that I know how to answer this problem, but I think a crisis is a great opportunity and we should be careful not to think that we've solved it. I think we haven't.

0:58:16.3 SC: Okay. They're very, very good to hear. Or very, very interesting to hear. I mean, maybe it'd be nice to have solved it, but we take what we can get. And like you say, the crises are opportunities in this field. So that is a good thing. But I guess the feeling I'm getting then is, there is this relationship between, I wanna say, space-time and reality, but maybe that's a pregnant way of putting it. There's this question of what exists and how we should think about the world. And I think it's very natural for most people to think of space and stuff in it as existing. And in some sense, this idea of the holographic principle for black holes, where you can think of them as having all the information on the horizon, but maybe there's an interior if you jump in. And also the AdS/CFT version, which is sort of the inside out version where we're inside the horizon and it's infinitely far away and there's all of our information is there. Both of these are undermining the idea that there is stuff located at points in space. Right? Quantum mechanics or quantum gravity seems to be a bit more subtle than that. And the AdS/CFT correspondence is saying there's two totally different ways of talking, which in those two ways of talking, puts stuff and space on very different footings.

0:59:32.0 RB: Yeah, I agree with everything you've said, but I don't think that this in itself is very shocking or unusual. I mean, I think that the history of physics is a story of how we have found new concepts that allow us to think about phenomena on a deeper level. But that doesn't mean that what we had before was wrong, nor does it mean that the new concept is the final word and that's how somehow things really are. Right? I mean, it seems pretty obvious to me that this debate about what's real, I mean, to me anyway, is completely meaningless. What we can ask about is, what are efficient ways of describing nature? What are... Yeah, what are economical ways of explaining the data that we have, of explaining experiments we can do? And that's what changes over time. So, a good example is, let's say, the motion of the planets, right? So already in ancient times, there was a pretty good theory of that by Ptolemy.

1:00:50.2 RB: And it was pretty complicated, but it kinda did the job reasonably well, allowed you to predict where they were going to be the next days. It's a pretty big success. And so we could say, okay, but these drawings that he made with the sun first going around the planets, and then, there are gonna be these epicycles and that is... That was obviously very complicated, would have been much easier if you just put the sun in the centre and let the planets go around it. And it would have been more to our liking. We know today that that's the more efficient way of thinking about it. But it wasn't really wrong. It wasn't wrong, because you're perfectly free to take the point of view that you're in the middle of the world and the sun is going around you and then the other planets are going around the sun while the sun is going around you. That doesn't give you the wrong answer. That's actually what we see in the sky, right?

1:01:43.4 SC: I can see the headlines now. Berkeley professor comes out with a paper [chuckle] with an eccentric view of the cosmos. Alright.

1:01:51.1 RB: That... Sorry, that train left a long time ago. I mean, this is just a question of what's more economical. It's not a question of what's right or wrong. You can certainly describe the world in that convoluted way. It's just... It's kind of painful, tedious. And more importantly, it makes it harder to make progress after that. Right? It was a lot harder to understand. For example, I don't think Newton could have gone from Ptolemy to his force law that tells you why the planets move like that around the sun.

1:02:27.8 SC: Right.

1:02:28.4 RB: But once you had Kepler, first of all, the refinement that it's not just circles, but ellipses. And then you had the sun in the centre. It's much easier to figure out like, okay, what do I have to put in to reverse engineer the force that is making the planets do that thing? It's much easier once you have a simple picture of what's happening. And that's why that was so vital. It's vital for progress that you think about it in a simple way and not in a convoluted way. But was Kepler wrong once Einstein discovered that the planets actually don't quite move on these ellipses?

1:03:00.6 RB: Because yeah, in some sense, he was wrong, but it was a better explanation and simpler. And it was, yeah, with fewer ingredients, explained more data. So, that's always the progress. And I don't think that the status of general relativity is any different fundamentally from the status of Ptolemy or of Kepler. It's just more powerful. It explains a lot more things with fewer ingredients. And it's still alive. It's been tested over and over, most dramatically recently by the discovery of gravitational radiation from black hole mergers and other compact objects merging. It's a fantastically successful theory, but I think in physics, we never ask, is this real? We can ask, you know, what's better?

[chuckle]

1:03:49.9 SC: I'm perfectly happy to ask what's real. I think that's what I'm very interested in doing. But otherwise, I do very much appreciate the operationalizing and simplifying like, what gets us understanding. But let me ask almost the same question, but in a slightly more down to earth way, which is more sympathetic to the philosophy you just put forward. The AdS/CFT correspondence, which as you've correctly said, is not our world. We live in a different world than the anti-de Sitter world. But nevertheless, it posits an equivalence between a description that has a certain number of dimensions of spacetime with an anti-de Sitter kind of universe and one fewer dimensions of space time at the boundary with no gravity at all. So my question is, if that were the universe, right? If we really did live in AdS/CFT, would we live in ADS or would we live in CFT? [chuckle] Would we see a universe with gravity and anti-de Sitter space or would we see a universe with no gravity and one fewer dimensions or could there be both or is that even a sensible question?

1:04:58.6 RB: I think it is a sensible question. And what I was trying to say... I guess I didn't really close the deal in what I said earlier. What I was trying to say is that that question is exactly analogous to asking, is gravity a force that keeps the planets going around the sun or is gravity the curvature of spacetime and the planets are just trying to go as straight as possible in this curved spacetime? Well, for most purposes, those are mathematically equivalent statements. Now, if you want extremely accurate descriptions of the motions of some of the planets, like that of Mercury over a hundred years, then in fact, it turns out that one of them gives you the correct answer and the other one is just a little bit wrong. So, one is a better approximation than the other.

1:05:44.2 RB: So, what's interesting, right, is that at the quantitative level of explaining experiments, at least as far as the solar system is concerned, there's almost no difference between these two descriptions. But from the conceptual viewpoint, they couldn't be more different. It's surprising that it's possible for them to even be remotely similar in any kinda situation in terms of outcomes, but they are. And so in those settings where they give you the same answer to... You know, as good an approximation as you need, you can go back and forth between both descriptions, that's just equally good. It's up to you which one you like better.

1:06:21.0 SC: Okay. Now, I think now you're dodging a little bit too quickly here, because even if the AdS... I know, even if AdS and the CFT correspondence, the two sides are equally formally good, you notice one. Like, most of us, most of my friends think they live in a three-dimensional space. [chuckle] I don't know of anyone who goes, oh yeah, I live in the two-dimensional holographic dual to your space. There's something that is closer to the manifest image of the world. And is...

1:06:53.6 RB: Yeah, that's usually the worst theory, right? I mean, if you went by what we think is true based on everyday experience, there also wouldn't be any quantum mechanics and the speed of light wouldn't be the limit because why on earth should that be true? And I don't know, there shouldn't be a twin paradox. Lots of things are not like what we experience in everyday. I don't think that has anything to do with the question you asked me.

1:07:19.5 SC: The question is there's two different descriptions that have different numbers of dimensions of space.

1:07:22.5 RB: Yeah.

1:07:23.8 SC: Surely if there were living creatures in that universe, they would hit upon one of those answers before the other one.

1:07:30.3 RB: Oh, I'm sure they would... Well, okay, one of those... That's the same as for us, right? We've already hit upon classical gravity, the world being... That's the easy description that you discover first probably. I don't know, maybe they're very different from us. Their brains fire differently, but yeah, I would expect...

1:07:49.6 SC: The AdS/CFT creatures would probably first find themselves on the AdS side where there was gravity rather than on the conformal field theory side where there was not gravity.

1:08:00.9 RB: We can simplify this discussion by pretending for a moment that we actually did live in an asymptotically anti-de Sitter universe. Sorry, that was very technical. We live in one of these...

1:08:11.9 SC: Yup.

1:08:12.0 RB: Boxy AdS universes, because you could put our galaxy there and just don't put any of the other stuff. And it would have made absolutely no difference for the evolution of humans and everything would have happened exactly the same way, and we will be sitting here right now. And maybe we haven't measured yet what the universe looks like. You know, we're kinda slow that way and we're gonna build our first telescope tomorrow and we're gonna discover, oh, it's AdS. But at that point we will be in precisely this situation. We have a good theory of gravity, Einstein's theory. We've discovered quantum mechanics. We want to put them together. And maybe we've already discovered the AdS/CFT Correspondence. So we even have a good quantum theory of gravity. And now we look at our universe and we discover, oh, it's anti-de Sitter space. Bingo. We got super lucky. We live in that universe for which we already have a quantum gravity theory. Wouldn't that be nice?

1:09:00.3 SC: Okay. I think that you're begging an important question here, but I'm gonna table it till the next time we're on the same coast and I can get you beer and/or coffee and we can hammer this one out. Because I do wanna switch gears as we wind up back to the real world where we do live, where we have a positive cosmological constant. And one of the things that modern theoretical physics has to grapple with is this fact that we know so much about the counterfactual case with the negative cosmological constants in AdS/CFT and we would like to know more about the real world. And we seem to be struggling with that. Do you have strong opinions or do you have a way of phrasing why it seems to be so hard to do the analogous thing for the real world?

1:09:44.1 RB: I guess, nature doesn't like to throw us softballs. It's a really challenging situation, because for... The problem isn't just that we don't have a good quantum gravity theory for our own universe. The problem is worse because it's not totally clear what we would want that theory to compute for us. In many situations, like in AdS/CFT, it's possible to define sort of idealized exact observables that exist somewhere in the universe. Maybe they're not accessible maybe to humans with their finite resources, but at least in principle it's... You can imagine that you could always increase your resources and do better and better and approach this idealized kind of measurement, as well as you desire.

1:10:41.9 RB: And in our universe, it's not clear whether such a thing exists and what it would be. So, it's not totally clear what exactly we're aiming at. And that has something to do with the fact that anti-de Sitter space is like a box. It has a boundary and the boundary is a good place to go if you want to make things exact, there's a lot of space there. And you can build very precise machines and do very precise measurements. And in our universe, it's not at all like that. So that's one thing that really makes this challenge hard. But another thing, which is just my personal opinion, I guess, is that it's extremely unlikely that our universe is fundamentally of the type where you have a positive cosmological constant forever.

1:11:33.6 SC: Okay. I mean, that's a pretty strong statement you just made, given the lack of empirical knowledge about that.

1:11:39.8 RB: Yeah, yeah, yeah. So, one reason... There are two reasons why I believe that. One is a proposal that Joe Polchinski and I made some 20 years ago about what explains the small positive value of our... Of the observed cosmological constant. And that is, in my view, currently the only viable explanation of that value. And in that explanation, it is the case that there are many other possible values that the cosmological constant can take. It's just that we're stuck with one for a while. Sort of like the way that you can have a radioactive atom and it sits around for a billion years and then it decays into a different atom. These time scales can be very large, you can think there's nothing else in the world, but in fact, there is and one day our universe will decay to one with a smaller cosmological constant. And there is an enormous fundamental difference, even if that takes a very long time to happen. There's an enormous fundamental difference in what you might think a quantum gravity theory should look like, depending on whether or not that happens.

1:12:49.0 RB: The second reason why I think that will happen is a different observational reason, maybe a little bit more direct, which is actually an argument that Lenny Susskind made sometime around, and his collaborators, Kleban and Dyson, around 2002 or 2003, something like that. They just said, well, suppose that we do live eternally in this kind of universe forever. Well, that kinda universe turns into a box as well, but it's different from the anti-de Sitter box. It's called a de Sitter box, amazingly. And this de Sitter space is a warm box. Its walls, unlike those of anti-de Sitter space, have some fixed temperature that never goes quite to zero. And when you have a warm box, one of the weirdnesses of quantum mechanics is that everything that it can eventually produce as sort of thermal radiation, as sort of temperature garbage that gets sent into, you know, along your way, will eventually be produced.

1:13:52.4 RB: It might take a long time, but it's gonna happen. And in fact, if that box exists for an infinite amount of time, everything is gonna happen infinitely many times. And that isn't just confusing, but in a way that I think they argued very nicely, it's inconsistent with our observations. Or more precisely, in a theory that posits that our cosmological constant is never gonna go away. What we observe has unbelievably small probability, precisely the sort of situation that would normally cause you to reject a theory. You know, you've done some experiment, you got some data, that data shouldn't have happened according to that theory, so you chuck it out and find a better one. So, that's reason number two why I don't think we will forever be stuck with this positive cosmological constant. And of course, I think it's significant that those reasons both point in the same direction. They're consistent.

1:14:47.8 SC: That's basically the Boltzmann brain problem as my...

1:14:51.6 RB: Yep. That is sometimes called the Boltzmann brain problem.

1:14:55.6 SC: Okay. So...

1:14:55.7 RB: I like to call it an inconsistency between theory and observation, so you can reject the theory.

1:15:02.1 SC: I'm biting my tongue so hard, because there's so many things I wanna say, but look...

1:15:03.4 RB: I know, I know. But suffer.

1:15:06.2 SC: I'm just gonna indulge myself for the next one. [laughter] I do wanna sort of wrap it all up, because really, we're right close to something that I think is crucially important here. In that, as you already said very nicely, de Sitter space, the universe with a positive cosmological constant becomes like a box. There's a horizon around us. Eventually, all the galaxies float away and you enter empty space. The difference with anti-de Sitter space being that the box has a finite size, right? The horizon has a finite area around us. And so, one of the technical difficulties in doing in de Sitter what we know how to do in anti-de Sitter is that the boundary where our information lives holographically is not infinitely big in de Sitter space, right?

1:16:00.8 SC: It has a finite size and quantum field theories naturally have an infinite number of degrees of freedom. Or even if we want to go to super technical language, an infinite dimensional Hilbert space. Whereas the de Sitter box that we will eventually go to has a finite entropy, a finite number of quantum degrees of freedom. And then I asked you before, should we think about the horizon of a black hole as really being everything that's on it? So, if that's our future, if our future is, we empty out and we have a horizon around us with a finite number of degrees of freedom, we have a finite entropy, does that mean, which I think maybe the Dyson, Kleban and Susskind analysis thought of, that really the whole theory of everything only has a finite number of degrees of freedom, a finite number of quantum states?

1:16:50.7 RB: Yeah, that's a great question. I mean, this is why I thought this paper was so important. The reason... So, I think this was a very important question. Can it be that our universe is sort of the final word as far as this value of the cosmological constant is concerned and therefore, the number of states in whatever fundamental quantum theory describes it? There was a very nice argument that was made by Fischler and Banks, I think around 2000, that maybe that's the kind of quantum gravity we should be looking for, right? One where there's only a finite number of states, so very different from the kind of things that you were just saying. Quantum field theory always has infinitely many, no matter what the setting is, unless you put some explicit sort of discretization. And when Joe and I discovered what later was called the landscape of string theory, this... Our way of solving the cosmological constant problem, that was a proposal that, in some aspect of which I think troubled a lot of people and which was certainly regarded as quite radical.

1:18:00.9 RB: And, as a physicist, I mean, I think you're always supposed to start by trying to shoot down your own ideas. So, I spent the next two or three years, basically pursuing this idea that Fischler and Banks had proposed, that maybe the world works this completely other way where we have a finite number of states, and it is what it is because it's trying to make do with this finite number of states. And it seemed like definitely... You know, I'd seen a lot of worse ideas than that. And so, it seemed like it was worth thinking about it. And it was only this argument of Dyson, Kleban and Susskind that that theory is necessarily inconsistent, or at least I was compelled by this argument. I thought it was convincing enough that it's inconsistent with observation. And at that point, I guess I embraced the landscape and moved on.

1:19:00.4 SC: Yeah. [chuckle] So therefore, you would say you're happiest with the idea that there are an infinite number of possible quantum states in the universe, an infinite dimensional Hilbert space?

1:19:10.7 RB: I don't think... I guess, this is one of those differences between necessary and sufficient, right? So, if Tom Banks and Willy Fischler's idea was to sort of start with the idea that the Hilbert space, the number of possible quantum states is finite, and then say, well, maybe it's just that right number that gives us a universe like ours. And it couldn't have been any other way, because for some fundamental reason we're yet to discover, you're just handed this finite Hilbert space. And then, I think that this argument that this is inconsistent with observation tells us that that's not quite how it works. But once you're outside of the confines of that particular way of thinking about the problem, I think it becomes more difficult to say exactly what should replace it. I mean, if you put a gun to my head, I would say, yeah, to the extent that a quantum gravity theory is gonna be described, in terms of standard quantum mechanics, which I don't think is a completely settled question, with a Hilbert space that's associated with it. My guess would be that that's an infinite dimension of Hilbert space. But now we're on a much less constrained territory where it's harder to be sure about how it plays out, I would say.

1:20:31.9 SC: I don't know if you're going to make it very far in physics with this sort of humble attitude that there are some questions you don't know the answer to. [laughter] You're gonna give people the impression there's still questions that we need to work on. I don't know. How are we going to get PR like this?

1:20:47.9 RB: Well, yeah, if we knew the answer to all questions, I'd be out of a job, so. Oh no, wait, I have tenure.

1:20:55.6 SC: There you go. Yeah, you could...

1:20:56.6 RB: Yeah, no, we'll figure it all out.

1:20:58.4 SC: I will figure it all out. No, I think you've done got a very, very good job of helping us understand how much progress we've made, but also how much there remains to be figured out. And I have been biting my tongue, but we have more things to talk about, I think, offline. I hope that the audience gets a lot out of this. So, Raphael Bousso, thanks very much for being on the Mindscape podcast.

1:21:15.8 RB: Thanks for having me.

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