Stephen Hawking made a number of memorable contributions to physics, but perhaps his greatest was a puzzle: what happens to information that falls into a black hole? The question sits squarely at the overlap of quantum mechanics and gravitation, an area in which direct experimental input is hard to come by, so a great number of leading theoretical physicists have been thinking about it for decades. Now there is a possibility that physicists might have made some progress, by showing how subtle effects relate the radiation leaving a black hole to what’s going on inside. Netta Engelhardt is one of the contributors to these recent advances, and together we go through the black hole information puzzle, why wormholes might be important to the story, and what it all might teach us about quantum gravity.
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Netta Engelhardt received her Ph.D. in physics from the University of California, Santa Barbara. She is currently on the faculty in the physics department at MIT. She recently shared the New Horizons in Physics Prize with Ahmed Almheiri, Henry Maxfield, and Geoff Penington, “for calculating the quantum information content of a black hole and its radiation.”
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0:00:00 Sean Carroll: Hello, everyone. Welcome to the Mindscape Podcast. I’m your host, Sean Carroll. For those of you who are physics fans out there, you will know that one of the very long-standing big picture puzzles in physics is quantum gravity, reconciling Einstein’s General Theory of Relativity, which is a theory of gravity, with the fundamental principles of quantum mechanics.
0:00:21 SC: And a problem with this puzzle is that we don’t have a lot of experimental guidance. In fact, the only experimental guidance we have is that classical general relativity seems to work very well, and quantum mechanics seems to work very well, so they’re somehow going to be reconciled some day. Something we do have, though, are thought experiments, which can help guide us in thinking about, well, if we do eventually manage to quantize gravity, what will it look like? What shape will it have? What will it teach us? What will be the fundamental ingredients?
0:00:54 SC: And the most important thought experiment we have is the Black Hole Information Loss Puzzle. This is something that was given to us by Stephen Hawking, who in the 1970s showed that black holes aren’t completely black. When you include quantum mechanics, they radiate, and eventually they’ll evaporate completely away into essentially information-free thermal radiation. The puzzle is that most of physics doesn’t work like that. Most of physics conserves information. Even if you throw a book into a bonfire, the information in the book is somehow, we think, encoded in all the heat and light that is made in the process of burning the book.
0:01:33 SC: Whereas if Hawking were right, then black holes are different. They destroy the information that gets thrown into them. A lot of us don’t believe that’s actually the right answer. We believe that the calculation that Hawking did has been incomplete. But it’s very, very hard, as it turns out, to figure out mechanisms that can somehow get the information out. So the hope is, that by looking for such mechanisms, we can learn something about quantum gravity even if we don’t have direct experimental evidence for it.
0:02:02 SC: And interestingly, there has been progress over the years, and in just the past year or two, there’s been what looks like very exciting progress in this quest to understand how the information gets out of evaporating black holes. So today’s guest is Netta Engelhardt, who is a professor of physics at MIT. She’s one of the people who has been involved in this research which seems so promising, and she’s also really, really good at bringing some abstract ideas down to earth.
0:02:31 SC: That’s important here, because I will tell you right ahead of time, this is a brain-stretching exercise, this podcast episode. We’re going to go pretty deep. We’re going to start very gently. It’s supposed to be understandable to everybody throughout the entire conversation. But we’re going to get into not only black hole evaporation and things like that, but the AdS/CFT correspondence, wormholes and the structure of quantum gravity entanglement, all that good stuff. It’s all going to appear here.
0:03:00 SC: I think it all does make sense. I think it is not yet fully formed. One of the things that Netta mentions is that we don’t yet claim to have the final answer. What we claim is to have some very interesting tidbits of information that might help us get to the final answer of how to quantize gravity. I think that makes this both an enjoyable and maybe even an important episode of Mindscape.
0:03:23 SC: Let me take this opportunity to give you the occasional reminder that we have a Patreon account for Mindscape, if you want to support us financially. I say us, it’s just me. You know it’s just me. So you can go to Patreon.com/seanmcarroll, if you want to give support at some level of support per episode. And most of the benefit of doing this is that you feel good that you’re supporting something that you like. But also, you get some more tangible benefits in the form of you get to ask questions at the monthly Ask Me Anything episodes, and also you get an ad-free version of the podcast if that’s important to you.
0:03:58 SC: So we appreciate the support, we appreciate all the listeners, whether you support us or not. We think it’s a great community to have here, the Mindscape listeners. I personally, Sean, thank you for coming along with me on this journey in so many different topics that we cover. I know we like the physics ones. We like all the other ones as well. I’ve been learning a lot. I really love doing this podcast. This is a fun thing. Thanks for sticking around. And let’s go.
[music]
0:04:41 SC: Netta Engelhardt, welcome to the Mindscape Podcast.
0:04:43 Netta Engelhardt: Thank you very much.
0:04:43 SC: We have ahead of us today an ambitious show [chuckle] by the standards of the podcast. We’re going to try to not only discuss some of the difficult ideas in theoretical physics, but very cutting edge ones. We’re talking about stuff that has literally been going on in the past year among some of the highest reaches of theoretical physics. And correct me if I’m wrong, but my impression is, the dust hasn’t settled yet, right? This is an area where we’re still in the midst of working things out, so we shouldn’t expect the final answers to emerge over the next hour or so.
0:05:13 NE: Absolutely. I would be amazed if we had final answers over the next hour.
0:05:17 SC: [chuckle] Okay. So you don’t have them already, and we’re not… We won’t be mentioning them. But yeah, who knows? A good idea could happen. That’s been known to occur. But why don’t we… We have to start somewhere. We can’t explain general relativity and black holes in full generality. So let’s imagine that the audience has heard of black holes. They’ve heard that gravity is the curvature of spacetime. They’ve even heard that Stephen Hawking showed in the 1970s that black holes give off radiation, that they have a temperature, that they’re not completely black.
0:05:44 SC: Something that they may have heard, but let’s try to explain, is the idea that as wonderful a proposal as it was, this discovery of Hawking’s that black holes will eventually evaporate, leads to puzzles, leads to problems, the information loss problem. So as well as you can, what’s the big problem? Why is it an issue that black holes evaporate away?
0:06:06 NE: Yeah, so that was a lovely introduction of the current status. So we have this prediction by Stephen Hawking that black holes evaporate, and if you take that prediction very seriously and you follow the calculations, you find that what we call information is lost. And this is in fact in contradiction with some of the basic laws of quantum mechanics, which we expect information to always be conserved. And what we mean by information here is very analogous to what you might imagine are bits encoded in a computer, just the quantum version, and we call them qubits. And the idea is that there’s some information about these qubits that simply disappears from the universe altogether when the black hole evaporates.
0:06:55 NE: Now, things can go into a black hole and they might not be accessible to us living outside of the black hole, but as long as they still exist somewhere in the universe, we say that the information in the universe has not been destroyed. But if the black hole has taken some information with it and then disappeared altogether, then that information is gone from the universe, and we really have a process in the universe that loses information.
0:07:19 NE: And this is catastrophic from a couple of different perspectives, one of which you can think about in the following. Physics is what we call a predictive science. Give us some information about what is happening now and we will tell you, oh, this thing will happen in the future. We’re not fortune-tellers, of course, but the idea is if some particle is behaving in some way now, if we know its properties now, we can predict what its behavior will be in the future. And this also works in the other direction. If you are telling us how things are now, then we should be able to tell you how things were some time ago.
0:07:53 NE: But the problem is that information is lost. That means that after the black hole has evaporated, it is impossible for us to reverse engineer what was happening some time ago. And so physics is no longer postdictive, as we call it, able to predict or postdict the past, which is truly catastrophic because it means that there’s a fundamental weakness in physics, which is something that we have not ever seen and have not been able to incorporate into our theories.
0:08:24 SC: I guess, I’m going to be a little bit of a devil’s advocate here so I’m not revealing my own sympathies, which I think are exactly the same as yours, but it’s my job to play, to give voice to the skeptics. When we invented quantum mechanics in the 1920s, we did away with the very precious idea that you could make exact deterministic predictions about future experiments. Maybe we should give up on the idea that postdiction is possible and physics is information-conserving. And no less a person than Stephen Hawking actually believed that that was probably the right answer for at least a little while.
0:08:57 NE: Definitely, but we did not give up determinism with quantum mechanics. It’s a very important distinction that even though we gave up the idea that something might have a definite state, say in the Schrodinger cat experiment, that the cat is either alive or dead before we’ve measured it. We may have given up on that, but we have not given up on determinism in the sense that a given quantum state evolves into some other quantum state by a process which we can describe. And so I would say that determinism is a unifying feature of everything that we have seen and all the theories that we’ve constructed to date.
0:09:35 NE: Now, it’s possible, and indeed Stephen Hawking subscribed to this for a long time, that information is in fact lost. But then we have to ask ourselves, how is quantum gravity a… What kind of quantum theory is quantum gravity that it loses information? Quantum gravity being the descriptor of the quantum mechanics and general relativity together. If it loses information, what do we have to modify about quantum mechanics so that this actually is a consistent theory.
0:10:04 SC: Well, this bit about determinism I want to clarify a little bit, because if we believe that the only thing that ever happened in the universe was the evolution according to the Schrodinger equation, the fundamental equation of quantum mechanics, then I agree it’s completely deterministic. And my good friend, Hugh Everett, who invented the many-worlds interpretation, thought that that was right, but there are other approaches to quantum mechanics where it’s truly not deterministic.
0:10:29 NE: This is true. So again, there are people who subscribe to information loss. And there’s currently no empirical experiment that we can conduct to determine which one is correct, information conservation or information loss. Although certainly, the recent developments point us in one direction rather than the other. I would say that many of us find information conservation much more palatable because it is something that allows us to keep the tenets, the principles of quantum mechanics intact.
0:11:02 SC: Yeah, I think that’s exactly right. But I do want to… Something that’s always bugged me. You’re just going to be the guinea pig for all of the things that have bugged me about the information loss paradox for 20 or 30 years now.
0:11:14 NE: Naturally.
0:11:16 SC: The time when quantum mechanics does not look deterministic is when we make a measurement. And we can argue whether or not really it is deterministic, we just don’t see it because there are other branches of the wave function or whether someone like Penrose would say that there is a true collapse of the wave function at that moment. But if the way that we teach quantum mechanics in textbooks said that information is lost when we make a quantum measurement, why are we so upset when information seems to be being lost when black holes give off radiation? Until we observe it, we wouldn’t know, and when we observe it, we collapse the wave function and it looks like information’s lost anyway.
0:11:56 NE: Yeah, so let me maybe make an analogous picture of what you’re describing. Suppose that I am an experimentalist working with some tabletop experiment and I have some quantum particles. And some… Maybe some of my particles escape away from my tabletop and I’ve lost information. It’s very analogous in the sense that there’s some interference, the edge of the table, perhaps, that has caused information loss. The difference is that my table is not the entire universe and it is a sub-system of the universe. And the information loss is reasonable when you’re looking at a sub-system, a subset, a wave function that describes some part of the universe rather than all of it. But it’s more troubling when you are literally describing everything in the known universe or everything in the universe, and nonetheless, information is lost. It raises the question of where does it go.
0:12:48 SC: Right. And in fact, as I indicated, I’m completely sympathetic to this point of view.
0:12:53 NE: Yeah.
0:12:54 SC: You’re, just to be clear, ’cause I think that listening to me on this podcast has maybe poisoned the mind of a lot of listeners, most working physicists don’t worry that much about the foundations of quantum mechanics. Do you think of yourself as a many worlds person, or a “I don’t really care about that much. Let’s think about black holes,” kind of person, or what?
0:13:14 NE: I would say I… Sometimes, I worry, but most of the time, I don’t worry.
0:13:19 SC: Yeah.
0:13:19 NE: Most of the time, I fall into the latter category.
0:13:22 SC: Right. The thing you just said about the universe doesn’t conserve information, certainly is Everett-sympathetic or something like that, but it may be it’s not exactly the same thing. Okay, anyway, good, I’ve gotten some of my itches scratched there, that was very helpful.
0:13:39 NE: My pleasure.
0:13:39 SC: But let’s just be clear on why it’s a problem. So we have a black hole, it’s evaporating. It seems clear why information would be lost in the sense that if I throw a book into the black hole, I can’t get it back. But now, the black hole completely evaporates away. What’s to say that the information that was in the black hole isn’t somehow subtly encoded in the radiation that comes out?
0:14:05 NE: Well, that is the hope. The hope is that somehow, there is information which is encoded, that the Hawking radiation actually encodes this information. Now, the calculation that Hawking did does not support this conclusion. And so you are left with two possibilities: Either you have to say where Hawking went wrong, what he failed to take into account, and where the calculation must be corrected. Or you are forced to conclude that information is in fact lost. And this is why we call it the information paradox because information loss is very problematic for the reasons we just described, although again, some people do subscribe to it. And on the other hand, you have a calculation which appears to be correct, and we don’t a priori immediately know what is wrong with it.
0:14:51 SC: Right, and so that’s why…
0:14:52 NE: Yeah, right.
0:14:53 SC: That’s why it’s different than just throwing the book into a bonfire, for example.
0:14:57 NE: Precisely, yeah, that’s exactly the difference.
0:15:00 SC: Somehow, that information in the book, it’s kind of weird. I think that maybe a lot of people don’t quite get how natural this is to physicists, but we would say that literally all of the information about where the ink marks were on the letters in the book somehow affects the light and heat and ash that comes out of the fire, and that doesn’t seem to be what happens in black holes.
0:15:21 NE: Exactly. If you think about it, supposed you had a really great computer that could simulate exactly how the bonfire works and it was able to miraculously somehow to track every single molecule in the whole process, every atom, every particle, then you would be able, at the end of the day, to say, okay, well, the information about the book was somehow encoded in everything that came out of the fire. But black holes appear to be different.
0:15:47 SC: Right, and there’s a lot of places we can sort of go to fill in this picture a little bit. Maybe it’d be useful to talk about the entropy of black holes, ’cause this is part of what Hawking invented. Not just that they give off radiation, but that means we can associate an entropy with it.
0:16:01 NE: Right, right, so yeah, so there was… The history of this, roughly speaking, is I have a personal favorite starting point, which is that there is this idea in general relativity that black holes don’t… That they’re completely described by certain simple quantities that you can measure, like their mass. And what this means is that there is no uncertainty about the black hole if you know, say, its mass or how fast it’s rotating. And there being no uncertainty in a mathematical way means that it has no entropy.
0:16:37 NE: So one of my favorite stories is about Jacob Bekenstein and his advisor, Wheeler, who gave him a problem to think about, which was if you take a cup of hot tea, that obviously has entropy, and you throw it into a black hole, how could… Did you manage to decrease the entropy of the universe? And if so, is this a violation of the second law of thermodynamics, which states that entropy must always go up? And at the time, Jacob Bekenstein was a graduate student, so he thought very long and hard about this and eventually, he suggested that, actually, it must be the case that black holes have entropy. And even though general relativity doesn’t seem to think so, that entropy must be a result of some deep quantum gravity mechanism. And I suppose it’s a favorite for me because I think of all of the problems I can give to my graduate students without being considered too hard of an advisor.
0:17:28 SC: Well, Wheeler, he must have been doing something right. His students turned out pretty good.
0:17:34 NE: Yeah, it’s true, it’s true. I’d be happy to emulate. [chuckle]
0:17:37 SC: Richard Feynman, Hugh Everett, Kip Thorne, Jacob Bekenstein, yeah, he did okay.
0:17:42 NE: He did okay, yeah. [chuckle]
0:17:44 SC: Maybe we should… I think that everyone who’s listening, or at least 90% of the people who are listening here have heard the word entropy and think they know what it means, but I bet that over the next few minutes, we’re going to have to be nit-picky about what is meant by entropy. Do you have a favorite definition in this context?
0:18:00 NE: Definitely. I like to… Well, I have some favorite mathematical definitions, but intuitively… [chuckle] The intuitive definition that I might give is that I would like to think of entropy as a measure of ignorance of some system. So I might know something about the system. For example, your hot cup of tea, I might know its temperature, I might know its volume, but I don’t necessarily know the location of every molecule at every moment.
0:18:27 SC: Right.
0:18:27 NE: And I would like to think of entropy, one of my favorite ways of thinking about entropy as the ignorance of where those molecules are, what they’re doing at any given moment. So ignorance about some aspect of the system you’re interested in, given that you might know some other things. You might know some larger quantities or even some smaller quantities.
0:18:47 SC: Yeah, and I love that way of thinking about it in this context because it brings us right to the beginnings of sort of a tension between the general relativity way of thinking and the, let’s say the microscopic way of thinking. Because just like you said, a black hole has no hair. Black holes are the same if you know what their mass charge and spin are, so there’s no way it classically should have entropy because there’s no information being lost. And so you could see why Wheeler would be worried. But… And so, I guess that the lesson is classical general relativity can’t be the right answer if black holes evaporate. If black holes didn’t evaporate, it would be fine, right? You would just say, “Well, that cup of coffee left the universe. It’s inside the black hole and the black hole will be there forever.”
0:19:33 NE: Right. As long as you’re willing to accept that the black hole has entropy, which is… Well, either that or you’re willing to give up on the second law of thermodynamics.
0:19:42 SC: Well, I guess, you could say… I’m just making this up as I go along, maybe you could say something like, if we have a black hole, the region outside the black hole of our universe is an open system, right? It can…
0:19:53 NE: Yes, that’s right.
0:19:53 SC: It can throw things away, and therefore, maybe there’s no reason to be too persnickety about the second law.
0:19:58 NE: That’s right, we can certainly think of it that way. We can also… We don’t immediately run into any problems if we just postulate that black holes do have entropy and it’s not… We don’t… We can accept that and without thinking about black hole evaporation a priori.
0:20:15 SC: Right. But it was Hawking’s annoyance with Bekenstein that led us to the invention of the black hole radiation.
0:20:20 NE: Yes, that’s right. I think, in fact, I think if memory serves, I believe that Hawking in fact set out to show that black holes do not actually have a temperature, and therefore, this entropy analogy is purely an analogy. I believe that’s the story I’ve been told. And what he ended up showing was actually quite the opposite, that they literally are thermal objects with a temperature and an entropy.
0:20:43 SC: Yeah, I think that’s literally the story that Hawking said in Brief History of Time, so it’s not like someone is attributing [chuckle] this to him. But okay. So maybe it’s not surprising, maybe it is, but when Hawking allows for there to be quantum effects near the black hole, they evaporate. And now, the universe is a closed system again because the black hole disappears, and now the entropy had to go somewhere, if you believe in the second law.
0:21:08 NE: That’s right, and yeah. And I suppose the crux of the matter is that if we think of entropy as measuring ignorance, then all of a sudden you’re ignorant about something even though you know everything about the entire universe once the black hole has evaporated. That’s the puzzle, or a puzzle, at least.
0:21:26 SC: Okay. So what is the reason why people just didn’t quantize gravity and solve everything straightaway?
0:21:31 NE: Well, you know. We would if we could!
[laughter]
0:21:34 NE: But at the end of the day a… Well, let me say this in this way. For a very long time, we thought that the only way to resolve really any aspect of the black hole information paradox is to actually have a full theory of quantum gravity that we understood from first principles, and one that we could use to describe the black hole evaporation process. And I suppose I’m jumping a little bit ahead, but one of the…
0:22:07 SC: Go ahead.
0:22:08 NE: One of the aspects of the recent developments over the past year-and-a-half or so that have been so miraculous is that we actually have not needed that kind of access to this deep mysterious regime of quantum gravity in order to be able to make tremendous progress on the black hole information paradox. And that’s what’s been causing so much excitement and ripples in the field of the black hole information problem.
0:22:33 SC: Yeah. In some sense, since we don’t have any data about quantum gravity, for the past, I don’t know, 50 years, 50 years? People have been… 45 years, people have been using the black hole information loss problem as the thing that we need to keep in mind when we try to quantize gravity. Is that a fair way to say it?
0:22:53 NE: Yeah, I would. That’s one way to say it. And some people have certainly attempted to tackle it head-on in several different ways, but I would say it was… I would describe progress on the black hole information paradox as something that comes in waves. Usually, there’s… We’re silent on it because it’s something that, yeah, we just kind of need to keep in mind when we quantize gravity or when we think about quantum gravity, something that needs to be resolved. And then all of a sudden, someone will have some insight.
0:23:19 SC: Right.
0:23:19 NE: And that’ll result in some frantic activity for a short amount of time as everyone thinks that maybe this is the time that we solve the paradox. And it sort of dies out for a while until it gets revised by some new insight. I think one of the really exciting things that have been happening the past year-and-a-half is that there have been a lot of progress, not just reformulating the paradox in different ways, but actually progress towards resolving it, and it doesn’t appear to be slowing down as far as I can tell.
0:23:49 SC: Not yet. That’s good. We’ve caught you at the right time.
0:23:52 NE: Yeah.
0:23:52 SC: Despite pandemics and things like that, we’re still making progress in theoretical physics. It’s good to know. But okay, so… But I like this idea that we’re not claiming to get a full quantum theory of gravity, but what we’re doing is using what we think we know about black holes to tease out properties that that theory should have. And if black holes are going to have entropy, which is what Hawking said, then it must be the case that black holes are not all the same, right? Or that there’s many, many, many different things that could be going on inside the black hole, just as a cup of coffee could have many, many different arrangements of its molecules.
0:24:31 NE: Absolutely, yeah. We have… And it’s just standing outside of the black hole, all we know is what we’re ignorant of. We know essentially how much information we might be ignorant of, but we don’t actually know what that information is.
0:24:43 SC: Do we have good ideas? Do you have a favorite idea for what the… As what we call the microstates of the black hole are? Is it like little pixels of quantum spacetime or something more subtle?
0:24:54 NE: I think that I… I am sufficiently confused about this point that I think that in certain cases, there have been… People have actually been able to count microstates. And I think in those cases, it’s fairly incontrovertible as long as you agree with the counting method and the theory or framework that they used, what exactly they’re looking at, although sometimes it’s very indirect. But I think in general, dynamical black holes, meaning black holes that change with time, I don’t know. I don’t know the answer to that, and I think it’s something that we are going to have to solve sooner or later.
0:25:31 SC: Yeah, I like to leave these open… I like to mention these open problems out here in hope that some young person listening to the podcast will grow up to solve them and then mention Mindscape in their Nobel Prize acceptance speech as inspiring their interest in this problem.
0:25:43 NE: Yeah, if you’re listening… If you’re listening and you have a solution to the microstate problem, you should definitely write it up into a paper.
0:25:51 SC: Exactly. Okay, so I think this is pretty good in terms of laying out the problem. We have these black holes. Classically, they all look the same, the story about evaporation and entropy seems to imply that actually there’s a lot of different microstates that look the same, but we don’t know what they are. Maybe if we knew what they are and how they relate to the outside world, they would explain how the information can get out. But is that a fair way of saying what the aspiration is? That somehow the process of evaporation preserves the information and puts it into the outgoing radiation?
0:26:26 NE: That would be what the… What we would want to see. We would want to see an explicit, precise mechanism by which the information that went into the black hole, information about the microstates of the black hole is encoded in the radiation that escapes it. That would be… That’s sort of the pinnacle of what we’re working towards.
0:26:48 SC: And part of the problem is just that if I do throw a book into the black hole and I sort of trace what happens to it, it goes deep into the center and hits a singularity. So just physically it seems to be far away from the horizon where the radiation’s coming from.
0:27:03 NE: Yes. That’s exactly right. So there’s a problem where it seems, how can be… There has to be some kind of a… It would appear to have to be some kind of a process that doesn’t respect causality, in order for information that went into the black hole to end up in the radiation. And so in particular, we say that the event horizon, we say is a point from which nothing can return, what that essentially means is that nothing can escape from inside the black hole to outside of the black hole. But clearly, what we’re seeing here is that somehow quantum gravity manages to still place the information from inside the black hole to outside of it, even though that would violate our notions of causality.
0:27:43 SC: Right. And this is again, maybe some place where it’s going to be useful to be careful and persnickety because, again, quantum mechanics gives us a kind of non-locality, right? There is this thing called entanglement, and it bothered Einstein ’cause it was a spooky action at a distance. So maybe we should explain what entanglement is and why that’s not just by itself enough to explain how information can come out.
0:28:08 NE: Yes. So entanglement, I suppose my favorite… Entanglement is very much a quantum phenomenon, so it’s one which is difficult to explain by analogy. Because to be completely honest, there isn’t really an analogy.
0:28:24 SC: Right. Not a good one. There are plenty of bad ones.
0:28:27 NE: Yeah, there’s no analogy that perfectly captures the meaning of entanglement. But I generally like to think of it as some kind of a correlation between two objects that are separated from one another. So you might imagine that you have a couple of coins, for example, and there is some mysterious law of nature that essentially tells you that whether you get heads or tails on one of your coins is… It is related to whether it’s heads or tails on the other coin. Even though the two coins are very far separated from one another. So it’s kind of correlation between two objects that are not able to communicate with one another is… It’s this type of non-locality that appears in quantum mechanics. And I don’t know, Sean, if you have any other analogies that you like to use that maybe make this somewhat more conceptual, but it is true that quantum mechanics does have in some sense a built-in in-locality, a non-locality in the sense of this entanglement across space.
0:29:34 SC: No, actually, I completely agree with your impression that the analogies fail and therefore I basically don’t use them. I say, imagine there are some spins and they’re going to be up and down, and you can measure them. And it’s exactly what you said, the spin is going to be spin up or spin down as analogous to the coin being heads or tails. The extra little bit, of course, is that with the coins, you have the idea that it is heads or tails, we just don’t know which, whereas with true quantum systems, it’s in a superposition. And it can be in a superposition of both, we don’t know which… Whether the spin’s going to be up or down, but we know if it’s one, then the other one is going to be the other way. And that’s the weird non-locality.
0:30:12 NE: Right, right. There’s an issue, where… A classical coin naturally has… It’s either heads or it’s tails. Whereas a quantum coin is simultaneously some percentage heads and some percentage tails. And if that’s not counter-intuitive enough…
[laughter]
0:30:28 SC: Yeah. Exactly.
0:30:28 NE: I’m sure I could come up with other things.
0:30:30 SC: Well, and this is also where it’s interesting ’cause I move back and forth between the sort of theoretical physics gravity communities and also the foundation of physics community, and they make a big deal about non-locality. But it’s always in this sort of Bell’s Theorem entanglement quantum sense. And the particle physicists and gravity people say, well, it’s really hard to explain how information comes out of black holes because you need some non-local transmission of information somehow. And maybe it’s worth explaining why that’s a different kind of non-locality, right? Like, we know that there’s a kind of non-locality in quantum mechanics, but that’s not enough, it’s not what you mean by the kind of non-locality you need to get the information out of a book that’s falling into the singularity.
0:31:15 NE: Right. I would say the crux of the matter is that there is a theorem in quantum information which tells you that you cannot use entanglement alone to send information, to transmit information. So it is not possible to send information without actually having… Having it traverse at least no faster than the speed of light between two objects, even if there is entanglement between the two. So entanglement is not enough on its own to send information. You have to supplement it with what is known as classical communication. Which is to say something that does not travel faster than light, it is not enough on its own.
0:31:56 SC: And that really bugs physicists, right? Like so… Is it safe to say that even before getting to your favorite, or the field’s new favorite ways of getting the information out, just setting up the problem, if you think that information does get out, you’re going to need some kind of non-locality, non-local transmission of information, and that’s not what we would expect from our experience with ordinary quantum mechanics or quantum field theory.
0:32:22 NE: Exactly, yeah, that’s… That is what is bugging us in a sense that there is a… We know that you cannot use entanglement on its own to just communicate this information, we know that you can’t do that, and at the same time, we have to be able to use something that… There has to be some way for the information to still get out, even though there is no… Let me put it this way, there is no way for anything that travels no faster than light to actually send the information out.
0:32:54 SC: Right, right. But you know, okay, so an ordinary quantum field theory, which we think is the best way we have of describing all the experiments we’ve ever done, really has locality built into its bones, but apparently, gravity is different somehow. And I bet that a lot of the listeners have heard this idea that there’s something called the holographic principle, that the world is really only two-dimensional and we’re just a projection of it. So that came out of thinking about the black hole information problem, right?
0:33:22 NE: The idea of holography or…
0:33:24 SC: Yeah.
0:33:25 NE: Are you referring to AdS/CFT or…
0:33:28 SC: Let’s start with the idea of holography, and then it gets sort of in your face at the AdS/CFT example, right?
0:33:34 NE: Yeah. Yeah, so this idea of the black hole as… The black hole event horizon is just a hologram which… Yeah, the idea being that somehow, even though it seems very strange, all of the information about gravity in some part of the spacetime is encoded on the boundary of it. So you might think, okay, I’m sitting in a room, and somehow if someone were just to look at all of the walls of the room, they would be able to completely describe everything that I am doing in the room right now, everything, all the objects that are sitting in the room, and that is a very… It’s a very strange idea, but it’s one that was born out of thinking about black holes, because the entropy of a black hole, for example, is something that you can compute knowing… Only by measuring only quantities that are on its boundary, on the event horizon. So there is a clear analogy there to the room and the boundary of the room, and in some sense, this is how the ideas about the hologram and the gravitational hologram came about.
0:34:42 SC: Exactly. And this is where it gets really trippy for me, because from Susskind and friends, we had Lenny Susskind as a podcast guest some time ago, I’m given to believe that I can think of the black hole in the traditional way as a region of spacetime, and if I go inside I can’t go out, and nothing special happens when I enter inside except that I’m doomed to eventually hit the singularity, but I can also, if I’m outside, think of everything inside the black hole as just living on its horizon, living on the boundary. And so there’s two different ways of talking that sound very different but are equivalent. Is that fair the way I put it?
0:35:22 NE: Yeah, and that’s a completely fair way to put it. And it’s one of the things that’s very beautiful about working with quantum gravity, is that you have these two different descriptions of the same system and they look completely different, and they are telling you different things that at the end of the day have to be one and the same. And part… Many of the insights that we have obtained about gravitational physics and quantum gravity in the past few years, in the past… Or more than a decade… A couple of decades, it’s… They’ve been a result of this duality, we call it, between two different descriptions that are really the same.
0:35:55 SC: Yeah. I think… And we’ll… This leads us right into AdS/CFT, which is perfect. But first, I want to sort of pause and sort of savor this for a bit, because it seems to me to be a huge implication that in some sense spacetime is overrated. Einstein really… The reason why spooky action at a distance bugged him so much is because he thought that without spacetime you can’t even sensibly talk about physics. And of course we have spacetime, but we’re saying that one single physical situation could have two very different spacetimey kinds of descriptions depending on how you want to look at it. So it can’t be the spacetime itself that is central or fundamental.
0:36:33 NE: Absolutely. Yeah, the spacetime is not fundamental. And in fact, there are different ways of seeing this. But we certainly think that if you zoom in enough, spacetime itself breaks down. It’s only an approximation, it’s an approximate notion that we see when we’re looking at it from far away. So to give an analogy, if you are listening to this and you’re sitting at your desk, maybe it’s made of wood, maybe it’s made of something else, it looks pretty solid, right, but if you’re… If you zoom in what you end up seeing is molecules, and it’s the same basic idea that spacetime is… It looks… Well, I guess maybe… It’s difficult to say what spacetime looks like, maybe you’ve seen those fabric diagrams. But general idea, time appears to be pretty continuous, space appears to be continuous to us, but if you zoom in enough, well, the expectation is that it breaks down into some more fundamental constituents.
0:37:27 SC: And I think just… I think it’s even worse than that, unless I’m misunderstanding, because I think when you say something like that people will think that it’s less radical than it is, the idea of like, I could have some fundamental discreteness… Or… There’s the Planck length and that’s the shortest distance, and really, it’s kind of like a lattice or a set of molecules or something. But this holography stuff says that, no, spacetime is just kind of like a way of thinking, an impression, a way of talking about something that doesn’t even have locations in space, if you come right down to it.
0:38:01 NE: It’s a convenient description. That’s all is.
0:38:03 SC: Yes. And there might be more than one for the same physical situation.
0:38:06 NE: That’s right, yeah, that’s exactly right. It is… You’re right, it is more radical. It’s easier to think about the discretization of spacetime at small scales, but just because it’s easier it doesn’t mean we get to get away with it.
[chuckle]
0:38:18 SC: And, good. So we’ve been teasing it a little bit, but probably the most dramatic manifestation of this, or at least the one we understand the best and, therefore, can appreciate its dramatic consequences, is this weird thing called the AdS/CFT correspondence.
0:38:34 NE: Yes. So I assume you want me to discuss it now that we’ve…
0:38:36 SC: That was my invitation.
0:38:37 NE: I think we’ve maybe, yeah, teased the audience enough at this point.
[laughter]
0:38:40 SC: No, I mean, ’cause even though I could try to explain it, but I think that, number one, you probably understand it better, but also hearing different people’s explanation of it, I think it’s always very, very useful.
0:38:51 NE: Yeah. So the AdS/CFT correspondence is an incredibly precise manifestation, as you said, of this dual nature of quantum gravity, that it admits multiple descriptions, all of which are really describing the same fundamental system. So what is the laboratory here? So the laboratory is that you can imagine quantum gravity in some sense sitting in a box. So we’ve put quantum gravity in a box. This is a place where we can maybe have a better conceptual understanding of it. The reason this duality is called AdS/CFT is that we call the box AdS. So we have this quantum gravity theory in a box. Maybe the box is, let’s say, has three spatial dimensions, and we like to say one time dimension, so four dimensions total in this box, and we can think of there are all these physical processes. Maybe there are black holes forming inside the box, they’re evaporating.
0:39:44 NE: And all of this can be described in the language of quantum gravity inside the box. And we don’t have the greatest control over that language, except in certain cases, where maybe it looks a lot like classical gravity. But it also admits a completely different description in terms of a theory that lives in one fewer dimension and has no gravity at all. It’s just a quantum field theory, that instead of living in four dimensions like the box, it lives in three dimensions, two spatial dimensions, and one time dimension.
0:40:12 NE: And there is a dictionary that relates processes and object in this quantum field theory to processes and constructs in the quantum gravity theory, even though this quantum field theory does not actually contain gravity, which is to say, this is a quantum field theory that does not interact with gravity. You can think of it, if you like, as living on just flat space, which is never curved and has nothing to do with any of this black hole formation or evaporation. This is an incredibly powerful tool because it tells us that, for example, if in this quantum field theory, information is not lost, then it is also not lost in the quantum gravity. No matter how much we may not understand how to fix Hawking’s calculation, it nevertheless gives us the conclusive answer that information is not lost in quantum gravity if it is not lost in this quantum field.
0:41:07 SC: And it’s amazing because it’s sort of, in the most in-your-face version of this, spacetime is not fundamental story.
0:41:16 NE: Yes, yes.
0:41:16 SC: You could say, well, okay, a black hole I could think of as the interior or just the boundary, but black holes are weird and extreme. And here’s an example where the whole theory can be thought of as quantum gravity in three-plus-one dimensions, or quantum field theory without gravity at all in two-plus-one dimensions, and you’re telling me they’re secretly the same theory completely.
0:41:38 NE: That’s right. There’s a whole dimension. Where did it go? There’s a whole gravitational theory, spacetime curvature, where did it go? Somehow, it’s all encoded in this quantum field theory. I think it’s remarkable. I’ve been working on it, I would say, my entire career, and I still find it remarkable.
0:41:55 SC: Yeah. And so let’s just get some of the naive questions out of the way. Aren’t there more points in a four-dimensional spacetime than in a three-dimensional spacetime? How is there enough information in a three-dimensional spacetime to reconstruct a whole four-dimensional spacetime?
0:42:10 NE: There is clearly not enough information in three-dimensional spacetime, but that doesn’t mean that there isn’t enough information in the three-dimensional theory of quantum fields. So there is something about the quantum fields, you could imagine… In certain naive situations, you could think of it as the energy scale of the system, that can result in this, that they actually describe this additional direction, this additional dimension, which is missing in this quantum field theory. So it’s not that the spacetime contains the information. The three-dimensional spacetime doesn’t contain the information about the four-dimensional spacetime. It’s the quantum field theory that lives in the three-dimensional spacetime that contains the missing, “missing” information.
0:42:51 SC: Very, very roughly, it’s almost as if the energy of what’s going on in the quantum field theory acts like an extra dimension, or from that, arises the extra dimension.
0:42:58 NE: Yeah, yeah. Exactly. In certain cases, you can actually make this very exact and precise.
0:43:03 SC: And so this is going to be another pet peeve of mine. It’s not a pet peeve, but a long-standing issue that I’m just always very puzzled about. The counting of degrees of freedom, degrees of freedom being how we just say, well, whatever the quantum stuff of which things are made, we don’t know what it is, but we’ll call them degrees of freedom. In quantum field theory, in any box, I can put an infinite number of degrees of freedom. There can be an infinite number of things that could happen inside that box, and therefore the entropy of that box could be… The entanglement entropy could be infinitely big. I guess, we didn’t say it out loud, but because there is entanglement, things inside a box can be entangled with things outside, and that contributes to the entropy because you don’t know what’s going on outside.
0:43:48 NE: Absolutely, yes, yes.
0:43:49 SC: But a black hole, which is supposed to be the most we can fit in a region, only has a finite entropy, and that suggests to me, maybe to you, that there’s only a finite number of things that can happen in a region of space where black holes are possible, where you can have gravity, where you’re not in ordinary quantum field theory, and that’s a dramatic departure from the usual way we think about quantum field theory as a quantum theory.
0:44:13 NE: Yes, absolutely. And part of it is the fact that we don’t have a continuum in gravity. So there’s a limit to how much you can squeeze, how many points you can squeeze into a space if each point has to have some fundamental length and fundamental volume to it. There’s a limit to how much you can put in space, so you can think of this as being partly a result of the fact that quantum gravity does not permit you to have a continuum of space.
0:44:41 SC: And that always helped me. Maybe it was just an emotional help rather than a technical physics theory help, but it helped me reconcile AdS with the CFT because CFT, which stands for conformal field theory, on the boundary doesn’t have gravity and therefore every little bit of that spacetime can have an infinite number of things going on, and the AdS, which stands for Anti-de Sitter space, is the theory with gravity. It’s infinitely big and it has an extra dimension, but it also has gravity, so you can sort of fit less into each region.
0:45:12 NE: Yes, definitely. And there are also various ways of, I suppose you could say in certain cases, the infinity is met, and so there is a sense in which things are infinite in the same way, but the entropy of a black hole is not one of those infinite things. It is actually finite.
[chuckle]
0:45:30 SC: Well, I guess this brings up a very important question, ’cause I do, I’m sure there are some string theory skeptics out there, AdS/CFT came about from the minds of string theorists. Does it rely on string theory, the conjecture, or is it just compatible with it?
0:45:44 NE: So in its very initial formulations in the initial incarnation, it was derived, well, derived is perhaps a very strong word, but it was shown as a consequence of certain types of string theory constructions. Now, today, we have seen so much strong evidence in favor of AdS/CFT that we take it to be a conjecture that’s in some sense independent of string theory, although certainly they are compatible with one another.
0:46:13 SC: Right.
0:46:13 NE: And a lot of aspects of AdS/CFT take inspiration from string theory, but I would not say that AdS/CFT relies on string theory.
0:46:24 SC: And okay, again, another little diversion, but again, this is the fun thing about podcasts, is that they’re not formal lectures so we can be a little bit more, let our hair down. Do you think of yourself as a string theorist?
0:46:36 NE: That’s a really hard one.
[laughter]
0:46:42 NE: This past year in the annual Strings Conference, Strings 2020, and the year before that, there’s always someone who asks, “What is string theory, what do we include under the banner string theory?” If you go to one of these conferences, these annual gatherings of the, of many of us in the community, many people go to these… You’ll see everyone from people who work on more formal aspects of quantum field theory, to people who work on general relativity, and also people who work on very formal mathematical aspects of string theory. And so I think that while you could define a string theorist as someone who literally computes the scattering amplitudes of strings, or someone who works on formal model building constructions or F theory, you could also be more liberal with your definition of a string theorist and say it is anyone who works on quantum gravity inspired by the perspective that comes from string theory. And if you go by that definition, then I would class myself as a string theorist.
0:47:42 SC: Right, I mean, it’s funny because I have had several string theorists on the podcast, I always ask them that question. No one has ever said, “Yes, I’m a string theorist.” [chuckle]
[chuckle]
0:47:50 SC: It’s always like, “Well, it depends what you mean,” but I think that’s important because it helps people who are not embedded as experts in the field to appreciate that the labels are not really what matters, right. We’re all doing whatever we can at the moment to try to figure things out.
0:48:05 NE: Exactly, we use whatever tools we happen to think are the most likely to help us move forward.
0:48:10 SC: Good, and so you mentioned a little bit how we should give credit to here to one Juan Maldacena who was the first person to suggest the AdS/CFT correspondence and how it came from string theory, but it sort of… It has a life of its own now, it’s grown up and left the house. How would you put the question of how sure we are that AdS/CFT is right? It’s not something… It’s hard to prove, right, because we know what a conformal field theory is, but we’re not completely sure what quantum gravity in Anti-de Sitter space is, so showing that they’re exactly the same is a bit tricky if you only know what one of them is.
0:48:47 NE: Right, so the correspondence has passed a number of highly non-trivial checks, and in cases where we can calculate things on both sides of the duality, they do agree. So in the limit where quantum gravity looks like general relativity, we can do calculations in the gravitational theory and if those, if that happens to be a limit where we can also compute certain things in the conformal field theory, then we can compare the two and we get agreement, and so this… The correspondence, it has passed a number of very non-trivial tests and checks. We have not proven it and we do need to be careful about that, but there is, in my mind, there is… I feel fairly confident that AdS/CFT modular, maybe a few small caveats and modifications, but by and large that the correspondence is genuine and correct.
0:49:38 SC: Right. Is it a plausible perspective that there’s something called conformal field theories, and those are perfectly well-defined, they’re some of the best defined quantum field theories we have, and in some cases, we’re very, very confident that you can think of what’s happening in such a theory as quantum gravity and Anti-de Sitter space, and so it’s not a balance between two equally rigorously defined theories, but it’s one theory with two different ways of looking at it.
0:50:05 NE: Certainly, that is one, that’s one perspective that we can take. I do, I am a proponent of the idea that quantum gravity admits an independent description of quantum, of conformal field theory.
0:50:16 SC: Okay.
0:50:16 NE: And that if we are able to actually find that description, then we will be able to have an independent check. And so there are some people who are simply saying quantum gravity should simply be, and Anti-de Sitter space, should simply be defined as this conformal field theory, and I think that I’m not ready to jump on that just yet.
[chuckle]
0:50:35 SC: Okay, good. Alright.
0:50:36 NE: I think that we should still be looking for an independent description of quantum gravity that comes about perhaps more naturally in variables that… In variables that more naturally give rise to general relativity in the appropriate limit.
0:50:48 SC: Good, alright, good. So those are my worries out of the way and we can get back onto the main track of our progress here. You mentioned that one of the nice things about AdS/CFT is that on the conformal field theory side, it’s just obvious that information is conserved, right. That is something we’re perfectly confident about?
0:51:05 NE: Yes, yes.
0:51:05 SC: Is there a simple way of saying why we’re confident about that?
0:51:09 NE: Well, we can literally look at the state of this conformal field theory, we can look at it very far in the past and we can just evolve it forwards using the way that we know things are evolved in this conformal field theory, and at no point is information ever lost. The entropy, you could say, never changes. It’s always the same.
0:51:30 SC: Good. And so…
0:51:30 NE: So information is not lost.
0:51:32 SC: And therefore people take this as evidence that if whatever happening in the conformal field theory is equivalent to something happening in AdS, when that something is a black hole, then we believe that information shouldn’t be lost when the black hole evaporates either.
0:51:47 NE: Precisely, yeah. So if this conformal field theory is able to describe an evaporating black hole, then it is clear that information is not lost.
0:51:56 SC: Good. And okay, but that’s sort of good to know and confirms something we wanted to be true, but is a little bit less than sort of actionable. So it’s telling us that the information does get out when the black hole evaporates, at least in AdS, we can talk about whether or not that’s true in wider circumstances, but it doesn’t really tell us how, is that fair?
0:52:20 NE: That’s right, yeah, this is not a time for singing paeans just yet. We are not ready to do that. Just knowing that the information is conserved, well, it’s not quite enough. So we could just as easily have all sat down in some secret cabal meeting and decided we all say information is conserved, so be it. But in order to have a resolution to this problem, we need to actually say how, how it happens. What is the process by which it happens? We need to do a calculation that actually shows, at least indicates that information is conserved in an incontrovertible way in terms of the quantities of the problem.
0:52:57 NE: For example, in terms of the entropy of the radiation, in terms of that… Doing a calculation that shows that the entropy obeys the information conservation, that it starts out at some value and it ends up at that value, that is the hallmark of information conservation. And in order to make progress, this is not the end point yet because we want to just understand things more broadly, but in order to even start making progress, that’s something that we need to do.
0:53:27 SC: Right.
0:53:28 NE: Or I should say something that we needed to do for a long time and have recently done.
0:53:33 SC: We’ve made some progress. Well, anyway, yeah, so I will delay just to build the dramatic tension and… ‘Cause I need to convey a personal story here, because this idea that AdS/CFT shows that, well, it should be information conserving all along. Even Stephen Hawking was pretty moved by that. He changed his mind. For a long time, he said information is lost and basically, because of AdS/CFT, he changed his mind. And he gave a famous talk about it, I think around the year 2004 or ’05, and it was at a time that was primitive enough in the internet that the talk was not broadcast or recorded, nor was there even a text of what he said available anywhere.
0:54:16 SC: And the New York Times wrote about it, and I asked Dennis Overbye at the New York Times, have you actually seen Stephen Hawking’s talk? The text of it? And he said, “Yeah, I’ll send you a copy of it.” They gave out a copy and so I asked permission and I posted the text of the talk on my blog. And this was the only place that it was available for a little while, so I helped get the word out there. But as you say, it still leaves us a little bit stuck as to what is actually going on. So now, I’m in a realm where you’re way ahead of me and I’m going to have to rely on you to help us out. Why or what is it that has given us new confidence or hope that we actually have an idea how the information is getting out, not just that it is?
0:55:02 NE: So we did a calculation, and I say, when I say we, I should name the people. So this was a set of two papers that came out the same day, one by Geoff Pennington, and one by Ahmed Almheiri, myself, Henry Maxfield and Don Marolf. And we did a calculation in the quantum gravity theory in the box that I will explain in a minute, that in fact, showed, we calculated the entropy and this calculation showed that the entropy actually behaves in a way that is consistent with information conservation. And this is not a calculation…
0:55:39 SC: So this is the entropy of the black hole that you’re calculating, or the entropy of what?
0:55:43 NE: Yeah, the… So we calculated the entropy. So there are two steps to this. First, we wanted to take a black hole that evaporates. And this was challenging in its own right because black holes in AdS, well, they don’t really like to evaporate very much. And if they do evaporate, then they’re difficult to describe. So first, we had to go through a number of steps in order to just get these things to agree to evaporate. But once we did, we actually were able to have analytical control, a tractable situation where we could use a particular proposed formula to compute the entropy of the black hole and… Or you could say the entropy of the radiation via a slightly different formula that as a function of time.
0:56:32 NE: And so what we found, which was extremely non-trivial, we found that the entropy of the black hole or the entropy of the radiation actually behaves in a way that has been shown by Don Page to be the way in which it must behave if the evolution conserves information, if the evolution of the black hole evaporation process conserves information. So this was an explicit calculation done in quantum gravity language that actually indicates very strongly: Here is information conservation.
0:57:07 SC: And by, when a physicist says something like extremely non-trivial, you mean basically like it could have gone otherwise, you didn’t sort of cook the books by putting it in there. When you start the calculation, you’re not sure where it’s going to go, and it ended up exactly where you hoped.
0:57:23 NE: Yeah, it was… We were actually… This was not the thing that we necessarily set out to calculate. We set out to, well, we set out to show that a certain quantum information theoretic protocol has a particular geometric realization. And the fact that we got this behavior was extremely exciting and it was… Oh, yeah, it was not something that we put in by hand at all.
0:57:49 SC: Okay, so you have… Good, so you have the black hole and it has an entropy, and you have the radiation and it has an entropy. And maybe this is going to be ambitious, but what do you mean by saying it evolves in the way you expected it to? Is it like the entropy gets transferred from the black hole to the radiation as it evolves?
0:58:09 NE: You could think of it that way, but it’s better to think of it like this. Let’s just think about the radiation for a second. So the radiation, when a black hole is young, when it’s first formed, the radiation is basically, we could say, oh, it just formed, it only just started evaporating. So we basically know everything there is to know about the black hole, everything there is to know about the radiation. So its entropy is very small. And then as the black hole evaporates, some things fall into the black hole, some of the radiation makes it out. The entropy grows because our ignorance grows. But if the black hole… If once the black hole evaporates completely. The… All the information got out, then the entropy should go back to zero after the black hole finished evaporating, because the ignorance is non-existent, because we know everything about the system.
0:59:02 NE: And this type of behavior where the entropy first increases and then decreases is something called the… It’s attributed to Don Page, it’s something called the Page Curve, which is what we think of it as a litmus test for information conservation. And so when we… When I say we calculated things and they behaved in this way, I literally mean we computed the entropy using a formula that Aron Wall and I proposed in 2014. And this exactly produced this type of behavior where it starts out at zero and it ends up at zero.
0:59:33 SC: And so if we didn’t have… What could have gone wrong? What is it that makes it non-trivial? What other kind of curve could you have gotten if things were not working out?
0:59:43 NE: So if you were to do the calculation that Hawking did…
0:59:46 SC: Yeah.
0:59:46 NE: Then what you would get is that the entropy would start increasing. And then as the black hole finished evaporating, well, the entropy would still be high because you lost information. So you still have ignorance about the system. Even though you have access to the whole universe, information was lost, so there is some ignorance. And so the entropy would have just continued to increase until the black hole evaporated and there would’ve just remained a constant. Because what we saw instead is that it did not do that, it did not follow what we call the Hawking behavior, but it followed the Page behavior. That is evidence of information conservation.
1:00:21 SC: Okay. But if I’m still being the devil’s advocate here, I’ll say, well, but that’s still in this AdS/CFT of context where you already had convinced yourself that information was conserved. So how did this extra little calculation help point you in the right direction?
1:00:36 NE: Good. So I have two things to say about that. First is that all of the evidence we had in AdS/CFT for information conservation came from the CFT. And this is a calculation that was done in the gravitational theory. So we used a gravitational prescription for the entropy and we computed the entropy using just what we knew about the quantum gravity theory. So this was a more direct calculation, which is what we’ve been looking for rather than this indirect derivation.
1:01:07 SC: Yeah.
1:01:08 NE: Now, this is the first thing I wanted to say. The second is that very exciting developments that followed that, which have said, okay, let’s try to derive this from not… From a different angle, from a different type of calculation. Let’s try to do this calculation, which is essentially this formula that I was quoting that in initial stages, Aron Wall and I derived it in 2014, and it was then modified later in 2019 for the radiation. Let’s try to derive that without assuming AdS/CFT. And let’s try to justify it. And so there are two… Multiple papers that followed up, but two that really come to mind, which is by a number of folks on the East Coast, a number of folks on the West Coast. In our field it goes by the East Coast, and the West Coast came first. Which is not to say that we’re pitted against one another. We all work together.
1:02:00 NE: In a certain class of models, which are admittedly toy models, but we do expect that they are very reflective of other cases, they actually derive this formula, this calculation, not assuming the AdS/CFT correspondence. Which means that it is much more robust than just being special to AdS/CFT. Where you can say, oh, this CFT already told us about this. The fact that we can derive it without AdS/CFT, and we can derive it just with access to quantum gravity and not with access to this alternative language of this CFT, suggests that we are on the right track to figuring out what is the exact mechanism that is responsible for the information getting out. Because calculating the entropy is important. It is a stepping stone. But again, the pinnacle, the thing that we’re looking for at the end of the day is this mechanism by which the information actually gets out.
1:02:58 SC: Okay. So when you say we did some calculations that do not rely on AdS/CFT, is it even possible to give us a flavor for how you did that? Would it have worked in flat space or a zero cosmological constant, which is not AdS? Or is it, you imported some ideas from AdS into a different context? Or you started anew? Could Stephen Hawking have done this?
1:03:22 NE: So I should say… I should issue a disclaimer that I was not on this East Coast and West Coast papers, but I’ve been following the developments as well. And the basic idea is that concepts from AdS/CFT were imported or that the calculations were inspired by developments in AdS/CFT. In particular, by a development that is attributed, that is due to Lewkowycz and Maldacena. And it is, however, not special to AdS/CFT. These insights are important, but they’re something we could, in general, use about gravity. They’re in some sense related to some older work about deriving the entropy formula for black holes, the gravitational entropy formula, which related to the event horizon in this area.
1:04:16 NE: It used a construct, something called a gravitational path integral. And in some sense, this is a case of the gravitational path integral striking again, where this idea, this construct, together with insights and intuitions and inspiration from AdS/CFT, together are combined to give this derivation. Now, could Hawking have done this? Well, it’s a question of whether Hawking could have derived, I would say, the… Could have given the Lewkowycz-Maldacena construction. I suppose that maybe that’s a question that’s more for philosophers.
1:04:52 SC: Yeah, okay. But you know what? I think that we should reward the listeners who’ve stuck around for the last hour and really give them some of the red meat here. Let’s explain what a path integral is and what the gravitational path integral is.
1:05:08 NE: Okay, would you like to take path integral while I think of how to formulate the gravitational path integral?
1:05:12 SC: Sure, I’ll try path integrals. Because I think it’s actually, even though it’s a very kind of abstract sounding idea, it’s probably the kind of thing that fans of popular level quantum mechanics have heard of, that Richard Feynman in his office one day, or I don’t know, in the strip club or wherever he was hanging out, said, you know, quantum mechanics, it can be thought of as a story of a wave function evolving over time. But there’s this feature that the more likely thing to happen is closer to the classical thing that would have happened. It’s not a complete disconnect between quantum mechanics and classical mechanics. So maybe, and I have no idea what actually gave him the idea, but he says, maybe everything happens. Maybe the particle, if you just think of a particle moving on a path, maybe in quantum mechanics… In classical mechanics, there’s just a path the particle moves on, and there’s this idea called the principle of least action, that it takes the best path, the path, the path that took the least action to get from one place to another.
1:06:18 SC: And Feynman says maybe in quantum mechanics you can think of the particle as taking every path, every wild, crazy path zooming around, zipping here and there, completely violating the laws of physics, and then you sort of add up, quantum mechanically, the contribution from all of those possible paths. And when you’re near the classical path, all the contributions add up and you get a big answer. And when you’re far away from the classical path, you get some positive contributions and some negative contributions, and they nearly cancel out. So quantum mechanics is sort of taking advantage of all of the different things you could imagine the system doing. And this is called the path integral because you have all the different paths and you integrate over everything that can happen in them. And you recover, it’s not like a new theory, you’re just recovering standard quantum mechanics in an imaginative way.
1:07:08 NE: Thank you. That was really beautiful.
1:07:10 SC: How did I do? Yeah, okay.
[laughter]
1:07:16 NE: So the gravitational path integral is kind of a similar idea, but for gravity. And let me parse that statement. So in the ordinary path integral, as Sean just said, we are talking about all possible paths between two points. In the gravitational theory, we’re talking about all possible geometries, all possible spacetime shapes that have a fixed boundary. So for example, imagine this box. We fix the boundary of the box, we make it rigid, but we allow any spacetime you want inside of this box. Any kind of funny shape, black holes, anything that pass these boundaries that are unchanged and unaltered. And we sum over all of these possible contributions without worrying about whether this spacetime solves the equations of Einstein’s theory of general relativity or not. But we expect that when it does, we get these very large contributions. And so, we are… This is what we would call a classical point. Even though here, you could say we’re always talking about something classical, this is the spacetime geometry. But here, the classical point is the geometry, the spacetime that obeys the Einstein equation.
1:08:35 NE: And one of the things that are simply miraculous about the gravitational path integral, which is different from the path integral in ordinary quantum field theory, is that it knows a lot more than it has any right to. We don’t know why it knows all of this. But somehow, even though… You can look at this gravitational path integral, and from it, you can calculate the entropy of a black hole. Even though this gravitational path integral, you didn’t put in the underlying fundamental equations of quantum gravity into it. You didn’t tell it what are all of the possible space… States of quantum gravity, it just kind of knows. It knows what the entropy of a black hole is. It knows the number of microstates. Even though in principle, it doesn’t really have a right to. It’s not clear why it knows, but it just kind of does and it’s truly miraculous. This is something that is… This is not new, that it knows the entropy, but the new aspect to the story is that it also knows about information conservation. You can use this gravitational path integral to compute the entropy of the radiation.
1:09:44 NE: And if you do that, then this gravitational path integral will tell you, oh, the information is conserved. It gets out somehow. How does it know? Why does it know? We have no idea. And in fact, I gave a seminar recently, and I actually opened with the question about what is the gravitational path integral doing?
1:10:06 SC: Right.
1:10:08 NE: What is it calculating? And how do we find out, how do we decode the gravitational path integral?
1:10:12 SC: And this is…
1:10:13 NE: I think that… Sorry, go ahead.
1:10:15 SC: Sorry, I was just going to say, this is, this anthropomorphizing of the gravitational path integral that it knows more than it should is a wonderful example of this idea of a non-trivial thing going on. One thing is that the gravitational path integral, rather than the path of a particle, we take an entire spacetime. So to us spacetime is a single path and we’re integrating over all the different spacetimes. But it could have been the case that you couldn’t understand, as we suggested early on, that understanding how the information gets out couldn’t be understandable until you had the final once and for all theory of quantum gravity. And in some sense, the gravitational path integral isn’t that, right?
1:11:00 SC: It’s a hope and a prayer approximation that we think might be good in certain big universe, nice, smooth, nothing going on dramatically circumstances, but here, it’s telling us more than we thought it was going to be able to figure out.
1:11:15 NE: Absolutely, yeah. It somehow is able to know the essence of this calculation, even though the gravitational path integral is something we can calculate just from the perspective of what we call semi-classical gravity, gravity with small quantum contributions where the quantum effects are not so strong that we lose control over it. And we can calculate it from that, and that calculation is telling us that the information is conserved, even though for a very long time we thought that the only way that we could see information conservation was literally, as you say, just having this big quantum gravity theory and action, describing it in full detail in all regimes. And miraculously, that’s not the case. We are able to make progress just from this miraculous gravitational path integral. I just find that fascinating.
1:12:01 SC: Yeah, no. [laughter]
1:12:01 NE: It’s miraculous to me.
1:12:03 SC: It’s always fun to be hearing about these advances in physics as they’re going on because once they’re gone… We always present them in ways that just seem inevitable, like, oh, of course. It had to be like this. But while we’re in the middle of them, like, holy smokes, this is amazing. How [laughter] does it know?
1:12:20 NE: Absolutely. Yeah, yeah.
1:12:22 SC: But there is…
1:12:22 NE: Yeah. It’s exactly like that.
1:12:24 SC: Yeah, but there is one thing I think that at least has been suggested as a bit of insight as to why the path integral knows. After all, so the path integral is saying if you want to say how spacetime evolves from one thing to another, you literally take into account contributions from every single kind of spacetime you can imagine that would connect the beginning and the end of the story you’re trying to tell. And so, presumably, the set of all spacetimes that connect the beginning to the end would include the W word. We haven’t said it yet.
1:12:55 NE: Uh-huh. Yes… What is that?
[laughter]
1:13:01 NE: I would say what is surprising. Sorry, if I interrupted you, please continue. I didn’t mean to interrupt you. [chuckle]
1:13:06 SC: No. I don’t want to be too coy here. I’m thinking about wormholes. I have heard that wormholes play a crucial role in getting the information out in the context of this story. And once you say that word, people… People have probably seen the little picture of a wormhole, they know the general idea, but they’re going to think that somehow you want to tell me that I throw the book into the black hole and it escapes outside via a wormhole. But I’m sure it’s not as easy as all that.
1:13:33 NE: Yeah, so… Let me think what’s the best way to explain this. So, just to address an earlier point you made, I would say what’s miraculous about the gravitational path integral is that even in this approximation where we think of it as roughly in terms of the spacetime geometry that satisfies the Einstein equation, where we approximate it as something that looks like that, we can still get the information that we need. So we don’t actually need to have access to all of those metrics, all of those geometries that don’t actually solve the Einstein equation.
1:14:06 NE: Now, regarding as to how the information gets out and how that’s related to these wormholes. So, these wormholes, the way that they contribute is in a calculation of the entropy rather than as a description of the spacetime on which the information is propagating, on which the Hawking radiation is propagating. So I would be hesitant to say that these wormholes are giving us the mechanism via which information gets out. Now, I say hesitant because I don’t want to strike too strong a position on this, simply because I know there will be others who will disagree with me.
1:14:51 SC: And also we don’t know, huh?
1:14:51 NE: And I want to present a fair view. [chuckle]
1:14:53 SC: Yeah, we’re not done yet. No one is sure.
1:14:55 NE: I want to present a fair view of the field here. So even though I think, in my opinion, that we have not uncovered the mechanism and we have not answered the question of how the information actually escapes, I am sure that there are some people who have ideas about the wormholes and how they’re related to the mechanism via which information gets out. I want to give credit to those people, even though I do not necessarily agree with that perspective.
1:15:21 SC: Well, I think people are exposed to various ideas in the popular media, so it’s important to sort of relate our ideas to each other. Lenny Susskind and Juan Maldacena famously suggested that whenever two particles are entangled, just like in ordinary quantum field theory, we can think of them as being connected by a microscopic quantum wormhole, ER=EPR. Is this kind of like that or related, or completely different or two sides of the same coin?
1:15:52 NE: It’s not like that. Lenny and Juan’s wormholes are what we call spatial wormholes. So this wormhole is a wormhole in space. If you look at a single moment in time, then you would see this wormhole as sort of the stereotypical diagrams connecting two different universes through a wormhole at any given moment in time. The wormholes that are discussed in the context of the gravitational path integral and the recent calculation of the entropy of the Hawking radiation are not like that. These are what are called spacetime wormholes. These are wormholes that are extended in time, and they bring up a number of problems for that reason, regarding… Well, maybe I won’t go into it because it’s rather technical, but they bring up a number of problems.
1:16:46 NE: And while Lenny’s and Juan’s wormholes are wormholes that we can think of as existing in the space itself, in the spacetime itself, connecting two particles, these wormholes show up pretty much only in the calculation of the entropy, so you need to calculate the entropy to see them rather than in the spacetime itself. So, I would say they are two qualitatively different phenomena, although it is striking that the wormholes are appearing here. And I will say that there are some models where one can talk about both and you could try to talk about both of these, but I don’t think there is a clear picture, a clear indication that they are related in an obvious way.
1:17:28 SC: Right. I very much appreciate your attempt to, your desire to not get too technical, but I’m going to spoil it.
[laughter]
1:17:37 SC: So let me say something and you can tell me whether I’ve completely missed the boat here, which is very possible. When Stephen Hawking and Jim Hartle back circa 1980, or I don’t know what year it was, they proposed what they call the wave function of the universe. And what they said, part of their idea was, what do you mean by a wave function? Well, you have… A wave function exists at a moment of time, right? The wave function evolves over time in quantum mechanics, so at any one time, you have a wave function. And for gravity, that wave function would presumably say, well, what is the geometry of space at that one moment of time? And what are all the quantum fields doing at the same moment? And they wanted to calculate that and they wanted to calculate it by doing the path integral, by doing what Feynman said. But when you actually… The thing about the path integral, as beautiful as the story is, the mathematics of it, and the ability to calculate it is just god-awful, right? Like nothing is well-defined, nothing is calculable, whatever.
[laughter]
1:18:41 NE: Yeah.
1:18:41 SC: And there is this trick that you can introduce, ’cause what you’re supposed to do is say, well, integrate up all of the spacetimes that match on to this particular wave function you’re looking at. But the trick is, instead of integrating all the four-dimensional spacetimes that match on to this condition you’re looking at, you can just say, well, I’m going to integrate over all four dimensional spaces, so I’m going to forget about spacetime. I’m just going to do what we call the Euclidean path integral because Euclid just talked about space, not time. And…
1:19:13 NE: Oh, you went there. [laughter]
1:19:15 SC: I did, I did. This is where I’m going. And so it was sort of like you could justify… It’s a trick. It’s a mathematical trick. And it’s very rigorously justifiable in certain simple cases in quantum mechanics, and it certainly has the smell of being correct in certain more subtle cases in quantum field theory. In quantum gravity, what they were doing with it, it just seemed to be a trick so they could get a finite answer at the end of the day, and it was very unclear why it had anything to do with the real world, but they suggested it did. Maybe they were right. And since then, I think we’ve become a little more comfortable with the idea that we can use this trick of calculating quantum gravity wave functions by integrating over the Euclidean path integral, the set of all the spaces that end up looking like what we want, instead of all the spacetimes that look like what we want.
1:20:05 NE: Yes.
1:20:05 SC: And that’s what you’re doing, isn’t it? That’s the kind of wormholes that you’re invoking.
1:20:09 NE: Yes, right. That’s what I was trying to sweep under the rug.
1:20:11 SC: I know. [laughter] And you were right to do so, but I just like to live dangerously here.
[chuckle]
1:20:18 SC: So Lenny and Juan have wormholes that are literally good old in spacetime wormholes, and you have wormholes that are in these fake Euclidean spaces that you used to calculate the entropy.
1:20:29 NE: That’s exactly right. Yeah, that’s exactly right. And these fake Euclidean spacetimes have more boundaries. There are more edges than our original spacetime, which means that these wormholes are connecting these… More edges than we have in our original spacetime, and therefore, it’s difficult to make sense of them in terms of the original spacetime that we’ve started with.
1:20:51 SC: Right. Okay, so what’s next? Where are we going from here? What are… I mean, you’re very, very kind. I should make sure that everyone in the audience knows how very, very thoughtful it is of you to appear on this podcast, ’cause I know that like in theoretical physics, like you said, there are fallow periods where like we’re wondering what to do. And then there’s like periods of amazing excitement where you just want to get working. And so you’re taking off time of your real work to be on here, but what are you going to turn to next once we’re done chatting here?
1:21:21 NE: Well, like I said before, I think that the gravitational path integral is something that we need to really think about. Why does it know what it knows and how does it calculate it? At the end of the day, we would like to give a complete description of how the information gets out. If you’re an observer who’s sitting outside the black hole and you have a bunch of beam splitters and mirrors and you’re measuring the radiation, what do you see? How do you see information conservation? How does that happen? And we need to be… We want to be able to describe those so we can actually put a rest to the information paradox. Of course, not for its own sake, but because having a paradox in quantum gravity is telling us that there’s something we’re thinking about wrong. So this is going to tell us a lot more about quantum gravity.
1:22:08 NE: And I think that we now have a quantity that we, no-one knows the answer, and it’s up to us to, in some sense, ask the path integral the right question in order to figure out what the answer is. So we have ascertained the path integral knows the answer. It knows how to give us the right answer every time, and we need to ask ourselves why. What is it actually calculating? What is this thing that it is doing behind the scenes that is giving the right answer? How do we compute that without using the gravitational path integral? How do we see it directly from the physics of quantum gravity? These are all questions that I think we have to answer if we want to get to the bottom of the information paradox.
1:22:46 SC: And at the end of the day, one could take the attitude that the information paradox is a motivation, but it’s not the goal in some sense, right? The goal is to understand much bigger questions, and this is just the sort of puzzle that we’ve been gnawing over for some decades now and trying to get there. Do you think there could be implications of this set of things we’ve discovered for things like the wave function of the universe or the big bang or whatever?
1:23:12 NE: Yes, I do. I do. So I think one of the most exciting things about the recent discoveries is that they’ve sort of lived up to our expectation that understanding the black hole information paradox better is going to teach us a lot more about gravity and quantum gravity. So the reason that we care about paradoxes in the first place is because they’re telling us that there’s something we’re thinking about wrong in terms of quantum gravity. There’s somewhere we messed up. And the hope is that in resolving them we’ll understand that better. Of course, it’s an abstract hope, but I think it’s fair to say that it’s starting to be realized.
1:23:44 NE: So for example, the inclusion of these wormholes, these Euclidean wormholes and the Euclidean path integral is mysterious in many ways, because it suggests that there is some very strange mechanism that describes gravity in full quantum gravity theory. So there’s been some suggestions for… And one way of thinking about it is there’s a possibility that, really, gravity is described by a collection of quantum theories, what we call an ensemble, rather than a single theory. There have been suggestions of some kind of… That there is some kind of an averaging that is happening in order to obtain gravity from these theories.
1:24:25 NE: And all of these different hypotheses that are currently under development, some papers have come out. Some people are working on them. I’m working on this. All of this is a consequence of the understanding that these Euclidean wormholes have to contribute and that they give rise to information conservation. And those insights are telling us something fundamental about quantum gravity, regardless of whether we care about the black hole information paradox or not. And so there is a clear sense in which the black hole information paradox is living up to what we had hoped, which is that if we gain true insight into it, then it’ll lead us on the path to understanding quantum gravity better.
1:25:04 SC: That is exciting. I’m excited. I think this is great. I think this is very, very…
1:25:07 NE: I’m really excited, too. [chuckle]
1:25:07 SC: Yeah, good, good, good. This is the fun part of what we do for a living. So with that in mind, I can’t think of a better place to end. Netta Engelhardt, thanks so much for being on the Mindscape Podcast.
1:25:17 NE: It was my pleasure. Thank you for having me.
[music][/accordion-item][/accordion]
Technical problems on playback.
As usual, a fascinating episode. So refreshing to listen to substantive discussion. A real oasis in the midst of the constant political prattle
Very amazing episode. That’s what seems best to say. Thank you.
“It’s not like you throw the book into the black hole and then it comes out through a wormhole” LOL
I understand just enough about this topic to appreciate how silly that would be. Fascinating stuff. Thanks!
Sean, I didn’t hear an introduction of Netta Engelhardt on YouTube
What if the black hole’s event horizon is like a measurement that in an Everettian sense splits the Schrodinger equation in divergent realities? Would that explain the loss of information in our perceptible reality, but maintain information in a many-worlds interpretation?
One of the most fascinating Mindscape episodes yet, Sean.
Thank you!
Really enjoyed this show. I will have to listen again though. Thanks for the show notes to, I can look things up for a better understanding of what you’re talking about. Xxx
I was disappointed that you did not ask Netta Engelhardt to explain:
1. How Cauchy surfaces can possibly be defined across points of black hole evaporation events, without which conservation laws (e.g. for information) cannot be defined?
2. How a teleologically defined surface, such as an event horizon, can be cogently employed in a deterministic theory?
3. How a supposedly analytic theory using geometric/gravitational path integrals can have a continuum of solutions when assuming unique boundary conditions?
What fun!. Tales from the frontiers of cosmological physics, from someone who does the math and conceptualizing– first hand! How welcome, and how exotic! Thank you for the fresh vicarious glimpse of the undiscovered country.
I am delighted to hear you and your guest discuss the importance of determinism in theoretical physics, but where does that leave Jenann Ismael (episode 80) who does not believe in either determinism or causation. I wish you has asked her about that.
I have been interested in theoretical physics and black holes in particular for a long time. I have ideas that I would like to try to hash out, but my math skills are terribly basic.
Does anyone have advice for where someone should start insofar as math courses so that they may begin exploring and creating equations having to do with this field?
I should say that I literally need to start somewhere around course 1 math, because that was the last math course I ever took.
Course names, links to good places to find courses online, Ted talk links…anything would be helpful!