← Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
349 | Daniel Harlow on What Quantum Gravity Teaches Us About Quantum Mechanics
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Because the only thing that should interrupt your listening is, well, nothing. Download the Amazon music app today. Hello everyone. Welcome to the Mindscape podcast. I'm your host, Sean Carroll. Many of us have heard the story of Albert Einstein, who in 1905 had his miraculous year where he wrote these wonderful papers about special special relativity, quantum mechanics, Brownian motion in atoms, things like that. But then it was 10 years later in 1915, that he put forward the general theory of relativity, the theory of space, time being curved and that's what gravity is, et cetera. So the idea being that the smartest physicist of the 20th century had about 10 years of really hard work and he came up with this earth shattering theory that changed our views of space and time and the universe. And it wasn't even continuous work. Einstein wrote a of papers on other topics during those 10 years. But that precedent kind of gives us an expectation, right? Like if that smarter person can take that long time, 10 years, pretty long time, then we shouldn't take too much longer to make huge progress ourselves in the most difficult questions we have. After all, maybe we're not as smart as Einstein, but if all of us in physics are working together on something, or many people are, perhaps progress should be kind of tangibly fast. You should see more improvements, more theories that really change things. Of course, I'm saying all this because that doesn't seem to be the case these days in fundamental physics. Famously, we have the standard model of particle physics for which the finishing touches were put on in the 1970s, maybe the 1980s. Very few Earth shattering new theories have come along in fundamental physics since then. We've had a couple of discoveries. Neutrino masses, the vacuum, vacuum energy. We've had some very good ideas that have been very, very useful in helping us connect the theories that we have to experiments and observations, and also some very good speculative ideas in the realm of string theory and other places. But still we don't have the answer. And this is decades later, when I say the answer, I mean the answer to moving beyond the standard model of particle physics, ideally including gravity into the quantum framework. Einstein's 1915 theory of general relativity was a classical theory of gravity, and we can't do much better than that right now. It's frustrating and it leads people to say what's wrong with these physicists? That they can't make progress. I've often said that the fact that we don't understand quantum mechanics perfectly well, that we can't agree on the foundations of quantum mechanics, might be holding us back. We, when it comes to understanding quantum gravity, mine is a minority point of view about that. I think the much more common strategy is to either dive into some specific theory, like string theory or even ads, cft, or to try to think about general puzzles and paradoxes like black hole information, quantum cosmology, things like that. And who knows where the right strategy will come from or which one will lead us to the right progress. That's why we have many different strategies going on at once. So today we're talking to Daniel Harlow, who is a physicist at MIT who thinks about quantum gravity in sort of the newfangled way. Some of the old fashioned stuff like the path integral that Stephen Hawking used to understand quantum gravity with the no boundary wave function of the universe, but also a bunch of brand new ideas like using quantum information theory and holography and entanglement and some very modern notions to understand quantum gravity. And Daniel and his Collab collaborators have recently turned their attention to cosmology. He, among others, Daniel was very active in thinking about black holes, the black hole information problem. And these days he's thinking more about the universe as a whole, as a quantum system. And fascinatingly, as we will hear in the podcast, it has led him to question how quantum mechanics itself is formulated. Sadly, it has not led him to simply accept the Everettian many worlds view of quantum mechanics. But, you know, maybe Everett is not right, we got to admit that. Or maybe there's some reconciliation to be had in the future of everyone's different views of quantum mechanics. Daniel and his collaborators are proposing a pretty dramatic different way of thinking about quantum mechanics, where thinking of the observer as special is part of the framework. Defining the observer as classical and inventing new rules for dealing with observers is is right there, front and center in a way that might resonate with Niels Bohr and Werner Heisenberg and the old folks who made up the Copenhagen interpretation, but hopefully in a way that it would be more well defined, let's put it that way. As Daniel is very, very quick to say, we don't know whether his approach is right, but it's absolutely something that is worth thinking about. And as a special treat for Mindscape listeners, Daniel and I talked about the idea that since we work on similar things, maybe we should just have a real conversation in the podcast. In other words, not try to explain anything we were talking about, just talk as if we were two physicists at the Blackboard. Of course. So I said no to that because I want to define our terms in a way that hopefully the broader audience can catch on to, hopefully be more educational. But in the last 15 minutes, we let our hair down and we just said we're going to talk like physicists. So if that's of interest to you, either for physics purposes purpose or just sociological purposes, you can listen in to us as we try to reconcile our differing points of view on quantum mechanics and gravity. So let's go. Daniel Harlow, welcome to the Mindscape podcast.
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Hi, Sean, thanks for having me.
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I can remember when I was a wee starting out physicist and I knew that there was this thing about quantum gravity that was a big puzzle. People didn't know how to do it. But it was an epiphany to me when I realized that even though we didn't have a fully blown theory of quantum gravity, we actually understand a lot about quantum mechanics and a lot about gravity. So it's nevertheless possible to sort of say things and make progr even without the once and for all theory being put forward. Do you think that's a relatively accurate way of thinking today?
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Well, I would put it this way. We know a lot about the world already, like you said, from gravity and from quantum mechanics, and it's very hard to write down a theory that's consistent with the data that we already have. So most ideas are ruled out almost immediately, in fact, including many of the ideas that I work on, because it's very hard to write down a theory that's consistent with everything. So sometimes I work in a world with one plus one space time dimensions instead of three plus one. Sometimes I have the wrong sign of the cosmological constant. But I think the reason why, nonetheless, I. I feel like progress is possible is that there is something universal about gravity that is not so much the case for the other forces of nature. You know, if you look at the standard model, you know, some of the fields feel electromagnetism, some of them don't, some of them feel the strong force, some of them don't. And they feel it in different ways. And, you know, if you wanted to have a Very simple, overarching description of that. It seems hard, you know, and people try, but so far we haven't succeeded in the standard model of particle physics is kind of a smorgasbord, I think. I don't remember exactly, but I think they're 19 dimensionless parameters in the standard model that you just kind of fit to data. And they're more.
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Measure them.
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Yeah, yeah, there's more discrete parameters also, like, you know, the representations, the things transform them or whatever. And gravity doesn't seem to have all that mess, you know, that's. And that goes back to Newton and Galileo and the equivalence principle. Right. Everybody basically feels gravity the same way. And that leads to this generality of arguments about gravity. So, for example, I often talk about black holes. Black holes are very interesting objects to think about in the context of gravity. And the only reason that black holes can exist is because everything feels gravity in the same way. Because if you had a particle that didn't feel gravity, it could escape from a black hole. Why not? The gravity is what's pulling stuff into the black hole. But if you could be neutral under gravity, then you wouldn't have a black hole. And so somehow there's a kind of inevitability to some of the features of gravity. You know, where we, we try all these different unrealistic models in the wrong number of dimensions or with the wrong cosmological constant or too much super symmetry is another one that we like. And somehow the gravitational part of all those theories look similar even though the, even though the sort of other details look different. And that gives us some confidence that, you know, whenever we do find that theory that actually is consistent with everything we know about the world and also includes gravity, that the things that we learn from these other models maybe will carry over to that model and maybe they'll even help us find it. Right. I mean, for me, that's kind of the hope is, you know, I'm trying to find that theory and I, you know, I have to, I have to practice a certain amount of humility, you know, despite the fact that I'm a theoretical physicist. Because, you know, this problem has been around for a hundred years and it hasn't been solved. And, you know, who am I to think that I'm going to solve it, you know, and probably I'm not going to solve it. But I feel like every day I learn a little bit more and I feel like each year I know things that I didn't know the previous year and, you know, they don't feel Arbitrary. They don't feel things like things that are just artifacts of this particular model that I was studying, or at least the things that are. I, you know, I try to. I try to not pay too much attention to those parts and focus on the parts that feel more general.
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And the uniqueness of gravity maybe cuts both ways. On the one hand, it does give us some hope that there's something robust to be said outside some particular model. On the other hand, I've often had the thought, again, tell me, you know, whether you think that this is a. A sympathetic thought or not, that we got lucky with all the other forces of nature in the sense that we could write down a classical theory and quantize it, and it might be hard, but eventually you figure out how to do that. And with gravity, that seems to be much harder, maybe because that's not the right thing to do. Maybe there's quantum gravity, but we need to start from the quantum side rather than the classical side.
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Well, right. So, I mean, there are, there are in some of these models of gravity, it does go like that, right? Like for quantum gravity with negative lambda and too much supersymmetry. You know, it's dual to some fairly conventional quantum field theory that has a Lagrangian, and you can quantize it and using, you know, essentially high school physics if you're good enough at it. But I actually kind of am somewhat sympathetic to the broader thrust of your question, is that maybe that's actually one of the special features of those models that isn't true more generally. And I think that that gets into. I think one of the questions that a lot of us are thinking about now. You know, if you do quantum gravity, there's two things that you want to think about in terms of making contact with the real world, at least the two most obvious things, which are black holes and cosmology. You know, quantum gravity should be important inside of a black hole and. And maybe also outside. If you look at the black hole for long enough and want to understand the evaporation process. And it should also be important near the Big Bang, you know, when the universe was very dense, you know, when trying to understand questions like where did the initial conditions of the universe come from? And something that we've learned again and again over the last 50 to 100 years of trying to do quantum gravity is that black holes are easier than cosmology.
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Oh, yeah.
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And for black holes, you know, that's because essentially you can sit outside the black hole and drop things into it and, you know, Naively, nothing comes out. But actually, once you include quantum mechanics, something does come out, the Hawking radiation. And you can see what comes out. And those are very fairly conventional kind of experiments. They're the same kind of experiments that people do with the Large Hadron Collider. They just cost a bit more, so we haven't done them yet. But in cosmology, you know, you're always part of the system. You know, it's not like you're on the outside looking in, trying to see how it reacts. You know, you're in the system. The system is interacting with you all the time. And it's not even clear what it would mean to have somebody or something that's outside the system. And that was actually an issue even going back to the early days of quantum mechanics, where if you look at the discussion of Bohr and Einstein or, you know, even to pick somebody who's, you know, widely respected. Landau in his textbook. Right in the beginning of Landau's quantum mechanics textbook, you know, he says, quantum mechanics is a theory for a quantum system interacting with a classical apparatus or observer. You know, which is the same thing that Bohr says. And I would say, although I guess you might disagree, that I don't really think quantum mechanics makes sense without that external observer. I don't think it's really science. It's mathematics, but it's not science. You know, for me, quantum mechanics is. Is an emergent theory in the limit where you have this external observer and apparatus which is sort of arbitrarily big and slow and careful, and that's who gets to measure the test, the probabilistic predictions of quantum mechanics to arbitrary accuracy. It's the person who's outside the system. And that relates to all this various puzzles about Wigner's friend and so on. And in cosmology, you don't have that crutch, you know, you don't. You don't get to say you have this sort of arbitrarily big, cold, slow, careful observer, you know, or apparatus outside of the system, you know, interacting with it only if and when it chooses, you know, and then. And then publishing papers and journals somewhere outside the universe. And so it's not really the setting where quantum mechanics makes sense. And until recently, I mean, I've actually believed this for a long time, but until recently, it sounds a bit like philosophy, which is not necessarily a bad thing. I know you like some of us.
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Yeah.
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I also was a liberal arts major and read quite a bit of philosophy. This episode is brought to you by Progressive Insurance. Do you ever find yourself playing the budgeting game? Well, with the name your price tool from Progressive, you can find options that fit your budget and potentially lower your bills. Try it@progressive.com Progressive Casualty Insurance Company and affiliates. Price and coverage match limited by state law. Not available in all states. Cash flow crunch Ondeck's small business line of credit gives your business immediate access to funds up to $200,000 right when you need it. Cover seasonal dips, manage payroll, restock inventory, or tackle unexpected expense expenses without missing a beat. With flexible draws, transparent pricing and control over repayment, get funded quickly and confidently. Apply today@ondeck.com funds could be available as soon as tomorrow. Depending on certain loan attributes, your business loan may be issued by Ondeck or Celtic Bank. Ondeck does not lend in North Dakota. All owns an amount subject to lender approval. But, you know, you feel better if you have equations to back up your philosophy, right? Sure. And, you know, until recently, I didn't really have equations to back up this idea of, you know, the observer being part of the system and cosmology is really different from the observer being outside the system in the black hole or in the LHC or in any of the other situations where we, we test quantum mechanics. And what we've learned in the last five to ten years is that. Well, I should say a little bit of the background. Right. So please. Yeah, going back to black holes for a minute. Yeah. So 50 years ago, Hawking proposed this amazing black hole information paradox where he just took, you know, the laws of physics as best we understood them in the, in the early 70s, and in fact, more or less as we understand them now, you know, general relativity interacting with quantum field theory, with, you know, the gravitational interaction, very weak. So you can work sort of in an expansion of weak gravitational coupling. And Hawking argued that that seemingly obvious way, at least obvious if you are in this business, a way of combining gravity and quantum mechanics leads to paradoxes when you try to apply it to black hole physics. And in particular, you have this paradox that a black hole behaves a lot like a system that has a finite, like an ordinary quantum system with a finite number of degrees of freedom, you know, finite, which is the number basically being given by the area of the horizon of the black hole divided by Newton's constant. You know, it behaves a lot like that. So, you know, it has an entropy and it has an energy. And if you throw things into the black hole, they sort of equilibrate in the same way that if you Threw things into a, you know, an oven, they would equilibrate, you know, and, and it even radiates thermally in the way that the oven would radiate thermally. It obeys the laws of thermodynamics. And so that all sounds good, except that if you really buy this approximation of quantum field theory and gravity just treated approximately in the limit of weak gravity, then it tells you that actually that's fake. Because although the black hole behaves as if it has a finite number of degrees of freedom, it actually has an infinite number because you can just fit an arbitrarily large amount of stuff inside of the black hole. So if you try to count the ways of, you know, preparing the system on some time slice, you get too many. And Hawking, you know, beautifully quantified that by showing that, well, if you let the black hole evaporate, then its area is getting smaller and smaller because black hole is getting smaller and smaller, so its number of internal degrees of freedom is getting seemingly less and less. If, if the entropy is actually counting the degrees of freedom, as Boltzmann told us that it should, and eventually the black hole is gone, and it seems like there should be no degrees of freedom. But then where did the information go about how the black hole was created, right? I mean, if you, you know, if you, you know, burn a piece of paper in an oven or something, then the what you wrote on the paper is still there in the oven, at least if the oven is very well isolated from the, the rest of the world. And if it's not, then the information is out there somewhere. But Hawking showed that this approximation of gravity weakly interacting with matter fields gives you the answer that that information has just gone. And so somehow, you know, you thought that the black hole had no degrees of freedom left, but when it evaporated. But actually, if that information had to go somewhere, then somehow it still has degrees of freedom somewhere or other. And so in the relativity community, what people usually say is that, well, it must have left behind a baby universe, the black hole. It sort of pinched off from our world when it shrank to zero size. But the interior of the black hole must be out there still somewhere, and that's where the information is. So if you talk to people like your old colleague Bob Wald, he'll tell you that's the resolution of Hawking's paradox. But, you know, then why, why did the black hole behave like only had this finite number of states if it could actually store a sort of arbitrarily large number by just sort of sending it off into the baby universe at the end. And so this was a puzzle that, you know, drove many people in the field over the last 50 years. And, and I would say over the last 10 years, it's a puzzle that we actually learned quite a bit about, you know, that there was actually what I view as positive progress. Now, you know, one always has to be careful about claiming progress in this field because, you know, as you said in the beginning, right, it's, you know, we don't have a theory of quantum gravity, so we don't, at least not one that's consistent with everything we know about the world. So, so, you know, when I say we learn things here, what I mean is that it's more of a mathematical thing. So, so Hawking said that there are three things that you might want which are, you know, basically that the black hole has a finite number of degrees of freedom, that it evolves in a way that preserves information, which in quantum mechanics we call unitarity and locality, meaning that what I do here in this room can't instantaneously affect what's going on in your office there in Baltimore. And Hawking said, you can't have all three. So that's the way I like to think about Hawking's paradox is he said there are three things you might want. You get to pick two. And in his version of it, you gave up on, in the way I presented that you give up on the finite entropy. He might have said, you give up on the unitarity. I think the more modern thing is Bob's thing where you give up on the finite entropy. Essentially you say there are so called remnants. The Bibi universe is a kind of remnant. But the view that many of us have converged on sort of gradually over the last 20 years is that you have to give up option three, which is locality. And the slogan that we use for that is that we say that space time is emergent, right? So space time is kind of what tells you where things are and when. And so when we say it's emergent, we mean that notion is only true in some approximation and only in certain situations. And, you know, it's okay. It's easy to say that it could have been said 50 years ago. I mean, the thing that I would say is newer is that we've developed the mathematics of emergent space time over the last, you know, 10, 15 years. And so we're feeling good, pretty good about ourselves. Now try to connect back to cosmology, right? Saying, okay, we figured out at least, so we showed at least it's possible to have 1 and 2 and then 3 star, where you say, so you say, okay, Hawking was right, you can't have 1, 2 and 3, but you can have 1, 2 and 3 Star, where 3 Star says that it's not local. Okay, the space time is emergent. But in order to detect that it's emergent, that it's not really local, you have to do something exponentially complicated. And so what we were able to show is that, okay, that's some kind of loophole. What we're able to show is that that loophole's enough. Okay? So if you can tolerate that, if you can say, okay, it's fine. If we break locality by doing something that's exponentially complicated in the entropy of the black hole. Exponential in the entropy of the black hole. We've never done anything like that. Right, we don't, you know, we've tested locality a lot, but not doing something that's exponentially complicated in the black hole entropy. So maybe that's okay. And then we showed that indeed you can have a mathematical model that has 1, 2 and 3 stars. So they're not in contradiction with each other.
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So let me, before we're getting back to cosmology, let me pause on that because I'm sure people are going to care about this a little bit. I mean, what is your level of confidence that we're on the right track vis a vis just the black hole information loss? Puzzled. Do you think we have it basically figured out or do you think that we're, we have positive progress but still a way to go?
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Yeah, well, I mean, so, so I, I think one should always be careful about declaring victory on 50 year old problems. So I don't want to declare victory on the black hole information problem. So the, the precise claim is that Hawking said you can't have 1, 2 and 3, and we showed that you can have 1, 2 and 3 star. Okay, now there are two remaining questions. One is how bad is it to only have three star and not three?
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So just. Again, because people don't necessarily remember, three star is really, really tiny violations of locality.
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Yeah. Unless you do something really complicated and then they can be large. Okay, that's right. So you know, one could worry that that leads to other problems. Right. And so you have to, you have to construct a theory that realizes that possibility and then convince yourself that it doesn't have other fatal problems. And we have constructed such theories, but they're not very Realistic. So you could worry that making them more realistic would somehow introduce some additional problems that are not present in toy models. And I can't rule it out. I bet against it, but I can't rule it out. But then. So that. That's a mathematical question. But to really declare victory, there's also the physics question which was, even if I have a theory that works, that doesn't mean it's right.
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Well, that's true.
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Eventually we, you know, we would want to use this theory to predict something that we can actually test. And, yeah, we're far from doing that currently.
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So is the idea of wormholes involved in this nonlocality?
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Well, that's one way of thinking about it. Yeah. So, yeah, there are several on ramps to this idea. My favorite on ramp is quantum mechanical and trying to think about how the approximate quantum mechanics of the black hole interior emerges from the fundamental degrees of freedom of the black hole. And so I phrase that as a relation between Hilbert spaces, as the, you know, so it's. It's phrased using the language of quantum mechanics, and wormholes don't appear. There's another approach to this which I would say is less fundamental but consistent with it, which is where you base everything on the gravitational path integral.
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Could you say just a little bit for the person on the street, what the gravitational path integral is?
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Right, of course. So quantum mechanics was originally formulated in a somewhat opaque way where you take the things that you observe, like the locations of particles and how fast they're going, and you realize them essentially as really big matrices, you know, that you can then multiply and add and so on.
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Heisenberg's ideas.
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Yeah, yeah, Heisenberg. Yeah, yeah. And I would say Schrodinger also is implicitly doing that. And there's nothing wrong with that. I mean, in fact, to some extent, I like that way of thinking about it more because it makes the physics more clear. But it's less intuitive than this other approach, which is Feynman's path integral approach, where instead of talking about these really big matrices, you instead formulate the calculation for predicting, say, the probability that a particle which is here at time T1, ends up there at time T2. Right. So there's a way of computing that using these really big matrices. That's usually the way we learn it first. But Feynman showed that there's this nice other way of thinking about it, which you can derive from the first way, where you just consider all the possible trajectories that the particle could have taken from Here at time one to there at time two, and you sum over them with some carefully chosen weight, which the weight actually is not so bad. I mean, it's something that you might have guessed even without deriving it. Based on the classical physics of the particle, there's some natural guess for what the weight should be. And Feynman showed that that guess is correct. And so there's this way where you can think of quantum mechanics, it's just summing over all the ways that the system could have gotten from configuration one to configuration number two in the appropriate amount of time. So in ordinary quantum mechanics, these approaches are equivalent. There's no big mystery. You can pick either one and use it. And when we teach, we usually teach both, because some problems are better in one approach and some problems are better in the other approach, although you can always translate them if you want to. But in gravity, the situation is more mysterious because in gravity, the path integral approach is not something that you can derive from the really big matrix approach. Usually we call it the canonical approach. Okay, the really big matrix approach, it's somehow stronger. It knows things that the canonical approach doesn't know. For example, it knows the number of degrees of freedom of a black hole.
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Yeah.
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You know, Givens and Hawking showed in the late 70s that by using the path integral approach to gravity, just summing over all the geometries to get from the initial state to the final state, if you sum over it in the way that seems most natural, it actually knows how many states the black hole has, even though, you know, if you tried to actually count those states by going to the canonical formalism, it wouldn't work. So somehow the path integral knows more about the structure of gravity. And, you know, that's something that was there in the 70s, but I would say it's something that's been even more appreciated in the last five or 10 years because people just keep finding more stuff that it knows. And so, you know, one of the exciting things was that from back in 2019, that it was realized that the path integral knows that the evaporation of the black hole is a unitary process. That information gets out. It knows something about that, you know, which is exactly Hawking's paradox. Okay? Now, as I said, though, for me, my. My approach to the. To the gravitational path integral, though, is that I think of it like the oracle at Delphi. It's something that you consult and it tells you the answer, but it's not clear that you don't always understand the answer that you're given. And actually I heard a talk by Don Merrilf last summer which had a nice historical analogy about this. So in the second Persian invasion of Greece, so Xerxes was coming to attack Athens. And so the Athenians went to the Oracle, Adelphi, to ask for advice. And the Oracle first gave them an answer which was very depressing. You know, basically like Athens will be destroyed. You know, it's, you know, you're going to lose, et cetera. And they were not happy with that answer. So they said, okay, well can't you at least give us something thing? And they said, then the Oracle said, the heart of Athens will be protected behind wooden walls. And so they took that message back to Athens and there were two camps of what it means. So there was a camp that said that, well, the Acropolis in the center of Athens originally had a hedge around it which was, you know, wooden. And so we should just, the defenders should go to the Acropolis and hold the line there and they'll be able to stop Xerxes. So that was one of the interpretations. The other one, I think it was maybe Themicostalis, I can't quite remember the name. His view was that the wooden walls are ships and so they should leave Athens, go out in their ships and attack Xerxes at sea. And so the, the second interpretation was correct. The first interpretation was wrong. And so the defenders who stayed in the Acropolis were all killed. Athens was burned to the ground, but the navy won a great naval victory over the Persians at the Battle of Salamis. And so that was an example where, you know, misinterpreting the oracle preserved, you know, proved fatal. Yeah, with the gravitational path integral the same. Right. So you have to know the lesson that you're learning from the gravitational path integral. And so, so, so I'm always, you know, want something that's kind of more fundamental from which I can realize the consequences of the path integral rather than sort of, you know, having it, you know, be the end of the story.
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And when you say the path integral in gravity knows certain things, presumably you mean like we can use it to calculate certain things and we get an answer that seems to depend on this fact that we didn't put in by hand.
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Yeah, yes, yeah, yeah. So for example, like in ordinary statistical mechanics, right, if you want to know the entropy of an ideal gas, you have to count the states. Yeah, you make a, you know, you treat it as, you know, non interacting particles and you count the states. Right. And that's what we teach undergraduates how to do. But somehow the gravitational path integral knows the entropy of a black hole without doing any state counting. It just tells you here's the answer. And the answer is correct as far as we can tell, right? For example, it's consistent with whatever we get from string theory and ADs, CFT and holography. And it's, you know, it's consistent with what you want from Hawking's sort of indirect arguments based on thermodynamics, but it never counts the states. And so this approach I said about trying to understand how the interior degrees of freedom are realized inside of the fundamental degrees of freedom is treating the states as actual states. And so to me it feels more fundamental than the sort of Oracle approach. This episode is brought to you by Progressive Insurance. Do you ever find yourself playing the budgeting game? Well, with the name your price tool from Progressive, you can find options that fit your budget and potentially lower your bills. Try it@progressive.com Progressive Casualty Insurance Company and affiliates. Price and coverage match limited by state law. Not available in all states.
- [38:04]
B
Ryan Reynolds here from Mint Mobile with a message for everyone paying big wireless way too much. Please, for the love of everything good in this world, stop with Mint. You can get premium wireless for just $15 a month. Of course, if you enjoy overpaying. No judgments, but that's weird. Okay, one judgment anyway. Give it a try@mintmobile.com Switch upfront payment of $45 for 3 month plan equivalent to $15 per month required. Intro rate first 3 months only, then full price plan options available, taxes and fees extra. See full terms@mintmobile.com Good. Okay, thanks. So. So if I can summarize it and you can tell me if I'm on the right track here. So we've made some progress understanding how information can be preserved in the evaporation of black holes. And there's different ways to sort of think about the formalism of that. One way is more or less strictly quantum mechanical and we're talking languages of Hilbert spaces and operators. And another one is more space timey and there's a path integral and you can still tell a convincing story. Maybe wormholes are involved, but our understanding there is a little bit less.
- [39:08]
A
Yeah, that's, that's what I would say. Okay, maybe not everyone in the field with would, would agree with me on that.
- [39:14]
B
It would be no fun if everyone agreed. That's okay.
- [39:16]
A
You know, of course I'm right and they're wrong.
- [39:18]
B
Eventually they'll learn.
- [39:19]
A
Yeah, yeah, yeah.
- [39:22]
B
Okay, so then should we return to cosmology so that, that gives us a good state of play for the black hole information. And actually, actually, maybe, maybe one last question there.
- [39:30]
A
Wow.
- [39:30]
B
For many decades now, some people have loved to think about the black hole information loss puzzle. And others have been like, why are you bothering with this? Why is this the thing that you're most interested in? And the answer has been, well, it's something that is a puzzle that we should be able to think about and learn something from, even if we're not observing it in our telescopes or whatever. So do I take it that we now have an argument that we have learned something from all these considerations?
- [40:02]
A
Well, I would certainly say we learn something. We learn that, you know, you can have 1, 2 and 3 star, and they can be self consistent. Yeah, I mean, I, I think, you know, in response to this kind of complaining. Right. I mean, this complaint could be made about quantum gravity altogether, right?
- [40:18]
B
It is, yes.
- [40:19]
A
And I think, yeah. The way I like to think about this, you know, is that. Yeah. So maybe, let me mention two historical examples. So maybe one that's well, very well known and one that's less well known. So. So Einstein, when he was formulating special relativity, spent a lot of time thinking about trains that move close to the speed of light. And we still don't have trains that move close to the speed of light, especially not in the United States. But it was still a good thing to think about because it was the situation where the paradoxes were most stark, you know, and so there was a tension between classical mechanics and electricity and magnetism, you know, Newtonian classical mechanics and electricity and magnetism. And yeah, you could see the paradox in some mathematical way. You try to write down the Lorentz transformation of the Newton's laws and it doesn't work and whatever. But, you know, that's too, you know, that's too abstract. You know, Einstein found a way to really put it in front of you and formulate it in terms of something you could actually imagine doing, you know, and you weren't going to do it. Right. He knew there weren't going to be trains going close to the speed of light, but he understood that if there were, you would have a problem and it would be a problem that would be very. It wouldn't be a small problem, it would be a big problem. And it's a pro. It's a problem that needs to have an answer. Okay. And, you know, so then once you understand the problem well enough, then you can try to find a theory that fixes it. And the hope is that once you have that theory, it'll make other predictions, they're more terrestrial in nature that you could imagine actually testing. But when you're trying to come up with the theory in the first place, I think a sort of undue focus on what can currently be measured is not constructive. You know, that, that comes later once you've understand the structure of the theory better.
- [42:25]
B
Yeah.
- [42:27]
A
So maybe just to mention the other example, because I think it's a lot of fun. So this is one of my favorite. So, so Maxwell, before he invented electromagnetism, won some essay prize competition in Cambridge called the Adams Prize. And the problem that he studied was the stability of the rings of Saturn. So this was a well known problem in those days because the rings of Saturn had been observed for more than 200 years at that point and they were still there. And you know, if you think about it like, you know, you try to have some giant disc just hovering there around the planet, you know, the, the, the sort of dumbest things you can think of for how the rings should work are not going to be stable. They're just going to follow, fall, collapse into the planet or dissipate or whatever. And you know, you know, the, I mean, I recommend actually that you, you read this essay, especially the introduction. It's really quite fun. So he begins by, by talking about how this is a completely useless problem, you know, because you know what astronomy is for, you know, navigation and agriculture. And you know, this, the rings are so far away, they're not helpful for these things, you know. But then on the other hand, we have to know, does classical mechanics work near Saturn?
- [43:57]
B
Yeah.
- [43:58]
A
And if it doesn't, that's huge. What does work near Saturn? Right. And that's what he says. And so, you know, he says from this point of view, the rings of Saturn are the most impressive astronomical phenomenon with the possible exception of the spiral nebula.
- [44:19]
B
That was going to turn out to be another big one.
- [44:21]
A
Yeah. Very pressing from Maxwell. Okay. And so then he, then he writes this, you know, whatever 80 page paper going through all these different options for how the rings could work and rejecting almost all of them on the grounds that they're not stable, with the only option remaining being that the rings are composed of individually orbiting satellites, you know, and I mean, now we know that's the answer. So it doesn't sound surprising, but if you think about it, it's not clear that that should be stable. Right. You know, because it's a, it's a many body system. And so, so what he does in the paper Is he shows that if you perturb the rings, you get dissipative waves that go around the wings, but they dissipate. And so the structure of the rings is stable. And so you know how long it took for this theory to be confirmed?
- [45:14]
B
I don't, but I bet it was a long time.
- [45:16]
A
Yeah, more than 100 years. Because, you know, the particles are pretty small, Right, Right. So we have to send a satellite to Saturn and sort of shoot a laser back to Earth so that you can get a measurement of the sizes of the, of the particles. But that didn't stop Maxwell from thinking about the problem. And what if he had found that there wasn't an option? I mean, maybe we would have had to modify classical mechanics. I don't know.
- [45:41]
B
I hadn't heard about that example before, but it's a great one. Good for Maxwell. He's going to go far. Keep an eye on that.
- [45:47]
A
Yeah. This is before he did all the E and M stuff.
- [45:50]
B
Right, right. Or the thermo stuff. Yeah. Okay. Okay, good.
- [45:55]
A
Yeah. So anyway, so that was. Yeah. So you want to go on to cosmology.
- [45:58]
B
I interrupted you when you were just warming up to the cosmological pitch here. I have things to say to hear Your, your thing first.
- [46:04]
A
Yeah, so. Right, so we, so, so, you know, so, you know, we're feeling good. Ourselves, good about ourselves. Right. We, you know, we, we learn this new things about black holes, whether you want to say it in terms of the path integral or this, this kind of more quantum approach. And you know, as I said, there's two things that you do with quantum gravity, and one of them is black holes, and the other one is cosmology. So that we, we think we learned something about black holes. So, you know.
- [46:33]
B
Yeah.
- [46:33]
A
Onward brave soldiers to cosmology. And almost immediately we found ourselves in
- [46:41]
B
hot water
- [46:44]
A
because if you take these ideas that work so nicely for black holes and give us all the answers that we like, they give us something in cosmology that when you first think about it, it sounds totally crazy. And what it is, is that it tells us that if you, you know, as I said, the path integral, for example, can count the number of degrees of freedom of a black hole. So let's use it to count the number of degrees of freedom for the whole universe as well. Why not? Right?
- [47:14]
B
Yeah.
- [47:15]
A
And so we try and, you know, there's various approaches in various contexts where you can try to do that counting, and the answer is always the same. And the answer is zero. There's zero.
- [47:29]
B
What else could it have been zero or infinity.
- [47:31]
A
Yeah, what else could it be?
- [47:32]
B
Right.
- [47:32]
A
Like, I mean, I get either zero or infinity, and it's not infinity. So zero. Yeah. And so, you know, there are various versions of the argument. I mean, maybe the most flippant one, also the least precise, but I can say it very easily. Right. So, you know, I mentioned holography and various places here. Right. So holography inspired by the quantum mechanics of black holes is this idea that if you're doing quantum gravity in a region of space time, then the fundamental degrees of freedom of the system are really living at the boundary of that region. And so this is inspired by this fact that the black hole entropy goes like the area, the surface area of the black hole. And so, you know, and you know, all these toy models that I was talking about are in some sense holographic. Know they're often in the context of ado cft. So. Well, okay, fine, so let's take the principle and apply it to the whole universe. Okay, well, so, so holography says that the fundamental degrees of freedom live at the spatial boundary. Now, now here, when I say cosmology, what I really mean is, I mean that, that you're living in a closed universe. You know, a universe that has no spatial boundary. You know, for example, we could be living the space could be a big three sphere. That's an example of a closed universe.
- [48:56]
B
So, and maybe, maybe it's worth saying that when we measure the curvature of space is pretty close to zero, but it could be like a tiny positive number, right?
- [49:07]
A
Yeah, that's right. But it's, it's not. So I think it's not so much about the spatial curvature because, you know, we don't know the large scale structure of the universe. And if there's eternal inflation going on, then what we measure is an accident of the bubble that we're in in terms of. Yeah. So, yeah, so I'm just gonna. Right. I mean, even in Decidor space, right. You can choose to slice it with closed slices or flat slices or open slices. I think it's probably. Well, at least conceptually, the closed ones are the easiest ones to think about because there are, you know, you don't have the IR divergences you could worry about in the other two cases. So. Yeah, so here, for, for now I'll just. I mean that I'm in a closed universe when I talk about quantum cosmology.
- [49:59]
B
Right.
- [50:01]
A
And then there's no spatial boundary. And so if holography says that that's where the fundamental degrees of freedom live that if there's no spatial boundary, there's no fundamental degrees of freedom. Now, you know, that argument, you know, probably somebody made that argument at a bar, you know, 20 years ago or whatever, and everyone was like, ha, ha ha, okay, you know, so if we just had that argument, you know, that probably wouldn't be enough to convince me. But, you know, what we learned over the last five years is that if you, you know, we have all these ways of doing calculations now about black holes and they all back up that are, you know, so that they really, you know, if you, they quantitatively tell you. Yep. Yeah, Indeed. That's what's going on. This episode is brought to you by Progressive Insurance. Do you ever find yourself playing the budgeting game? Well, with the name your price tool from Progressive, you can find options that fit your budget and potentially lower your bills. Try it@progressive.com Progressive Casualty Insurance Company and affiliates. Price and coverage match limited by state law. Not available in all states. Cash flow crunch Ondeck's small business line of credit gives your business immediate access to funds up to $200,000 right when you need it. Cover seasonal dips, manage payroll, restock inventory, or tackle unexpected expenses without missing a beat. With flexible draws, transparent pricing, and control over repayment, get funded quickly and confidently. Apply today@ondeck.com funds could be available as soon as tomorrow. Depending on certain loan attributes. Your business loan may be issued by Ondeck or Celtic Bank. Ondeck does not lend in North Dakota. All loans and amounts subject to lender approval.
- [51:35]
B
I mean, maybe again, just for the bigger audience out there, the. A closed universe is a weird thing. You know, it has no energy, it has no electric charge, it has no angular momentum. So maybe having no degrees of freedom is not the craziest thing in the world.
- [51:52]
A
Yeah, I mean, right. In some sense. But, you know, if you. If you take the laws of physics as we currently understand them and study them, in a closed universe, there are definitely infinite. There are infinitely many degrees of freedom. Freedom.
- [52:03]
B
Right. Starting from a sort of classical understanding and thinking about it. I mean, there's lots of things can happen in a closed universe. Our universe could be closed for all we know.
- [52:11]
A
That's exactly right. Yeah. I mean, that's why this is so shocking. Right? Is, you know, we could very well be living in a closed universe. You know, as you said, it's consistent with all the data that we have. And, you know, how does the richness of human experience fit into a theory with zero degrees of freedom? I mean, that's the real question. And, you know, so there, there are various responses you could have to this. Right. So, you know, probably the first response is, oh, there must be a mistake somewhere. Like, yeah, absolutely could. Right, could be. Right. But then immediately have to say why that doesn't kill all the stuff that we thought we learned about black holes. I don't, I don't, you know, necessarily like that option. I mean, of course I try hard to find the mistake because I should and I haven't yet. You know, another possibility is you could say, okay, well, this is just an argument that we don't live in a closed universe. Right. So you could certainly say that. And then the only response I can have is like, okay, but like, it's, it's pretty wacky for us to be able to learn something about the global structure of the universe without even looking out the window, never mind building a telescope. Right. You just wake up in the morning and say, oh, guess I don't live in a closed universe. You know. Now, now you might say, since it's you, that the arrow of time problem has some aspect of that.
- [53:25]
B
It's a similar thing. I do think so.
- [53:27]
A
Yeah. Yeah. And that is something that we're worrying about. Yeah, right. Yeah, but, so then, yeah, but at least sort of more conservatively, if you want to go by the usual philosophy that, well, we shouldn't be able to tell what's going on arbitrarily far away just by looking, looking, you know, around the room where we woke up, then you have to go for, you know, and you want to say the argument's not wrong, then the only option remaining is that somehow the richness of human experience is consistent with the universe having zero degrees of freedom. And I'm kind of currently on that team, actually.
- [54:06]
B
Yeah, right.
- [54:07]
A
And I, I think it. Actually, you know what I think. So the way I would think about it, based on, you know, relating it to the discussion that we had about quantum mechanics earlier. You know, when I'm, when I'm counting degrees of freedom, I'm using the usual quantum count of degrees of freedom, you know, which mathematically is the dimension of the Hilbert space.
- [54:32]
B
And so just to be again, super clear, like a single qubit has two degrees of freedom and a single, I
- [54:41]
A
would say it's one, but yeah, because, yeah, for qubits, usually I define it as the log base two.
- [54:46]
B
So, Baron, I'm just trying to get like the rough, like the expectations on the table. A particle, like an electron in a hydrogen atom has infinity degrees of freedom.
- [54:54]
A
Yeah, it's a little bit, yeah, that's a little bit subtle. Right, so. So yeah, we have to decide whether we're counting discrete or continuous degrees of freedom. So, so I would roughly speaking say they both have one disagree degree of freedom, but they're different kinds of degrees of freedom. There's continuous and discrete. But I think, yeah, probably when I say that, it's because I think that continuous particle really has a cutoff or something. I don't know.
- [55:18]
B
Again, I'm just trying to like, for the.
- [55:20]
A
Really what I'm saying here is the Hilbert space is one dimensional, so however you count, there are zero degrees of freedom.
- [55:26]
B
I just want in the minds of the audience to know that when we teach people quantum mechanics and we do a particle in a potential like the simple harmonic oscillator, the dimensionality of Hilbert space is very often infinity.
- [55:38]
A
Yeah, that's correct. Yeah, that's correct. Yeah. Yeah. And so thermodynamic, I think the issue is thermodynamically, we would say that's one degree of freedom. Like, you know, when you count, you know, when you do thermodynamics of the gas. Right. You know, continuous variables count as one degree of freedom in the equipartition theorem, for example.
- [55:55]
B
Yeah, but, but I guess maybe at the practical level when we say something that sounds technical, like the dimensionality of Hilbert space, we can think of it of as how many completely indistinguishable quantum states are there in this system.
- [56:10]
A
Yeah. I think the right way to, and probably the best way to say this, Sean, is we just say it's the number of distinct states of the universe.
- [56:16]
B
Numbers. Yes. Good.
- [56:17]
A
And so I'm saying there's there, the number is one. There's only one possible state of the universe. It could not be in any other state.
- [56:25]
B
Good.
- [56:25]
A
Now when you say it that way, it maybe actually doesn't sound so scary because. Okay, fine, then we're just in that state. Right. And so, and that, that's why, that's why you have to start thinking a little bit more about what do you really mean by state. Right. And so the key question in some sense is what happens when you do a measurement? Because in the quantum mechanics that I learned, what happens when you do a measurement is the state changes, you know,
- [56:55]
B
collapse of the wave function.
- [56:56]
A
Lapse of the wave function.
- [56:57]
B
Yeah.
- [56:57]
A
So they gets projected onto the results of the measurement and now it's in a different state. And you know, you don't have to say it that way. You know, I'm I'm happy to say that you got entangled with the apparatus and so on, but that still is a different state. So being in many worlds won't get you out of that one.
- [57:17]
B
Right. Well, by the way, so when you say a single state, you don't mean start with a single state and let it evolve with time. There's just one state.
- [57:28]
A
Yeah. Although as you said, because the energy is zero in a closed universe, the time evolution is not so interesting. So.
- [57:36]
B
Yeah, but that's another, another thing that seems to be at odds with our straightforward image of the world where you see things changing with time.
- [57:44]
A
Right. But that one we kind of has a more conventional answer which is just you. Well, what do you really mean by time? You don't actually mean some God given time, you know, ticked by some divine clock. You mean the time that's, you know, ticked by your watch.
- [58:01]
B
Right.
- [58:02]
A
And, and that, that has evolution even in a closed universe. Yeah. So somehow. Yeah, so somehow that one at least usually we think is not so mysterious. But, but, but saying that, you know, there are no, there's only one state, no other state is possible.
- [58:19]
B
Yeah, only one possible state the universe could be in.
- [58:22]
A
It's not that you happen to be in one state, it's that that's the only state you could.
- [58:26]
B
There's no facts about which state you're in. That's.
- [58:29]
A
Yeah, yeah. There's no question to be answered about which state you're in because there's just one.
- [58:33]
B
So how are we going to get out of this? This sounds bad.
- [58:35]
A
Yeah, it sounds bad. Right. So my, my understanding of this currently, although now I have. So, so, you know, as, as we go on in this conversation, what I say becomes more speculative and idiosyncratic. You know, now we're getting into the regime where, you know. Yeah. There are lots, with lots of opinions about this subject and I'm just giving
- [58:58]
B
you mine the bleeding edge.
- [59:00]
A
Yeah. I would say that the reason we got this answer of one state is because we're trying to apply quantum mechanics to the whole universe. And that's only correct if there's an observer who's outside of the universe looking in. You know, that's who quantum mechanics is for. And the one state is telling you that there's not an observer outside looking in for a closed universe. You just have whatever it is in the universe and you have to make a theory out of that. And you know, you're, that can be you, that can be me, you know, all of us, you know, the apparatus, everything is all there, part of the system. And so we need to develop a theory that like, that lets us do physics that way, you know, and that theory won't quite be quantum mechanics. It'll look like, you know, it'll approximately be quantum mechanics in some limit that we can discuss. But, you know, it won't, it won't be quantum mechanics on the nose. Yeah.
- [60:09]
B
So, okay, I mean, how, how close are we to having such a theory?
- [60:16]
A
Well, we, I mean, there are models that are proposed, right? Like we give models that we can do calculations in. You know, I think one, one of the aspects, which I like a lot, although it's also controversial, is the question of, you know, we want to have some emergent description of the cosmological world that we're living in. How, how, how good does that description need to be? What are the errors in that description? You know, what, what controls the ambiguities that arise from this one state and so on. So a naive guess, you know, if you just talk to a sort of randomly chosen theoretical physicist, theoretical physicist, is that the mistake should be something like E to the minus the entropy of the de sitter space that we currently. And you know, they should be exponentially small and the Newton constant in some cosmological units, which, you know, so the, the entropy of the decision we currently live in is 10 to the 120. So we're talking about E to the minus 10 to the 120 effects, right? That's the sort of usual scale we would guess for non perturbative quantum cosmology effects. Okay. Now the models that we have where we try to build this rule of how to account for the observer as part of the system don't work to that level of accuracy. And actually they can't for a very interesting reason, which is that. Well, let's imagine. So let's say we have this theory with one state and now we're going to take the limit G Newton going to zero.
- [62:03]
B
G Newton is Newton's constant of gravity.
- [62:05]
A
Yeah, yeah, Newton's the Newton constant, the strength of gravity. So we just gradually turn off gravity. Well, so say we make it half as much as it is currently. Well, the Hilbert space dimension is still one. Okay, so let's go to a quarter. Well, okay, still one. Okay, let's divide it by 10 trillion. Still one. And then somehow when it gets exactly to zero, then you go from one to something big. And so there's some crazy discontinuous thing that happens when G goes to zero. And how can that, to me that's the really fun thing about this problem, is that the problem sort of persists all the way to turning off gravity. And my interpretation of that is that really this problem is getting at these foundational questions in quantum mechanics. So it is getting at problems that actually exist even when g Newton is zero. And the way that that works out in the models that we have is that the entropy of the observer becomes important. So, so, so, you know, I've, so this is, so I'll do an experiment here with you, Sean, today, a sociological experiment. So I, I, I've observed a bimodal response from physicists about the following statement. So I think I can guess which one you're on, but I'll. Let's try. So I claim that science as a concept is approximate with a lower bound on the error given by e to the minus the entropy of the observer.
- [63:42]
B
Well, I think, Sorry, I'm going to weasel out here. I don't mean to, but there's science in the sense of the best possible comprehensive description of the universe, and there's science in the sense of our knowledge of what that description is. Which one of these do you mean?
- [63:59]
A
Right. And so usually what we say, so, Right, so, so, yeah, and just to motivate this a little bit, right? Like, you know, you can't even write down a number to more precise accuracy than that, right. Because you just don't have enough bits. Right? And, you know, you, you, you know, you can't believe anything to accuracy better than that because it could be a figment of some crazy fluctuation in your, you know, in your brain or your memories can just fluctuate into totally different configurations at that scale.
- [64:27]
B
Right?
- [64:27]
A
And so the standard response to this is, okay, fine, but just make s observer bigger, you know, and when you're not doing quantum cosmology, that's fine. You just, the river is outside the system. You make them bigger, you make them slower, you make them, you know, more careful. And there's a limit where all these effects can be removed. But in quantum cosmology there isn't. And so my claim is we now actually have to, you know, there is a fundamental limit. Right? And so you said, Right, there's, when you said the best possible science, you were taking s observer to infinity. And my comment is that you're not allowed to do that in quantum cosmology. So, so we've got to deal with this, you know, possibility of your memories fluctuating in weird places. And the journal that you're reading, the ink rearranging to say something then.
- [65:15]
B
Yeah, that seems to be an epistemological question, not a metaphysical one, but I, I think that's okay. Let me mention to the audience that is listening here that Daniel had the wonderful idea when we started that we could just make no concessions at all to the audience and just talk to ourselves as physicists and let the audience eavesdrop in. And so I'm going to declare as the director of the podcast, that we're going to do that now that we've had a good time for an hour, trying to be clear to the audience. But let's take a few minutes and just not even try to be understandable to the audience, because I want to dig into this thing about. I mean, you made a statement a long time ago at the beginning of the podcast, anyway, and that I've heard people like Neymar Khani Hemed also make, that I think is implicit very much in what you just said. The idea that it's a very Heisenbergian or Borean statement, that quantum mechanics isn't complete without positing an external observer. And, you know, this, this strikes deeply to my ever ready and heart as, as, you know, like quantum mechanics, I think observers are part of the quantum state, and I have no trouble describing them that way. Indeed, this is what motivated Everett to invent many worlds. Quant, the problem of quantizing cosmology. So how. How. I feel like it's bad that you're giving up too quickly on just describing the world quantum mechanically and including us within it. How, how devoted are you to that?
- [66:44]
A
Well, I'm certainly. No, but I am including us. As, I mean, as I said, it's crucial to include us as part of the system. Right. So for me, indeed, the whole thing is that we are part of the system. Right? Yeah, it's the question, you know, so. So the rules that I'm thinking about do treat us as part of the system. Okay. The question is, do they treat us the same way they treat everything else in the universe or not? Or do we get some special treatment because we're the ones who's doing the science? And so my current understanding. Is that we should be treated differently because we're the ones that are doing the science. And there's a quantitative way of doing that where basically you just. So I keep the observer as part of the system, but in doing calculations using the one state, I always subject the observer to. To a decohering channel that essentially averages over their microscopic degrees of freedom to make them classical. And that's because it's not because I think that the observer actually is classical. It's because I don't think the concept of an observer makes sense if you don't do that. You know, and I, I, I think this is related to this Wigner friend.
- [67:58]
B
Yeah.
- [67:59]
A
Stuff. Right. Where you know, you know, from a purely, you know, every point of view nothing ever happens. Right. Like the, the measurement result never actually happens. You know, it's just the system gets entangled and it could be unentangled and there's no sense in which the definite outcome was selected.
- [68:17]
B
Right. Right.
- [68:18]
A
And you know, which, which by the way, you know, since you described yourself as having an Everetting heart, I can't resist just making one snide comment about it. Right. So I think a true dyed in the wool Everettian does not think that quantum mechanics happens in Hilbert space. I think they think it happens in a vector space.
- [68:35]
B
I don't understand. Hilbert space is a vector space.
- [68:38]
A
Yeah. But it has an inner product. And so the question is, do we need the inner product or not?
- [68:42]
B
Yes.
- [68:44]
A
Why? You're just evolving unitarily and we, we don't need to use the word unitarily. You're evolving linearly. You're evolving invertibly. Right. Why not just involve invertibly in a vector space? Why bother talking about an inner product?
- [68:57]
B
Ah. I mean, I think that the unitary evolution preserves the inner product. So you could even.
- [69:03]
A
But who cares? What do you, what is the, does the inner product mean anything?
- [69:07]
B
I mean, you certainly use it.
- [69:08]
A
What do you use it for? You only know one thing that we use it for, which is the Born Rule.
- [69:12]
B
The Born rule. I use it for that. That's important.
- [69:14]
A
Everydians don't believe in the born rule, so.
- [69:16]
B
No, we derive the Born rule.
- [69:20]
A
No, but you can't.
- [69:21]
B
I can. I've written papers, they got published saying
- [69:23]
A
I did other people, but I think they're always sneaking it in the back door. So. Because by using the inner product. So as soon as you use this inner product, you've introduced an additional axiom.
- [69:34]
B
We have to use the inner product. I mean, you're making me wonder, could I derive the inner product just from the evolution law by saying that the inner product is the one that is conserved. Proved.
- [69:45]
A
Yeah. So. So the thing is, I think that you can. Let me put it this way. So I think it's not hard to argue that if quantum mechanics is going to have a probabilistic interpretation, then the born rule is the one. It has to be.
- [69:59]
B
I agree with that.
- [70:00]
A
But that's not the question. The question is why would it have a probabilistic interpretation at all, right? And I think if you just have the Schrodinger in an equation and nothing else, then I would say you just have an invertible evolution in a vector space and there is no additional structure on that vector space that's physical. Okay? Now I think that's wrong. I think that quantum mechanics has an additional axiom that's not the Schrodinger equation, which tells you that there's a physical inner product. And the reason it's physical is because of the Born rule, which is there in the list of axioms, okay? And I don't think that that can be escaped from. And I also, that immediately begs the question of, so the Born rule defines these real valued probabilities with infinite precision. Who are those for? Who gets to use those real valued probabilities? I would say who gets to use them is that external observer who's looking at that system from the outside. Because the person who's in the system with a finite number of degrees of freedom does not deserve those real valued probabilities, okay? Because they can't make use of them. Or at least they can only make approximate use of them.
- [71:09]
B
I say, yeah, look, you're the one who's going to put a lot of approximations in your most comprehensive way of talking about necessary.
- [71:16]
A
But that's the thing is in quantum mechanics, in quantum cosmology, it's necessary. So, you know, when you're not doing quantum cosmology, you have this crutch of having an arbitrarily good observer outside, and you have to free your mind from that to do quantum cosmology. And I think that quantum mechanics crucially relies on that crutch. And so I think what we're doing in quantum cosmology is not going yet going to be the standard quantum mechanics that we learned in the textbooks. Now I do want to emphasize though, because there's something I didn't finish saying earlier, that this rule, so I talked about this thing that you can't do science to better than e to the minus S observer. So in this model is what you can show is that these models where you have the one state and then you use this decoherence rule where you treat the observer with a, you know, subject them to a decohering channel on the pointer basis. Since we're in the last 15 minutes,
- [72:11]
B
I can say, I know I'm not going to tell anyone what that means, but I know It, Yeah, they can, they can Google it, they can chatgpt it.
- [72:17]
A
Right, right, right. So then what happens mathematically is that effective field theory emerges, but only up to errors that are suppressed by E to the minus S observer. And now the question is, is that good enough? Okay, Is that good enough? Are we willing to accept the emergence of semi classical physics only up to errors that are of order E to the minus S observer? That sounds totally nuts, right? I mean, this is like a very speculative and radical thing to claim, but it's the least bad of the options that I currently see in front of me. And in some sense I think it's poetic. Right. Because why should science be better than E to the minus S observer? You know, and normally we don't have to worry about that, but in quantum cosmology we have to worry about it. And that's actually what the theory is giving us. Right. That's what the one state rule is giving us, is that we get effective field theory up to E to the minus S observer.
- [73:15]
B
So just to. Yeah, just to fill that in a little bit, because I'm not sure if we ever quite got this on the table. You're positing you have the single state describing the actual universe. That's fundamental physics. Then you have this effective field theory kind of thing with a bajillion degrees of freedom and the observer lives there and all the work is being done by like a map from that theory to the single fundamental state.
- [73:42]
A
Yeah, yeah, that's right. Yeah.
- [73:44]
B
And so I guess, I mean, look, the theory might be right. I'm at the moment holding on to good old quantum mechanics in Hilbert space, because I like it. Would you say that your setup is at the moment well defined?
- [74:00]
A
Well, in the models it's well defined. Yeah.
- [74:02]
B
But as a general framework, maybe.
- [74:05]
A
Well, I mean, there's different standards of evidence there. Right. Is QCD well defined?
- [74:14]
B
No, but ever ready in quantum mechanics is I have a Hamiltonian, I have a Hilbert space.
- [74:18]
A
Yeah. So I would say the rules are well defined here in the sense that I can do precise calculations and get answers. Now, what's approximate is the semi classical physics that emerges from it. But the actual calculations are numbers. Yeah.
- [74:36]
B
And you don't have branches in your theory. You would have essentially a single stochastic world in that effective description mapping onto the fundamental one.
- [74:46]
A
Well, I mean, there you can confirm the predictions of quantum mechanics. Right. So you know, you can do the double slit experiment and so on and get the answer that you like. Yeah, but there's, I would say there's not a sense in which there's this set of this Hilbert space of possible states that the universe could be in with some unitary evolution or something. Right.
- [75:07]
B
But when I do a Stern Gerlock experiment and I measure this bin to be down there is in, in your theory there's not another branch of the wave function where I measured it to be up?
- [75:17]
A
No, not fundamentally, but I still get the same result of experiment up to E to the minus S observer.
- [75:23]
B
But it seems like. So there's some, it's like I'm trying to relate it to other things that we, that we thought about in foundations of Quantum Mechanics. It seems like there is some. It's almost like a objective collapse model in which like there is true stochasticity in determining what is the branches which of the single possible Everettian branches is the real one.
- [75:48]
A
Yeah, but it's observer dependent. And so I think, but I actually, so I mean, for me, I always believe that the collapse of the wave function is subjective. I mean that's the sort of, to me the obvious resolution of Wigner's friend, for example. So my rule is that the wave function collapses for you when you learn the result of the experiment. And the reason I like that rule is not because, I mean it's certainly possible that I. Well, not actually possible, but theoretically possible that even after you learn the result of the experiment I from the outside could, you know, recohere you and the apparatus and everything, you know, but still for you, I would say the result happened when you learned it. And that's because you became sort of irreversibly decohered with the result in the sense that any operation which recohered you would also disrupt this convenient fiction that, you know, you have free will and are forming memories that have a life that makes sense and so on. Right.
- [76:42]
B
Yeah.
- [76:43]
A
And so I think, you know, that's why I say science, you know, this idea that there's this shared reality that we do experiments and we write papers and agree and so on. That's all sort of based on mutual decoherence that we share together. And when, when you have a world where stuff can just be undone, then these ideas are not going to be infinitely precise. And so I feel the traditional formalism of quantum mechanics is too precise to account for a world where nothing really precisely happens.
- [77:15]
B
I think it's giving up something prematurely, but it could be right. I could be holding on to something past its prime. I'm not sure. I do think, yeah, there's a lot of puzzles Here and it's new and you're very, very prudent. Etc about like not over claiming. So we'll have to see where it goes.
- [77:37]
A
Yeah, I don't know. I don't know. I mean, I'm doing the best I can.
- [77:39]
B
Yeah, sure. Of course. I do think, you know, I mean, there are related issues about the emergence of time. I mean you seem to point to saying like, well, we thought about that. We can, we can deal with that. Even in a static wave function, we can figure out ways that time emerges. I'm actually hung up on. I think that most of the ways that people use to get that to work are cheating and we really need to think harder about that. I don't know if you know about the clock ambiguity work that Andy Albrecht did.
- [78:08]
A
No, I mean I certainly believe that clocks are ambiguous. Yeah. I mean sometimes the power goes out and their clock could be made in Switzerland or it could be made in China.
- [78:17]
B
Well, there's this famous paper that people refer to by Page and Wooters.
- [78:21]
A
Right, Yeah, I know about that. Yeah.
- [78:22]
B
Right. And they decompose Hilbert space into a clock and the rest. And they show that blah, blah, blah, you can get what looks like time evolution in the rest of the universe. Yeah. And Andy's point is that if I do a different factorization.
- [78:37]
A
Yeah.
- [78:38]
B
Of the same Hilbert space in the same state into clock and rest, he shows that you can essentially get any effective Hamiltonian you want.
- [78:45]
A
Yeah, I mean, I think I, roughly speaking agree with that. Right. And that, that's why I think it's important to. That's why I think it's important that it's the observer who's treated specially. Right. And you know, and, and you know, because so, so in, in our paper we had three axioms for observers.
- [79:01]
B
Yeah.
- [79:01]
A
So I can tell you our axioms. So the first was that the observer, you know, semi classically should have some finite number of degrees of freedom and they can do physics up to E to the minus that number of degrees of freedom. Okay. That's axiom number one. Axiom number two was that they should be classical in the sense that they have a stable pointer basis that's stable under interactions with the environment.
- [79:29]
B
Okay.
- [79:30]
A
Again, I don't think it makes sense to have an observer that's not classical.
- [79:34]
B
I'm on board with that.
- [79:35]
A
Yeah. I mean, approximately classical, of course, sure. Right. And then finally the third rule was that observers are never pure. Now of course I don't mean that, you know, in the Catholic sense or whatever. Right. I mean it in the sense that they're always entangled with the rest of the universe. So, so you can't have an observer who's just sort of sitting there in a pure quantum state by themselves because you just. That's not, that's not how you get observers, you know? Yeah, they're. They're produced out of the world that they live in in a way that they're entangled with the rest of the universe. And because they're classical, it'll be the pointer basis. Will be the basis where their density matrix is diagonal.
- [80:19]
B
So they can't start pure and then become entangled.
- [80:21]
A
No, okay. No, no. Not, not, not, not. Not. By the rules that we were playing by. Like this calculation that said that you got. So this calculation that shows that you got effective field theory up to E to the minus S. Observer uses all three of these.
- [80:34]
B
Yeah, okay.
- [80:35]
A
Assumptions.
- [80:36]
B
So I guess I'm sure you have better things to do, but the paper I want you to write is, can you formulate this setup? Forgetting about quantum gravity, forgetting about cosmology, Just like. Tell me the setup in the most basic quantum mechanical terms. Like, you're proposing that there can be some foundational one dimensional Hilbert space and some effective huge dimensional Hilbert space, and you have some rules. What is the most general formulation of what those rules that would be graspable by someone working on the foundations of quantum mechanics?
- [81:12]
A
Yeah, I mean, I think, I think, roughly speaking, what I would say is you just, you take quantum, take the, take the quantum mechanics you like, but whatever state you have, hit it with a decohering channel on the pointer basis of whichever observer is doing the physics before you compute anything else.
- [81:30]
B
And I mean, again, maybe you're right. That just sounds so non fundamental.
- [81:38]
A
Yeah, but that's why it's radical. Right? I mean, so in some sense. Right. I mean, I think, by the way, if I said that to Bohr, he would be totally happy.
- [81:45]
B
Oh yeah, he would.
- [81:46]
A
That's what I was saying all along. Now you finally gave me the equations for.
- [81:49]
B
You had the technobabble. Yeah.
- [81:50]
A
Or if you looked at Lando. Yeah. Like, I mean, if you read the beginning of Lando like that, that's what they're saying. They just didn't write the equations for it, you know? So I mean, and that's why I said that. I mean, that's why I like this aspect, that even when I take gnu into zero, I still get something non trivial. Okay. On the other hand, clearly, like in practice, doing this does not change anything in terms of what we actually do. Because like we are indeed very classical and so we're already decohered and so decohering us more doesn't do anything. Right. And you know, in daily life. Right.
- [82:23]
B
But this hitting us with a decohering channel, is that something that we do as part of the description or is that literally part of the laws of nature?
- [82:31]
A
Part of the laws of nature. So that's the change. Yeah. So in the traditional approach to decoherence, the reason this happens is because of your interaction with the environment. Now the problem in quantum cosmology is that that environment is also part of the closed universe. And so that environmentally induced decoherence is not enough. But if nothing else, I can just say it's a mathematical fact that if the laws of physics do the decoherence, that is enough.
- [82:56]
B
Yeah.
- [82:57]
A
To resolve the one state problem and give you emergent semi classical physics. Now, I don't know whether it's correct.
- [83:03]
B
Yeah.
- [83:03]
A
Mathematical fact that it works and you know, it seems, you know, kind of better motivated to me than anything else anyone has proposed to make sense of this one state business.
- [83:16]
B
I mean, it's almost like you're letting the observer fundamentally be an open system.
- [83:24]
A
Yeah.
- [83:25]
B
And do you worry about, I don't know, experimental bounds on maintaining coherence or energy conservation or just do you predict that all those effects are so tiny we don't need to think about it?
- [83:37]
A
Yeah. I think it's all at the scale of E to the minus S observers. I mean, maybe one other thing I'll say though, since I can say to you now, since we're then. So one fun thing about this, you know, remember in the 90s, right. There was all this talk about black hole complementarity.
- [83:53]
B
I do.
- [83:54]
A
Where you have the observer inside the black hole and the observer outside the black hole and they don't have to agree on things. Right. And one of the problems with all that was that there weren't equations for that. And then later that idea was attacked by amps and, and Nathur and others. But you know, this is actually a rule that gives you different rules for different observers and you can, you can study that case. Right. So you can take a black hole that's completely evaporated. Right. And you have, I mean, by the way, one of the ways of seeing how the one state comes from the evaporating black hole is basically, well, you have an evaporating black hole. Semi classically it does leave behind this baby universe. Okay. But let's say that, well, that baby universe is a closed universe. So it only has one state Right. So then if that's so, then basically the holographic encoding of that one state is just a rank one projection. So the information goes into the black hole, it hits that rank one's projection and bounces off, goes through the entanglement in the Hawking modes out to the Hawking radiation. And that's how the state is pure. Right? So the fact that the Hawking radiation is pure is like crucially tied to the fact that the baby universe has a one dimensional Hilbert's body space. This is why I'm very hesitant to give it up is because, you know, if I make it two dimensional now the Hawking radiation is a little bit mixed. If I make it three dimensional it's even more mixed. And so, and so it's just intimately connected the this unitary black hole evaporation in the one state. And so anyway, now you can say, okay, so now let's do the classical complementarity thing. I have an observer that falls into the black hole. I have an observer who stays outside. Okay? So the, and I'm going to use my observer rule for both. All right? So the answer so and I'm going to use them both to answer the question of is the Hawking radiation pure? Okay. And so the, the outside observer gets the answer that it's pure. The inside observer gets the answer that it's mixed. And they get different answers because the laws of physics are different for the two observers. And so if, and in fact I can, I can even make it more precise. Right? So, so when you say you measure the entropy, probably I really mean the second Reny entropy or second something. So you do the swap of the two states.
- [86:02]
B
Okay?
- [86:03]
A
And so so Hawking would say that the second Rani entropy outside is E to the minus the entropy of the initial black hole, roughly speaking, actually a bit more because it's an entropy, it's not adiabatic process. But okay, okay, so a bit smaller than E to the minus S of the initial black hole, the inside observer does the same calculation. They get E to the minus S observer. Oh, sorry, I said it back. Sorry, sorry, I said it exactly backwards. Backwards. The outside observer gets one because the state is pure. Sorry. So the outside observer measures the unitary S matrix. So they find that makes you feel better. So the swap expectation value is 1. The inside observer gets E to the minus S observer, which is consistent with E to the minus S black hole. Because they can't do physics to better than E to the minus S observer. Okay, and so that's how it works, right? And so you get. So then both of them have answers that are consistent. You know, the inside observer gets an answer that's consistent with having this nice entanglement across the horizon. At least enough of it to account for their experiences. Because there's an s. Observer amount. The person outside sees that it's pure. And so now we have a mathematics of black hole complementarity that sort of works basically in the same way that this thing resolves the semiclassical physics of the closed universe.
- [87:18]
B
Okay.
- [87:19]
A
And so. So, you know, it's sort of.
- [87:20]
B
It hangs together to very.
- [87:22]
A
Yeah. Connects to various things that we like. Yeah. You know, which, again, doesn't mean it's correct, you know, I have no idea. Indeed. Like you said, it's crazy. You know, I don't know if it's either too crazy or sort of just crazy enough. I don't know.
- [87:35]
B
Well, you know, I've often said that maybe we just have no right to expect that we understand quantum gravity. Given that we clearly don't understand quantum mechanics. But I didn't plan on having to change quantum mechanics to make it work. So I'm glad that someone is. Yeah, well, no, look, I'm glad that someone is pursuing that. And if you turn out to be right, it would. It would indeed be a lot of fun.
- [87:56]
A
Yeah, I hope so. I don't know. Let's see. Take a while, probably. I mean, of course, eventually, we hope to. Right now, this was all pretty floating around, right? I mean, we have to see to what extent this connects into more concrete theories. String theory and whatever. And how can we turn this into real predictions and so on. So it'll be a while before we know. And maybe something better will come along. I don't know.
- [88:21]
B
Full employment. We're not going to run out of fun things to say. So, Daniel Harlow, thanks very much for being on the Mindscape podcast. This was great fun.
- [88:28]
A
Yeah, thanks, Sean. Nice to talk, as always.