349 | Daniel Harlow on What Quantum Gravity Teaches Us About Quantum Mechanics

Introduction

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Einstein's Theory

1:00Hello, 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 relativity, quantum mechanics, Brownian motion and 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, etc. So the idea being that the smartest physicist of the 20th century had about 10 years of really hard work,

1:36and 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 lot of papers on other topics during those 10 years. But that precedent kind of gives us an expectation, right? Like if that smart a 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,

2:09or many people are, progress should be kind of tangibly fast. You should see more improvements, more theories that really change things.

Current State

2:19Of 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 energy. We've had some very good ideas that have been very, very useful in helping us connect the theories that we have

2:51to 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.

3:21It's frustrating, and it leads people to say, what's wrong with these physicists if 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 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,

3:52or 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.

Daniel Harlow Interview

4:09So 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 collaborators have recently turned their attention to cosmology.

4:44He, 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've got to admit that. Or maybe there's some reconciliation to be had in the future of everyone's different views of quantum mechanics.

5:20Daniel 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 right there, front and center, in a way that, you know, 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.

5:51As 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, you know,

6:21define 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 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.

Black Holes

7:01Daniel Harlow, welcome to the Mindscape podcast. Hi, Sean. Thanks for having me. I can remember, you know, 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 progress,

7:31even without, you know, the once and for all theory being put forward. Do you think that's a relatively accurate way of thinking today?

7:40Well, I would put it this way. You know, 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.

8:16Sometimes I have the wrong sign of the cosmological constant. But I think the reason why, nonetheless, 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.

8:46And 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. And the standard model of particle physics is kind of a smorgasbord. I think, I don't remember exactly, but I think there are 19 dimensionless parameters in the standard model that you just kind of fit to data. And they're more discrete. And they measure them, yeah. Yeah, there's more discrete parameters also,

9:17like, you know, the representations that things transform in or whatever.

9:22And gravity doesn't seem to have all that mess. Because, 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.

9:56Because if you had a particle that didn't feel gravity, it could escape from a black hole. Why not, right? 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 try all these different unrealistic models in the wrong number of dimensions or with the wrong cosmological constant or too much supersymmetry is another one that we like.

10:28And somehow the gravitational part of all those theories look similar, 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.

10:59And, you know, 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 100 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.

11:29They 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, you know, I try to not pay too much attention to those parts and focus on the parts that feel more general. 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 sympathetic thought or not,

12:02that 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 we eventually 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.

12:24Well, right. So, I mean, 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

12:55is 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.

13:27You know, quantum gravity should be important inside of a black hole 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 we try and understand questions like where did the initial conditions of the universe come from?

13:52And 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. Oh, yeah. 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.

14:24And 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 at the Large Hadron Collider. They just cost a bit more. So we haven't done them yet.

14:41But 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

15:11even 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 is, you know, widely respected Landau, you know, 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

15:42that 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 an emergent theory in the limit where you have this external observer and apparatus, which is sort of arbitrarily big

16:13and slow and careful, you know, and that's who gets to measure the, you know, test the probabilistic predictions of quantum mechanics to arbitrary accuracy. You know, it's the person who's outside the system, you know, and that relates to all this various puzzles about Wigner's friend and so on.

16:33And in cosmology, you don't have that crutch. You know, 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.

17:00And so it's not really the setting where quantum mechanics makes sense, you know, and until recently, you know, I mean, I've actually believed this for a long time, but until recently, you know, it sounds a bit like philosophy, which is not necessarily a bad thing. You know, I know you like some of us. Yeah, I also I also, you know, was a liberal arts major and philosophy. When you've got a one track mind, you go where the cravings take you. Welcome to racetrack.

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Hawking's Paradox

19:03you 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 in 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 test quantum mechanics. And what we've learned in the last five to ten years

19:34is that, well, I should say a little bit of the background, right? So, please, yeah. Going back to black holes for a minute.

19:45Yeah, 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 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

20:15gravitational 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

20:46that 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.

21:00You 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 it even radiates thermally in the way that the oven would radiate thermally and it obeys the laws of thermodynamics.

21:24And 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.

21:54So 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 the black hole is getting smaller and smaller so its number of internal degrees of freedom is getting seemingly less and less if the entropy is actually counting the degrees of freedom as Boltzmann told us that it should

22:25and 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 what you wrote on the paper is still there in the oven at least if the oven is very well isolated from 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

22:57with matter fields gives you the answer that that information is just gone and so somehow you know, you thought that the black hole had no degrees of freedom left 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 in the relativity community what people usually say is that well it must have left behind a baby universe you know the black hole it sort of pinched off

23:28from our world when it shrank to zero size but the the interior of the black hole must be out there still somewhere and that's where the information is so you know if you if you talk to you know 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 it it 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

23:58and so this was a puzzle that you know drove many people in the field over the last 50 years 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

24:28quantum 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

24:58which in quantum mechanics we call unitarity and locality meaning that you know what I do here in this room can't instantaneously affect what's going on 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 you know there are three things you might want you get to pick two and you know in his version of it you gave up on in the way I presented it you give up on the finite entropy he might

25:29have 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 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

25:59when 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 you know now I'm trying to connect the back to cosmology right saying okay we figured out at least you know so we showed at least it's possible to

26:30have one and two and then three star where you say so you say okay Hawking was right you can't have one two and three but you can have one two and three star where three 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 is enough okay so if you can tolerate that if you can

27:01say okay it's fine if we break locality by doing something that's exponentially complicated in the entropy of the black hole right exponential in the entropy of the black hole you know 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 one two and three stars so they're not in contradiction with each other so let

Emergent Space-Time

27:26me before we're getting back to cosmology let me pause on that because I'm sure people are gonna care about this a little bit I mean what is your level of confidence that we're on the right track these would be the just the black hole information loss puzzled you have it basically figured out or do you think that we're we have positive progress but still a way to go yeah well I mean so so 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

27:56so the precise claim is that Hawking said you can't have one two and three and we showed that you can have one two and three star okay now there are two remaining questions one is how bad is it to only have three star and not three three so just again because people don't necessarily remember three star is really really tiny violations of locality yeah unless you do something really complicated and then they can be large okay that's right so you know

28:29one 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

28:59can'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 that's true 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 so is the idea of wormholes

29:30involved in this non-locality 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

30:04that as a relation between Hilbert spaces as you know so 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 could you say just a little bit for the person on the street what the gravitational path integral is right of course so so quantum

30:37mechanics 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 Heisenberg's ideas yeah Heisenberg yeah

31:08yeah 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 to for you

31:39know 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 show 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

32:10which the weight actually is is not so bad I mean it's it's it's something that you might have guessed even without deriving it it just based on the classical physics of the particle there's some natural guess for what the weight should be and and Feynman showed that that guess is correct and so that there's this way you 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 you know in the in the appropriate amount of

32:40time so in in ordinary quantum mechanics you know these approaches are equivalent there's no big mystery you can pick either one and and use it and you know 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

33:11integral 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 um it's somehow stronger it knows things that the canonical approach doesn't know for example it knows the number of uh degrees of freedom of a black hole yeah you know gibbons 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