The Unreasonable Effectiveness of the Klein Bottle | Janna Levin

0:00 There is no general relativity. There is no space-time. There is only the quantum threads, the embroidery, the threads out of which you embroidered this illusion of a continuous space-time. Professor Janna Levin, along with co-author Brian Greene, published two papers just last month exploring what it would mean for our universe to be compactified on one of the most bizarre objects in the history of math, a Klein bottle. This is a non-orientable surface with surprising physical properties, potentially explaining the origin of matter. Matter that composes you. Is this related to self-referentiality and unprovability? On this channel, I, Curt Jaimungal, interview researchers regarding their theories of reality with rigor and technical depth.

0:48 Most approaches to CP violation, the matter-over-antimatter asymmetry that is the reason we exist rather than annihilate, put in that violation by hand as tuned parameters. Janna Levin's papers don't. The geometry of the universe breaks the symmetry. Today, we discuss what Gödel has to do with the universe, black holes as elementary particles, and even ER equals EPR, piggybacking off of the previous Juan Maldacena podcast on this channel as well. The question underneath everything is, what if the deepest laws of physics are not laws at all, but geometry? Professor, is the universe a Gödel sentence about itself?

1:34 So, this is something I've definitely struggled with. I think the early universe, the creation of the universe, the idea of setting initial data for the universe, all of that sounds really self-referential. It sounds like the laws of physics are trying to say something about their own genesis. And that ingredient, the self-referential ingredient, is kind of a flag that you might be getting into Gödelian territory. I've never actually formalized this intuition, though I talk about it occasionally, and occasionally I'll talk to somebody plausible who can help me struggle through it. It's always good to have a collaborator. But I haven't written it down yet, in some sense. I haven't written down that Gödelian expression. But it does seem to harken back to those original ideas about there not being a theory of everything.

2:24 Ah, okay. Well, we've got to shut this interview off right now, because that's the channel's name. All right. You can add a question mark. Perfect, perfect. Now let's think about this, because a Gödel sentence describes its own unprovability. So it's not merely a self-referential sentence. Do you mean to say more like the universe may be a self-referential sentence, or is there something Gödelian about it? Yeah, I think it's both. So let's just go back to Gödel for people who haven't thought about it for a while. There was famously the liar's paradox, which certainly Gödel would have been aware of, in which the liar says, "this is a lie." So if it's a lie, it's true. If it's true, it's a lie. And you have this paradox that exists in language. And I think metaphysicists were sort of lightly, not overly concerned about this,

3:11 but what Gödel did, which was to bring this to absolutely the next level, was to mathematize the idea. So he moves from "this statement is untrue or a lie." He doesn't do that. He actually formulates "this statement is unprovable." And he mathematizes that concept. He says, essentially, that there is a true statement about a proof belonging within an axiomatic system that cannot be proven to be true, which is, of course, the claim of the statement. So the statement is true, but unprovable. And that is not inherently paradoxical or inconsistent. So Gödel says, look, I'm going to preserve my faith in the consistency of this axiomatic system,

3:58 but I did just show that not all true statements, even in algebra, can be proven to be true. And that's fantastic. Now if you look back at the time when he was doing this, the great mathematician Hilbert had made a call to all mathematicians, not to prove all infinite true statements, which is impossible, but to at least render the fairly obvious assumption that all true statements could be provable, to at least ensure that that was the case. And in fact, Gödel comes along and does the opposite. So in some sense, Gödel's work doesn't talk about paradoxes. It's perfectly consistent within mathematics. But it is nonetheless stunning because it suggests that there can

4:44 be no such thing as a theory of everything for mathematics. You cannot prove some statements simply by marching through the axioms of certain mathematical structures, that there are things, even among the numbers, that we simply will never know, that we can't know, true things that are unknowable. And I think that was a shock to mathematicians, but also it should continue to interest physicists whose, of course, big ambition is to have a theory of everything. So what can I do about the early universe this way? Could it be that the early universe,

5:31 somehow, the consistency of the initial data and the laws of physics are preserved? There are relations that are true, but unprovable. Now, could it be — okay, so two questions here. You can take whichever one you like. Could it be that the laws of physics or the initial conditions are inconsistent, whatever that would mean? Okay, so that's one horn, one question. And then my second question is, what would the Gödel sentence, supposing this is true and more than just a flowery analogy, what would the Gödel sentence of the universe's formal system be? Like the sentences in a sentence in a certain language. So I'd like to think that the laws of physics and the universe itself and the way that the universe is crunching, possibly an algorithm, crunching this initial data forever,

6:22 that that is consistent. That is, of course, the paradigm of physics. If that's not consistent, then we've got something really, really bad on our hands. And I think Gödel would have said the same thing about algebra. He said, I'm going to accept the consistency, but the unprovability, as opposed to saying, this is inconsistent. So I think it could be the same thing, perfectly consistent laws of physics, just ones that don't allow us to prove certain aspects of the initial conditions. What would the statement be like? Again, I've never really tried. So what Gödel did, which was so amazing, is he invented this code where every symbol, every number, every operation,

7:09 including a parenthesis, got a code, received a numerical code. And so every proof could be mathematized as just a relationship among numbers. Very simple algebraic relationship. So I've never gone to the depths of trying to actually do this. But I mean, now you're kind of inspiring me when we get off the phone not to go to yoga, but instead to try to structure the sentence. But I think if we look at "this statement is unprovable," which is the kind of English translation of what Gödel did, it would be something like, "these initial conditions cannot be predicted by the laws of physics."

7:55 Ah okay. I would say that that kind of parallels Gödel's structure. It is both self-referential, and it can be true but would intrinsically therefore be unprovable, because you can't get to it through the laws of physics. So, the laws of physics — it's usually thought of as the laws of physics, and then we have initial conditions or boundary conditions or what have you. And they're separate. It's been a long struggle, yeah. If the Gödel statement is a statement in the laws of, like, a law itself, then if it's referring to the boundary conditions, it wouldn't technically be self-referential. I would say, if you're really talking about the creation of the whole universe, you can't play that game. Like, I can get away with it if I'm teetering a

8:44 ball on the top of a hill. And I say, look, the laws of physics are Newtonian mechanics. And I'm externally to that adding in the initial data. But if I want the system to be the entire universe, I just don't think you can get away with that. And I think that we felt the resistance about why initial data is so strange when we want to apply it to the whole universe. That's been a long problem people have thought about for a long time. Hartle and Hawking, principles for the initial state of the wave function of the universe. Trying to say, maybe it's not a choice, maybe there's not a range of initial data, there's only one possibility, and the possibility is set by the laws of physics. That seems more holistic to me.

9:34 I think we have an initial data problem whether we like it or not, if you're going to talk about the entire universe. So that's why I think therein lies, at least... And again, with Gödel's, once Gödel proved this statement was unprovable, a whole slew of things followed, like uncomputable numbers with Alan Turing. It was just the tip of the iceberg. Now we know that there's an infinite set of uncomputable numbers, numbers about which we will essentially know nothing. But they're numbers. They have facts about them. But they're not numbers we can write an algorithm to predict. They're not numbers about which we can know their intrinsic properties. It's just simply a list of random digits. And

10:22 the universe could be like this. The initial data could just be the tip of the iceberg. Okay, well, let's talk about Penrose, AI, and consciousness. Okay, fun. I just saw Roger — I like to call him Sir Roger, although sometimes the British tease me for that because it's so formal. Apparently, when someone is knighted, you don't call them Sir Penrose, you call them Sir Roger. And I think it's quite endearing to call him Sir Roger. But I saw him recently, we had a conversation together at Oxford just in October, and he remains one of the most interesting people I've ever known. Great. I'll place a link to that on screen and in the description as well. So, he also ties uncomputability to consciousness and says that AI is not conscious. Computers may never be conscious.

11:10 Now, you also take the view that AI, current AI, is not conscious, I imagine, for a different reason. So, I want to spell out where do you agree with Roger and where do you diverge with Sir Roger? Yes. Well, I'm not sure of all of his dimensions in that. Last time I spoke to him, we were actually talking about black holes, in fairness. But I think from my point of view, AI isn't yet conscious. I am not a person who thinks consciousness is substrate-dependent. I don't see a barrier to consciousness in a different material. That strikes me as really odd. I can imagine it being way too hard for us to simply algorithmically program. I can imagine that. I can imagine that this whole thing going on with these biological systems took billions

11:58 of years to evolve and are just very complex, and so we're kind of stuck with biology because nature did this for us through evolution. But I can't find a logical reason to preclude the possibility that it's conceivable that there could be consciousness in a different substrate. So I'm not against AI consciousness as a possibility. I just believe we're so far off, even though I am stunned by LLMs. They're incredible, man. And I'm not a big person using AI for emotional nor intellectual support, but man, what a search engine. It is unbelievable. This thing

12:47 does talk to me. It won't stop using scare quotes. I can't get it to stop doing that. What do you mean? So anytime an LLM wants to say something metaphorical, you'll find a lot of them will put quotes around the word. And I keep saying, I understand what a metaphor is. You don't have to keep putting a quote around this word. Like, the universe "chooses" — if we wanted to say, the universe chooses a state, it will put quotes around "chooses." I find that I can't disabuse it from this habit. Do you have custom instructions on them? So, I'm not that deep into it. I think I have tried that because this is such a pet peeve of mine. I see. But anyway, I'm just a newbie in some sense to this whole thing.

13:36 My pet peeve is it's not X, it's Y. It's not that the universe cycles, it's that the universe does this and that. It's so frustrating. And then the em dashes. Right, the em dashes. I probably have a bit of a bad habit with em dashes myself. Yeah, but that's because LLMs are trained on you. You train the LLMs. Right, right. I mean, there's a lot of things to complain about the LLMs and what it's doing to society, you know, and how people are less and less original every day and more and more average. And how can we innovate if we're simply copying ourselves frozen at a particular moment in the history of humanity? You know, all of this stuff. But that's not the big questions. The really interesting questions are these ones about consciousness. And so I guess what I feel about it is,

14:24 if I think about human beings as being a series of chemicals interacting according largely to electromagnetism — largely, right? It's usually large molecules forming DNA, RNA, and proteins, and all of this stuff happening just on the basis of electromagnetic interactions. Really basic laws of physics. At what stage does that become human consciousness? Of course, one of the most tremendously thorny and elusive questions that humanity's ever asked. So I don't see why we're expecting the LLMs or any AI for us to be able to solve that problem

15:10 before we can solve this problem. Like, we don't understand how this happened. I still cannot, in a laboratory, go from molecules interacting electromagnetically to comprehending why there's an interiority and a sense, an imagination that hallucinates the color red. That absolutely evades us. So as a physicist, where do you stand on the hard problem? So David Chalmers is a good friend. It's funny because David Chalmers has basically become superb at dismantling any attempts to solve the hard problem. That's his job. He is this gatekeeper, and no matter what solution you come at him with,

15:56 he's going to dismantle your attempt to solve the hard problem. Sometimes I have other friends in neuroscience who think that it's just a total red herring, that it's just really not the question we should be asking, and it's just silly. It's the how question. So we can say where, what, who, when, why. We can answer all of these questions about consciousness somewhat. It's evolution, where it happened, where the biological correlates are, and all of these things are answerable. Nobody thinks that those are the hard problem. The hard problem is how. Like, how does a photon hitting my eye and triggering some

16:42 electromagnetic interaction along some fibers result in me imagining, hallucinating the color red? Nobody knows that. And nobody's come, in my opinion, anywhere close. And when people try, they're really usually answering a why question. Human beings evolved consciousness. Why? Well, because our compute is low. We don't have infinite compute. We struggle to understand all of this data. So we evolved a mechanism to approximate really quickly. I can, out of the corner of my eye, know it's a baby. Out of the corner of my eye, I know it's a tree. Or a car is speeding at me. All of that consciousness is a really good tool with low compute. This approximate

17:32 hallucination I have allows me to survive and very quickly with very approximate understanding. And so I understand a lot of the whys. You can talk about whether emotions are important or the unconscious. All of this is why stuff. It's all interesting. But none of it really explains how. How I have an interiority and how I have this hallucination of the world. And I think it's a fascinating and wonderful thing. We're all obsessed with our hallucinations of the world. It's everything to us, right? But I would say that I sometimes wonder a stronger thing, which is if a machine has tremendous compute, like practically infinite compared to us, will it need to evolve consciousness? Is

18:21 there any reason why it would have to? Or can it just continue to do perfectly well by pretending, by simulating consciousness the way an LLM does, a large language model? And that, I don't know, maybe consciousness is a crutch AI won't need. And so it will never develop. You know, I have a bone to pick with you. Oh, please. I can hang up now and take my toys and go. I subscribe to The Economist. Their science and their AI coverage is among the best I've found anywhere. And I say that as someone who reads plenty of it. I'll give you some examples. They just ran an analysis on how attitudes towards science are changing in American politics and what this means for research

19:08 and funding in scientific institutions moving forward. This sort of high-quality reporting is fantastic. They even covered how dark energy may be weakening over time. Now, if that holds up, it completely changes our understanding of the universe's fate. If you watch this channel, those are exactly the kinds of questions that we explore every week. I subscribe to The Economist because their science and their AI reporting regularly surprises me with how deep it goes. And they're also, of course, known for global affairs, both political and economic reporting. They are top-tier, and interestingly and flatteringly, TOE is one of the only podcasts that The Economist partners with. So as a listener, you get an exclusive 35% off. That's not a deal that they have just anywhere.

19:55 Head to economist.com/TOE to subscribe. That's economist.com/TOE for 35% off. Do you think Dr. Squatch, Burt's Bees, or Native are small wholesome operations? Think again. They've all been swallowed by private equity. This channel, Theories of Everything, unlike other channels, is not owned by private equity, and I'm glad that Van Man, today's sponsor, also has that as a value. They're at the epicenter of the pushback. Let's play muckraker for 10 minutes with their ingredient list. Take a look at other brands' ingredient lists, and you'll find the same corporate slop wearing different labels. Van Man started the tallow trend a few years back with grass-fed tallow moisturizers,

20:40 and they've been crushing it since. You may have noticed that Curt's been looking extra dashing and handsome lately. I've been using Van Man's tallow cream, in fact, this one here. And I've been using their sweet onion shampoo. I even love how their packaging is a joy to open, look at that. Now, here's the thing about tallow. The fatty acids are nearly identical to the oils in your own skin, so your body recognizes it. One use, and you'll feel the difference. It's softer, it's smoother, there's no filler garbage. It replaces lotion, night cream, wrinkle cream, even Neosporin and diaper balm. Actually, right now I even have their lip balm on. And it's not just for men, even though it's called Van Man. My wife loves it as well, and when I put it on, I always go, "I'm Van Man." So whether you're a refined philosopher or an artist or researcher in physics, it will assuage

21:29 dry, cracked skin overnight. Powerful enough to heal and safe enough to spread on toast. Ready to ditch the corporate chemicals? Go to vanman.shop/CURT and use code CURT, C-U-R-T, for 15% off your first order. That's vanman.shop/CURT, code CURT. Van Man, real ingredients, no exceptions. I'm Van Man. I recently signed this book deal with Penguin. Penguin is fabulous. Penguin is wonderful. Yes, yes. So in it, I made this analogy to averted vision. And I haven't heard anyone make that analogy before. And also, I have the characters of Gödel and Turing as well. And then I see, oh gosh, Janna Levin just beat me to it. I gave a lecture a couple days ago at the Mind at Large conference,

22:17 which is a conference on panpsychism. And I was saying that, look, some phenomenon may be such that when you try to look at it directly, it actually disappears. Right. And I think that's akin to looking at something directly, not seeing it, feeling it in a sense by not looking at it, but then you try to make it explicit and then it disappears. And then

23:06 I saw that you also made a similar analogy and I was upset with you. I'm so sorry. Yeah, that's in A Mad Man Dreams of Turing Machines, where truth is just like that. You can see it, but only out of the corner of your eye. And it disappears when you try to look at it directly. I think it's a beautiful analogy for what happens. What I was trying to do in A Mad Man Dreams of Turing Machines is admit that you could not get to the truth of the stories of these lives in an axiomatic way, simply as though rolling from theorem to theorem, listing biographical facts. I couldn't write, in other words, nonfiction and get any closer to the truth about them,

23:53 in the same way that Gödel's true statement can't be arrived at through theorems. And I felt that that underscored sort of this idea of, well, sometimes our human narrative, which destroys things in the process of telling the story, is as close to the truth as you're going to get. You can only get to it out of the corner of your eye, you know. Yeah. So well, now I'm looking forward to your book. Is it fictionalized? No, no, no. I wanted to bring people to the frontier of physics because people keep thinking the frontier of physics is string theory, it's AdS/CFT. And I'm thinking that's 20 years, 30 years old. Like, what's the frontier? As I was going through this, I was thinking, okay, because I'm not a physicalist, but I'm not an idealist either. I'm not a monist

24:39 in the sense of any traditional sense of the word, but I'm philosophically homeless. I don't know what I am. I just am unconvinced of all the mainline positions. Well, there's always more to be done. I mean, it's almost this idea that we should be re-approaching theories and ideas and saying them different ways and each person having a unique approach. You know, this idea that, oh, the novel's already been written, there's no new novel. Of course, that's absurd. It's almost like saying, well, let's not make more human beings because a human being has already experienced the world. So nobody else should experience the world. And, of course, that's not what we actually believe. We actually believe that each experience of the world is unique and brings something and experiences something unique.

25:25 Klein bottles. Klein bottles, yeah. Well, I'm a little obsessed with them. Can I show you? I have a little Klein bottle. Oh, I should have brought my glass Klein bottle. I have this. Can you see this little Klein bottle? Yeah yeah. I actually have a glass 3D Klein bottle. So my friend's an artist, Andrea Lauer, and she makes these little things for me for various events I do or ideas I'm thinking about. It's really kind of a fun collaboration. But this, of course, is not really the Klein bottle. This is what the Klein bottle looks like if I force it to live in three Euclidean dimensions. I have to really mess it up. Okay. The Klein bottle, as it lives in two dimensions without forcing it to embed in three,

26:14 is a very symmetric object. It's very symmetric. Now, some symmetries are lost, but not all symmetries are lost. So the idea of the Klein bottle, if it lives in just 2D, it can be a perfect square, meaning it's as wide as it is high. And I can't do that here. It's all messed up. It looks like it's smaller and bigger. I've had to change the local geometry in order to represent the global topology. But you can have both if you stick in two dimensions. So then you're really playing a video game. The idea, for instance, let's take the simpler structure, the torus. In the torus, if you exit the right face of,

27:02 let's say, a square, you re-enter the left face, just like a video game. It's no big deal. You fly off one edge, you re-enter the other edge. It's just a rule of how those edges are glued. You can do the same thing in the video game, going off the top of the screen and re-entering the bottom of the screen, right? And if I want to see what that looks like to me, my three-dimensional self wants to say, well, what does that look like? I want to lift it into three dimensions. I want to glue the sides, make a cylinder. Then I want to take the ends of the cylinder, and I want to glue those together and make a donut. And I go, oh, look, the torus is a donut. But in doing so, I've changed its local geometry. I've made it shorter on the inside and longer on the outside and shorter around the donut part. And all of that's false. All of that's a false projection of what I did to force it to show me the object

27:52 with which it is topologically equivalent. So the surface of a donut is topologically equivalent to the real torus, but the real torus lives just in two dimensions. I never lift up the sides. The real torus can be equally wide as it is high. So the Klein bottle is just like the torus, except when I glue the sides together I twist the sides by 180 degrees. So in other words, let's say this twist happens when you're going out the top. If I go out the top, I come back in, and I have a left-handed glove. It comes back in the bottom, flipped into a right-handed glove. I'll be showing some animations on screen over this, so don't worry. Okay cool. Yeah, so that makes the Klein bottle. It's completely compact. And it is

28:42 what's called non-orientable because when I go one journey around the Klein bottle, it's almost as though, because of this twist, I've come to the inside of the Klein bottle. There's no real inside or outside. And if I go back around, I'm on the outside again, and that's a continuous surface, so it's as though it has no well-defined inside or outside. Okay, now the donut does. I can tell what's inside the donut versus what's outside the donut. The Möbius strip or the Klein bottle, which is the 2D analog — it's not orientable in that sense. And because it has this funny left-right property, if I take a left-handed glove one time around, it's now a right-handed glove. It doesn't fit my left hand anymore. I have to send

29:30 it around the universe another time for it to come back and now fit my left hand. And they're just fascinating little spaces. The original idea for working on them recently was I wanted to make a ray gun where you shot left-handed particles into the Klein bottle. So you had a universe as we know it, three dimensions of space, one dimension of time, large spatial dimensions, plus two additional dimensions that were wrapped up into a Klein bottle. And those dimensions exist everywhere, but they're hard to access because maybe they're small. Maybe we live on a brane. There could be various reasons why we don't notice that they're there. Wait, sorry. Can you repeat that? What's the structure of our large dimensions,

30:17 and then where do the Klein bottle dimensions live? Yeah, so at every point in our space, just like at every point in our space there's up, down, left, right, forward, backward, there's also these two other dimensions at every point in space, and they're wrapped into a Klein bottle. And so everywhere I am, in principle, if the bottle was large enough, I should be able to stick my hand in there and watch it come back right-handed. My right hand will come back left-handed. I see. But it's possible that it's just too small for me to do that. And the common analogy is imagine you lived on a very, very, very thin straw, and you were bound to that straw. You might think the universe was only one-dimensional. And it might take the whole other straw dimension inflating before you realized, oh, wow, there's this other dimension

31:05 that I live on that I could go round and round. And if I make it big enough, I might even think I lived on a flat plane. I might lose the sense that I lived on a straw altogether. So it could be that those dimensions are just really small and we think we only live in three, but we really have five spatial dimensions. Got it. And maybe that's the reason, or maybe there's another reason why we can't access them. Like, we're bound via some interactions to the three-dimensional space, and that's like a brane. Sometimes that's called a membrane, a high-dimensional membrane in this five-dimensional space. And we're glued to this membrane, so we just, even if that space is big, the Klein bottle's big, and our whole membrane is moving through the Klein bottle. Our whole

31:50 universe, all the galaxies, everything stuck to this vast universe that we see is moving through this higher-dimensional Klein bottle. We just don't even notice it. That is a possibility, too. Yeah. So, firstly, physicists tend to not like non-orientable surfaces because you can't put spin on them. You can put pin. So, I want you to tell us the difference between spin and pin and why this is not as much of a concern as we thought. Yeah. So we're not the originators of the mathematics of pin structures, but spin structures are just a way that people understood they could do things like put fermions or spin-half particles in a universe. And this is what the Dirac equation

32:40 describes for us. It describes the evolution of a spinning particle in ordinary space. We don't put anything topological on it. We don't assume it's finite. Just three nice dimensions. The Dirac equation was originally written in three plus one dimensions, including time, four dimensions. The problem with non-orientable manifolds is people thought, oh yeah, maybe you can't orient the spin structure either. You know, there is an orientation to the spin structures, and so maybe they just can't live there. But it was shown that you have different structures called pin-plus and pin-minus depending on the boundary conditions for the fermion, meaning does the fermion field come back to itself on one trip around the non-orientable space,

33:30 or does it come back to minus itself? Because that's not an observable, you can't tell the difference. So both are possible outcomes of taking one full trip around the space. And simply it's just been shown that those structures exist, so there's a reassurance that you can do the Dirac equation even on these non-orientable manifolds. It is not an obstruction. You talked earlier about obstructions. It is not an obstruction to building fermions. So we know we can build fermions. We have trouble building what's called chiral fermions. And chirality is this left-handedness versus right-handedness. Chirality describes your handedness. And we know that particles do come in a hand. It's a peculiar thing that left-handed particles interact weakly and that the right-handed

34:22 counterparts behave differently. So we want to be able to build left-handed particles because the laws of physics that we observe are partial to left-handed particles. We don't know why. But it turns out it's really hard to build chiral fermions. So there are reasons why we kind of want to restrict the world that we observe to this brane where we can have chiral fermions, where we don't have this problem of the left and right being mixed up in these non-orientable manifolds. Because if you're a left-handed particle and you travel into this higher dimension, you come back right-handed. That seems really bad because now you've broken something about the gauge symmetry, right? Because you've broken something in a really bad way that's

35:13 inconsistent. So we're trying to understand many things about these higher dimensional spaces. I thought they might do us some good in that we could take left-handed particles, shoot them into the extra dimension, have them come back right-handed, and by their right-handedness they would be non-interacting. Hmm. And so I thought, oh, that's kind of cool. You've made something dark. You've made something that was interacting, and you've made it non-interacting. So you've turned off, you've made it dark. Or effectively, as I often say, and many people say, it's better to call things invisible, because you've made them invisible, not dark. They don't cast a shadow, they're just technically invisible.

36:00 And I thought this was a really cool idea, but instead what we got was something really different. And I really should say I have the most fabulous collaborators in this. This is work with Brian Greene and Massimo Porrati, who is just absolutely brilliant, a particle physicist and string theorist, and Dan Kabat, just an incredible talent in particle physics and string theory. And I'm sort of the space person, you know. I call them my guys, you know, and it has been one of the greatest pleasures of my research life to work with them and just run into the cloud of ideas and try to find our way through. But yeah, so what we ended up finding was equally really exciting,

36:45 but completely unexpected, at least to us, at least to me. I can't speak for them. Tell me about what you bring to the table and what Brian brings to the table. What are the relative strengths of everyone? What's your dish at the potluck? You know, it's all different. Brian and I have worked together for many years, as have Dan and I, Massimo a couple of years, just a wonderful collaboration. Sometimes one of us just sees something the others aren't seeing. It's just... we are all bringing different things, but it's not stark. It's not like, this person calculated this section of the paper. It's not like that. So everyone has a global view. In some more astronomy fields than in theoretical physics, people will be, I did this data analysis, and I did these

37:34 figures in this larger paper. I think for us, we all have to have the whole view. And so what we're bringing for each other is sometimes challenging, pressure testing the ideas. Each of us will bring different ideas to the table and we'll work on them as a group. And I think sometimes you really want to be pressure tested by your collaborators in your group and not go out there without having fortified your ideas and really crossed your T's and dotted your I's, doing all of this. A lot of what we're doing is pushing on it and pressuring it. And then streamlining. I think for a long time we just didn't know what we had. So you're going to your friends and saying,

38:21 is this a mistake? I'm calculating this. I can't get it to go away. Am I making a mistake? We all know lots of ways of calculating. Do you see a calculational error? Or do you see a different way of doing this calculation? And sometimes we'll have two different ways of doing it and getting the same result, which is really important. So yeah, I would say that. And really, it's just a lot of fun to get together for a few hours, and there's always some point where people will walk past my door, and we're all in here, and we're all quiet. Nobody's talking. Why? Because you're thinking? We're all thinking. And it's a really funny thing. Does it look tense from the outside? They think you're upset with each other, or what?

39:07 I think physicists are used to this phenomenon, but people who are not physicists remark on it. The strange phenomenon that you'll get together, there's a flurry of talking, flurry of activity, and then it could be 10 minutes of utter silence. And no discomfort. Until somebody kind of picks up a piece of chalk and meanders over and says, "Well, what if..." and it starts. But yeah. So I think what has been interesting is that what we discovered is that these spaces violate certain symmetries that you would have had. So if you're starting with a two-dimensional sheet of paper before you've glued it together, and that sheet of paper is infinite,

39:53 so you imagine two extra infinite dimensions, you should have this symmetry under translations. You expect the universe to be the same wherever you are, and you don't expect to have parity violation, which is this violation of this handedness, this left symmetry gets broken. And something else subtly gets broken. You can also break charge symmetry, which says that the universe or the laws of physics look the same for the particle and, let's say, the antiparticle. The topology can break that for you. So it gives you something that we actually know we have, which is an asymmetry between matter and antimatter that we don't know

40:38 how to explain. We don't know why after the Big Bang there weren't equal proportions of matter and antimatter, why those proportions didn't come together and annihilate and obliterate into light and thereby leaving us an empty universe devoid of certainly human beings, planets, stars. And we've been trying to understand this, why there's something instead of nothing. And actually, the Klein bottle is just a simple example of a space where the geometry of the universe breaks the symmetry and can preferentially favor matter over antimatter. It would explain why there's something instead of nothing. So it does some funny things.

41:26 I remember the doubt before launching this podcast. What if no one listens? What if I'm wasting my time? If you've ever felt that way about starting a business, Shopify is the partner that turns uncertainty into momentum. They power millions of businesses and 10% of all U.S. e-commerce, from Allbirds to Gymshark to brands just getting started. No straggler left behind. Shopify's AI tool writes your product descriptions fully and it enhances your photography, it builds you a stunning store from hundreds of templates. Forget about the dormative haze of bouncing between separate platforms. Shopify puts inventory, payments, and analytics under one roof with the propriety of a true commerce expert. Their award-winning 24/7 support means you're never alone, and that iconic purple ShopPay button — it's the backbone

42:18 of their checkout, the best converting on the planet, turning abandoned carts into actual sales. It's time to turn those what-ifs into wins with Shopify today. Sign up for your $1 per month trial at shopify.com/TOE. That's shopify.com/TOE. Half of my day is spent in conversations and research, the other half is spent trying to remember what was said and read. That's where Plaud comes in. P-L-A-U-D. I have far too many thoughts. I always tell myself that I'm going to remember them and then I almost never do. It's incredibly frustrating. But I've been using Plaud for many months now, and it's a huge game changer. It's actually ridiculous. I've noticed that this channel's output,

43:06 Theories of Everything — if you've also noticed that it's increased in quality and clarity over the past few months, if it's improved at all, Plaud is responsible for a non-trivial chunk of that. I would say something like a 5% gain in thinking, and that workflow compounds fast. If you're in knowledge work, you know how valuable even incremental small 1%, 2% changes are. This trounces that. What I like is that it removes friction. I'll use the Note Pin S when I'm walking, moving around, or just thinking out loud. It's hands-free. I don't have to look at a screen and I can stay present with the world. I don't have to worry that I'm going to drop my phone. Then I use Note Pro in more structured settings, when I actually want to capture and organize conversations more deliberately. So instead of ideas slipping away, everything is captured, processed, and then turned back into something

43:52 usable. It's basically a system for extending one's working memory into the real world, and if you know anything about intelligence, intelligence is highly correlated with working memory. So if your work depends on conversations, research, business, medicine, law, this kind of thing matters far more than you'd expect. They're also serious about privacy and security, SOC2, HIPAA, and GDPR compliant. If you want to check it out, go to plaud.ai and use code CURT. Now, does it just permit CP violations or does it predict? Like, what would be the difference between permitting and predicting? Yeah. So I would say first we said it permits. That's the first step. And there again,

44:39 all kinds of different boundary conditions you can impose and they all lead to slightly different predictions. And so some of the spaces predict this violation and some boundary conditions won't, but you really just need one. I just need one. And then to predict, I do think, is another layer, because then you have to say, well, how do I interact with this higher dimensional space? And now to have prediction requires more understanding of the cosmology. So do all of our fundamental quantum fields permeate the higher dimensional space? Or are we stuck to a brane? And so then these details start to

45:27 become important in the actual cosmology of how you convert the breaking of the symmetry into the cosmological consequence you want, like there's more matter over antimatter. And that's... I wouldn't say it's a prediction. I think you're trying to match a model to what we observe. So if I have a brane and the brane moves through this Klein bottle, it interacts with this in a way that breaks the symmetry, and so you're predicting the way the interactions are written. You can predict all kinds of interactions, and the model will select values for the... you'll be fitting your model to

46:16 the observations kind of thing. So I'd say it's not exactly predicting, it's allowing. Permitting. I see. It is more permitting. And then the model building uses that permission to do what it wants. If I recall correctly, there was a footnote about you weren't able to find a pin-minus structure on the boundary conditions with charge conjugation. It was... yeah, with charge parity, we weren't sure... Yeah, even I can't remember the exact statement. There's a famous line — do you know this play, Proof? No. It's a famous play. Tell me about it. It's about mathematicians, where the father in the play is a Fields Medal-winning mathematician,

47:08 and the daughter is following in his footsteps, but nobody believes she's written her proof. Her own sister doesn't really believe her, and she says, "Well, here, I'll show you proof, I'll walk you through it." And she says, "But you have to give me my notebooks." And the sister says, "Well, why would you need your notebooks if you wrote the proof?" She's like, "It's not a muffin recipe. I need my notes to talk you through the proof." It's not a muffin recipe. So that's a great line. So sometimes Brian and I joke about that. It's not a muffin recipe. Who has the notes? We've got to look at our own notes. But yeah, for the charge parity, we couldn't be sure that we had a minus boundary condition,

47:55 essentially, that we can enforce a minus boundary condition. We kept getting the pin-plus structure. It might be that there's just a phase that one could add. We're not saying we've proven it can't be done. And what's the significance of that? I don't think it's particularly significant. I just think that the topology and the boundary conditions force you to use certain spin structures. That's all we know. Maybe somebody who's worked on the spin structures specifically, really deriving them, would find some big significance in it, but I think it might just be with charge parity that you're forced to use a spin structure. I don't think... it's a little surprising. We kept going around in a circle on it.

48:42 So you just mentioned branes, and people who are listening may know of branes from string theory. Are you just borrowing a tool from string theory, but this particular approach is not string-contingent? It just uses a tool? That's exactly right. Yeah. So I like to say string theory requires extra dimensions, but extra dimensions don't require string theory. And so, this could be any fundamental model that could have this kind of dimensionality. The CP violation would be broken by the geometry. Nothing stringy about that. Even brane worlds don't have to be stringy, though they did come — they were motivated by the idea that beyond strings you had higher dimensional membranes, and maybe we'd be stuck on one of these membranes. And that's

49:28 why we don't notice the extra dimensions, as opposed to requiring that the extra dimensions be small. It's very clever stuff, but all of it can migrate outside of the stringy context. But the brane world was just a simple way to show proof of concept by example. Just to say, look, I can actually show you that I can calculate an asymmetry in particles if I invent a coupling where they live on a brane. And as the brane moves through the Klein bottle, it gets these bursts of particle production. And it notices where it is in the Klein bottle because some of the symmetries have been lost of the space. And it was really just a way of

50:15 showing how you could get particle production and how you could get the main ingredients that are required for creating matter over antimatter. But you don't necessarily need a brane scenario to do it. It was just a very clean demonstration of how to exploit the fact that these topological spaces could be CP-violating, charge parity-violating. I see. Yeah. It was just a demonstration. Yeah. Okay, so let's see if I got this correct. You're not claiming that our four dimensions, our three plus one, is a Klein bottle. You're saying that our potentially five plus one, with the extra two dimensions, is somehow a small Klein bottle. I mean, well,

51:01 you were actually thinking, how can I violate CP symmetry? Okay. And then this is one way. You're not saying that this is necessarily how the universe is. You're using this as a tool. And you're concerning yourself with CP violation because you want to know about baryogenesis. And there are three conditions. And so one of the main conditions that has been unsolved is about CP violation. Is that roughly correct or am I off track? That's roughly correct. No, no, you're... I think that's about right. There's a bigger picture. One is saying those large dimensions that we live in could also be topologically wrapped up. We just don't know it because it's so big. The universe is so big that we're just unaware of that. So I think that there are multiple things beyond the CP violation that the extra dimensions can do

51:50 for you. So having the extra dimensions, Klein bottle being a simple example, could do things for you like give you dark energy, which is something that we had talked about in previous papers. And the way it can do that is because a small space has a quantum energy associated, again, with the topology of the space called the Casimir energy. And this is a well-known result. We can see Casimir energies in the laboratory by trying to confine two electromagnetic plates. We find that there's a pressure between them because of the difference in the energy between plates where there's a boundary because of the plates versus if there were no plates. That's called a Casimir energy. You can trap energies by forcing a boundary condition. And topology forces

52:39 a boundary condition on the vacuum in such a way that it creates a quantum energy that is different than you would have in infinite space. So it can create a quantum energy. That quantum energy would be felt everywhere. And that is what we think of as a dark energy. Dark energy is this weird vacuum energy that's felt everywhere. We don't know why it has the value it has. But it could be that extra dimensions are a way of trapping that energy for you. So it could give you dark energy. There's reasons to think it could contribute to dark matter models as well. That excitations in the extra dimensions could be acting as kind of dark matter particles.

53:27 It could also be, as we found here, that the same mechanisms are also giving you the CP violation and explaining matter over antimatter. So it's an all-stop shop. Potentially. And this ray gun — is that a pipe dream or was that an actual... you were hoping to make it an experiment? We... I think we can shoot left-handed particles and have them come back right-handed. I don't think those particles can be the dark matter for subtle reasons, having to do with being unable to make chiral fermions in the higher dimensions. So anything that can go into the extra dimension left-handed can come out right-handed. That I'm confident of. And the space can do that for us. And thereby, you might say, oh, it makes something dark. But then we would say, oh,

54:15 we have a problem making chiral fermions that interact in a chiral gauge theory at all because they're always mixtures of left and right. They're always mixtures. So I can't make them only left and only interact left-handed. And so that problem is a problem. So I think it works. We had more problems than we solved with that particular... But again, it doesn't have to be a Klein bottle. It could be a different topological space that breaks CP violation. So I think the idea is that it's more general than any specific claims about

55:00 the specific space. It's a general result in that sense. In other words, the shape of space might have a lot to do with the universe that we live in. You know? It's just pretty interesting. Is the shape of space what's exciting you right now? Is that where your mind is at? I have always loved that topic. I think we could also say something like, we'll learn what the geometry of the large dimensions must be by looking at the shape of the small dimensions. That's also very exciting. The idea that maybe in the early universe, there was a democracy of these finite dimensions. And what we're really trying to understand is why did three spatial dimensions get so big? And the others, however many there may be of them, stayed small or inaccessible. And that,

55:54 if there is this causal relation between why the other dimensions are small and why these are big, it might mean that we could, by probing particle physics, understand the shape of the universe on the largest scales. That stuff, I thought, has always been exciting. I am thinking about it some more because I think that this topic has given us a lot of really interesting results that are potentially very fruitful for cosmology. So yeah, I'm still thinking about some offshoots of that. But I also do black holes. I think the joke for me is that when I work on black holes, for me that's like concrete reality. I'm being practical.

56:43 Yes yes. So sure, I'm still thinking about black holes. So why don't you walk us through some of the recent results in, say, black hole information, like the Page curve or the island formula? Well, I know less about the island formula, but I'm sure your audience has heard about this a lot. But I think it's always for internal consistency worth sort of stating the problems. The problem, of course, being Hawking's provocation that black holes, just by doing a little sprinkling of quantum mechanics just outside a black hole, not doing anything dramatic like quantum gravity — just this has got to be true — a little bit of quantum mechanics on a mildly curved space-time.

57:30 And black holes are mildly curved if you make them big enough. I think that surprises people. But it's the same as saying the Earth, when it's really big, looks flat locally. The bigger it is, kind of the less you notice the curvature. So you're in this mildly curved region around a big black hole and you have a little quantum mechanics. And the black hole steals one of the particles that come out of a quantum vacuum fluctuation. And it doesn't sound like such a big deal. It's perfectly consistent with quantum mechanics. If we want to take a step back even from there, we can say, look, the Heisenberg uncertainty principle tells us that I can never know for sure where a particle is exactly, but that also means I can never know for sure that it's not there. So Heisenberg uncertainty seems

58:20 to require the possibility of particles kind of frothing around. So I can have empty space, but by Heisenberg uncertainty, I can make a particle and its antiparticle, an entangled pair, in precisely such a way that they cancel each other's details so that they can go back to the vacuum again. What I can't do is make a particle with spin a half and a pair that has spin one. I can't do that because they can't cancel each other. I have to make a half up with a half down. They can cancel each other. Spin goes away. Positive charge with negative charge. They can cancel each other. Charge goes away. But they have to be paired so that they neutralize each other perfectly. This is perfectly consistent with what we mean by a vacuum. It doesn't necessarily mean it's exactly empty. It doesn't necessarily mean it has no energy. It really means that on average,

59:10 it's got no charge, no spin, no color, you know. So anyway, a particle-antiparticle pair comes up. The black hole can steal either one. It doesn't matter if it's the particle or the antiparticle. And it can steal it in such a way that the other one is left outside of the event horizon, no longer has its pair. It can't neutralize. It can't get rid of its charge or its spin or any of its other details. It can't go back to the nothingness from whence it came. And so now it lives. It's stuck. It's stuck out here now. And that particle escapes to infinity, far away, and some observer from far away sees this particle. Maybe it's a photon. Maybe it's an electron. Maybe it's a positron. And it says, oh my gosh, the black hole just radiated a particle, because that's kind of what it looks like.

59:59 Right. But from the black hole's perspective, nothing came from inside. This is crucial. So whatever went into the black hole is not making it out. And that's a disconnected story, according to the original story that Hawking was telling. And now you have the following provocation, which is that, look, eventually the black hole is shedding its mass as it's absorbing these particles. And we can talk about why it gets less massive and not more massive when it absorbs these things. I'll talk about that in a second. But it will get less massive. The energy will be conserved. But eventually the curtain is yanked up. The black hole has evaporated. It's given off all of its mass to this form of Hawking radiation. And the curtain's gone. The event horizon's gone. And if the event horizon's gone,

1:00:47 I'm no longer protected from this terrible confusion about what happened inside the black hole. I should be able to see what happened to all the stuff that fell into the black hole. And it seems this great crisis that the stuff that went into the black hole seems to be gone, but it's not the same stuff that was radiated away. Those were two separate things. And this is what led to the famed information loss paradox. Quantum mechanics says you cannot destroy information. What happened to the stuff that fell in? It's not in the radiation that came out. That's really bad. And general relativity says, well, nothing can get out of the event horizon. So by the time the event horizon is yanked up, it's too late. The stuff, you know, it's over. So nothing can make it out. So this leads to a real conflict, a real paradox.

1:01:37 Well, so this is all very interesting stuff that everyone's thinking about now. So the standard story is that there's some event horizon, let's just imagine it as a wall, and the black hole, the black holiness is over here, and nothing can come out, but then the regular space is over here. And that there is some pair production that occurs here. And from the outside, we see something come out of the black hole. But from the black hole's perspective, something just falls in. So why would it be that the black hole is evaporating rather than getting larger? Because from the black hole's perspective, more is just coming in. Right. Sometimes you'll have people say, oh, it absorbed the negative mass particle. That's not right. There is no negative mass particle. It's not absorbing negative mass and thereby getting lighter. But the difference is that time and space, in some sense, have switched place.

1:02:25 So from outside, I might say that's a positive energy particle, my pair, that fell in and it was directed spatially inward in momentum. But because of the relativity of space and time in the interior of a black hole, you say, oh no, that negative momentum is a negative energy. I call that the time direction. I call the direction which it's moving the time direction. And it is imparting negative energy. What you're calling negative momentum, I'm calling negative energy. That's totally fine. So you don't have negative mass particles. You haven't violated anything. It's just the relativity of energy and momentum directly reflects the relativity of space and time. And so you actually absorb, in your frame of reference, in the interior of the black hole,

1:03:15 a negative energy, and the black hole gets lighter. So it's completely consistent. Yeah. Do you have a preferred resolution to the black hole information paradox? Or do you not even see it as a problem? So for instance, Sir Roger, when I spoke to him about this, he said, why do people put up so much of a fuss? Maybe information is destroyed in black holes. I see no reason why not. Yeah. He's not the only one. I think the relativists tend to be like, I can live with that. And the particle physicists are the ones who say, I cannot live with that, and nor should you be able to live with that. You should not. I don't care. You should not be able to live with this. I think there is definitely a resolution. I don't think it's just, ah, information's

1:04:05 destroyed and it's no big deal. I don't think that's the case at all. And I think, in fact, it's this gift we have. It's like the siren song. It's like the two laws that we love so much are signaling their demise and telling us where to look. They're guiding the way. So I think it is the most wonderful direction for fundamental physics. I don't think it's a waste of time. But I think that the answer — and I'm not actively working on this, although I'm mostly just chatting with people about it, but I'm observing from afar — I think the answer to this will really be a big deal. It will really be a big deal. And we are already seeing that in some of the ideas that are floating around, which I suspect are probably right. Lenny

1:04:50 Susskind's holography, Juan Maldacena's AdS/CFT. These are all, I'm sure, on the right path. But if you take a step back and you say, we still don't nitty-gritty have the answer, what it seems to suggest is that — and this is even harder in the context of what we were just talking about — we can't even trust the dimensionality of the universe as a firm fact. Holography says it might look three-dimensional, but really you only need two. And all of this is an illusion. And it is granted that the two can be interpreted in a different language as though it's three, but you only really need the two. And this is what AdS/CFT is all about, the anti-de Sitter space and the conformal field theory.

1:05:37 I think the answer is that I might have a universe in a box, but it's exactly translatable into a universe just on the lower dimensional boundary. Those are equivalent worlds. So I think the things it's saying about the nature of reality are really big things. It's not like, oh, now I know how to quantize the metric. Now I know what the indivisible unit of space-time is, and now I can just do normal quantum gravity. I don't think we're going to get quantum gravity. I think we're going to get something else. And that's why I love watching that. Yeah. Let's linger on black holes. So you said something — if I'm recalling correctly, and as you know, I haven't had much sleep the past couple weeks. I'm

1:06:23 in a horrible bout of insomnia, which you've also suffered with. Yeah, so sorry about that. Oh yeah. We'll talk about that later on. If anyone's listening and you're going through something similar, we'll get to that. Yeah. Some practical tips from Janna. You've solved it. You told me. You promised me. Oh, I have not. You can cure me. Okay. But if I recall correctly, you said something about, you've dismissed fuzzballs or soft hair and firewalls, if I recall correctly. Oh, yeah. And that ER equals EPR cannot follow the chalk or doesn't follow chalk. Something like that. I would pick those apart. So I would say, I think there's something to ER equals EPR. And I'm not going to go into great detail because I don't think it's there yet, either. I think even the people who I'm learning

1:07:08 this from are struggling to formulate it in a more precise way. So I'm not going to pretend I'm going to do better than that. But I think there's something to ER equals EPR. The idea being that, oh, maybe when I entangled a particle with its pair that fell into the black hole, that that thing that fell in is, like, by a wormhole actually also the particle on the outside. And so now those being entangled too isn't violating the monogamy of entanglement. Like, I think there's something there, got to be honest. But firewalls are a little bit different. Firewalls are what provoked people like Lenny Susskind to think harder again about something that they thought they had made real progress on.

1:07:59 So, for Lenny for a while, I think — and again, I don't want to speak for him. Lenny can be really intimidating, so I don't want him yelling at me or anything.

…