Theories of Everything with Curt Jaimungal - Dark Dimensions: NEW THEORY Unifying Dark Matter & Dark Energy

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Starting point is 00:00:40 Visit amex.ca slash y amex vary by card other conditions apply the dark matter Which is this bread and butter of this mysterious mass in the universe and the dark energy? Which is pervading everywhere, and we have no idea we think are related Dark dimensions F theory and what lies beyond space-time? cumran vafa professor of science at har, whose doctoral advisor was Edward Witten, proposes a revolutionary idea that could either unify or break decades of physics research. His theory suggests dark matter and dark energy, comprising 95% of our universe, might be manifestations of the same underlying phenomenon.

Starting point is 00:01:25 Come with me into the heart of the universe, both observable and not, where the nature of the cosmos hangs in the balance. Professor Vafa, welcome. Thank you. I want to know what got you into math and physics. Well, when I was a child from the very elementary schools, I remember loving math. So math was always part of my excitement

Starting point is 00:01:50 about intellectual excitement. But physics kind of gradually got into it in the sense that I started looking around things like looking at the moon. And I remember I was second grade when I was wondering why the moon isn't falling down on the earth. And what I found amazing was that it didn't bother people around me, that fact that there's something up there like kind of suspended. And it is kind of like, I didn't know, I don't know how

Starting point is 00:02:17 to put my finger on it didn't seem to intellectually bother them to want to know the answer to it. So these kinds of things from the beginning kind of attracted me to nature and understanding how it works. That gradually became my excitement about physics as a whole and fundamental physics later on. And luckily for me, my interest in math and physics matched in terms of the requirement of the activity. So I'm very happy that I'm in this field now. Would you say that your love for math is greater than your love for physics now, or vice versa? I think to me math and physics are inseparable actually. I mean the way for me my thinking of mathematics in terms of objects and things is physical.

Starting point is 00:03:02 So for me math is part of physics and to me even though math has its own language and you can apply it to many things nothing to do with physics, for me it comes to life through physical objects. So to me math and physics are not separate. Contrast that for me for one of your colleagues who may be a mathematician who doesn't view math in a physical manner? How do they think? Of course, they, they, you have to ask them. I'm not saying everybody should view it the way I do, obviously. I'm saying that's, to me, math is something not so different from physics. In fact, when I want to really feel what the math is telling me, I imagine physical objects or physical things and what it encapsulates. So to me, math and physics can be a good relation in terms of enhancing one another So of course math can have its existence independently of physics and physics kind of Orthogonal not completely from math, but to me as the way I look at them is they are not separable

Starting point is 00:03:58 Have you ever talked to any of your colleagues or just mathematicians and asked them? Okay How is it that you're thinking about this problem and then you you were able to see that, hey, actually, there's something that if you're a physicist, you would be able to discern this phenomenon more easily or maybe the opposite, you would be misguided because of your physical intuition and they're not. Well, we often discuss with mathematicians, for example, joint collaborations. So I am sometimes in the situation you just mentioned where

Starting point is 00:04:25 I have to explain why this idea that to a mathematician might sound strange or unmotivated or why this result should hold is very natural from physical perspective and try to explain why. So yeah this happens quite often and that's the excitement of it. Namely things which are unintuitive from mathematical perspective becomes intuitive only from a mathematical perspective becomes intuitive only from the physical perspective. Of course, there's sometimes the reverse. That is, things that are from a mathematician's perspective natural from physical perspective

Starting point is 00:04:53 may look unnatural. So that's why to me trying to view these as a unified thing is actually helpful. I try to view them as two different parts of the same thing. Just as the Mariana Trench plunges to depths of 11,000 meters, concealing ecosystems we've barely glimpsed, our universe harbors its own vast, unexplored realms. Marine scientists estimate that we've mapped less than 20% of the ocean floor, and cosmologists face an even more daunting challenge. Roughly 95% of the universe's energy mass content eludes our understanding.

Starting point is 00:05:33 The cosmic abyss isn't composed of water or rock, but rather what physicists call dark matter and dark energy. Their gravitational effects shape galaxies and accelerate the universe's expansion, yet they remain invisible to our most sophisticated detectors. Can you give an example for math where it seemed unmotivated but it seemed natural coming from physics other than mirror symmetry? And then for the opposite where it seems unnatural in physics but it's highly motivated in math and ended up being correct. Things that in math they're not mostly from physics there are there's a huge

Starting point is 00:06:11 number of them the question is whether you want it technical or non-technical or whatnot to me mirror symmetry that you meant you you kind of disarmed me with is actually the most beautiful example of that. Well the reason is that that's the most common example, common in our circles. Well, I think I probably should explain that because I was at the center of that circle. So I should explain what happened actually

Starting point is 00:06:33 in that interaction. Sure, sure. So I was explaining to my colleague, Yao, who was my colleague here at math department, the fact that from physics it seems natural, this is before we conjectured mirror symmetry, that there should be as many Calabias as positive Euler characteristic as negative one for Calabia threefold, which is a prediction of mirror symmetry. And he kind of found it very odd that we were saying something like this. And he asked, why are you thinking this way?

Starting point is 00:07:06 I said, well, there's from physical perspective, it's natural because there's no natural definition of the sign of this operator and you can choose either side. There's no canon, there's no God given choice. Therefore, different choices give you the opposite choices. And so therefore from physics, reconstructing geometry will land in one or the other Calabi, you cannot distinguish which one. He said, well, that doesn't sound too right to me because we know more of negative Euler characteristic

Starting point is 00:07:30 Calabi than positive. So there's no symmetry from the known example. So despite that, we conjectured it. So it wasn't like something was unintuitive, something was against the mathematical evidence. Ah, right. And nevertheless, we were so sure of it, we conjectured in my paper with Wolfgang Lerfe and Nick Warner.

Starting point is 00:07:47 Yes. So that's an example and that later on we had no non-trivial example other than six-dimensional tori. So non-trivial examples came later. The trivial example existed, but non-trivial ones wasn't there. But our motivation was basically simple examples and the general idea. But this happens again and again. So the things that fit together in some particular way in different physical ideas motivate a way of thinking which comes to mathematical statement, which might sound strange to a mathematician at first, and now it's not. Can you give one more example?

Starting point is 00:08:27 So examples of kind of math that a mathematician finds interesting or not. I mean, there are different kinds of things that mathematicians might find exotic. For example, let me go back to, well, let me say before, it depends on whether you're interested in the content which is mathematical or the content which is physical. I will give you a first surprising physical content which to a mathematician sounds strange. So if you explain to a mathematician that algebra or groups can explain why time dilates or length contracts as Einstein's theory of relativity shows, special relativity, they find no connection between simple group and this and that and this amazing fact that lengths contract and time dilates.

Starting point is 00:09:22 For them, that physical reality does not connect with that other fact they know about, the group theory of transformations, which we call Lorenz Group. So they understand one piece of it, but why that means the other one for them is a total mind-boggling thing. So if you try to say, no, this means that, and how does it mean that, and what does it imply and what else it could mean and so on is shocking. And so therefore it depends on how you want to kind of package it. It's physically exciting, mathematically exciting or other ones.

Starting point is 00:09:53 But mathematical excitements are many examples. Other ones are, for example, mathematicians are interested in counting curves. Counting by curves I mean how surfaces fit in some geometries. It's very hard for them to do that. Mirror symmetry was one way to actually do this. But regardless of mirror symmetry we found again from a different physical reasoning that the way these numbers are working, conspire in a particular way to give you certain rational numbers, even though they are counting,

Starting point is 00:10:30 they manage themselves into a non-trivial rational number. This is something that my colleague, Rajesh Gopakumar and myself found, how to unpack these rational numbers to decipher integer quantities out of them. So we told our mathematical colleagues that if you compute this rational number that they knew how to in principle formulate,

Starting point is 00:10:50 and if you do this operation on them, you can extract some integers out which actually are counting some things. And for them it was shocking and they said, how, why, where is that coming from? Again, that came from understanding of these objects from physical terms. So there are many examples like this.

Starting point is 00:11:05 Another example has to do with aspects of gauge theories. So we were interested with Witten in studying instantons for four manifolds. So this involves studying very non-trivial questions of geometry of bundles, gauge bundles, gauge bundles or connections which add in self-dual and considering self-dual gauge connections on them. And we were interested in computing on these spaces, the space of these instantons,

Starting point is 00:11:36 they're Euler characteristic. And again, from a physical reasoning, we knew that or we were expecting that if you stack them up, instanton number one, two, three, four, they form a function. And this whole function has amazing properties, it's called modular transformation properties. So we told mathematical colleagues that we are looking for this structure and we don't

Starting point is 00:11:57 know whether these numbers are computable or not. And they were surprised that we are even looking for such a structure. And the first few examples that we found along these lines were already shocking. And now the math community, a lot, there's a lot of research trying to understand these invariants that we defined in my work with Witten. So there are many examples like this and I can go on and on, but I do not know whether that's within the range of interest of your listeners. You just mentioned some invariant. What was its name?

Starting point is 00:12:27 This is, I mean, they call it now the Vafav-Witten invariance, but it is the invariance having to do with four manifold and instantons on them. Yes. Also, when you're referring to invariants, the one about rational numbers counting them, that's called the Gromov-Witten invariance, if I'm not mistaken. Please explain, what are the Gromov-Witten invariance if I'm not mistaken. Please explain what are the Gromov-Witten invariants? Actually, I should have said it. The rational numbers I was telling you is the Gromov-Witten invariants. So what we learned with, what we suggested with Gopal Kumar was how to unpack these rational numbers, the Gromov-Witten invariants into integers, which is now called the Gopal Kumar Gopal Kumar invariants. numbers, the Gromov-Witten invariance, into integers, which is now called the Goffa-Komarov-Baffa

Starting point is 00:13:05 invariance. That repackaging of that rational numbers in terms of integers was something that was surprising for mathematicians and that's what we found. You mentioned that there are self-dual connections and I'm unsure why is it that self-dual or anti-self-dual connections are so important? And is it only important in four dimensions? Well, there are similar things in different dimensions, but the four dimensional one, the self-dual connections are most interesting in four dimensions because the notion is really makes sense only in four dimensions. The dual of a gauge, the curvature of a gauge bundle is two form only in four dimensions.

Starting point is 00:13:43 So therefore it makes sense to say self-dualed or not. Only four dimensions. The reason they are interesting is that they give you critical points of Yang-Mills theory. The minimum energy configurations in a given sector. So for each given sector you can ask what is the... So first of all, the space of gauge connections on a manifold splits into different spaces. In each one, you can ask what is the minimum energy configuration, or in physical language, what is the minimal action configuration, and they end up being self-tooled ones. So it's like a ground state of the gauge connection in that sector. Of course, in the trivial sector, the ground state means you turn off everything gauge field

Starting point is 00:14:24 is zero, nothing. But in the the other sectors you have to turn them on and the self-tour ones are the ground state. So they basically are the ground states of the each configuration of the gauge connections. So having studying the ground states in each topological sector is of course natural. Okay so physics can be seen as a history of revolutions. I remember you mentioned this once and one of the revolutions is that the constancy of the speed of light or the Earth is not the center or the solar system is not the center even and then you said that the next revolution was well among others but one of them is that point particles may not be points they may be extended objects aka string theory. Now do you see there being another revolution that needs to occur

Starting point is 00:15:06 within string theory itself? Oh, it has to because our understanding of string theory is certainly incomplete. We do not have a, we just have pieces of what the theory is, not the full formulation of it. So yes, of course, there's got to be a better formulation of this theory. We have, I would say that what we have learned is the analog of the wave mechanics before we had quantum, we had pieces of wave mechanics like de Broglie had for quantum mechanics without having shown the equation. So I think we are, we are, we don't, we are not there yet. String theory promised a unified so-called theory of everything,

Starting point is 00:15:42 but its landscape has proven far more rugged than physicists have anticipated. Some hail it as our best shot at understanding the universe and others dismiss it as untestable speculation better relegated to the funding bodies of mathematics, not physics. Well, obviously if you knew the answer you would be publishing on it, but you probably have some hunches. So what's your what do you feel like is the assumption in string theory that may be overturned shortly? Obviously, if you knew the answer, you would be publishing on it, but you probably have some hunches. So what's your, what do you feel like is the assumption in string theory that may be overturned shortly? Well, overturned is not the, I don't think we have something which is, which is in the

Starting point is 00:16:16 form of a, of a laws of like Maxwell's laws that you can say this can be wrong or this can be right. String theory is a collection of examples of consistent solutions to quantum gravity. Those are not going to be overturned because we have changed all about them and they make sense. What we don't have is a unifying framework of what brings this whole thing together. So it's not something to be overturned, but something to be developed. I would say it's not that's not that it's like saying that how do you how do you just to? Say the other way suppose you want to say how would you overturn the brogles wave wave statement? You don't overturn it you basically develop it you develop it to quantum mechanics. That's what string theory is right now

Starting point is 00:16:57 I see so of all the papers that you've worked on professor. What do you feel like is the one you're most proud of? Of all the papers that you've worked on, professor, what do you feel like is the one you're most proud of? It's hard to say. I think I enjoy every paper I write. At least, you could say not all of them with equal love, but I think overall, it's not as easy as to say, I like this paper and not the rest or this is my top one and not the rest. It's not like that. I think one thing that is perhaps it's not quite appreciated by a non-scientist is that it's not just one paper which does anything. One paper might be a summary of many other papers that you have done or thought about.

Starting point is 00:17:37 And you might kind of summarize or get to aha moment in one paper, that's true. But it didn't come in vacuum. And that fact is I think sometimes missed. You think, oh, this is the great paper. No, no, no, no, no. This is built upon a lot of laborious other papers which don't get much recognition.

Starting point is 00:17:56 And so I have the same feeling about my own works that some of them are just building up towards the crescendo and suddenly one paper, if I'm happy with this because of those other works, which may say may say oh who cares about that paper but those are the beginning of of the thinking so I wouldn't I would not want to encourage that culture of thinking that there's this paper I like Speaking of crescendos sir there's F theory and I understand it may not be you may not consider it the crescendo of your work maybe you are working on else, but why don't you tell us what's exciting that you're working on currently?

Starting point is 00:18:28 There are other directions that I find equally interesting or maybe even more, aspects having to do with engineering quantum field theories from string theory, how do you get them from string theory or engineering black holes from string theory. Again, I find very interesting or understandings, aspects of topological strength from string

Starting point is 00:18:45 theory, what do they mean, these mirror symmetry, another example. All of these I find equally exciting and not a single thing, like F theory for me is one thing. I wouldn't say actually right now I'm working on a very different area of string theory, which I will call, I can talk about later with you, but called the Swamp Land Program, which is now what I'm most excited about. So there's, there are parallel, I mean, there are many things which kind of interrelate and have interconnections. It's not one thing that determines my excitement about the subject.

Starting point is 00:19:15 Okay. So F theory has multiple time dimensions and we're going to get to that, but I want you to first outline what are some of the issues why people historically didn't consider there to be more than one-time dimension? F-theory suggests that there are two extra dimensions in the game in some hidden form, but that existence of these two extra dimensions is not clarified in what form, and it's not necessary for using this framework. So there's this thing called the F-theory framework, where you can use that to construct solutions to string theory. That's a robust statement and it does not include extra time or anything else.

Starting point is 00:19:51 In my paper, when I wrote the first idea about the F-theory, I also suggested that these two extra dimensions that are hidden in some form, they more naturally have one space and one time direction, and that's why the notion of two times came in. It wasn't necessary for my discussion. So the idea that there are, so the F-Therese has made the fame for having two time directions, that's actually kind of irrelevant for the discussion.

Starting point is 00:20:17 The F-Therese construction really does not require extra time dimensions. So it's two directions that are extra, that are unspecified, they could be too spatial, they could be too time, a total of three time dimensions. So it's two directions that are extra that are unspecified. They could be too spatial. They could be two times a total of three time dimensions. It could be, but it doesn't actually matter. It could be and it could be well and my suggestion is one space and one time, which means two all together two times. Yes, exactly. So it's not since that time this that space does not directly enter the discussion. It's just an art. It's kind of like a partial

Starting point is 00:20:47 hidden aspect of the constructions as if there's two extra dimensions. Would there be something other than space and time that it could be? So that is to say we look into these two blocks that it could be a space one, it could be a time one, we don't know where to put the blocks. Well since it's not formulated in a way that has a physical properties of the rest of the space and time, it certainly is not of the usual type. So, yes, whatever it is, it's not of the usual space and time. That's part of it because we know how the usual space and time looks like and these

Starting point is 00:21:19 are not one of those. So, there should be something a little different about these two if they are in some sense physical. And what makes them different? Well, the symmetries. They don't have the symmetries to make them part of it. You cannot rotate our space to that space. So the rotation of our spatial direction to these extra dimensions doesn't make sense. So the theory does not allow that. So therefore, it's not part of it. Hear that sound? That's the sweet sound of success with Shopify.

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Starting point is 00:23:38 string theory. If somebody told you, okay, you have studied string theory, tell me what did you learn? What it is that this quantum gravity is all about, this is what SwampLand is trying to do. It's exactly the lessons we are supposed to have learned from studying string theory. Now what does that exactly entail? Quantum gravity is very different from the rest of quantum field theories. So if you take particles like quantum quarks and electrons and how they interact in the context of gauge theories, we have beautiful theories which describe them very nicely. Quantum chromodynamics describes the theory of

Starting point is 00:24:16 strong interactions. Quantum electrodynamics does the same for electricity. And there's the electricak force which is another kind of gauge force which is also does as equally a good job for describing the weak forces. Naively one might have thought the gravity is of the same type you can take the gravity and do the same thing you do with these other forces and that just doesn't work and part of the reason it doesn't work is that a lot of the notions of quantum field theory breaks down when it comes to gravity. Quantum field theory has a hierarchical structure in terms of short and large distance physics.

Starting point is 00:24:53 And the idea is that you're always interested in large distance. What happens at large distance, not at microscopic scale? So you kind of integrate out what we say or basically average out what's happening at short distances to come up with an effective description at larger distances. Sometimes we call this the effective field theory perspective about how things are emerging. This idea works beautifully in corner field theories. Namely, you start with a given large distance physics and ask what kind of symmetries are operative at that scale. large-distance physics and ask what kind of symmetries are operative at that scale. And using symmetry arguments, you can more or less write down what the physical action looks like. Except that you don't need to know what was the short-distance

Starting point is 00:25:34 physics leading to this theory. So you just ignore it because it's not relevant for your question. So we learned the fact that if you're interested in describing large distance, by and large you can forget what's going on in short distance. And that is why quantum theory has become so powerful because you can just take symmetries and write whatever you want and at the larger scale, deal with it. Even if you don't know the details at short distance, that does not affect your calculation at large distances. Very powerful idea. This idea totally fails for quantum gravity.

Starting point is 00:26:07 The idea of separation of scales of short and large, microscopic and macroscopic, is what doesn't work for quantum gravity. And the idea why it doesn't work is kind of, one could kind of see why. So let's do the Gedanken experiment. Like you want to describe what happens at short distances. What we do in particle physics is to take two particles

Starting point is 00:26:30 and accelerate and toward each other with ever higher energies. Why? Because when they go at higher energies, they can probe shorter and shorter distances. The distance scale you probe is inversely proportional to the energy in the central mass of such a collision. So therefore you go at a higher and higher energy,

Starting point is 00:26:47 collide them to see what's going on at shorter distances, namely what comes out of such a process of scattering these particles, what is created gives you a hint about what's happening at higher and higher energy scales or shorter and shorter distance scales. This is the idea of quantum field theory. If you try to do this for quantum gravity, this begins to work the same way that we think

Starting point is 00:27:11 about quantum field theory. You take energies of the particles who go higher and higher until you go to such high energies that something totally unexpected happens. What happens is that instead of particles coming out, suddenly nothing comes out. So you hit them at a very high energy and what happens instead is that you create a big black hole. Yes.

Starting point is 00:27:33 A black hole is a solution to Einstein's equation, which is described by long distance physics, not short distance physics. So you are interested in understanding what's going on in short distance and the physics told you, sorry, you cannot go any further than this. After this scale, everything is becoming bigger. So higher and higher energies is now translating to higher and higher distances, which is opposite to the way of thinking that we had. In other

Starting point is 00:27:58 words, high energy and low energy kind of are connected. The discussion of separating the short and large distances in this way fails. So the idea of the effective field theory fails in quantum gravity precisely because of black holes. So the black holes run the show in this case. So this is why quantum gravity is very special. Now I come to SwampLand.

Starting point is 00:28:19 So this was just a background about the connection between quantum gravity and why is it so different from quantum field theory. So you say, okay, so okay they are related, but what does this relation really mean? How do you actually use this fact? What is the description? This means that you cannot just say I have this and this symmetry in long distances, write down for me the action. That you cannot expect to work. String theory tells you that you cannot expect to work. String theory tells you that is in fact does not work.

Starting point is 00:28:48 In other words, if you just studied with the symmetries, you would have thought about the many, many, many more possibilities than you can actually get from quantum gravity. The short distance physics tells you not all of the things that you thought are okay are actually okay. There's a conspiracy between that short distance and large distance, which is not apparent

Starting point is 00:29:06 to a field theorist point of view. How do we know this? String theory. So the examples that we have learned from string theory tells us that the things that we get, no matter how we change, so in the string theory, we choose these extra dimensional geometries

Starting point is 00:29:21 because string theory is more than, in more than four dimensional space-line. These extra dimensions have their own geometries that we can pick. Calabi-Yau, this manifold, that manifold, G2 manifold, spin 7 manifold, whatever. You choose it and you see what physics comes out. You change the manifold, changes the physics. So you say, okay, I want to see different physics. I want to get this kind of physics. Can you give it to me? The answer is physics, I want to get this kind of physics, can you give it to me? The answer is almost always no. The kind of physics you get are very, very restrictive. In fact, among the set of all possible conceivable physical theories that you may have been interested in getting,

Starting point is 00:29:56 the ones that you actually get are measure zero. The ratio of what you can get to what you want to get or you could have wanted to get is zero. That means it's basically minuscule possibilities of what are actually consistent theories with gravity. So our perspective of what is this fails. Now. Wait, is that a theorem? Well, we have a lot of evidence. No, there's a lot of evidence for what I just told you.

Starting point is 00:30:20 And so in different examples, it's a theorem. Depends on how precise a question you wanna ask. So I will give you a few examples of this. To try to understand what are these restrictions is what we call the Swamp Land Program. Swamp Land Program tells you out of these possibilities, which ones are not good, Swamp Land. Now, the other ones are good.

Starting point is 00:30:42 There were the ones which are not bad, we call them landscape. So you might say, why are we looking for swampland instead of landscape, which is what the good ones are. The point is that the landscape are measure zero. So it's like saying you have a points on a plane and you wanna find these points. Well, good luck.

Starting point is 00:30:58 What you can eat more easily say is, well, you draw a line and say to the left, there are points to the right, there are not. Much easier to do that than to say there is a point exactly there. So Swampland program is trying to find these lines, kind of ideas like to the left is okay, to the right is bad, and this and that. So this narrows what is possible. It doesn't pick you those points because those are very difficult, because they're very rare. So that's the solving program is to understand these lines.

Starting point is 00:31:25 And I will try to tell you some of these lines or these Swamp Land criteria that we have found over the years. So the first one, which actually happened even before the Swamp Land program started was started even back in the, I don't know, 40s or 50s, 1940s or 50s by Wheeler and collaborators, which is the statement that no quantum theory of gravity

Starting point is 00:31:44 has symmetries other than gauge symmetries. In other words, you cannot have symmetries in quantum gravity without having electrical fields associated with them. In our universe, we have, of course, electric charge, which is conserved, but that has electrical field with it. So what this statement is that you could not have at the universe where there's electric charges

Starting point is 00:32:07 with no electrical field coming out of it and the charges are still conserved. That is a no-no, that's not possible. Now from the viewpoint of an effective field theorist like you and I, it sounds perfectly fine, why not? Why can't you have objects you can count but has no electrical field on it? Says quantum gravity says no, you cannot.

Starting point is 00:32:24 So this is almost at the status of a theorem. Why do we think so? Well, because we have ideas having to do with black holes, which tells you that if this was not the case, you would get into trouble because you can send one of these charges to the black hole and black hole evaporates and you get rid of that charge. So therefore you violate the conservation of charge. So symmetries get disappeared through the black hole evaporation process. And so there are arguments like that. So when you say, can you prove it?

Starting point is 00:32:52 Of course it presupposes we have a framework or principles to prove, but we don't have those. So I cannot tell you, I can prove it because I don't have the Euclidean principles like the axioms of Euclid or whatnot. So I cannot give you such a proof. But to the extent that we believe the evaporation of black holes works the way we do, which we are very sure of, this is a proof that there is no global symmetries.

Starting point is 00:33:13 Another example is weak gravity conjectures that we have, which we have a huge amount of evidence, which says in any conceivable quantum theory of gravity, gravity is always the weakest force. It's not just in our universe. You could not have had any consistent theory of physics for which gravity was not weaker than other forces. That sounds again strange from a viewpoint of effective militaries because you can imagine having two electrons. So the hierarchy problem is then the hierarchy inevitability? No, the hierarchy is more more more specific question. hierarchy

Starting point is 00:33:47 just says why is this case so much smaller? It could have been just the factor of 10 smaller. Oh, I see. Okay. hierarchy says why is it why is the factor of 10 to the 19 or 10 to the whatever smaller, that's a different one. Here, we're just saying the scale is lower, but we didn't say how much lower but it goes in the direction of making hierarchy possible, let's say. It goes in that direction, but it doesn't tell you you have to have a huge hierarchy. So this idea of the weak gravity conjecture, if you think about it, it's a little strange why it's true.

Starting point is 00:34:17 Because if you imagine you have two electrons, if you put them at a distance r relative to each other, there's a repulsion between them which Coulomb taught us. It goes like a square of their charge divided by distance squared. Like we call E squared over R squared, the distance squared. But there's also a gravitational attraction between them which goes like their mass times mass over R squared. That's Newton's gravitational attraction.

Starting point is 00:34:44 It goes like M squared r squared. So gravitational attraction is m squared r squared, electrical repulsion is e squared r squared, and we are saying repulsion always wins. In other words, m is always smaller than e. Well, you could have imagined that electrons mass was much higher and it would have been the other way. But we say, no, no, no, no, the theory of gravity would not have worked. You see, that's a positive surprise because you would have thought there's no reason a priori the mass

Starting point is 00:35:13 of the electron has anything to do with its charge. This is no, it better be smaller than its charge in the appropriate units, in the fundamental units in physics. So these kinds of ideas, and these are just two examples, there are many more examples. Yes. Perhaps I will say one more example, because it's also one of the most remarkable examples, which relates to duality symmetries of string theory. This statement, which I find probably the most difficult

Starting point is 00:35:40 to see from an effective field theory predictions or perspective, is what is called the distance conjecture or duality conjecture. The statement is that if you take parameters in your theory, first of all, all the parameters in your theory are dynamical. Now, what does that mean? That means when we usually think about constants

Starting point is 00:35:59 of nature or numbers and so on, we are saying there's no such thing in physics. That means that things that we think are constants or numbers are actually can be changed. They're dynamical. You can change them in one region of space to be bigger or smaller. It's not fixed numbers. Okay, so constants become fields. Constant become fields or more precisely the expectation value of certain fields. Right. Okay. Even the speed of light?

Starting point is 00:36:21 Speed of light is not, we view it in a fundamental unit as one, so we don't even talk about it. It's not the speed of light we view it as one, it's not changing for any discussion that you're working. In other words, speed of light is not a, let me make it more clear. So in your theory, you don't need to have a parameter for speed of light, that just sets the units for us. So something else will change, but that will change with respect to the speed of light. Yeah, you could try to do that, but all the parameters

Starting point is 00:36:49 in the theory will be somehow related to fields. Now, if you take, if you, so now I haven't stated what distance conjecture or duality conjecture is. It tells you that if you take this field and take the value of this field to extreme values, small or large, that means in your physical theory it might have been a coupling becomes extremely small or extremely large, something like that.

Starting point is 00:37:18 You always, your theory always breaks down, always. That's a surprise. That means the extreme limits means something breaks down. Yes. Now, what do I mean by breakdown? It means that if you go to far away corners of these extreme parameters, you get a tower of particles,

Starting point is 00:37:36 which used to be very heavy, becoming lighter, lighter, lighter, and lighter. And as you go to extreme values, these give you an infinite tower of light particles. Very, very little mass, separated from each other by little masses, and so you have a huge number of particles that you had ignored, because back in the middle of the field space, they were very massive, so you could have ignored them. But when you're going to these extreme parameters, they become so light you cannot ignore them.

Starting point is 00:38:03 And if you try to incorporate them one by one, you cannot succeed because there are infinitely many of them. So therefore, if you go far away to the left or to the right or anywhere, any direction you go, your description breaks down. So what happens, a new description comes over and takes over incorporating those degrees of freedom,

Starting point is 00:38:22 which is not your original description at all. It might mean that some dimensions opened up. It might mean that some extra particles or strings are in the game that you have completely no idea about. This gives us what we call the dual description. So the duality in physics, I just explained to you in a language of this form, is of this form.

Starting point is 00:38:41 You start somewhere, you go one limit, you find one description, which is what we call one duality frame. If you go the other direction, you get a completely different perspective, another duality frame. So these physics between them are describing the same physics, but at different extreme regions of parameter space. So this is the duality or distance conjecture, which is also another example. And this does not have to be true without gravity. It's only there if you have gravity. So quantum gravity changes the whole rule.

Starting point is 00:39:11 The rules of quantum field theory are not applicable. And that's, I think, the most exciting thing we have learned in string theory. String theory tells you that the paradigm that the particle physicists have been operating for the hundred years is wrong, is wrong, is badly wrong, because they thought they could ignore the short distance away from large distance. We have learned that you cannot decouple them.

Starting point is 00:39:34 The short and large are intricately connected when it comes to gravity. And this is crucial because potentially a lot of the puzzles of particle physics, like hierarchy problem, like all these puzzles that particle physics has difficulty with, that try to use supersymmetry to answer, for example, so it didn't work. So many of these puzzles, which doesn't look natural to particle physicists, is because they had ignored gravity in the discussion. And the reason they ignored gravity was kind of benign. They said, look, gravity is a weak force.

Starting point is 00:40:07 It is not strong until you get to plank energies. And we are not in our accelerators. We are nowhere near plank energy. So forget about that. So we were just talking about other particles. Forget about gravity. They thought that not thinking about them is perfectly fine because the energy that we are doing is not related to that.

Starting point is 00:40:24 They were not thinking about the connection I told you about black hole, the higher energy and low energy are intricately linked with each other. And that picture is what is, I think, at the root of failure of particle physics to try to explain a lot of these fine tuning or hierarchies that appear. Are particle physicists still thinking that we don't have to incorporate gravity? There's a group, it's beginning to change. So, and I do know that there's a number of particle physicists are now becoming cognizant of this fact. For example, my colleague here, Matt Rees, is an example of such a group of particle physicists

Starting point is 00:40:56 who appreciate the importance of the quantum gravity as being in the mix to get insights into particle physics questions. So there is drawing, but still by and large, I think the majority of particle physics, unfortunately are not as much familiar with this. And so it's gradually getting to them. But I think it will get, because it's kind of, it actually gives their field of vitality

Starting point is 00:41:19 to make predictive powers, because as I just told you, the number of possible allowed ones are measured zero so therefore this gives you predictive power so if you understand what these rules are yes it will give you what paragraph is like because they are looking for such paradigm so I think they will they will when they get to learn a bit more about it I think they will they will appreciate it even more so in other words usually in a treasure map you have X marks the spot, but we don't have the X. If we had the X, we'd have the answer. But if you can exclude parts of the map, so you can encroach on what is the viable region,

Starting point is 00:41:56 then you say, okay, so we don't have to dig across the whole earth. We can just dig in this guy's back alley in Panama. Exactly, exactly. And so sometimes what happens is that you get lucky. Like, you know, the thing is the X is on the left of this line, but the experiment finds it very close to this line and you didn't know whether it's going to you. Sorry, you find it very much along a line here somewhere and you don't know whether it's going to be past this or not. And you say, no, no, no, it cannot be past that. But the experiment says that it cannot be so much to the left either. So therefore you're kind of stuck on that line or very close to it.

Starting point is 00:42:31 So in this way becomes predictive, even though it sounds like you're just excluding something combined with experiments, it actually can become predictive and that's what we have been using it for. So while the Swamp Land has a negative connotation to its name, it's actually positive because you want to be able to exclude more and more exactly. it for. So while the swampland has a negative connotation to its name, it's actually positive because you want to be able to exclude more and more. Exactly. So when you use the word consistent earlier, when you say that look, we're excluding what's inconsistent. Inconsistent means what? Inconsistent means it does not have a short distance completion. That means

Starting point is 00:43:02 it looks fine at large distances, but there's no full theory which you can answer to questions like what happens at high energy scatterings. It will have answers to some region but not the rest. It doesn't fit together. So you don't have a complete picture. It doesn't work. Okay, because the way mathematicians use the word consistent or inconsistent is that if you have a theory that's inconsistent, you can predict everything because you have A and not A at the same time. But that's not the sense that physicists mean inconsistent when they're speaking about this theory of quantum gravity is inconsistent.

Starting point is 00:43:31 No, it is the same. It is the same. It is the same. It means that suppose I give you a theory for which you study the scattering of particles of some energy E, and it looks perfectly fine and everything is good, but you don't know how to compute when E is very large. And somebody says, no, no, no, the E that you picked, if you try to do that, at large energy,

Starting point is 00:43:49 it gives you nonsensical answers. The answer becomes blows up or becomes zero or something which doesn't make any sense. Therefore you say, well, that means that your other one is wrong. So A and not A also in that sense means if you thought this A, then you're saying and the other one is wrong.

Starting point is 00:44:03 So in other words, you get one side or the other not working So if you if you wanted the way it works at long distance the short distance doesn't work So it is some does something like a and not a at the same time I see that as unintuitive, but I don't see that as inconsistent. So if someone predicts infinity, I don't see that as being inconsistent I see that as being not not corresponding to our world, but mathematically you don't see that as being inconsistent. Can you help me out? No, no, no. I'm not explaining. I'm not perhaps explaining myself clearly to you. So suppose

Starting point is 00:44:33 you have drawn a line and you draw a straight line. Suppose you draw just giving a boring example. You're drawing a straight line. And for physical reasons, suppose this is something that has to be positive, like a mass of a particle or something, you're drawing as a function of a parameter a straight line. And this mass should, the particle should have a positive mass everywhere. But you have studied it far away along the real line

Starting point is 00:44:58 and you find that as you change this parameter, it linearly grows with that parameter. You say, good, I'm done. The mass of the particle goes linearly, it's finished. And then somebody comes and tells you, no,. You say, good, I'm done. The mass of the particle goes linearly, it's finished. And then somebody comes and tells you, no, no, no, no, it's not finished. If you go to the other regime, it's negative mass. It doesn't make any sense. That's what I'm saying. So the thing that you thought, the thing that you thought is fine, it doesn't work on the other side. In that example, the difficulty is that you said

Starting point is 00:45:22 for physical reasons in the beginning, you preface this with for physical reasons we have to assume the mass is positive. So that's what I'm getting at. No, not physical. I mean, I'm just saying suppose in your physical theory, you come up with a physical theory which says, oh, mass grows linearly and in this regime is positive and that's worked perfectly fine, you're done. For large for some regime of parameters and your theory doesn't tell you anything about the other regime, but your prediction is that it should be linear. Yes. But then somebody comes and tells you

Starting point is 00:45:51 that cannot be because of the silly fact that if you take this and continue to negative, the mass will become negative, and that's not allowed. And that's all. And therefore, that simple fact that in this, I'm giving you a little bit of a silly example so that I can illustrate the point. In one regime, you know how to do a computation and you think it's fine, but actually fails because you're not looking at the totality of the question.

Starting point is 00:46:15 So it's inconsistent as a whole. So it ends up inconsistent. So one side is like large distance physics and the other one is like a short distance physics. If you take something at large distance physics and you study it, you may not know that you're assuming something about short distance which is not allowed. Okay, now is that because the the short distance comprises the long distance or vice versa? No, they are connected. They are connected. You see, I was trying to give you the black hole example. You could not have ignored it. You couldn't say they're independent. I see. They're connected because the higher and higher energy gives you bigger and bigger distances.

Starting point is 00:46:47 So they're somehow related. What you thought that you're probing at short distance actually ends up being large distance. Higher energy knows about large distance, not short distance. So what happened there? So that paradigm was wrong that one was using. So that's what has, so it's a revolutionary,

Starting point is 00:47:04 in some sense, really revolutionary. That is, the ideas that we thought about scales, short and large separation, is actually badly wrong and it is actually in some sense a good development because that leads to predictive power for us. Well, let me see if I understand by taking your silly example and making it even more silly. So let's take this cup and let's say, look, this cup must comprise, if you were to zoom in elements that have mass because this guy as a whole has mass. But if you keep zooming in and your theory then tells you that there's negative mass

Starting point is 00:47:36 there, well, the way that you get the total mass of this cup is by integrating so you should get something that's negative mass. However, you have the observation that has positive mass. So there's an inconsistency there. Would that be correct? Yes. Yes. Okay, so let's talk about classical versus quantum. Is the notion of classical versus quantum fundamental? And if not, then why not? No, it's not fundamental. Classical and quantum can be interchanged and that mirror symmetry is an example of it. So something which appears classical to one perspective can be quantum to another perspective.

Starting point is 00:48:06 Because the analog of Planck constant can itself be a parameter. And if you go to very strong, large values of that Planck, then the duality example I was telling you about gives you some other description opening up. So sometimes that becomes a classical picture of somebody else. So something which is highly quantum to one perspective becomes classical to another.

Starting point is 00:48:27 It's a part of duality example. Professor, what would you say is the definition of string theory? Let me preface this. So in other words, if someone hands you a theory, how do you know this is a string theory? Is it that it has extended objects? Is it as simple as that? No, I wouldn't say that. I would say string theory attempts to describe consistent quantum gravity theories. String theory has landed on what we think

Starting point is 00:48:52 might be the only constant theory of quantum gravity. But the Swamp Land program that I am studying, for example, does not assume that. So we are open to the possibility that there are other consistent theory of quantum gravities. But we have all the evidence we are, in other words, what I mean by that is that we don't want to say just because string theory cannot give you this physical reality that cannot be obtained, period. We try to see if you cannot rule out a physical reality by some other reasonings like black hole physics, beyond string theory, which is not to do with string theory per se, which rules that theory out or not.

Starting point is 00:49:28 So string theory could be therefore, in some sense be derived if everything that is allowed ends up being what you can get in string theory. If the totality of what is allowed is exactly equal to what string theory gives you, then string theory is the only game in town. But we are not assuming that. And in fact, I think it's healthy not to assume that. We want to assume quantum theory of gravity. So, consistency of a quantum theory of gravity.

Starting point is 00:49:53 That means gravity is well defined with the properties involving black holes, with other particles, with the consistent set of rules of scatterings and objects and all that. So we have a set of rules that we can check, whether they are consistent, and that's what I mean by quantum gravity being good. If you handed me one of those, I would start asking questions like scatter this, do that, do this, to see if it's consistent. And maybe in some regime I see some extended objects,

Starting point is 00:50:18 because that's one of the things that I expect, and then maybe a string, maybe a membrane, maybe something else. So therefore these are the tests I will run this object or theory that you give me about. So string theory by now, I think is, I would say at least to me and many of my colleagues, convincingly, perhaps possibly the only theory

Starting point is 00:50:40 of quantum gravity, but it's always I think good to be open-minded in possibilities of other possible theories that could exist. I think it's also, if you even want to understand just string theory, having this perspective is good because it tells you what are the fundamental things in string theory, what makes string theory tick, what are the basic reasons or ideas that go into it? So you have to step back away from string theory to try to get that formulation. What are some of the other theories that may compete with string theory to describe our universe that you feel like perhaps you don't feel like they're on the right track? Otherwise

Starting point is 00:51:17 you would switch gears and just start publishing it. I don't think there's anything comparable to I mean you hear sometimes loop quantum gravity in this I think they're just it's just far off about what we are talking about. So I wouldn't say even on par. So yeah, I don't think, I didn't think right now there's any game in town other than string theory, but I think we should keep it open-minded. Not that we have found one, but I'm just saying the possibility of having some other structure that's consistent with gravity, we should be open to it. But right now I think all the evidence is

Starting point is 00:51:50 pointing towards that. For example, in the context of Swampland, we are finding that the rules that seem to be consistency of black hole physics, unitarity, evaporation, all the things that we think should be true regardless of whether it's string theory, when you use them, you narrow the space of theories down and you find a lot of the cases that we know how to narrow them down, you end up to be exactly the same set you get in string theory. And so that to us begins to smell like, okay, that's the only game in town. So we are now deriving pieces of it. So with enough supersymmetry, with high enough dimensions, we actually have accomplished that. That we can actually push this to a classification of possible things and it exactly matches what string theory gives you

Starting point is 00:52:30 So we are very happy with with the fact that now we are finally beginning to con quote-unquote derived string theory from some first principles Practically speaking what would it mean to keep one's mind open about other quantum theories of gravity or other unifications of gravity with a standard model? Like does that mean a grant body for like an additional grant body or additional department? Like practically speaking, what is meant? No, no, I will tell you how it will appear. Suppose I'm studying possible consistent theories of scattering of gravitons and I find I study them and I find some framework I become so smart I managed to exactly solve what are the allowed possibilities and I find there are only two possibilities in

Starting point is 00:53:14 Ten dimensions one of them gives you exactly the answer is string theory and the other one is not But it looks perfectly consistent Okay That other thing is whatever you want to call it, it's not string theory therefore. And so therefore we would have found another theory. So if we were there, but more and more the way we are doing it, we're always being narrowed down only to the one corner, which is what I can recognize, which is string theory. Not in everything we have done that, but in high enough supersymmetry with high enough dimensions, we are

Starting point is 00:53:42 being cornered to the string corner. And so this is what we call the string lamppost principle. Sometimes the people told us, well, you guys are studying only string theory and you might be suffering from the lamppost effect. That is, you're only seeing things string theory gives you. But if everything that we're getting is part of that lamppost, that is everything.

Starting point is 00:54:05 That's what we are finding. And this thing we're calling the string lamppost principle. That is, there is nothing else other than the lamppost of strings. When people talk about quantum gravity and you go to different lectures, there's often, well, what we do is we sum over the geometries, like you sum over different paths in the Feynman integral. Is that the correct approach to quantum gravity? You sum over the different possible metrics? At some level, it seems perfectly okay, but not at fundamental level.

Starting point is 00:54:35 I don't think we have a fundamental definition of quantum gravity. At large distances, it might be like that, and you take pieces. But if you come to a short distance like tank scale, I don't think that's the correct description. At distances for which the space-time geometry itself is a highly bubbly quantum form of geometries bubbling off and so on, I don't think you should think about the summing over geometries, because the notion of geometry doesn't make sense.

Starting point is 00:54:59 So you're in a regime where geometry is not even a good approximation. So therefore, I think in some regimes it might be that, but not as a whole. I don't think the notion of distance and metric is universally makes sense. Help me with this because one way that I wasn't able to ever square why summing the possible metrics

Starting point is 00:55:17 is a viable option is because in order to define a fermion, you have to define a section of a spin bundle, which if you need a spin bundle, you need the orthonormal frame bundle, and that requires a metric in and of itself. So if we're varying the metric, then I don't know what it means to define a fermion that hasn't sat right with me. Well first of all, there are different things that you can think about fermions. Fermion you can define by a local transformation of space.

Starting point is 00:55:46 Now, local does not necessarily mean plank in this sense. You can take a piece of your space, large enough for which you can describe the notion of geometry, and then you can, in that notion, describe the notion of fermion as you do a rotation and you see if the fermion picks up a sign or not. So that you find out how does it transform on the rotation.

Starting point is 00:56:06 That's only the notion in which there is a geometry. Otherwise, the fermion does not exist separate from geometries, it exists at a given point in your space and time. So to the extent that your space time is bad, your notion of fermion might also become bad. So you can only, so you are self-consconsistent in the regime for which you have a geometry, then you can define a fermion perhaps or other objects living on it. If that

Starting point is 00:56:32 object that doesn't live anymore, then what, then you should not be able to define that fermion the way you used to do. It should be a completely different way of doing whatever it is, depending on what is the object that replaces it. You know earlier you were saying, look, there are different gauge fields for electricity magnetism and the weak force and the strong force and some people want to incorporate gravity like that. So what is meant when people want to incorporate gravity

Starting point is 00:56:54 in a similar manner? People say gauge gravity, quote unquote gauge gravity. What does that mean? You know, gravity is gauging the few morphisms symmetry. So the few morphisms is a symmetry of a manifold. The theomorphism means that you can choose any coordinate system and gravity gauges it means that that symmetry should be respected locally.

Starting point is 00:57:14 You can take your coordinates and change them different places, different ways. That's what we mean in physics when we say we gauge it. So in mathematics, we just say that, oh, all you're saying is that the local chart, coordinate charts and different ones are independently chosen? Yeah, that's all I mean. Your physics should be independent of that. So in Yang-Mills when we gauge we say that there's SU3 cross SU2 cross SU1 and then that's like a principal fiber bundle and G is that group. So are you saying that to gauge gravity

Starting point is 00:57:44 you still take as the base manifold M, but then you gauge, like you put fibers of the different morphism group? Well, yeah, what I'm saying is that tangent bundle of the manifold is canonical. You don't give it any more. You don't choose the analog of G, because the manifold is there, the tangent space is fixed.

Starting point is 00:57:59 So that's different. For gravity, just as another difference with gauge forces, the gauge forces you artificially have to with another structure like a principal bundle. Yes. A group manifold. No, because once you give me a Riemannian manifold, you have given everything you need to give me. So for the geometry of that space is itself the metric, namely, that's what it is.

Starting point is 00:58:18 So you don't need to say anything. Of course, you could say, oh, you're talking about tangent bundle. Yeah, you can think of it that way if you want. Metric is a structure on tangent bundle, connection on tangent bundle and so forth. What is your superpower? What does that mean? So what I mean is that Witten explicitly said that his superpower isn't mathematical prowess, though he has that.

Starting point is 00:58:41 What it is, is deciding on what problems to work on. What do you see as your secret sauce? What makes Vafa Vafa? Well, trusting my intuition, I think. And trusting my intuition over formalism. I don't trust formalism. I trust my intuition. So my intuition might clash with formalism and then I'll go with my intuition, not

Starting point is 00:59:00 the formalism. So I think that's what, if there's any difference is that. And so if my intuition goes against conventional wisdom, I'm not afraid of stating it. Mirror symmetry is an example of that. How do you decide what problems to work on? Is it just intuition? Intuition. I cannot explain what makes me think one is better than the other, but my intuition guides me. What if we've been chasing a ghost? For decades, dark matter has been physics' elusive quarry.

Starting point is 00:59:29 Invisible, yet supposedly everywhere. It's the cosmic glue holding galaxies together. Or so we thought. What if cum run Vafa is correct? What if dark matter doesn't exist as we imagine it? Vafa's theory hinges on the cosmological constant, the energy density of empty space. In anti-desider space, with a negative cosmological constant, this energy is attractive, just like gravity.

Starting point is 00:59:56 In the universe that we inhabit, it's a desider space that is repulsive, driving cosmic expansion. Wafa proposes that what we call dark matter and dark energy are manifestations of the same phenomenon tied to the nature of dissider space itself. This unification arises from string theory's Swampland conjectures, which suggest that not all effective field theories can be consistently coupled to gravity. Specifically, Wafa is explaining that the apparent fine tuning of the cosmological constant

Starting point is 01:00:29 is teaching us about the dark sector of the universe. And what is it that you're working on now? Swampland principles. So I'm understanding this. To me, as I said, right now I'm, well, I have been starting the idea around 2005, this Swamp Land program, and ever increasing number of physicists, especially young crowd, are actually working on this with, so it's become a very active community of physicists trying to decipher what we have learned from strength theory.

Starting point is 01:01:01 You see, I think you ultimately want to say what does string have to do with the real world? And I think a lot of the efforts in string theory, even though they are interesting, they seem to be going away from connecting to the real world. And I think trying to reshape back, focus back, our attention from principles of we have learned

Starting point is 01:01:23 about string theory to the real world is what I find exciting. And surprisingly, you can do this and that's what we are beginning to do. And so some of these ideas about the Swamp Land we have actually now used to make a very bold prediction which is potentially observable in the next few years. And so I will try to explain

Starting point is 01:01:44 where this bold prediction comes from. So I told you about when you take extreme parameters in your theory, you always end up with getting a tower of light particles. Yes. Well, you could have asked me, really? I know an extreme parameter, tell me what does it correspond to,

Starting point is 01:01:58 namely dark energy. The dark energy in fundamental units of physics is 10 to the minus 122. It's so small. It's extreme. Okay, what is your tower? You see, this question is, it just sounds like a benign question. Like, am I claiming there's extreme? Okay, it's extreme. This is extreme. Tell me what's happening here.

Starting point is 01:02:19 Just that way of reasoning pushed us to a direction which suggested that yes, there must be a light tower in our universe and that light tower we identify with dark matter. So in other words, the dark matter which is this bread and butter of this mysterious mass in the universe and the dark energy which is pervading everywhere and we have no idea, we think are related. It is the extreme power, extremeness applied to dark energy or this distance or duality which suggests there must be a tower.

Starting point is 01:02:51 Now you could say, what is this tower? Where is this tower? How do you actually, what is the mass scale? What do you, how do you see it? So combining this, this general idea I told you with other observations, it turns out there's only one possibility. The possibility is that there is one of the dimensions of the microscopic dimensions

Starting point is 01:03:09 are actually bigger than the rest and of the scale dictated by dark energy and that energy scale amounts to about a micron, one thousandth of a millimeter. So we are saying that there is there must be one of these dimensions bigger than the rest of the order of one thousandth of a millimeter micron. But our universe, the three plus one dimensional space time, which we are living in in terms of electrons, quarks and all that, are in a hyperplane in this higher dimension. So you imagine you have one higher dimension, but we are on a hypersurface on that, stuck on that, and the size of that is about a micron. So we got this from just applying the Swampland Principle, the distance conjecture, which I tried to explain why it's so natural from the physics perspective, because the duality of string theory demands it. So if you just tip it and say, okay, let me assume without knowing exactly how I get my universe from string theory, just that idea, what does it imply?

Starting point is 01:04:10 You immediately get these kind of predictions and the micron scale size of this extra dimension is actually observable potentially in our universe because they have gone off to 30 microns and they haven't seen it. So how do they see it? Well, they put two particles and they measure the force between them. If the force goes like 1 over r squared, then you're in three dimensions. If it goes like 1 over r cubed, then you're in four dimensional space.

Starting point is 01:04:40 So you have grown in space dimension. So they want to see if the force becomes stronger. The force of? Gravity. Of gravity. So I'm saying that the Newton's gravitational force law being one over r squared becomes stronger for higher dimensions. But if the extra dimension has a micron scale, and if you are separated more than a micron scale, you won't feel the extra dimension. It looks like three dimensional. But if you bring it closer so that you can feel the extra dimension, if you're within less than a micron. Yeah that's super interesting. One of the questions that I had was going to be, look is there something about the extra dimensions of string theory that necessitate compactifying to something extremely small? And you're saying no,

Starting point is 01:05:19 this is relatively large, no it's a micron but that's relatively large. This is extremely large in some sense, surprisingly. I'm saying this is not that string theories forces you. This is observation combined with the Swampland idea. So in other words, we are, we are, as I explained, sometimes you have an idea that, okay, you should not be to the left or to the right of this line, et cetera. That's like the distance conjecture that if you go for large distance in the field space, you hit a tower of light particles. But then you say, oh, but I know in our universe, lambda is

Starting point is 01:05:47 blah and blah. What does that imply? Then you can use this. So it doesn't tell you lambda or the cosmology constant had to be small, but if it is small, then you can use it. And would this say that dark matter is several particles? It's not just a single one? It's a tower of them? Well, so the tower that I'm talking about turns out to be one particle, namely just graviton. Now, you might say, wait a second, graviton is massless. But three plus one dimensional graviton is massless, but four plus one dimensional graviton

Starting point is 01:06:14 is not massless because the graviton can have waves, oscillations in the other direction. This tower I'm talking about is nothing but oscillations of graviton. So it unifies gravity with dark matter. So dark matter is nothing but excitations of the graviton, which is why it's weak, weakly interacting because gravity is weakly interacting. So the dark matter becomes a tower of this graviton, which is weakly interacting anyhow. So it unifies dark matter with graviton and dark energy into one package. Does this then have a name like a separate?

Starting point is 01:06:47 Dark dimension. We call this dark dimension scenario. Yes, so dark dimension scenario is a scenario that there's one extra dimension opening up and this is coming from this Swampland idea I just told you. So there are a few other predictions that this makes about cosmology, in particular about axion physics and other things that are potentially also very interesting. And ultimately it's an answer to a kind of an answer to a question that Dirac was asking. Dirac had noticed that different scales in physics

Starting point is 01:07:15 has bizarre relations by factors of 10 to the 30, 10 to the 20, 10 to the 40, these big numbers. And he was saying, it looks like they are not related by factors of two or three, they are related by powers. What is the reason for this? So in the context of swampland, we have actually seen exactly the reasoning for why they are powers.

Starting point is 01:07:34 And more than that, we find things are given by powers of 1 12th of the cosmological constant. So things come in chunks of lambda to the 1 12th, and that's about 10 to the minus 10. So you get 10 to the minus 10, 10 to the 10 to minus 10, 10 to minus 20, 10 to minus 30, etc. And these give you the different scales in physics. One of them gives you the higher dimensional Planck scale, the other one gives you the weak scale, another one gives you the neutrino scale, the other one gives you the large scale of physics, the large size of the universe. So all of these kids fit into this hierarchical fashion given by the dark energy. So the dark energy gives you the, gives you a unifying principle about all these different scales. This dark dimension theory, when did it occur to you and your collaborators? Like how long was the time? It gradually developed.

Starting point is 01:08:18 It gradually developed. So the distance conjecture was started around 2006. Ah, okay. The fact that you go, but then we applied the distance conjecture started around 2006. Ah, okay. The fact that you go, but then we applied the distance conjecture to the case of cosmological constants in another paper. I think that was 2018. And then a few years past, we tried to think about cosmological aspects of it. And then we gradually were going in the direction, and in the 2022 it led to the actual say, why not?

Starting point is 01:08:43 Combining this gives you that. So the idea came gradually, it could have done been done much faster What do you think about dissitter quantum gravity? well quantum gravity dissitters seems to have a problem of stability and So so a lot of these ideas in the context of swamp and seem to point towards the idea that dissitter space With positive energy cannot be stable Well, the question would be okay, if they are not stable,

Starting point is 01:09:06 what is the scale of, what's the time scale of the instability? And what we think is that the time scale of the instability is itself set by the sitter. That means it's what we call the Hubble scale. So for example, if you take that in our universe, it suggests that the scale in which the universe will unwind or the dark energy will unwind is roughly the age of the universe, current universe. So that is kind of interesting because it will tell you that the dark energy has a

Starting point is 01:09:33 time scale associated with it also and we don't know if the recent observation of DESI which the dark energy survey which tried to see whether dark energy is constant or not they seem to have some indication that dark energy survey, which try to see whether dark energy is constant or not, they seem to have some indication that dark energy is actually changing and decreasing with time in the same kind of time scale as one would naively think along the lines I'm talking about.

Starting point is 01:09:54 So these kinds of ideas tell you that dark energy is actually dynamical and actually evolving potentially in time. It's certainly not stable. So quantum gravity of the sitter should not exist in the sense of a complete the sitter. It could be just patches, short time maybe, but not in the long term. In the long term, it will decay.

Starting point is 01:10:16 So does that mean that our universe, which is the sitter, will decay? Yes. Correct. We expect our universe not to be stable. In fact, I think every string theory I think every string theorist believes that. We just don't know exactly the time scale. The arguments emanating from swamplands suggest that the time scale is given by the Hubble, which is roughly the age of the current universe. So that's the kind of a time scale.

Starting point is 01:10:40 You're saying that the age of the universe is the expected age of a decider universe to collapse? Yes, up to the log factor, which I didn't tell you about. So in other words, there's the age up to a logarithmic correction. So if you want to get the upper bound, we think it's like two or three trillion years. OK. So it's about, it's upper bound. We don't think it's going to be more than two or three trillion years. This is again, this is an idea from Swampland which has less of an evidence because we don't have examples of this from string theory. So we have extrapolated what we know to get this. It's what's called the trans-Planckian censorship conjecture. So this is one of the things that we are trying to gather more evidence for. Check it to see if it's correct, if it's not correct and so on. But the idea suggests that there's this upper bound. But at any rate, all the examples we know in the context of strength theory,

Starting point is 01:11:29 which has dark energy, is always unstable. The question is whether how unstable they are. And that's what we are trying to figure out. Why did you call that a problem? Because when I asked, just to reiterate, when I asked, okay, what do you think about dissitter quantum gravity? You said the problem is that it's unstable. Why is that a problem? Yeah, because

Starting point is 01:11:46 This is there when people talk about this it there they mean Everlasting this is there if you're just having a piece of this it there then that's different So in other words, there's a time this is there has a time axis Okay, so if you take the curvature or the scale of the sitter and extrapolate in time, we're saying it won't last So therefore it's not the sitter you call it the sitter or the scale of the sitter and extrapolate in time, we're saying it won't last. So therefore, it's not the sitter. You call it the sitter or not, it becomes ambiguous. So professor, to end, I want to know what is a mystery that you think about on a daily basis?

Starting point is 01:12:16 Well, trying to see what we can find theoretically to check this idea of dark dimension right now. These days, I'm mostly consumed about trying to understand how we can confront string theory with reality. I'm hoping that in my lifetime, there will be experiments which will hopefully show us how string theory works in real world. Yes, you said that many of your colleagues,

Starting point is 01:12:37 not all of them, but many of them may have gone too abstract or gone too in the way of forgetting about this universe and you're trying to bring them back with the Swamp Land Program or the Weak Gravity Conjecture in particular. So can you expand more on that? What is this delineation between people who don't have a tether on physical reality, though they think they're studying physics, it's called theoretical physics? No, no, no.

Starting point is 01:13:01 I wouldn't say they don't have tether on physical reality. I think they think we don't have enough tools to study physical reality. I think they are under that impression. They think that's unapproachable right now with our techniques. So let's do abstract stuff for which our techniques might apply. That's their mindset. And I disagree with that mentality. I think we do have a number of ideas and techniques which does apply to our universe and that's our difference. Otherwise I don't think they're untethered to reality. They are. They just don't think that we do have enough of the tools. So it's like a jigsaw puzzle and you feel like

Starting point is 01:13:34 we have the pieces already to put it together. They say don't waste it. We don't have, exactly. That's the right way of saying it. I think we have enough of the jigsaw pieces right in the place to figure out some of the rest that are crucial. Uh-huh and last question at what time did we have enough of these pieces of the jigsaw like what was the last piece that you're like okay from this point we had enough to infer if we were

Starting point is 01:13:57 only clever enough I mean we have more mathematical tools now but physically speaking the experimental results that were enough to allow us to infer the rest of the picture. Well, the dark dimension is when I got convinced that we may have a chance, because that was a scale which was coming from the relation of dark energy with a particular physical scale that we can actually see in our universe, was motivated by abstract principles of string theory. So this connection that one thing leads to this concrete thing, like, wow, of course, there's a very extremely tuned pan-amteron universe, the dark energy.

Starting point is 01:14:28 Why don't we apply it? It was kind of daring to say, well, there's a tower. Where is that tower? Nobody saw this tower. And suddenly, you remember that in two problems always come together. Problems come in pairs. And the two problems were one is what is dark matter? And other one is what does this tower have to do with anything? Yes, that's super interesting to me because dark matter and dark energy were always misnomers to me because they don't a priori have anything to do with one another. But then in the popular press they said they're both dark and so most people think there's some association, but you're actually compromising that. Yes, we are saying they are related. They are unified into one object, into this dark dimension. The existence of this large length, micron scale length, relatively large, is the manifestation of dark energy. And the long wavelengths of gravitons on them is the dark matter.

Starting point is 01:15:19 So the tower of light, dark matter, gets related to the size, which is set by dark energy. So dark energy and dark matter gets related to the size which is set by dark energy. So dark energy and dark matter gets related. The mass of the dark matter gets pegged to the value of dark energy. Well professor I'm going to leave the paper I'm gonna leave the set of papers on this subject by you and your collaborators on screen right now and in the description for people who want to find out more. Thank you for spending so much time with me. Thank you thank you for interviewing. Have a good time. Firstly thank you for spending so much time with me. Thank you, thank you for the interview. Have a good time. Firstly, thank you for watching, thank you for listening. There's now a website, kurtjymungle.org,

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Theories of Everything with Curt Jaimungal - Dark Dimensions: NEW THEORY Unifying Dark Matter & Dark Energy

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