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Cumrun Vafa: Dark Dimensions is the NEW THEORY Unifying Dark Matter & Dark Energy
July 19, 2024
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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
Kamran Vafa, professor of science at Harvard, 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. Come with me into the heart of the universe, both observable and not.
When I was a child from the very elementary schools, I remember loving math, so math was always part of my excitement about intellectual excitement.
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 to put my finger on it didn't seem to
Intellectually bother them to want to know the answer to it. So these kind 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 of the Activity so I'm very happy that I'm in it 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. So for me math is part of physics and to me even though math has its own language and you can apply 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, you have to ask them. I'm not saying everybody should view it the way I do, obviously. I'm saying that to me, math is something not so different from physics. In fact, when I want to really see 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.
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 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 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.
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.
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 number of them the question is whether you wanted technical or non-technical or what not 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 in that interaction. So I was explaining to my colleague Yao, who is my colleague here in the math department, the fact that from physics it seems natural
This is before we conjectured mirror symmetry, that there should be as many colabias as positive Euler characteristic as negative one for colabia threefold, which is a prediction of mirror symmetry. And he kind of found it very odd that we are saying something like this.
He asked, why are you thinking this way? 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 Calabria cannot distinguish which one. He said, well, that doesn't sound too right to me because we know more of negative Euler characteristic Calabria 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. Right. And nevertheless, we were so sure of it, we conjectured in my paper with Wolfgang Lerfe and Nick Warner. 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 material 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?
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 mathematics 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, you know, simple group and this and that and this amazing fact that, you know, lengths contract and time dilates.
For them that physical reality does not connect with that other fact they know about the group theory of transformations which we call the rents group so 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 depends on how you want to kind of packages. It's physically exciting, mathematically exciting or or other ones. But mathematical excitements are many examples. Other ones are comes, for example, mathematicians are interested in counting curves. Counting by curves, I mean how surfaces fit in some geometries.
This is 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 you're counting, 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, 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 another example has to do with aspects of gauge theories. So we were interested with written and studying
instantons for four manifolds. So this involves studying very non-trivial questions of geometry of bundles, gauge bundles, or connections on which admins self-dual and considering self-dual gauge connections on them. And we were interested in computing on these spaces, the space of these instantons, their Euler characteristic. And again, from a physical reasoning, we knew that or we were expecting that if you stack them up,
Is it on number 1234 they form a function and this whole function has amazing properties was called modular transformation properties. So we said we we told mathematical colleagues that we are looking for this structure and we don't know whether these numbers are computer 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 with it. 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?
This is, I mean, they call it now the Vafov-Witten invariance, but it is the invariance having to do with 4-manifold and instantons on them. Yes. Also, when you're referring to invariance, 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? Actually, I should have said it. The rational numbers I was telling you is the Gromov-Witten invariance.
So what we learned with what we suggested with Gopal Kumar was how to unpack these irrational numbers, the Gromov-Witten invariance into integers, which is now called the Gopal Kumar Bafa invariance. That's that's 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 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
The curvature of a gauge bundle is two-form only in four dimensions, so therefore it makes sense to say self-dual or not only in 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 mineral action configuration? And they end up being self doable. So it's like a ground state.
of the of the of the gauge connection in that sector. Of course, in the trivial sector, the ground state means you turn off everything gauge field is zero nothing. Yes. But in the other sectors, you have to turn them on and the self two ones are the ground state. So they basically are the ground states of the each configuration of the gauge connections. So having having studying the ground states in each topological sector is, of course, natural. OK, 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 within string theory itself?
Oh, it has to, because our understanding of string theory is certainly incomplete. We do not have, 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, 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? Well, overturned is not there. I don't think we have something which is which is in the form of a laws of like Maxwell's laws that you can see 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. It's like saying that how do you, just to say the other way, suppose you want to say how would you overturn the Broglie's wave statement.
You don't overturn it. You basically develop it. You develop it to quantum mechanics. That's what the string theory is right now. 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? It's hard to say. I think I enjoy every paper I write, at least
Now you could say not all of them would equal love, but I think overall it's not as easy as 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 and you might kind of summarize or get the 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 a great paper. No, no, no, no, no. This is built upon a lot of laborious other papers which don't get much recognition. 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, oh, who cares about that paper? But those are the beginning 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 something else, but why don't you tell us what's exciting that you're working on currently? There are other directions that I find equally interesting or maybe even more if athletes 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 strings from string 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 Call the Swamp Land Swamp Land program, which is now what I'm most excited about. So there's their parallel I mean there are many things kind of interrelate and have interconnections. It's not one thing and
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. It does not include extra time or anything else. In my paper, when I wrote the first idea about the FDA, I also suggested that these two extra dimensions that are hidden in some form, there's 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 theory has made a fame for having two time directions, that's actually kind of irrelevant for the discussion. The theory of 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. It could be, but it doesn't actually matter. It could be. And it could be. And my suggestion is one space and one time, which means two altogether, 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,
Like a partial hidden aspect of the constructions, as if there is 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 physical properties of the rest of the space and time, it certainly is not of the usual time. 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 on time looks like and these are not one of those. So there should be something a little different from 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.
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Earlier when asking about F theory and how it may or may not be the crescendo of your work and you outlined quite a few different directions like the Swampland and and black holes. Can you please pick one of them? Pick one of those topics. Let's say the Swampland. Let's just talk about the Swampland. Why is it that the Swampland has you so fired up right now? Well, Swampland is for me exciting because it's the executive summary of all I have learned from 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 interior theory of strong interactions. Quantum electrodynamics does the same for electricity. And there's the electric weak force, which is another kind of gauge force, which is also does as equally 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. And the idea is that you're always interested in large distance. What happens at large distance is 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 quantum field theories. Namely, you start with a given 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 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 physics 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
That does not affect your calculation at large distances. Very powerful idea. This idea totally fails for quantum gravity. 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 and accelerate them 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 center of mass of such a collision. So therefore you go at a higher and higher energy, 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 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, 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 transiting to higher and higher distances, which is opposite to the way of thinking that we had. In other 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. So this was just a background about the connection between quantum gravity and why it's so different from quantum field theory. So you say, OK, so OK, they are related. So 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 on this symmetry in short long distances right now for me the action that you cannot expect to work. String theory tells you that is in fact does not work.
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 OK are actually OK. There's a conspiracy between that short distance and large distance, which is not apparent 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 this extra dimensional geometries because string theory is more than in more than four dimensional space time. These extra dimensions have their own geometries that we can pick. Kalabiya, this manifold, that manifold, G2 manifold, spin seven manifold, whatever you choose it. And you see what physics comes out. You change the manifold changes the physics. So you say, OK, I want to see a different 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, 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, is that a theorem? Well, we have a lot of evidence. No, there's a lot of evidence for what I just told you. And so in different examples, it's a theorem depends on how precise a question you want to 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. They 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 want to find these points. Well, good luck. 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 take you those points because those are very difficult because they're very rare. So that's the song program is to understand these lines. I will try to tell you some of these lines or the Swampland 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 has symmetries other than gauge symmetries. In other words, you cannot have symmetries in quantum gravity without having electrical fields associated with them. Like 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 a universe where there's electric charges 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?
Since quantum gravity says no, you cannot. 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? 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.
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 theories because you can imagine having two electrons. So the hierarchy problem is then the hierarchy inevitability.
No, the hierarchy is more specific question. Hierarchy just says, why is this case so much smaller? It could have been just the factor of 10 smaller. Oh, I see. OK. 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 tells you 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, 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 scores 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 electrical charge electrons mass was much higher and it would have been the other way.
But we say no, no, no, the here 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 of the electron has anything to do with its charge. This is no, it better be small than its charge in the appropriate units and the fundamental units in physics. So these kind 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 to see from an effective 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 of nature or numbers and so on, we're 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 are 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?
Speed of light is
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 in the theory will be somehow related to fields. 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. 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, 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 as we 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. And if you try to incorporate them one by one, you cannot succeed because they're infinitely many of them. So therefore, if you go far away to the left or to the right or anywhere in any direction you go, your description breaks down. So what happens?
A new description comes over and takes over incorporating those degrees of freedom, 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 the language of this form, is of this form. 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 different extreme regions of parameter space.
So this is a 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. 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. 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, someone 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. 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're 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.
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?
who appreciate the importance of the quantum gravity as being in the mix to get insights into particle physics question. So there is there is growing, 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 their field of vitality to make prediction predictive powers, because as I just told you, the number of possible allowed ones are measure zero.
So therefore, this gives you predictive power. So if you understand what these rules are, yes, it will give you what part of this 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,
exactly evermore so you can encroach on viable region 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. Sometimes what happens is that you get lucky. The X is on the left of this line, but the experiment finds it very close to this line and finds 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, 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. 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.
Inconsistent means it does not have a short distance completion. That means it looks fine at large distances but there's no full theory which you cannot answer to questions like what happens at high energy scatterings.
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. 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 pick, if you try to do that at large energy 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 then you are saying the other one is wrong. 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 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, I 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 you have drawn a line and you draw a straight line. Suppose you draw just giving a boring exam. Sure. 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 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, no, no, no, it's not finished. If you go to the other regimes 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 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 work perfectly fine. You're done. For large for some regime of parameter and your your theory doesn't tell you anything about the other regime. But your prediction is that should be linear. Yes. But then somebody comes and tells you 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,
The fact that simple fact that in this I'm giving it a little bit of a silly example so that I can illustrate the point and one regime you 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. 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 as large as in 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 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. 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 it's a revolutionary, 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 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 interchange, and that mirror symmetry is an example of it. So something which appears classical to one perspective can be quantum to another perspective. 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. So part of duality exam. 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 quantum, consistent quantum gravity theories. String theory has landed on what we think 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 constant theory of quantum gravities, but we haven't. 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 strength. There is nothing to a string theory per se, which rules that theory out or not.
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.
Consistency of a quantum theory of gravity 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 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 of quantum gravity, but it's always, I think, good to be open minded in possibilities of other possible theories that could exist.
It's also if you even want to understand just string theory, having this perspective is good because it tells you how for what are the fundamental things in string theory. What are what it what it what makes string theory take? 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 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 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 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.
So we are very happy with the fact that now we are finally beginning to derive string theory from some first principles.
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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.
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 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'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 that one corner, which is what we recognize, which is string theory. Not in everything we have done that, but in high enough supersymmetry with high enough dimensions, we are 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. 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 OK, but not at fundamental level. 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. 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 universally makes sense.
Help me with this because one way that I wasn't able to ever square why summing the possible metrics 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
Well, first of all, there are different things that you can think about fermions. Fermion you can define by a local transformation of space. 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 you find out how does it transform under rotation. 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 are self-consistent. In the regime for which you have a geometry, then you can define a fermion perhaps or other objects living on it.
If that object that doesn't live anymore, then what then you should not be able to define that Fermi on the way you used to do should be a complete 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 in a similar manner? People say gauge gravity, quote unquote gauge gravity. What does that mean?
No, no, gravity is gauging diffeomorphism symmetry. So diffeomorphism is a symmetry of a manifold. Difffeomorphism means that you can choose any coordinate system and gravity gauges it means that that symmetry should be respected locally. 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 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, you still take as the base manifold M, but then you gauge like you put fibers of the morphism group? Well, yeah. So what I'm saying is that tangent bundle of the manifold is canonical. You don't give it any, we don't choose the analog of G because the manifold is there, the tangent space is fixed. So that's different for gravity.
And just as another difference with gauge forces and 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. 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. 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 the formalism. So I think that's what if there's any different 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. 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. In the universe that we inhabit, it's a desider space that is repulsive, driving cosmic expansion. Vafa proposes that what we call dark matter and dark energy are manifestations of the same phenomenon tied to the nature of desider space itself.
This unification arises from string theory Swampland conjectures, which suggest that not all effective field theories can be consistently coupled to gravity. Specifically, Vafa is explaining that the apparent fine-tuning of the cosmological constant is teaching us about the dark sector of the universe. And what is it that you're working on now? Swampland principles.
So to me, as I said, right now, well, I have been starting the idea around 2005, the Swamp Land Program, and ever increasing number of physicists, especially young crowd are actually working on this. So it's become a very active community of physicists trying to decipher what we have learned from strength theory. You see, I think you ultimately want to say what does strength 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 that we have learned 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 swampland 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 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? And maybe dark energy. The dark energy in fundamental units of physics tend to the minus one hundred and twenty two.
It's so small. It's extreme. Okay. What is your tower? You see, this question is just sounds like a benign question. Am I claiming there's extreme? Okay, it's extreme. This is extreme. Tell me what's happening here. 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 condition which suggests there must be a tower. Now, you could say what is this tower? Where is this tower? How do you actually, what is the mass scale? How do you see it? So combining 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 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.
And but but our universe the three plus one dimensional space time which we are which we are living in in terms of electrons corks and all that are in a hyper plane in this higher dimension so you imagine you have a you have one higher dimension but we are on a hyper surface on that stock on that and the size of that is about a micron.
So we got this from just applying the Swamp Land Principle, the distance conjecture, which I try 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, OK, let me assume without knowing exactly how I get my unit from string theory, just that idea, what does it imply? 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 one over R squared, then you're in three dimensions. If it goes like one over R cube, then you're in four dimensional space. So you have grown a 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 at higher demand 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, 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 theory forces you. This is observation combined with the swampland idea.
So, in other words, 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, etc. That's like the distance conjecture, that if you go a 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 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? 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 is not massless because the graviton can have waves, oscillations in the other direction.
This part I'm talking about is nothing but oscillations of Graviton. So it unifies gravity with dark matter. So gravity 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 these 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 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 the 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 and physics has bizarre relations by factors of 10 to the 30, 10 to the 20, 10 to the 40. What these big numbers and he was saying it looks like they are not related by factors of two or three. They are related like by powers.
What is the reason for this? So in the concept of swampland, we have actually seen exactly the reasoning for why there are powers. And more than that, we find things are given by powers of one twelfth of the cosmological constant. So things come in chunks of lambda to the one twelfth. And that's about 10 to the minus 10. So you get 10 to the minus 10, 10 to the minus 20, 10 to the minus 30, etc. And these give you the different scales in physics. One of them gives you the
Higher dimensional plank scale. The other one gives you the weak scale. Another one gives you the neutrino scale. Another 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? How long was the? It gradually developed. So the distance conjecture started around 2006. But then we applied the distance conjecture to the case of cosmology constants in another paper. I think that was 2018.
and then in 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 combining this gives you that so the idea came gradually but it could have done been done much faster. What do you think about de Sitter quantum gravity? Well quantum gravity de Sitter seems to have a problem of stability and so a lot of these ideas in the context of swamplands seem to point towards the idea that de Sitter space
With positive energy cannot be stable. Well, the question will be okay. If they are not stable, 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'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 time scale associated with it also and we don't know if the recent observation of Desi which
The 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 about along the lines I'm talking about. 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 sitter. It could be just patches, short time maybe, but not in the long term. In the long term, it will decay. 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 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. You're saying that the age of the universe is the expected age of
A dissident universe to collapse up to the up to a log factor, which I didn't tell you about. So in other words, there's this 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 so so it's about since it's upper bound, we don't think it's going to be more than two or three trillion years. This is this is again, this is an idea from Swampland, which has less of an evidence because we don't have examples of dissident from string theory. So we have extrapolated what we know to get this.
So this is one of the things that we're 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, which has dark energy, is always unstable. The question is whether how unstable they are. And that's what we're 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 the sitter quantum gravity? You said the problem is that it's unstable. Why is that a problem? Yeah, because when people talk about the sitter, they mean everlasting the sitter. If you're just having a piece of the sitter, then that's different. So in other words, there's a time, this 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,
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, not all of them, but many of them may have gone to abstract or gone to in the way of forgetting about this universe and you're trying to bring them back with the Swampland 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.
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 they just don't think that we do have enough of the tools. So it's like a jigsaw puzzle and you feel like 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 in the right in the place to figure out some of the rest that are crucial.
Last question, at what time did we have enough of these pieces of the jigsaw? What was the last piece that you're like, okay, from this point, we had enough to infer. If we were only clever enough, we have more mathematical tools now, but physically speaking, the experimental results were enough to allow us to infer the rest of the picture. 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 palm to our universe and dark energy. 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 the other was what is 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. Yes, we are saying they are related. They are unified into one object into this dark dimension. This the 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. 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. 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 going to 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 watching, thank you for listening. There's now a website, curtjymungle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like.
That's just part of the terms of service. Now, a direct mailing list ensures that I have an untrammeled communication with you. Plus, soon I'll be releasing a one-page PDF of my top 10 toes. It's not as Quentin Tarantino as it sounds like. Secondly, if you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself
Plus, it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm, which means that whenever you share on Twitter, say on Facebook or even on Reddit, etc., it shows YouTube, hey, people are talking about this content outside of YouTube.
which in turn greatly aids the distribution on YouTube. Thirdly, there's a remarkably active Discord and subreddit for theories of everything where people explicate toes. They disagree respectfully about theories and build as a community our own toe. Links to both are in the description. Fourthly, you should know this podcast is on iTunes. It's on Spotify. It's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from rewatching lectures and podcasts.
I also read in the comments
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▶ View Full JSON Data (Word-Level Timestamps)
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"text": " 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."
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"text": " Kamran Vafa, professor of science at Harvard, 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. Come with me into the heart of the universe, both observable and not."
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"text": " When I was a child from the very elementary schools, I remember loving math, so math was always part of my excitement about intellectual excitement."
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"text": " 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 to put my finger on it didn't seem to"
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"text": " Intellectually bother them to want to know the answer to it. So these kind 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 of the Activity so I'm very happy that I'm in it in this field now"
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"text": " 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. So for me math is part of physics and to me even though math has its own language and you can apply to many things nothing to do with physics,"
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"text": " 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, you have to ask them. I'm not saying everybody should view it the way I do, obviously. I'm saying that to me, math is something not so different from physics. In fact, when I want to really see what the math is telling me, I imagine physical objects or physical things and what it"
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"text": " 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."
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"text": " 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 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."
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"text": " Well, we often discuss with mathematicians, for example, joint collaborations. So I am sometimes in the situation you just mentioned where 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."
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"text": " the same thing."
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"text": " 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."
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"text": " 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?"
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"text": " 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 number of them the question is whether you wanted technical or non-technical or what not 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"
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"text": " I think I probably should explain that because I was at the center of that circle so I should explain what happened actually in that interaction. So I was explaining to my colleague Yao, who is my colleague here in the math department, the fact that from physics it seems natural"
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"text": " This is before we conjectured mirror symmetry, that there should be as many colabias as positive Euler characteristic as negative one for colabia threefold, which is a prediction of mirror symmetry. And he kind of found it very odd that we are saying something like this."
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"text": " He asked, why are you thinking this way? 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 Calabria cannot distinguish which one. He said, well, that doesn't sound too right to me because we know more of negative Euler characteristic Calabria than positive. So there's no symmetry."
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"text": " from the known example. So despite that, we conjectured it. So it wasn't like something was unintuitive, something was against the mathematical evidence. Right. And nevertheless, we were so sure of it, we conjectured in my paper with Wolfgang Lerfe and Nick Warner. 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."
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"text": " The material 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?"
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"text": " 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."
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"text": " I will give you a first surprising physical content which to mathematics 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, you know, simple group and this and that and this amazing fact that, you know, lengths contract and time dilates."
},
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"end_time": 615.811,
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"text": " For them that physical reality does not connect with that other fact they know about the group theory of transformations which we call the rents group so 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"
},
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"start_time": 616.408,
"text": " 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 depends on how you want to kind of packages. It's physically exciting, mathematically exciting or or other ones. But mathematical excitements are many examples. Other ones are comes, for example, mathematicians are interested in counting curves. Counting by curves, I mean how surfaces fit in some geometries."
},
{
"end_time": 663.968,
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"text": " This is 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."
},
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"text": " Even though they are you're counting, 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, and if you do this operation on them, you can extract some integers out which actually are counting."
},
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"start_time": 690.367,
"text": " 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 another example has to do with aspects of gauge theories. So we were interested with written and studying"
},
{
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"index": 30,
"start_time": 710.196,
"text": " instantons for four manifolds. So this involves studying very non-trivial questions of geometry of bundles, gauge bundles, or connections on which admins self-dual and considering self-dual gauge connections on them. And we were interested in computing on these spaces, the space of these instantons, their Euler characteristic. And again, from a physical reasoning, we knew that or we were expecting that if you stack them up,"
},
{
"end_time": 759.787,
"index": 31,
"start_time": 739.019,
"text": " Is it on number 1234 they form a function and this whole function has amazing properties was called modular transformation properties. So we said we we told mathematical colleagues that we are looking for this structure and we don't know whether these numbers are computer or not and they were surprised that we are even looking for such a structure and."
},
{
"end_time": 782.193,
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"start_time": 760.282,
"text": " 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 with it. 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?"
},
{
"end_time": 808.899,
"index": 33,
"start_time": 783.029,
"text": " This is, I mean, they call it now the Vafov-Witten invariance, but it is the invariance having to do with 4-manifold and instantons on them. Yes. Also, when you're referring to invariance, 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? Actually, I should have said it. The rational numbers I was telling you is the Gromov-Witten invariance."
},
{
"end_time": 829.497,
"index": 34,
"start_time": 809.497,
"text": " So what we learned with what we suggested with Gopal Kumar was how to unpack these irrational numbers, the Gromov-Witten invariance into integers, which is now called the Gopal Kumar Bafa invariance. That's that's repackaging of that rational numbers in terms of integers was something that was surprising for mathematicians. And that's what we found."
},
{
"end_time": 854.155,
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"start_time": 830.52,
"text": " 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 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"
},
{
"end_time": 879.633,
"index": 36,
"start_time": 854.548,
"text": " The curvature of a gauge bundle is two-form only in four dimensions, so therefore it makes sense to say self-dual or not only in 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."
},
{
"end_time": 890.811,
"index": 37,
"start_time": 880.23,
"text": " In each one, you can ask what is the minimum energy configuration or in physical language, what is the mineral action configuration? And they end up being self doable. So it's like a ground state."
},
{
"end_time": 921.049,
"index": 38,
"start_time": 891.22,
"text": " of the of the of the gauge connection in that sector. Of course, in the trivial sector, the ground state means you turn off everything gauge field is zero nothing. Yes. But in the other sectors, you have to turn them on and the self two ones are the ground state. So they basically are the ground states of the each configuration of the gauge connections. So having having studying the ground states in each topological sector is, of course, natural. OK, so physics can be seen as a history of revolutions. I remember you mentioned this once."
},
{
"end_time": 944.377,
"index": 39,
"start_time": 921.425,
"text": " 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 within string theory itself?"
},
{
"end_time": 972.073,
"index": 40,
"start_time": 945.196,
"text": " Oh, it has to, because our understanding of string theory is certainly incomplete. We do not have, 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."
},
{
"end_time": 994.07,
"index": 41,
"start_time": 973.916,
"text": " String theory promised a unified so-called theory of everything, 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."
},
{
"end_time": 1020.333,
"index": 42,
"start_time": 995.452,
"text": " 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? Well, overturned is not there. I don't think we have something which is which is in the form of a laws of like Maxwell's laws that you can see this can be wrong or this can be right. String theory is a collection of examples"
},
{
"end_time": 1047.91,
"index": 43,
"start_time": 1020.742,
"text": " 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. It's like saying that how do you, just to say the other way, suppose you want to say how would you overturn the Broglie's wave statement."
},
{
"end_time": 1068.285,
"index": 44,
"start_time": 1048.37,
"text": " You don't overturn it. You basically develop it. You develop it to quantum mechanics. That's what the string theory is right now. 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? It's hard to say. I think I enjoy every paper I write, at least"
},
{
"end_time": 1098.865,
"index": 45,
"start_time": 1069.258,
"text": " Now you could say not all of them would equal love, but I think overall it's not as easy as 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 and you might kind of summarize or get the aha moment in one paper. That's true."
},
{
"end_time": 1125.435,
"index": 46,
"start_time": 1099.206,
"text": " But it didn't come in vacuum. And that fact is, I think, sometimes missed. You think, oh, this is a great paper. No, no, no, no, no. This is built upon a lot of laborious other papers which don't get much recognition. 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, oh, who cares about that paper? But those are the beginning of the thinking."
},
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"end_time": 1131.22,
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"text": " So I wouldn't I would not want to encourage that culture of thinking that there's this paper I like."
},
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"text": " 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 something else, but why don't you tell us what's exciting that you're working on currently? There are other directions that I find equally interesting or maybe even more if athletes 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."
},
{
"end_time": 1188.114,
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"text": " Aspects of topological strings from string 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 Call the Swamp Land Swamp Land program, which is now what I'm most excited about. So there's their parallel I mean there are many things kind of interrelate and have interconnections. It's not one thing and"
},
{
"end_time": 1217.773,
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"start_time": 1188.387,
"text": " 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"
},
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"end_time": 1244.514,
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"text": " Where you can use that to construct solutions to string theory. That's a robust statement. It does not include extra time or anything else. In my paper, when I wrote the first idea about the FDA, I also suggested that these two extra dimensions that are hidden in some form, there's 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."
},
{
"end_time": 1257.21,
"index": 52,
"start_time": 1244.889,
"text": " So the idea that there are, so the theory has made a fame for having two time directions, that's actually kind of irrelevant for the discussion. The theory of construction really does not require extra time dimensions."
},
{
"end_time": 1281.476,
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"start_time": 1257.363,
"text": " 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. It could be, but it doesn't actually matter. It could be. And it could be. And my suggestion is one space and one time, which means two altogether, 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,"
},
{
"end_time": 1311.015,
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"start_time": 1282.022,
"text": " Like a partial hidden aspect of the constructions, as if there is 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 physical properties of the rest of the space and time, it certainly is not of the usual time. So yes, whatever it is, it's not of the usual space and time."
},
{
"end_time": 1337.841,
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"start_time": 1311.664,
"text": " That's part of it because we know how the usual space on time looks like and these are not one of those. So there should be something a little different from 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."
},
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"text": " Hola, Miami! When's the last time you've been in Burlington? We've updated, organized, and added fresh fashion. See for yourself Friday, November 14th to Sunday, November 16th at our Big Deal event. You can enter for a chance to win free wawa gas for a year, plus more surprises in your Burlington. Miami, that means so many ways and days to save. Burlington. Deals. Brands. Wow! No purchase necessary. Visit BigDealEvent.com for more details."
},
{
"end_time": 1392.398,
"index": 57,
"start_time": 1367.227,
"text": " Earlier when asking about F theory and how it may or may not be the crescendo of your work and you outlined quite a few different directions like the Swampland and and black holes. Can you please pick one of them? Pick one of those topics. Let's say the Swampland. Let's just talk about the Swampland. Why is it that the Swampland has you so fired up right now? Well, Swampland is for me exciting because it's the executive summary of all I have learned from string theory."
},
{
"end_time": 1415.845,
"index": 58,
"start_time": 1392.91,
"text": " 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."
},
{
"end_time": 1443.08,
"index": 59,
"start_time": 1416.186,
"text": " 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 interior theory of strong interactions. Quantum electrodynamics does the same for electricity. And there's the electric weak force, which is another kind of gauge force, which is also does as equally good job for describing the weak forces."
},
{
"end_time": 1472.568,
"index": 60,
"start_time": 1444.65,
"text": " 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. And the idea is that you're always interested in large distance. What happens at large distance is not at microscopic scale."
},
{
"end_time": 1503.148,
"index": 61,
"start_time": 1473.524,
"text": " 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 quantum field theories. Namely, you start with a given 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."
},
{
"end_time": 1533.2,
"index": 62,
"start_time": 1503.933,
"text": " Except that you don't need to know what was the short distance 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 physics 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"
},
{
"end_time": 1559.189,
"index": 63,
"start_time": 1533.677,
"text": " That does not affect your calculation at large distances. Very powerful idea. This idea totally fails for quantum gravity. 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."
},
{
"end_time": 1589.275,
"index": 64,
"start_time": 1559.821,
"text": " What we do in particle physics is to take two particles and accelerate them 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 center of mass of such a collision. So therefore you go at a higher and higher energy, collide them to see what's going on at shorter distances, namely what comes out of such a process of scattering these particles"
},
{
"end_time": 1615.145,
"index": 65,
"start_time": 1589.548,
"text": " 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 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."
},
{
"end_time": 1633.882,
"index": 66,
"start_time": 1615.418,
"text": " 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, a black hole is a solution to Einstein's equation, which is described by long distance physics, not short distance physics."
},
{
"end_time": 1660.043,
"index": 67,
"start_time": 1634.172,
"text": " 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 transiting to higher and higher distances, which is opposite to the way of thinking that we had. In other words, high energy and low energy kind of are connected. The discussion of separating the short and large distances in this way fails."
},
{
"end_time": 1687.756,
"index": 68,
"start_time": 1660.606,
"text": " 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. So this was just a background about the connection between quantum gravity and why it's so different from quantum field theory. So you say, OK, so OK, they are related. So what does this relation really mean? How do you actually use this fact? What is the description?"
},
{
"end_time": 1700.367,
"index": 69,
"start_time": 1688.319,
"text": " This means that you cannot just say I have this on this symmetry in short long distances right now for me the action that you cannot expect to work. String theory tells you that is in fact does not work."
},
{
"end_time": 1730.759,
"index": 70,
"start_time": 1701.015,
"text": " 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 OK are actually OK. There's a conspiracy between that short distance and large distance, which is not apparent 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"
},
{
"end_time": 1758.729,
"index": 71,
"start_time": 1731.135,
"text": " So in the string theory, we choose this extra dimensional geometries because string theory is more than in more than four dimensional space time. These extra dimensions have their own geometries that we can pick. Kalabiya, this manifold, that manifold, G2 manifold, spin seven manifold, whatever you choose it. And you see what physics comes out. You change the manifold changes the physics. So you say, OK, I want to see a different physics. I want to get this kind of physics. Can you give it to me? The answer is almost always no."
},
{
"end_time": 1786.357,
"index": 72,
"start_time": 1759.531,
"text": " 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, 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"
},
{
"end_time": 1813.473,
"index": 73,
"start_time": 1786.766,
"text": " This fails. Now, is that a theorem? Well, we have a lot of evidence. No, there's a lot of evidence for what I just told you. And so in different examples, it's a theorem depends on how precise a question you want to 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,"
},
{
"end_time": 1841.152,
"index": 74,
"start_time": 1813.933,
"text": " The other ones are good. They 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 want to find these points. Well, good luck. 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."
},
{
"end_time": 1864.036,
"index": 75,
"start_time": 1841.766,
"text": " 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 take you those points because those are very difficult because they're very rare. So that's the song program is to understand these lines. I will try to tell you some of these lines or the Swampland criteria that we have found over the years."
},
{
"end_time": 1893.933,
"index": 76,
"start_time": 1864.599,
"text": " 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 has symmetries other than gauge symmetries. In other words, you cannot have symmetries in quantum gravity without having electrical fields associated with them. Like in our universe, we have, of course, electric charge, which is conserved."
},
{
"end_time": 1915.452,
"index": 77,
"start_time": 1894.292,
"text": " But that has electrical field with it. So what this statement is that you could not have a universe where there's electric charges 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?"
},
{
"end_time": 1941.681,
"index": 78,
"start_time": 1916.152,
"text": " Since quantum gravity says no, you cannot. 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."
},
{
"end_time": 1965.845,
"index": 79,
"start_time": 1942.312,
"text": " And so there are arguments like that. So when you say, can you prove it? 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."
},
{
"end_time": 1994.718,
"index": 80,
"start_time": 1966.22,
"text": " 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 theories because you can imagine having two electrons. So the hierarchy problem is then the hierarchy inevitability."
},
{
"end_time": 2023.268,
"index": 81,
"start_time": 1995.913,
"text": " No, the hierarchy is more specific question. Hierarchy just says, why is this case so much smaller? It could have been just the factor of 10 smaller. Oh, I see. OK. 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 tells you it doesn't tell you you have to have a huge hierarchy."
},
{
"end_time": 2052.671,
"index": 82,
"start_time": 2023.951,
"text": " So this idea of the weak gravity conjecture, if you think about it, it's a little strange why it's true, 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"
},
{
"end_time": 2077.961,
"index": 83,
"start_time": 2053.217,
"text": " times mass over r squared. That's Newton's gravitational attraction scores 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 electrical charge electrons mass was much higher and it would have been the other way."
},
{
"end_time": 2107.995,
"index": 84,
"start_time": 2078.916,
"text": " But we say no, no, no, the here 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 of the electron has anything to do with its charge. This is no, it better be small than its charge in the appropriate units and the fundamental units in physics. So these kind 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"
},
{
"end_time": 2127.261,
"index": 85,
"start_time": 2108.575,
"text": " Which I find probably the most difficult to see from an effective 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"
},
{
"end_time": 2154.241,
"index": 86,
"start_time": 2127.961,
"text": " Dynamical. Now what does that mean? That means when we usually think about constants of nature or numbers and so on, we're 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 are 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?"
},
{
"end_time": 2168.626,
"index": 87,
"start_time": 2154.633,
"text": " Speed of light is"
},
{
"end_time": 2196.664,
"index": 88,
"start_time": 2168.933,
"text": " 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 in the theory will be somehow related to fields. So now I haven't stated what distance conjecture or duality conjecture is. It tells you that if you take this field,"
},
{
"end_time": 2223.08,
"index": 89,
"start_time": 2197.073,
"text": " 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. 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"
},
{
"end_time": 2239.462,
"index": 90,
"start_time": 2223.507,
"text": " If you go to far away corners of these extreme parameters, you get a tower of particles, 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."
},
{
"end_time": 2269.65,
"index": 91,
"start_time": 2240.64,
"text": " Very, very little mass separated from each other by little masses as we 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. And if you try to incorporate them one by one, you cannot succeed because they're infinitely many of them. So therefore, if you go far away to the left or to the right or anywhere in any direction you go, your description breaks down. So what happens?"
},
{
"end_time": 2289.019,
"index": 92,
"start_time": 2270.52,
"text": " A new description comes over and takes over incorporating those degrees of freedom, 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."
},
{
"end_time": 2311.698,
"index": 93,
"start_time": 2289.514,
"text": " So the duality in physics, I just explained to you in the language of this form, is of this form. 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 different extreme regions of parameter space."
},
{
"end_time": 2337.824,
"index": 94,
"start_time": 2312.176,
"text": " So this is a 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. 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."
},
{
"end_time": 2366.049,
"index": 95,
"start_time": 2338.2,
"text": " 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. 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, someone didn't work,"
},
{
"end_time": 2396.63,
"index": 96,
"start_time": 2366.886,
"text": " 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. 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're 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."
},
{
"end_time": 2412.637,
"index": 97,
"start_time": 2397.005,
"text": " 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."
},
{
"end_time": 2429.923,
"index": 98,
"start_time": 2413.319,
"text": " Are particle physicists still thinking that we don't have to incorporate gravity?"
},
{
"end_time": 2459.531,
"index": 99,
"start_time": 2429.923,
"text": " who appreciate the importance of the quantum gravity as being in the mix to get insights into particle physics question. So there is there is growing, 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 their field of vitality to make prediction predictive powers, because as I just told you, the number of possible allowed ones are measure zero."
},
{
"end_time": 2484.292,
"index": 100,
"start_time": 2460.23,
"text": " So therefore, this gives you predictive power. So if you understand what these rules are, yes, it will give you what part of this 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,"
},
{
"end_time": 2492.927,
"index": 101,
"start_time": 2484.821,
"text": " exactly evermore so you can encroach on viable region then you say okay so we don't have to dig across the whole earth"
},
{
"end_time": 2517.91,
"index": 102,
"start_time": 2493.217,
"text": " We can just dig in this guy's back alley in Panama. Sometimes what happens is that you get lucky. The X is on the left of this line, but the experiment finds it very close to this line and finds 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, it cannot be past that."
},
{
"end_time": 2533.524,
"index": 103,
"start_time": 2517.91,
"text": " 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. 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."
},
{
"end_time": 2561.596,
"index": 104,
"start_time": 2533.814,
"text": " Inconsistent means it does not have a short distance completion. That means it looks fine at large distances but there's no full theory which you cannot answer to questions like what happens at high energy scatterings."
},
{
"end_time": 2573.422,
"index": 105,
"start_time": 2562.125,
"text": " The way mathematicians use the word consistent or inconsistent is that if"
},
{
"end_time": 2598.234,
"index": 106,
"start_time": 2573.763,
"text": " 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. 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."
},
{
"end_time": 2626.169,
"index": 107,
"start_time": 2598.575,
"text": " And somebody says, no, no, no. The E that you pick, if you try to do that at large energy 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 then you are saying the other one is wrong. 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 something like A and not A at the same time."
},
{
"end_time": 2654.104,
"index": 108,
"start_time": 2626.732,
"text": " 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, I 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 you have drawn a line and you draw a straight line. Suppose you draw just giving a boring exam. Sure. You're drawing a straight line."
},
{
"end_time": 2679.599,
"index": 109,
"start_time": 2654.633,
"text": " 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 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."
},
{
"end_time": 2706.561,
"index": 110,
"start_time": 2680.06,
"text": " And then somebody comes and tells you, no, no, no, no, it's not finished. If you go to the other regimes 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 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,"
},
{
"end_time": 2734.155,
"index": 111,
"start_time": 2706.971,
"text": " You come up with a physical theory which says, oh, mass grows linearly and in this regime is positive and that's work perfectly fine. You're done. For large for some regime of parameter and your your theory doesn't tell you anything about the other regime. But your prediction is that should be linear. Yes. But then somebody comes and tells you 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,"
},
{
"end_time": 2763.609,
"index": 112,
"start_time": 2734.462,
"text": " The fact that simple fact that in this I'm giving it a little bit of a silly example so that I can illustrate the point and one regime you 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. 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 as large as in physics and you study it you may not know that you're assuming something about short distance which is not allowed."
},
{
"end_time": 2790.111,
"index": 113,
"start_time": 2764.189,
"text": " Okay. Now, is that because 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. 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?"
},
{
"end_time": 2813.012,
"index": 114,
"start_time": 2790.606,
"text": " So that paradigm was wrong that one was using. So it's a revolutionary, 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."
},
{
"end_time": 2830.299,
"index": 115,
"start_time": 2813.012,
"text": " 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 there, well,"
},
{
"end_time": 2859.94,
"index": 116,
"start_time": 2830.913,
"text": " 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 interchange, and that mirror symmetry is an example of it. So something which appears classical to one perspective can be quantum to another perspective. Because"
},
{
"end_time": 2886.886,
"index": 117,
"start_time": 2860.247,
"text": " 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. So part of duality exam. Professor, what would you say is the definition of string theory?"
},
{
"end_time": 2913.063,
"index": 118,
"start_time": 2887.363,
"text": " 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 quantum, consistent quantum gravity theories. String theory has landed on what we think might be the only constant theory of quantum gravity. But the Swamp Land program that I am studying, for example, does not assume that."
},
{
"end_time": 2941.374,
"index": 119,
"start_time": 2913.473,
"text": " So we are open to the possibility that there are other constant theory of quantum gravities, but we haven't. 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 strength. There is nothing to a string theory per se, which rules that theory out or not."
},
{
"end_time": 2963.183,
"index": 120,
"start_time": 2941.869,
"text": " 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."
},
{
"end_time": 2977.056,
"index": 121,
"start_time": 2963.797,
"text": " Consistency of a quantum theory of gravity 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"
},
{
"end_time": 3004.667,
"index": 122,
"start_time": 2977.654,
"text": " 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 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"
},
{
"end_time": 3022.415,
"index": 123,
"start_time": 3005.179,
"text": " I would say at least to me and many of my colleagues, convincingly, perhaps possibly the only theory of quantum gravity, but it's always, I think, good to be open minded in possibilities of other possible theories that could exist."
},
{
"end_time": 3042.329,
"index": 124,
"start_time": 3022.824,
"text": " It's also if you even want to understand just string theory, having this perspective is good because it tells you how for what are the fundamental things in string theory. What are what it what it what makes string theory take? 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."
},
{
"end_time": 3071.715,
"index": 125,
"start_time": 3043.302,
"text": " 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 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 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"
},
{
"end_time": 3096.118,
"index": 126,
"start_time": 3072.363,
"text": " 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 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,"
},
{
"end_time": 3123.558,
"index": 127,
"start_time": 3096.374,
"text": " 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."
},
{
"end_time": 3132.159,
"index": 128,
"start_time": 3123.985,
"text": " So we are very happy with the fact that now we are finally beginning to derive string theory from some first principles."
},
{
"end_time": 3161.903,
"index": 129,
"start_time": 3133.131,
"text": " This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state."
},
{
"end_time": 3187.551,
"index": 130,
"start_time": 3162.722,
"text": " 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."
},
{
"end_time": 3212.722,
"index": 131,
"start_time": 3188.063,
"text": " 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 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's not string theory therefore and so therefore we would have found another theory"
},
{
"end_time": 3228.234,
"index": 132,
"start_time": 3213.097,
"text": " So if we were there, but more and more the way we are doing it, we're always being narrowed down only to that one corner, which is what we recognize, which is string theory. Not in everything we have done that, but in high enough supersymmetry with high enough dimensions, we are being cornered to the string corner."
},
{
"end_time": 3256.34,
"index": 133,
"start_time": 3228.814,
"text": " 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. 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."
},
{
"end_time": 3284.821,
"index": 134,
"start_time": 3257.381,
"text": " 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 OK, but not at fundamental level. 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"
},
{
"end_time": 3313.558,
"index": 135,
"start_time": 3285.333,
"text": " 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. 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 universally makes sense."
},
{
"end_time": 3340.555,
"index": 136,
"start_time": 3313.712,
"text": " Help me with this because one way that I wasn't able to ever square why summing the possible metrics 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"
},
{
"end_time": 3364.889,
"index": 137,
"start_time": 3341.186,
"text": " Well, first of all, there are different things that you can think about fermions. Fermion you can define by a local transformation of space. 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."
},
{
"end_time": 3394.753,
"index": 138,
"start_time": 3365.623,
"text": " So you find out how does it transform under rotation. 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 are self-consistent. In the regime for which you have a geometry, then you can define a fermion perhaps or other objects living on it."
},
{
"end_time": 3422.978,
"index": 139,
"start_time": 3394.923,
"text": " If that object that doesn't live anymore, then what then you should not be able to define that Fermi on the way you used to do should be a complete 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 in a similar manner? People say gauge gravity, quote unquote gauge gravity. What does that mean?"
},
{
"end_time": 3444.104,
"index": 140,
"start_time": 3423.882,
"text": " No, no, gravity is gauging diffeomorphism symmetry. So diffeomorphism is a symmetry of a manifold. Difffeomorphism means that you can choose any coordinate system and gravity gauges it means that that symmetry should be respected locally. 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."
},
{
"end_time": 3457.005,
"index": 141,
"start_time": 3444.565,
"text": " So in Yang Mills, when we gauge,"
},
{
"end_time": 3484.633,
"index": 142,
"start_time": 3457.346,
"text": " 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, you still take as the base manifold M, but then you gauge like you put fibers of the morphism group? Well, yeah. So what I'm saying is that tangent bundle of the manifold is canonical. You don't give it any, we don't choose the analog of G because the manifold is there, the tangent space is fixed. So that's different for gravity."
},
{
"end_time": 3514.36,
"index": 143,
"start_time": 3485.145,
"text": " And just as another difference with gauge forces and 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. 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?"
},
{
"end_time": 3539.309,
"index": 144,
"start_time": 3515.384,
"text": " What does that mean? So what I mean is that Witten explicitly said that his superpower isn't mathematical prowess, though he has that. 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."
},
{
"end_time": 3564.292,
"index": 145,
"start_time": 3540.043,
"text": " So my intuition might clash with formalism and then I'll go with my intuition, not the formalism. So I think that's what if there's any different 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."
},
{
"end_time": 3592.637,
"index": 146,
"start_time": 3565.282,
"text": " What if we've been chasing a ghost? For decades, dark matter has been physics' elusive quarry. 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."
},
{
"end_time": 3616.34,
"index": 147,
"start_time": 3593.097,
"text": " In anti-desider space with a negative cosmological constant, this energy is attractive just like gravity. In the universe that we inhabit, it's a desider space that is repulsive, driving cosmic expansion. Vafa proposes that what we call dark matter and dark energy are manifestations of the same phenomenon tied to the nature of desider space itself."
},
{
"end_time": 3642.005,
"index": 148,
"start_time": 3616.698,
"text": " This unification arises from string theory Swampland conjectures, which suggest that not all effective field theories can be consistently coupled to gravity. Specifically, Vafa is explaining that the apparent fine-tuning of the cosmological constant is teaching us about the dark sector of the universe. And what is it that you're working on now? Swampland principles."
},
{
"end_time": 3670.128,
"index": 149,
"start_time": 3642.381,
"text": " So to me, as I said, right now, well, I have been starting the idea around 2005, the Swamp Land Program, and ever increasing number of physicists, especially young crowd are actually working on this. So it's become a very active community of physicists trying to decipher what we have learned from strength theory. You see, I think you ultimately want to say what does strength have to do with the real world?"
},
{
"end_time": 3699.753,
"index": 150,
"start_time": 3670.606,
"text": " 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 that we have learned 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 swampland we have actually now used to make a very"
},
{
"end_time": 3728.558,
"index": 151,
"start_time": 3700.742,
"text": " bold prediction, which is potentially observable in the next few years. And so I will try to explain 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? And maybe dark energy. The dark energy in fundamental units of physics tend to the minus one hundred and twenty two."
},
{
"end_time": 3759.701,
"index": 152,
"start_time": 3729.94,
"text": " It's so small. It's extreme. Okay. What is your tower? You see, this question is just sounds like a benign question. Am I claiming there's extreme? Okay, it's extreme. This is extreme. Tell me what's happening here. 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,"
},
{
"end_time": 3787.483,
"index": 153,
"start_time": 3760.128,
"text": " 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 condition which suggests there must be a tower. Now, you could say what is this tower? Where is this tower? How do you actually, what is the mass scale? How do you see it? So combining this general idea I told you with other observations, it turns out there's only one possibility."
},
{
"end_time": 3811.681,
"index": 154,
"start_time": 3788.387,
"text": " The possibility is that there is one of the dimensions of the microscopic dimensions 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."
},
{
"end_time": 3833.643,
"index": 155,
"start_time": 3812.363,
"text": " And but but our universe the three plus one dimensional space time which we are which we are living in in terms of electrons corks and all that are in a hyper plane in this higher dimension so you imagine you have a you have one higher dimension but we are on a hyper surface on that stock on that and the size of that is about a micron."
},
{
"end_time": 3862.995,
"index": 156,
"start_time": 3834.684,
"text": " So we got this from just applying the Swamp Land Principle, the distance conjecture, which I try 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, OK, let me assume without knowing exactly how I get my unit from string theory, just that idea, what does it imply? You immediately get these kind of predictions and the micron scale size of this extra dimension is actually observable potentially in our universe."
},
{
"end_time": 3889.206,
"index": 157,
"start_time": 3863.37,
"text": " 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 one over R squared, then you're in three dimensions. If it goes like one over R cube, then you're in four dimensional space. So you have grown a space dimension. So they want to see if the force becomes stronger, the force of gravity."
},
{
"end_time": 3906.152,
"index": 158,
"start_time": 3889.718,
"text": " Of gravity, so I'm saying that the Newton's gravitational force law being one over r squared becomes stronger at higher demand 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."
},
{
"end_time": 3934.753,
"index": 159,
"start_time": 3906.647,
"text": " 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, 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 theory forces you. This is observation combined with the swampland idea."
},
{
"end_time": 3958.524,
"index": 160,
"start_time": 3935.247,
"text": " So, in other words, 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, etc. That's like the distance conjecture, that if you go a 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 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."
},
{
"end_time": 3983.66,
"index": 161,
"start_time": 3959.462,
"text": " And would this say that dark matter is several particles, it's not just a single one, it's a tower of them? 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 is not massless because the graviton can have waves, oscillations in the other direction."
},
{
"end_time": 4012.841,
"index": 162,
"start_time": 3984.087,
"text": " This part I'm talking about is nothing but oscillations of Graviton. So it unifies gravity with dark matter. So gravity 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 these 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 dark dimension? We call this dark dimension scenario."
},
{
"end_time": 4031.135,
"index": 163,
"start_time": 4013.524,
"text": " Yes, so dark dimension scenario is a scenario that there's one extra dimension opening up and this is coming from the 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"
},
{
"end_time": 4050.981,
"index": 164,
"start_time": 4031.596,
"text": " Ultimately, it's an answer to a kind of an answer to a question that Dirac was asking. Dirac had noticed that different scales and physics has bizarre relations by factors of 10 to the 30, 10 to the 20, 10 to the 40. What these big numbers and he was saying it looks like they are not related by factors of two or three. They are related like by powers."
},
{
"end_time": 4074.77,
"index": 165,
"start_time": 4051.391,
"text": " What is the reason for this? So in the concept of swampland, we have actually seen exactly the reasoning for why there are powers. And more than that, we find things are given by powers of one twelfth of the cosmological constant. So things come in chunks of lambda to the one twelfth. And that's about 10 to the minus 10. So you get 10 to the minus 10, 10 to the minus 20, 10 to the minus 30, etc. And these give you the different scales in physics. One of them gives you the"
},
{
"end_time": 4095.23,
"index": 166,
"start_time": 4074.77,
"text": " Higher dimensional plank scale. The other one gives you the weak scale. Another one gives you the neutrino scale. Another 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."
},
{
"end_time": 4115.128,
"index": 167,
"start_time": 4096.084,
"text": " This dark dimension theory, when did it occur to you and your collaborators? How long was the? It gradually developed. So the distance conjecture started around 2006. But then we applied the distance conjecture to the case of cosmology constants in another paper. I think that was 2018."
},
{
"end_time": 4143.899,
"index": 168,
"start_time": 4115.759,
"text": " and then in 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 combining this gives you that so the idea came gradually but it could have done been done much faster. What do you think about de Sitter quantum gravity? Well quantum gravity de Sitter seems to have a problem of stability and so a lot of these ideas in the context of swamplands seem to point towards the idea that de Sitter space"
},
{
"end_time": 4171.903,
"index": 169,
"start_time": 4144.258,
"text": " With positive energy cannot be stable. Well, the question will be okay. If they are not stable, 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'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."
},
{
"end_time": 4183.558,
"index": 170,
"start_time": 4172.466,
"text": " So that is kind of interesting because it will tell you that the dark energy has a time scale associated with it also and we don't know if the recent observation of Desi which"
},
{
"end_time": 4203.729,
"index": 171,
"start_time": 4183.814,
"text": " The 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 about along the lines I'm talking about. So these kinds of ideas tell you that dark energy is actually dynamical."
},
{
"end_time": 4224.155,
"index": 172,
"start_time": 4204.104,
"text": " 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 sitter. It could be just patches, short time maybe, but not in the long term. In the long term, it will decay. So does that mean that our universe, which is the sitter will decay? Yes."
},
{
"end_time": 4248.029,
"index": 173,
"start_time": 4225.282,
"text": " Correct. We expect our universe not to be stable. In fact, I think every string theory 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. You're saying that the age of the universe is the expected age of"
},
{
"end_time": 4277.159,
"index": 174,
"start_time": 4248.37,
"text": " A dissident universe to collapse up to the up to a log factor, which I didn't tell you about. So in other words, there's this 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 so so it's about since it's upper bound, we don't think it's going to be more than two or three trillion years. This is this is again, this is an idea from Swampland, which has less of an evidence because we don't have examples of dissident from string theory. So we have extrapolated what we know to get this."
},
{
"end_time": 4299.002,
"index": 175,
"start_time": 4277.5,
"text": " So this is one of the things that we're 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, which has dark energy, is always unstable. The question is whether how unstable they are. And that's what we're trying to figure out."
},
{
"end_time": 4327.927,
"index": 176,
"start_time": 4299.718,
"text": " Why did you call that a problem? Because when I asked, just to reiterate, when I asked, okay, what do you think about the sitter quantum gravity? You said the problem is that it's unstable. Why is that a problem? Yeah, because when people talk about the sitter, they mean everlasting the sitter. If you're just having a piece of the sitter, then that's different. So in other words, there's a time, this 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,"
},
{
"end_time": 4357.619,
"index": 177,
"start_time": 4328.302,
"text": " 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."
},
{
"end_time": 4379.497,
"index": 178,
"start_time": 4358.763,
"text": " Yes, you said that many of your colleagues, not all of them, but many of them may have gone to abstract or gone to in the way of forgetting about this universe and you're trying to bring them back with the Swampland 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"
},
{
"end_time": 4399.497,
"index": 179,
"start_time": 4380.111,
"text": " physical reality, though they think they're studying physics, it's called theoretical physics."
},
{
"end_time": 4429.019,
"index": 180,
"start_time": 4399.94,
"text": " 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 they just don't think that we do have enough of the tools. So it's like a jigsaw puzzle and you feel like 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 in the right in the place to figure out some of the rest that are crucial."
},
{
"end_time": 4452.295,
"index": 181,
"start_time": 4429.94,
"text": " Last question, at what time did we have enough of these pieces of the jigsaw? What was the last piece that you're like, okay, from this point, we had enough to infer. If we were only clever enough, we have more mathematical tools now, but physically speaking, the experimental results were enough to allow us to infer the rest of the picture. The dark dimension is when I got convinced that we may have a chance."
},
{
"end_time": 4477.773,
"index": 182,
"start_time": 4452.671,
"text": " 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 palm to our universe and dark energy. Why don't we apply it? It was kind of daring to say, well, there's a tower. Where is that tower?"
},
{
"end_time": 4489.906,
"index": 183,
"start_time": 4478.166,
"text": " 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 the other was what is this tower have to do with anything."
},
{
"end_time": 4513.2,
"index": 184,
"start_time": 4490.299,
"text": " 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. Yes, we are saying they are related. They are unified into one object into this dark dimension. This the the existence of this large length"
},
{
"end_time": 4533.114,
"index": 185,
"start_time": 4513.626,
"text": " Micron scale length relatively large is the manifestation of dark energy and the long wavelengths of gravitons on them is the dark matter. 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. The mass of the dark matter gets pegged to the value of dark energy."
},
{
"end_time": 4548.387,
"index": 186,
"start_time": 4534.019,
"text": " Well, Professor, I'm going to leave the paper, I'm going to 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."
},
{
"end_time": 4564.735,
"index": 187,
"start_time": 4549.701,
"text": " Firstly, thank you for watching, thank you for listening. There's now a website, curtjymungle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like."
},
{
"end_time": 4591.135,
"index": 188,
"start_time": 4564.923,
"text": " That's just part of the terms of service. Now, a direct mailing list ensures that I have an untrammeled communication with you. Plus, soon I'll be releasing a one-page PDF of my top 10 toes. It's not as Quentin Tarantino as it sounds like. Secondly, if you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself"
},
{
"end_time": 4608.439,
"index": 189,
"start_time": 4591.135,
"text": " Plus, it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm, which means that whenever you share on Twitter, say on Facebook or even on Reddit, etc., it shows YouTube, hey, people are talking about this content outside of YouTube."
},
{
"end_time": 4637.875,
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"text": " which in turn greatly aids the distribution on YouTube. Thirdly, there's a remarkably active Discord and subreddit for theories of everything where people explicate toes. They disagree respectfully about theories and build as a community our own toe. Links to both are in the description. Fourthly, you should know this podcast is on iTunes. It's on Spotify. It's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from rewatching lectures and podcasts."
},
{
"end_time": 4657.824,
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"start_time": 4637.875,
"text": " I also read in the comments"
},
{
"end_time": 4681.271,
"index": 192,
"start_time": 4657.824,
"text": " and donating with whatever you like. There's also PayPal. There's also crypto. There's also just joining on YouTube. Again, keep in mind it's support from the sponsors and you that allow me to work on toe full time. You also get early access to ad free episodes, whether it's audio or video. It's audio in the case of Patreon video in the case of YouTube. For instance, this episode that you're listening to right now was released a few days earlier."
},
{
"end_time": 4701.715,
"index": 193,
"start_time": 4681.271,
"text": " Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?"
},
{
"end_time": 4719.855,
"index": 194,
"start_time": 4702.176,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal."
}
]
}No transcript available.