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Peter Woit: Unification, Twistors, and the Death of String Theory
December 6, 2023
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
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You cannot play any games about this. You have to admit that this is wrong. I think especially for mathematicians to come in and see an environment where there's guiding ideas that people haven't really worked out and a lot of things are known do not work for known reasons but people are still acting as if this is not true and trying to figure out how to do something and make career for themselves.
Peter Wojt is a theoretical physicist and a mathematician at Columbia University. He's been an influential figure in the ongoing debates surrounding string theory. His critiques, as articulated in his book, Not Even Wrong, strike at the heart of many popular assertions about this framework. Professor Wojt also has a widely read blog in the math and physics scene called Not Even Wrong, so it's the same name, and the links to all resources everything mentioned will be in the description as usual. We take meticulous timestamps and we take meticulous show notes.
In one sense, the problem with string theory is the opposite of the problem of fossil fuels. With fossil fuel companies, you have a goal, let's say it's to wash your clothes, and you're able to achieve that goal, but you produce negative externalities. Whereas string theory has plenty of positive externalities, but arguably achieves little toward its initial goal. Professor White introduces a novel toe approach called Euclidean twister unification. You may recognize that term twister as it's primarily associated with Roger Penrose. Twisters provide an alternative to space-time descriptions in quantum physics.
Peter's application of twisters is in the Euclidean setting, and he talks about how this significantly changes the playing field. It opens up a connection between gravity and the weak interaction, because space-time in this formulation is inherently chiral. We also talk about spinners and Michael Atiyah. You know how some people are Christian mystics or Muslim mystics? Well, Atiyah seems to be a spinner mystic.
We alternate between technical and more intuitive discourse. If you're new to the Theories of Everything channel, this is Par for the Course, and my name is Kurt Jaimungal. Usually what we do is we interweave between rigorous, steep technicality, and then periods of explaining the intuition behind what was just said. In other words, you can think of it as high-intensity interval training for the mind. Recall the system here on Toe, which is if you have a question for any of the guests, whether this guest or from a different Toe podcast,
Welcome, Professor.
Thank you so much. It's an honor to have you. I've been wanting to speak to you for almost two years since you came out with Euclidean Twister Theory or Euclidean Unification Theory, and well, here you are. Well, thanks. Thanks for having me on. I'm looking forward to the opportunity to be able to talk about some of these topics. I've certainly enjoyed some of your other programs. The one with my friend Edward Frankel recently was really spectacular.
Thank you. That's all due to Ed, of course. What are you working on these days? What's your research interest? There's something very specific. I'm just in the middle of trying to finish a short paper about an idea which I'm not quite sure what it is. I guess I've for now entitled the
The draft of the paper is titled, Space Time is Right-Handed. There's a slight danger it'll change conventions. It'll end up being that space time is left-handed, but I think it will stay right-handed. It's related to the twister stuff that I've been working on for the last few years, which I'm still quite excited about. There's one kind of basic claim at the bottom of what I'm trying to do with the twisters, which is
I think to the standard way of thinking about particle physics and general relativity and spinners, it's initially not very plausible. I should say one reason that it took me a long time to get back to the Euclidian twister stuff from some early ideas years ago was that I didn't actually believe that this basic thing that I needed to happen could happen.
I think lots of other people have had the same problem with this. The more I looked into the twister stuff, the more I became convinced that something like this had to work out. More recently, the last few months, I've come up with an understanding in much simpler terms, not involving twisters, just involving spinners, about the really unusual thing that's going on here. I think that I've
I've been trying to write up an explanation of the basic idea, and I think it's a fairly simple one. As I've been writing it up, I keep thinking, well, wait a minute, can this really work? There's no way this can actually really work. But the more I've been thinking about it, the more I've been convinced, yes, this actually does really work. I'm hoping within the next few days to have a
a final version of that paper. Well, not a final version, but a version of that paper I can at least send around to people and try to get comments on and also write about it publicly on my blog. I read the paper. Thank you for sending it. What you have is a very, it was very early draft of it, which made even less, hopefully the, I'll have something that will make more sense will be what all the public will see, but we'll see. Yeah. Do you think spinners are more simplified or easy to understand than twisters?
Oh, yeah. So spinors are really very basic, very, very basic things. I mean, every, you know, every elementary particle like electrons are just the way you describe them. They're spin would have nature is as spinors. You have to electron wave functions are spinors. And so they're in every, you know, every physics textbook or every if you do quantum mechanics, you do quantum field theory, you have to spend a fair amount of time to spinors. So
Spinners are very, very basic things. I spent a lot of my career thinking about them, trying to better understand them. I keep learning new things. In the last few months, I realized something about them, which I think is new, at least I'd never seen before. This is what I'm trying to write about. They're very fundamental objects. It's a little bit hard to
I can give you a whole lecture on spinners. I'm not sure how much of that you want or where you want to start with that. Right. Well, there's one view that we can understand them in quotes algebraically, but that doesn't mean we understand what spinners are. So that's the Michael Attia approach where he says it's like the letter I, the complex I, the imaginary I back in the fourteen hundreds or fifteen hundreds. It's only now or a couple hundred years later you realize what they are. And so, sure, we have many different ways of describing spinners mathematically.
but it's still a mystery as to what they are. Do you feel like we understand what they are or there's much more to be understood more than the formalism?
If you try and do geometry of any kind or Riemannian geometry, expressing everything in terms of spinors instead of in terms of vectors and tensors gives you a very different and in some ways more powerful formalism but one that people are not that used to and it has some amazing properties. It's kind of deeply related to
the notions about topology and k-theory and the Dirac operator gets into it. So the thing that made Atiyah really most famous, his index there was Singer. It's basically saying everything comes down to a certain kind of fundamental case and that is the fundamental case of the Dirac operator and spinners. So he was seeing the spinners kind of at the
as this really kind of central thing to the most important thing that he'd worked on. And so there's a lot to say. So there's a lot known about spinners, but there's also a lot, it's a little bit mysterious where they come from. I think the new stuff that I've been more, so I've been thinking about that a lot over the years, but the new stuff that has gotten where I think there's something new that I see going on is
Not the general story about spinners, but a very, very specific story about spinners in four dimensions. So you have spinners in any dimension, any dimension you can write down spinners and they're useful. But in four dimensions, some very, very special things happen. And the other very, very special thing, interesting thing that's going on in four dimensions is that from the point of view of physics, there's two different
Signatures that you're interested in you're interested in either spinners in the usual kind of four dimensions where all four dimensions are the same and you're just trying to do Euclidean geometry in four dimensions, which I might sometimes call Euclidean spinners or you're interested in spinners of the sort that you actually observe in relativistic quantum field theories where the geometry is that of Minkowski space. So sometimes refer to those as Minkowski spinners. And so you have two different versions of four dimensions, one
What is it your
Understanding or your proposal that the world is actually Euclidean and it's been a mistake to do physics in a Minkowski way when we wick rotate, we see that as some mathematical trick and you're saying no, no, no, that's actually the real space. That's real quote unquote, even though there's something imaginary about it. And the Minkowski case was the mistake like an analogy would be we operate in USD and then for some calculations, it's easier to go into yen.
And we think that the actual world is operating in the United States and the calculations are just something to make the numbers easier. And then you're saying, no, no, no, what's really happening is in Japan and it's been a mistake to go into the USD or the USD is just to make the math easier. So is that what you're saying or no? Well, so this goes back more to the Euclidean twister stuff. Yes. So there. Well, it's been well known in physics that you really kind of that
There's a problem in Minkowski's space-time. If you try and write down your theory in Minkowski's space-time, the simplest story about how a free particle evolves, you write down the formulas for what's a free particle going to do, what's its propagator, and you see that it's just ill-defined. You've written down a formula which mathematically is ill-defined. It needs more information in order to actually be a well-defined formula.
and I mean technically if you look at any physics book you'll see they're saying well you know we're going to do the answer is this integral and you look at this integral and this integral is going straight through two poles poles and uh you know that's just ambiguous you don't know what how to define such an ambiguity is about how you define such intervals so the one they ask what you've always known you have to do something like rotation you have to do something you have to
get rid of those ambiguities. And one way of getting rid of those ambiguities is, you know, analytically continuing and making time a complex variable, analytically continuing it, analytically continuing maybe to Euclidean signature, and there the formulas are well defined. So it's um, yeah, I'm not sure. I'm very comfortable saying one of these is real and one of these is not. It's the same. It's the same formula. It's just, you have to realize that
To make sense of it, you have to kind of go into the complex plane in time and you can, if you things are analytic, if this is a holomorphic function in time, you can either evaluate what happens at a measuring time or you can make time real, but you have to take the limit in a certain way moving, like perhaps starting with a measuring time and then moving analytically continuing a certain direction to get
a real time. But that's a standard story. That's not me saying this. That's a standard story. And then there's a, how do you, what sense do you make of this? Is this just a mathematical trick? Which a lot of physicists will say, well, that's just some kind of weird mathematical trick. It's not, it has nothing to do with reality. Or do you take this more seriously? So what's always fascinated me is more, is that it's fairly clear what's going on if you just talk about
scalar fields. If you talk about particles with spin zero or fields that transform trivially under rotations, what happens when you go to imaginary time is quite interesting and in some ways tricky, but it's very well understood. But it's never actually been very well understood what happens when you have spinner fields. And this is the problem is that
The spinners in Euclidean signature and spinners in Kowski signature are quite different things. And so you can't just say, oh, I'm going to analytically continue from one to the other because they're not related. Anyway, it's very unclear how you're going to do that. And so there's also a similar story in twister theory. You can do twister theory in Kowski space time, which is what Penrose and his collaborators mostly did, or you can do it in Euclidean
Signature space time, which is what a Tia and a lot of other people and mathematicians have done and and and in principle the two are related by analytic continuation, but the way that works is quite um, you know, I think it's much it's much subtler than you expect and uh, and so and what i've been interested in, you know, most recently this this business about um, it really is a claim That the standard way of thinking about how you analytically continue between these two different kinds of spinners is um
you're making kind of a wrong choice when you do that and there's a good reason for the standard choice you're making when you normally when you do that but there is actually another choice you can make which is that instead of working with spinners which are kind of symmetric between there's two different kinds which by convention you can call right and left handed or positive and negative chirality and the standard set up treats this question
What I've realized recently is it looks like it's quite possible to make this setup completely asymmetric so that you
You just described spinners using these right-handed or positive chirality spinners. You just don't use the left-handed ones at all in your construction of space-time. You can do that, it appears to be, and that's why this paper is called space-time is right-handed. Is it the case that you could have called it space-time is chiral and you could have equivalently described as left-handed or is there something specific about right-handedness?
No, it's a matter of convention. To say it a little bit more technically, the Lorentz symmetry group is this group called SL2C. It's two by two complex matrices, determinate one. What you realize is if you work in complex version of four dimensions,
The symmetry group is two copies of SL2C and you can call it a plus copy and a minus copy or you can call it a right copy and a left copy but there's two of them. And the standard convention in order to get analytic continuation to work out the way people expected has been to say that the physical Lorentz group
that we that corresponds to our real world is is not chirally symmetric it's it's kind of a diagonal which is you use both the right and left and you have to complex conjugate when you go from one side to the other but it kind of the lorenz group the sl2c lorenz group we know is supposed to sit as kind of a diagonal thing which is both right right and left but um what i'm kind of arguing is that no you can actually set things up so that the
The Lorentz group is just one of these two factors. It could have been the right factor, the left factor. You have to make a choice of convention. So it is very much a chiral setup. But the strange thing about this is you only really see this when you complexify. If you just look at Minkowski's space-time, you don't actually see this
Anyway, you don't see this problem or you don't see this ability to make this distinction. It's only when you go to Euclidean space-time where the rotation group really does split into two completely distinct right and left things, or if you go to complexified space-time where you have this two copies of SL2C, it's only in those contexts that you actually see that there is a difference between choosing the diagonal and choosing the right-handed side.
So for SL2C, you call that the Lorentz group. Is that technically the double cover of the Lorentz group? Yeah, people use both terminology. If you're going to work with spinners, you have to use the double cover. But yes, it's also... Yeah, sometimes you might want to say that SL3-1 is the Lorentz group and this is the double cover. But mostly you're interested in working with spinners and then you have to use the double cover, really. Yes.
So is there a reason that triple covers or quadruple covers aren't talked about much? Is it just because of experiment, there's nothing there? Well, it's more the mathematics that they don't. There is, I mean, there is, you know, any the rotation groups of any kind, you know, have this to have this twofold nature, there is this spin double cut, there is this heavy spin double covers.
In many cases, one way of seeing this is just a basic topology. The topology of rotations has a plus and minus thing in it and you have to do something about that. So there aren't any kind of known mathematically interesting triple covers, etc. Now, in the standard model, the way that
It's written in bundle languages that it's a principal bundle, and then the gauge groups are the structure groups. And then for general relativity, you have a tangent bundle. And then some people say that the gauge group of GR is the diffeomorphism group. But is there a way of making that into a bundle, like a principal bundle with a diffeomorphism group? How is one supposed to understand that as a bundle construction?
Yeah, yeah. Anyway, there's a lot of different ways. There's several different ways of thinking about geometry and about Romanian geometry. Yeah, and this starts to get a complicated subject. Maybe the best way to... Well, thinking in terms of different morphism groups is something you can do.
I it's actually not my favorite way of doing this kind of geometry and for for the reason is that it um well maybe let me just say something about about an alternate way of uh of thinking about geometry which which seems to be more powerful maybe actually to motivate this a little bit better sure if you just think about different morphism groups
It's very, very hard to understand what spinners are and where they come from. You really kind of can't see them at all if you're just thinking about the diffeomorphism group of a manifold. So the other formulation of geometry, going back to Cartan, which makes it much easy to see where spinners are going and is a lot more powerful in other respects, is to think not about
not about a manifold, but about a bigger space, which is a bundle that for each point in the manifold, you consider all possible bases for the tangent bundle. It's also called frames. And so this is sometimes called the frame bundle. And so it's kind of saying if you want to understand geometry, you should look at the points of space and time, but at the same point,
You also got to think about the tangent space and you should think about the possible bases of the tangent space and the so-called frames. So you should always kind of think, instead of bringing all your formulas in terms of local coordinates on the manifold, you should think about your problem as being a problem that lives up on the frame bundle and that you're not just at a point in space time, but you've also got a frame.
But then you have to be careful to kind of work kind of equivalently that you have, you know, you can, you can change your choice of frame, you can rotate your frames. So you have, you kind of work up in the frame bundle, but equivalently with respect to rotations or whatever that, so that's a, that gives a lot more structure to the problem. In particular, it allows you to easily say what spinners are, which you couldn't if you just talk about it. So, um, so,
Anyway, there's a lot more we could say, but if you're more for some groups and that, but just in terms of the relation to the spinner stuff, maybe to forget about it, to say it that way. It's not that you have to do something quite different if you're going to talk about spinner. Right. OK, now the problem you were working on earlier that you said you weren't sure if it would have a solution and you're finding that it does. What was it in the early part of the conversation what you're working on your research interests?
Well, do you mean, right at the beginning where I'm still what I'm still confused about? Yeah. Okay. It seemed to me that you were saying you're solving the problem. Oh, yes. Yes. I think it could be solved. You're surprised. So this actually I mean, this was actually it goes back to when I was graduate student or postdoc of his first
Occurred to me look, you know, actually, maybe to kind of explain how this all came about. So I was a graduate student at Princeton and I was working on lattice gauge theory. So we're working on this kind of formulation of Yang-Mills theory on a lattice. And so you can actually do computer calculations of it. And so I was trying to understand, you know,
There's a lot of interest in topological effects in Yang-Mills theory, and I was trying to understand how to study those in the kind of numerical calculations on the lattice. And then, so I made some progress on that. But then the next thing that really occurred to me was exactly spinners came up. Besides having Yang-Mills theory on the lattice, we also want to put spinner fields on the lattice. So there's this really beautiful way of putting
gauge fields in the lattice, Yang-Mills theory, which kind of respects the geometric nature of the gauge fields very, very nicely. It's kind of the Wilson's lattice gauge theory. But there isn't, if you try and put spinors in the lattice, a lot of very mysterious things happen. And again, in some sense, the problem is that if you're just looking at this lattice that you've written down, it's clear kind of what the discrete analogs of vectors are and of planes and of
you know, of those things, but it's very, very unclear what the, you know, since you don't really have a good way of thinking about spinners in terms of kind of standard geometry of, you know, lines, planes, etc. You don't really know how to put the spinners and lattice in a way that respects their geometry. And if you try to write down the formulas or do anything, you run into a lot of weird problems. There's a lot of anyway, there's a long story about what happens if you spinners and lattice.
Yeah, so there's one thing you find is that there's no consistent way to put a single kind of fermion in the lattice. That if you try and do it any way you know of doing it produces all these extra versions of the same thing and you have to somehow disentangle those. That's part of the problem. But that's when I started thinking about the geometry of spinners and
some ideas about putting them on the lattice. And then what I was seeing, I started to see that, wait a minute, you know, if you, so this is all happening in Euclidean space where the rotation group is a copy of two SU2s. There's again a left-handed one and a right-handed one, if you like. And what I was seeing really was that the, some of the choices, the geometry I was trying to use to put these things in the lattice gave me kind of
Things occurring and kind of multiplets that had the same SU2 structure as what you see in a generation of electroweak particles. So in a generation of electroweak particles, for instance, you have a neutrino and left-handed neutrinos and you have right-handed and left-handed electrons, for instance.
And those have certain transformation properties under the SU2 and under a U1. And those were the same ones that I was seeing when I was trying to construct these spinners. So it seemed to me, if you can think of part of this rotation group, this SU2, as an internal symmetry, as the symmetry of the weak interactions of the Weinberg's law model, then you could actually
Anyway, you got all sorts of interesting things to happen, but the thing that this, but making this idea work really required that some explanation of why in Euclidean space, what you thought were space-time symmetries that really broke up into half space-time symmetries and half an internal, internal symmetries, which didn't affect space-time. So I never,
This is what, for many years after looking at this, I was like, well, this just can't work. I mean, you can't, if you just look at the whole formalism for how you've set this up and, you know, both of these SC2s have to be space-time symmetries. You can't, they're both going to affect space-time. You can't get away from that. Other people didn't see this as a problem? No, no, I think everybody saw this as a problem. I mean, I think anybody who ever looked at this idea of trying to get
you know one of the part of the four-dimensional rotation symmetry to be an internal symmetry has probably backed away backed away from it for the same reason saying well wait a minute this can't you know i just can't see how that could actually happen that that you have to you're telling me this should be an internal symmetry which doesn't affect space time but looks to me that you're rotating space time with it so you can't do that and so this so this is what um
many years kind of kept me from going back to those ideas. And as I learn more about quantum field theory, actually one motivation as I was teaching this course on quantum field theory and quantum field theory in the back of my mind is, okay, you know, as I go along and teach this course, I may not explain this to the students, but I'm going to very, very carefully look at the formalism and I'm going to understand exactly how this analytic continuation is working of these spinners. And I'm going to
and I'm going to see that it looks like this has to work and I'll finally understand why and then I can stop thinking about this. But as I was teaching this, as I was looking at this, I never actually saw the argument for why this has to be a space observatory. It looked like it had to, but you couldn't quite pin down why.
Anyway, so then when I went back to the twister stuff, I became convinced that if you think about everything in terms of twisters, then the whole twister setup is naturally chirally asymmetric. From the twister point of view, this kind of thing looked a lot more plausible and I got more interested in it again. But it's only very recently, the last few weeks, the last couple of months that I've kind of
I have a very good understanding of exactly why it seemed that why I was right. This should be impossible. There is a standard assumption that you're making, which makes what I wanted to do impossible. But it's also possible to not make that assumption and do something else. And that assumption is? It's the symmetry between right and left. It's kind of when you go between Minkowski and Euclidean,
spinners you know the the setup that you use to analytically continue do you do that in a setup which is um which is right left symmetric and and if you want the setup to be holomorphic then you have to you have to use the right left symmetric one but what i saw so simultaneously i realized yes you can yeah yes i mean this in the standards
There was a very, very good reason that I and everyone is skeptical that this can make sense, but there also there actually is a way around it. You can just decide, OK, I'm going to I'm going to just use right handed spinners and I'm going to and you can get you can get a theory that makes sense. I don't know if I'm jumping ahead, but I recall in one of the lectures that I saw online of you and you were giving the lecture, I believe Cole Fury was in the audience. You're saying that what we have to use are hyper functions.
Yeah. Am I jumping ahead because you're saying it's not going to be holomorphic? No, but actually hyper functions are really part of the holomorphic story. They're not. Hyper functions are really just saying, so what I was saying when I was trying to explain this business about, you know, why about WIC rotation and that things were
That if you write down the standard formulas, you end up with something in the Caskey space time, which is ill defined. Okay. And then you have to use, you have to define it via re-rotation or analytic continuation. There's just another way of saying that more with putting in a more interesting mathematical context is to say that the things that you're looking at him in Caskey space time are not actually normal functions there, or they really are
What they are best thought of as hyper functions. In this case, they're hyper functions which are just kind of boundary values of analytic things as you approach the real line. So the hyper function story is just kind of part of the standard. It's really part of the rotation story. This latest thing I'm trying to do actually gets away from analytic continuation.
You really, I'm really, I'm still kind of, you know, trying to wrap my head around exactly what the implications of this are, but you are, you're not doing the standard sort of analytic continuation anymore. The standard sort of way of analytically continuing, which uses all four space time dimensions, that you're not doing that. You're doing something different and it's unclear.
Yeah, anyway, I mean, if you start writing out formulas, you'll still get the same story with hyper functions. But what prompted you to then go look at twisters? And by the way, is it called a twister formalism or twister formulation? I don't know. Either one is I don't know if those are used interchangeably. I hear, for instance, that there's different quantum formalisms like Vigners or interaction or path or categorical. But then sometimes I hear, yeah, the categorical formulation of quantum mechanics. I'm like, OK, you get the idea.
Well, the thing about twisters is they're not actually... Maybe a good thing to say about twisters is we don't actually know exactly what their relevance is to the real world. If you have a well-developed idea using twisters for describing the real world and you wanted to contrast it to other
similar descriptions you might want to say oh this is the twister formalism or maybe twister formulation i don't know but it's a little bit but either one is a little bit premature in terms of physics that we don't actually know what exactly how the twisters are related to the real world so it's not like you can translate a real world problem to twister formalism and then back well you can so maybe
Twisters are a bit like spinners. They have some of the mathematical properties of spinners, but they do something more interesting. They're kind of a higher dimensional thing. Maybe one of the best things to say about them is that they're very useful. If you want to understand Minkowski's space-time, this is what Einstein figured out. You can use
Minkowski's geometry, Minkowski metric, if you want to talk about vectors and metrics and tensors, or if you talk about Minkowski space-type spinors if you want, that's what I've been most interested in. But the other interesting thing about our theory is when we write them down in Minkowski space-time, theories of massless fields and things like Yang-Mills theory,
They have this bigger invariance group than just under rotations and translations, they're conformally invariant. So the geometry of Christos really comes into its own if you're trying to describe, to understand the properties of space-time under conformal transformations.
Anyway, so that's kind of a motivation. So if you don't care about conformal transformations, you may not be very interested in spinners. But if you really want to understand, you know, what is, how do I write down my theories? And how do I have a version of you, of Mitkowski space time that where the conformal group acts
in a nice linear fashion where everything works out and the spinner, now you can call it a formalism or a formulation, but it's a way of doing conformal geometry. It really comes into its own. So spinners go, I mean, twisters go way back and this really was mainly Roger Penrose is doing in the 60s and he was very interested in using them to understand
You know, things happening in Minkowski's Space Time and especially the conformal invariance of these things. And so there's a huge amount of effort and a lot of beautiful things discovered during the 70s, especially by him and his collaborators in Minkowski's Space Time. And then Atiya realized that you could take this over and do some very, very interesting things in
Romani and geometry and Euclidean space time. Yeah, so I was you know, I kind of learned about this geometry the response that sentence could be said about a Tia in the most general form and then a Tia realized you could use this for underscore with geometry. Yeah. Yeah. Yeah. So it's but anyways, so I've been kind of aware about twisters for a long time, but I, you know, I didn't see
Anyway, I actually wrote a very speculative paper a long, long, long ago about this, and it mentioned the connection to twisters, but there's just a lot about them that I didn't understand back then. It took me many years to understand, and especially the relationship between Euclidean signature and Mancassi signature spinners, how they're related. That's quite a tricky story, which would take me a long time to understand. So you have the splinter in your
thumb for decades about the space-time symmetries and them acting not just on space-time. What happened in 2020 and 2021? One thing that happened in 2020 was COVID. In your mind, what happened in 2019 then? No, but this is actually relevant because actually in 2020, I was much more
And I was thinking of this stuff, but yeah, but yeah, but in 2020, all of a sudden, you're kind of, you know, you're at home, you're at home a lot that you're just sitting there and I office at home and I don't have a lot of all the usual distractions or whatever. And so and so that actually actually gave me some of the more time to kind of think peacefully about about some of this stuff and make some and make some progress. Yeah. So I'd have to, I mean, I,
How does it fit? Is there a way of explaining it? Maybe the best thing to say about Twister theory is that it really
It really kind of naturally wants to be a theory of complex space-time. And this is the thing, if you say I'm going to study four dimensional complex space-time and I'm interested in its conformal group and things like that, then the Twister story is actually very, very simple. You're basically just saying that there's a four complex dimensional space and a point in space-time is a complex two-plane in that four dimensional space. So points
Anyway, yeah, so instead of thinking of the way of normal thinking of some space with these points where you got to think about just think about the complex two planes and complex four dimensional space and and you know everything is kind of drops out of that and and that there is one there's a beautiful relation of that story to the theory of spinners is that and this is kind of the relationship between the theory of twistered and theory of spinners
In twister theory, a point in four-dimensional space-time is a complex two-plane. That's the definition of what a point is. But that complex two-plane, that kind of tautologically answers the question of where do these spinners come from? Because the space of spinners is a complex two-plane. So from the standard point of view,
As I was saying, if you just think about the diffeomorphism group, it's very, very hard to even say what a spinner is. So where are these weird complex two planes coming from? Well, from the point of view of twister theory, it's purely tautological. It's just, you know, the two plane is a point. So the spinner, the spin one half two plane, complex two plane, which is describing the spin of an electron is exactly
That's exactly what the definition of a point is. A point in twister space or a point in space-time? A point in space-time. Twister space is a four complex dimensional thing. The points in it correspond to various structures in space-time, but the complex two planes in it correspond to the points in space-time. That's one of the basic
Yeah, so then is the statement that the points in space time are the same as spinners or the points in space time or the structure of space time gives rise to the structure of spinners and vice versa or are none of those statements correct? I think both of them. I mean, it really is telling you twister theory is really telling you that it's a it's a way of thinking about space time in which
And sorry, this is four dimensional space-time. Four dimensional space-time, yeah. Yeah, yeah, yeah. It's a way of thinking about, yeah, so Twister theory is very, very special to four dimensions. It doesn't really work in other dimensions. But it really is, it's a way of thinking about space-time in which, you know, the occurrence of spinners and their properties are just completely tautological. They're just built into the very definitions. Sociologically, why do you think it is that Penrose's Twister program
Firstly has been allowed to continue because many other programs just die out if you're not loop or string or causal or asymptotic. Like there's just four as far as I can tell. Five with Penrose. So why is it alive? And then why hasn't it caught on? Well, for I mean, or maybe you disagree, it's not alive. No, no, no, it's very much it's very much alive. It's very much alive and still. But and so there's an interesting kind of history. But but a lot of it was really
So he had this idea and he's raised places to explain how he came up with it and he was very, very struck by this. And so he quite successfully at Oxford built up a group of people working on this. And so it was a good example of how normal science kind of works sociologically. Somebody comes up with a good idea and they actually build a group of people around them and
People do as people do more work, they learn more interesting things about this more people get interested. So, you know, he always, you know, throughout the 70s, I would say into the 80s, there always was a quite healthy group of people, you know, working on Penrose or people somehow having some relation to Penrose collaborators were working on this. So it was anyways, but perfectly normal science. It wasn't it wasn't so clear, though, how to get
Some things were very clear. Some things were clear that this was really a beautiful way of writing down conformally invariant wave equations and studying their properties. The beauty of the idea and the power to do certain things was known, but it didn't seem to be necessary or have any particular connection to specific problems in particle physics. Particle physicists would look at this and say, well, that's nice, but
You know, I don't, that doesn't actually tell me anything. You know, if I need, if I needed to do some conformally invariant calculations, I might be able to use that, but it's not actually telling me something really that, you know, really knew I can't get elsewhere. Um, and, and then, you know, and then in the eighties, you also had, uh, you know, a Tia got into the game and there's a lot, a lot of mathematicians got into it through the, um, the relations to the, on the Euclidean side. So, you know, it was, uh,
Especially among mathematicians, mathematical physicists, it remained a very active area and it still is to this day. A lot of it was based in Oxford but also a lot of other places. But in terms of its implications for physics, I would say the thing that
I think Penrose and his people trying to connect this to physics in an interesting way, they kind of ran out of new ideas or some things that they could do, but they couldn't actually get any kind of really killer app if you like. From my point of view, I don't know if I can, I think
Anyway, I don't know if I'll ever be able to convince them or what they think of it these days. But the problem was that they were thinking of connecting this to physics purely from the Minkowski spacetime side. So they're looking at Minkowski spacetime twisters, Minkowski spacetime spinners. And those, the twister theory just didn't, if you just look at Minkowski spacetime, you don't see
You don't see the sort of new things, which I'm finding interesting, which I think tell you something new about particle physics. You don't see this kind of internal, the fact that one of these factors can be an internal symmetry. You just can't see that in Mikowski's space time. And then there's some other more technical things about, better not get into that, but there's kind of a
Well, it's okay. The audience is generally extremely educated in physics and math. Yeah, I would actually, well, maybe to connect this to what I'm saying, right, is I think, you know, also the way people think about general relativity in, I mean, Caskey's signature, general relativity is not a chiral theory. It's supposed to be left right invariant, parity symmetric theory. So the problem with thinking about general relativity in terms of twisters
is that your setup is completely chiral. If you try and do gravity with it, you end up with something that's not quite the right theory of gravity. It's kind of a chiral version of gravity. Anyway, this is a very interesting story. I think Penrose always referred to this as the googly problem. Something about cricket. In cricket, there's something about how
You can see from my point of view that was always
That's evidence of exactly what I'm trying to say now that, well, space-time is right-handed. Yes. Yeah. So it's a related problem. So Penrose and the people around him, I think, put a lot of effort into trying to revamp twister theory into something chirally symmetric. Now, why would they want to do that if the standard model isn't? Well, they weren't really trying to describe the standard model. They never really have it.
They thought twisters were a way of thinking about space-time, so they wanted to do general relativity. And general relativity is not a chiral theory. So they were trying to find kind of a, how do we get rid of all this chirality? And they never were really successful at that. So you're saying it's a pro, not a con. Yeah, exactly. It's a feature, not a bug. Yeah. Right, right. But one interesting, fun thing about the sociology, though, is that what...
The idea that you could use twisters to do general relativity and perhaps quantize it, that was always something which Penrose and his people were working on. But most physicists, I think, felt that wasn't really going anywhere. This wasn't going to work. And maybe Witten was an example of somebody, I think, who really could see the mathematical power of these ideas and how important they were as new ideas about geometry.
Again, that's a general statement that can be said, and then Ed Witten saw the power of this mathematics, dot, dot, dot. Yeah. I'll say so he I think even going back to a postdoc, he had learned about twisters, he was trying to do some things with it. But um, but he never kind of but he that he that actually finally finally found something and this was about 20 years ago. And what became known as the twister string. So we actually became he found a way of kind of writing
Yeah, a different way of writing down the perturbed calculations in Yang-Mills in terms of a sort of string theory, except it's a very different kind of string theory than the one that's supposed to be the theory of everything. And it's a theory where the string lives in twister space. So Ritten wrote this really kind of beautiful, very, very beautiful paper about twister string theory. And so since Whitten is talking about twisters, of course, all of a sudden there's a lot of
Physicists who were never had anything good to say about twisters all of a sudden are rushing out to learn about twisters. There's been an ongoing story of this twister string story which is a lot of people have done a lot of things but again a lot of it hasn't really worked out the way people
Well, like, and for the same reason as Pender, that Pender's always had that the people are trying to find quantize a chirally version, a chirally symmetric version of general relativity using this thing. And that's not what it really wants to do. So anyway, but that's kind of that's sociologically very important about why most high energy physicists, you know, have more have heard about twisters and don't and often have nice things to say about them is because of the twister string.
There are quite a few questions that I have. One is, the particle physicists' repudiation of twister theory or just distancing from it because it's not useful to them, is that something that they also slung at string theory or were they more embracing of it? Earlier you said that the particle physicists
weren't initially adopting string theory, sorry, twister theory, because it didn't provide them with anything that's new. You said, well, okay, if we need to do some conformally invariant calculation, we'll use twister theory. Yeah. But at the same time, string theory is known, or at least colloquially known for not producing what's useful to high energy physicists, but useful outside of high energy physics, like to mathematics, or maybe condensed matter physics.
What I'm asking is around the same time when they were distancing themselves from twister theory, you're not using it. Were they then embracing of string theory or they gave the same critique? Well, okay, so we have to you should start talking about string theory. Yeah, that's a kind of a complex, this kind of complex story. And it has the whole story of particle physics and string theory. That that's pretty well pretty much completely disconnected from from twisters because
The issues about why people were doing string theory or why they might or might not want to do string theory really had nothing to do with twisters. Twisters is a speculative geometric framework, and then twisters make a small appearance due to Whitten at one point 20 years ago, but that's about it.
Maybe we can start talking about the whole string theory and particle physics business, but I'm not twister. Anyway, just twisters. It seems like a bad place to start. I'm not trying to mix up twisters with it. What I just meant to say was it's interesting what gets accepted and what doesn't. Yeah. And so why was string theory accepted? Take us through the history of that. And also you could tell people who may have just heard the term, the name, sorry, Ed Whitten, but all they know about him is that he's a genius, but they don't realize that influence that he has.
This is a good place to start. Witten is really central to this story. I think the short summary of the history of this subject of particle physics was that by 1973, you had this thing called the Standard Model, which was this incredibly successful way of talking about particle physics and capturing everything that you see in
When you do high energy physics experiments, and the story, you know, when I kind of came in, it feels like I went to start learning about, probably started reading books and things about what's happening in particle physics, probably right around the mid, late 70s, mid 70s. I went to college in 75 and I spent most of my college career, a lot of it learning about the standard model and this stuff. And then, so by, but by the time I left grad,
Grad school, by the time I left college, 1979, and I went to graduate school at Princeton, people were starting to get, people had now spent, let's say just six years, let's say, trying to figure out how to do better than the standard model. And one thing is how to find some kind of new
Anyway, how to do better the standard model as a theory of particle physics, but also but one thing is the standard model doesn't give you a quantum theory of gravity. So the other thing was, how do we get a quantum theory of gravity? So these were kind of the big problems are already in the air. And Witten, you know, so Witten is a genius and he had been a grad student at Princeton. He actually came to Harvard as a postdoc, I think in 77, 78. And I met him when he was actually was a postdoc.
And he quickly started doing some really amazing things. I went to Princeton in 79. A year or two later, he went directly from a postdoc at Harvard to becoming a full professor at Princeton, becoming a professor at Princeton very quickly, and he was there. And so the years I was in Princeton as a graduate student were from 79 to 84, and those were years
People I think were getting more and more frustrated. There were lots of ideas coming up, but every idea that people kind of tried to do better than the standard model or maybe to quantize gravity really didn't quite work. And people were kind of cycling every six months through. There's some new idea, you'd work on it for six months or a year and people start to realize, well, this doesn't really do what we want to do, let's find something else. So there were a lot of new ideas, but nothing
There was this idea that was very unpopular, that very few people were working on, to try to quantize gravity and unify it with the particle physics through string theory. And so it was people like John Schwartz and Michael Green were working on this, but it was a very small group of people.
There wasn't much attention being paid to that. But Winton was paying attention. I think one thing to say about him is that besides being very, very smart, he's also somebody who can read people's ideas or talk to them and absorb new ideas very, very quickly. So he was also spending a lot of time looking around trying to see what other ideas are either out there. And this was one that he got interested in.
But for various reasons, technical reasons, he thought, you know, there's a technical reason, so-called anomaly calculations about why this is not going to work out. And what happened right in the fall of 84, I actually went to as a postdoc to Stony Brook. And right around that time, Green and Schwartz had done this calculation that showed that these anomalies canceled except
There's some specific case where these anomalies canceled. Witten then became very excited about the idea that you could use in that specific case of this so-called super string theory. Witten heard about this and said, the reason I had my mind why super string theory couldn't work as a unified theory
And now it looks like maybe you can get around that. So he kind of then started working full time on trying to, you know, come up with models or understand SuperStream models that you could use to do unification. And so throughout kind of, I was now at Stony Brook, but I was kind of hearing reports of what's going on at Princeton and throughout late 84, 85, 86, this was, you know, Witten and the people around him, this is what they were working on. And they were, you know,
They had a very specific picture in mind. It was that the super string only is consistent in 10 dimensions, so you can get rid of four of them by the so-called Calabi-Yau Compactification and hopefully there's only a few of these Calabi-Yau's and one of those is going to describe the real world and we're going to have this wonderful, beautiful, unified theory using this kind of six-dimensional geometry of Calabi-Yau's and we're going to have it within the next year or two. That was the way they were thinking.
and you know a lot of the people you know friends and colleagues of mine who you know were doing kind of the thing that you would often do is go down and go you know when you're in Princeton go talk to Whitten and say here's here's what I'm working on you know can you what do you think about this and I got several of them reported back to me yeah you know I went down to Princeton I talked to Whitten and
he said well you know what you're working on that's all very nice well and good but you know you really should be working on string theory because that's actually you know where all the action is and that's really and you know we're almost going to have the theory of everything there and you kind of work on string theory so you know this just had a huge effect so and um and this was called the so-called first super string revolution and you know uh there's kind of there's a story over the next five or ten years of how you know
People were brought into this field and some people were always skeptical, but it gained more and more influence and became institutionalized during the decade after that. In some sense, the weird thing that's hard to understand in strength theory is why once it became clear these ideas really weren't working out, why didn't this just fall by the wayside and people go and do something else?
So what do you see as the main physics, physical problem or even mathematical problem of string theory? Do you see it as, well, how do we search this landscape or how do we find the right manifold, the six dimensional Taylor manifold? Yeah, I think that was always the thing that bothered me about it from the beginning, which I think is the fundamental problem.
And it's a fundamental problem whenever you decide to use higher dimensional Riemannian geometry. I mean, this actually goes back to Einstein, Einstein and these Clutes of Klein models. People have often said, okay, well, we had this beautiful theory of four-dimensional geometry in Einstein's general relativity, and we had this particle physics stuff going on, which seems to have some interesting geometry to it, so let's just add some dimensions and
and write down a theory in five or seven or ten or whatever dimensions and then do geometry there and that's going to solve and that's going to be the unified theory so I mean this is sort of thing Einstein was thinking about but um if you start thinking about this the problem is you realize that these kind of internal dimensions that the the geometry of particle physics and the geometry of special relativity are quite different they're not um
You know, there are these metric degrees of freedom in four dimensions. And if you try and you don't really have those in like in the standard model, you just have things like that. So if you put those sort of dynamical variables into there, the ability for these for these other dimensions by the four went to all the you have a vast
You've hugely increased the number of degrees of freedom and you have a theory where you have to now explain why all this extra geometry which you've put in there and which you're only trying to get a kind of small kind of very rigid kind of couple pieces of information out. Why are all these infinite number of degrees of freedom? How can you just ignore them? You have to find the dynamics
Consistent dynamics for them and then you and that consistent dynamics has to explain why you don't see them Yeah, and and so that's always been the problem with like Kaluza Klein models and with Any kind of extradimensional models and and string theory just kind of has this problem in spades in here You know your instead of feel sort of point particles you have springs They have a huge number of new degrees of freedom You have to say that well the string vibrations are all happening at such high energy as we can't see them and
and then they're trying to use the fact that superstrings have very special properties in 10 dimensions and they're trying to use that to argue that our strings are moving in 10 dimensions and that 4 are the ones we see and 6 are going to be described particle physics. It becomes a very complicated theory you have to write down
in order to kind of make any of this work and make any of this look like physics. And from the beginning, there was kind of no story about why is anything that looks like the real world going to drop out of this? And why that? And that's still the case 40 years later. And the whole thing just suffers from this problem that you don't
You don't actually have the theory. When you say that you have a string theory and people say, oh, we have this mathematically elegant, well-defined, unique theory, they're talking about that's not a full theory. That's a perturbative limit of a theory. And so what they really need in order to answer the questions they want to answer is they need something more general, a non-perturbative kind of general version of string theory.
Sometimes people, we all call it M theory. So if you want, we can call it M theory and they need an M theory and nobody knows what M theory is. No one has come up. You can write down a list of properties that, you know, M theory is supposed to be some theory with this list of properties, but you can't actually write down a theory. And so on the one hand, you don't actually have a real theory that you can nail down and say, this is a theory, we're going to solve it and look at the solutions and see if they look like the real world.
So what you what people end up doing is saying, well, we don't really know what the theory is. Let's assume that but it seems that maybe there's one that has some properties that look like the real world. So let's work with that and and then try to constrain, see what constraints we can get out of it will tell us, you know, are we seeing something like the real world? And then they just end up finding that, no, there aren't really useful constraints that you can get almost anything out of it. So you get this landscape of all possibilities. Yes, yes.
and then you know twenty years ago things got very weird when people just started say well you know instead of saying that normally if you have a theory it can't predict anything because you know almost everything is a solution to it you say okay well that was a bad idea and you move on but instead you saw people saying oh well that's it just means the real world is you know all of these possible things exist in the real world the multiverse and yeah and just for
You know, for anthropic reasons, we happen to live in this random one. And, you know, I mean, anyway, it's the fact that anyone ever took any of that seriously is just still kind of, I don't have any explanation for it. It's just, yeah. Okay. So to summarize, somewhere around, this is not a part of the story that was said, but somewhere around the 1960s, some amplitude called the Veneziano, I think, Veneziano. I don't know how to pronounce it. Just read it.
That was the first inklings of string theory and it had to do was come up with because of the strong force. They were trying to solve something that it was forgotten about. And then around the 1980s, there were some other problems with string theory that were solved. And so this is the Green Shorts anomaly cancellation. Yeah. And then some people say that that was the first revolution. But it's also more accurate to say that that precipitated Ed Witten to take it seriously. And then that's what precipitated the first string revolution. Yeah.
Okay, then from there, then you realize that there are different ways that something like five to the 100 or 10 to the 500 or some extreme amount that if you're to do some calculation, all those books behind you, the amount of words ever written, not just books ever published, words ever written, I think easily letters ever written, like single letters, it would be like saying find this one letter,
Well, that...
Actually, maybe go back to one thing and say, yeah, so this is one part of the story I didn't say is that your string theory had originally come out as a potential theory of the strong interactions. And that actually was one reason Winton, I think, was looking at it is that so one of the open problems that the standard model left open was, how do you solve the strong? We have this strong interaction theory, but how do you solve it? And it looked like maybe you could you could use the old ideas about strings to solve it and
I actually spent a lot of time learning about strings as a graduate student because of that and I was ready to win. But the problem with this kind of multiplicity of solutions of string theory is that it's not just that there are too many of them, it's just that you don't actually have a definition of the problem. This kind of drives me crazy. People often talk about, well, the problem is that we don't know how to put a measure on the space of solutions
a string theory. And if we could put a measure that we could figure out, you know, maybe it's concentrated someplace, right? And that would be great. But I keep pointing out that the problem is not that you don't have a measure of the space. The problem is that you have no idea what the space is. As I was saying, you know, to even define what a string theory solution is, requires knowing precisely what M theory is. You don't know it. There are no equations anyone could write down, which
If we were smart enough and could find all the solutions to this, these are all the solutions to string theory. You just don't have that. So all of the things that you do have, like you can go out and say, well, maybe it's these gadgets and you have 10 in the 500 of them or whatever. Those are all just kind of cooked together possible approximations to what you think might be a string theory solution.
There are solutions to some equations you've written down, which are not the equations of string theory. There's something you wrote down and think maybe these things have something to do with string theory. So the problem is much worse than any of these practical problems of there's too many of these things. And now it's become kind of an industry that, well, let's apply machine learning techniques to this. You're just applying
Does this frustrate you? Yes. This data is garbage. You basically do not actually know what your problem is so you're cooking up something which you can feed to a computer but it actually is known to be garbage and you're doing processing on this and producing more garbage and getting grants to do this and going around telling people that you're looking for the
Or the universe. I mean, it's real. That's just utter nonsense. I'm sorry. Many people don't know because they don't know the history. But since 2010s, it's become somewhat cool to dunk on string theory, at least in the popular press. Maybe not inside academia. But you were alone. You and Lee Smolin were lone wolves. Early lone wolves. Yeah, yeah. Can you talk about that and talk about some of the flak you took? Maybe still take?
Yeah, anyway, it was certainly a very strange experience, a very strange time. But, you know, I think the thing to say is that, you know, throughout, you know, I was never, I was always fairly skeptical about string theory, but, you know, initially for many years, my attitude was, well, you know,
Who knows? It's certainly very smart. These people are going to, sooner or later, they'll figure out for themselves, either they'll figure out this works or they'll do something else. But then, just as time went by, years went by, and this was just not happening. You had more and more popular books. I have to confess, maybe in some sense, it's somewhat of a reaction to Brian Greene, who is my friend and colleague here at Columbia. He did a very, very good job with PBS specials convincing
the world that this was a successful, this was an idea on the way to success when it really wasn't. So I thought, okay, well, somebody should sit down and write a book about what the real situation here is. And it's not like when I talk to people privately about this,
You know, I would say that people who are not string theorists mostly would, would, would say, yeah, you know, yeah, you're probably right. This is not, this doesn't seem to be going anywhere, but you know, whatever. And then the, um, and people, and when I talked to string theorists, I have plenty of string theorist friends, they would often say, yeah, you know, yeah, there are a lot of huge problems and we, we just, we don't really know anything better to do right now. So we're going to keep doing this, but yeah, yeah. All these problems you're pointing out are really, uh, uh, yeah, they're real. And, um, so what's wrong with that?
Well, the weird thing I think was this disjunction between the private opinions of people, what people were saying to each other privately, and what you were saying in the popular press. One aspect of this was people not wanting to publicly criticize something.
I think the subject became more and more ideological and the string theorists started to feel kind of in battle. They were very well aware that a lot of their colleagues thought what they were doing was not working. On the other hand, they became more defensive and a lot of people I think felt
would tell me, yeah, I agree with a lot of your saying, but yeah, but don't quote me on this publicly. I don't want to get involved in that mess and alienating a lot of my colleagues. Anyway, I have this weird status that I'm actually in a math department, not a physics department. I don't have a lot of the same reasons that you don't want to
I spent a lot of time thinking about this stuff. I started writing this in around 2002, 2003. The book was finally published. It was a long story, but it finally got published in 2006. In the meantime, Lee Smolin had been writing
a book. He was coming from a different direction. Trouble with physics? Yeah, the trouble with physics. And he had his own motivation. So it was trying to write something I think more general and sociological, but with this as an example. And I think the way he describes it, the example kind of took over the general theory. And so he ended up also writing a book about string theory. And the books ended up coming out at the same time, which I think
You know, it was kind of a force multiplier there that, you know, people, if one person is writing a book, which says, well, you know, a lot of the things you're hearing, you're hearing are not right. Or people say, well, that's just one person's opinion. But if two people do it, I think everybody's like, oh, you know, there must be something to this. And so I think that the combination of the two books, I think it did have a lot of effect on them. It did make a lot of people realize there was a problem here.
It made a lot of the string theories much more defensive. It also caused a lot of young people thinking of doing string theory or people doing string theory to decide to move on to something else. People very often tell me about effects this book had on them or other people they knew in terms of their decisions about what to do with their research or their career. The book is called Not Even Wrong, the links to
All resources mentioned will be in the description, including this book. So you mentioned that your colleagues would talk to you privately and then they would say something else to the popular press. Now, when you say popular press, are you also including grant agencies with that, like just the public in general? Because it's not just a popular science issue. It's also a grant issue where the money goes. Yeah. So it's not just the popular press. And to be clear, I should say it's not that they would say one thing, one place. It's just,
they would carefully just not say, you know, that there are things that they would say in conversation with me or I think in conversations with other people, not just me, that they would just say, okay, this is not something that, okay, sin of commission versus omission. Yeah, it's not like they were going out and saying, oh, strength theory is going great. It's just that, you know, anyway, they were, they were, they were not kind of, they were not saying this is really appears to be a failure. But, uh,
Yeah, but you're right. This issue kind of occurs at all levels from the very, very popular press, from kind of television specials to more serious popular press, what gets into Scientific American, what gets into now we have
quantum magazine, which are more serious parts of the press aimed more at the public, all the way down to exactly what do you write in grant proposals, whatever, or if you're trying to explain to some kind of funding person or something about what's going on in your subject.
What do you say about string theory? I think everybody, whatever you're working on, you're often forced by this business of getting your students a job or getting a grant to go right up to the boundary of what's defensible and being optimistic about what you're doing. That's what string theorists have certainly
always been always been doing you can argue you know in many cases it's not different than what other other scientists do but it's um i think the thing which i had i have to say i have found more and more disturbing the reaction of and and it started when my book came out and i think we smell it is some reaction the um.
I think both of us were expecting a much more serious intellectual response to the issues we were raising. We were raising serious technical questions and we were getting back personal attacks. From people in the community or from the public? From people in the community.
You know what you're getting from people who don't in the public don't know much about this year, you're getting some completely random combination of people who are annoyed because you're saying something different than what they heard and other people who become your fan because you're saying something different. And so you end up with a huge number of fans who you don't necessarily want as your fans. But anyway, the yeah, so both of us were expecting, you know, that, you know, we put a lot of effort into making a
You know a serious intellectual case about what these problems were and instead of getting a serious response we were getting You know, you know these kind of personal attacks of how dare you say this and so for instance, you know There's one prominent blogger who says who would write these endless blog entries about what's wrong with peter white and what he's doing and and at some point I was trying to respond to these and at some point I realized you know
What this guy's talking about is nothing to do with what I actually wrote in my book. And then he actually kind of publicly admitted that he refuses to read the book. So anyway, this kind of blew my mind. How can you be an academic and engaged in academic discussion, intellectual issues, and you're spending all this time arguing about a book and you're refusing to read it? I mean, how is this really crazy?
And that was a string theorist or just a colleague? A string theorist, yeah. Speaking of Brian Greene. Oh, sorry, continue please. Yeah, no, it wasn't Brian Greene. No, no, no. I didn't mean to suggest that. No, no, no. But anyway, that's just one example. And I think this is an ongoing, I think, disturbing situation that people are just not, people are kind of
defending that field and continued and researched there with just kind of refusing to acknowledge the problems or to have kind of serious discussions of it. I think you're on your last thing with Edward Frankel. I think it's kind of funny because I know him and I actually was out visiting him in Berkeley in June or something and we're talking about things and he told me, oh, Peter, I'm going to go to the strings conference and it's the first time I've been to a strings conference.
He knows all these people and he knows a lot about the story and I think he knows me well enough.
I'm not a complete fool and I have a somewhat serious point of view, but maybe I'm really a bit too extreme about this. But then he went to this conference and then after when it comes back, he gives me a call and says, Peter, I didn't realize how bad it really was. You're right. This really is as bad as you've been saying. So anyway. What was bad? The exuberance of the young people or the old people telling
misleading the younger people into a useless pit or like what was what was bad? Yes, it is as bad as you say. Well, I think what's what's bad is it is really just this kind of this kind of refusal to admit I mean, this is a field which influxes serious problems, things have not worked out, these ideas really have failed to work. And instead of admitting that some ideas have failed and moving on, people will just kind of
keep acting as if that's not true. Sorry to interrupt. I'm so sorry. So why would Edward expect an admittance of the failure of string theory at a strings conference? I think one thing to say, part of the story about him is he's a mathematician. So mathematicians, if you do mathematics, the one thing you have to be completely clear about is
What you understand and what you don't understand and what is a wrong idea and what is a right idea? You know, and if something doesn't work and is wrong you have to You can't play a game. You cannot play any games about this This is you know, you have to admit that this is wrong and so I think especially for mathematicians to come in and see an environment where there's you know The kind of guiding
ideas that people haven't really worked out and a lot of things are known, do not work for known reasons, but people are still kind of acting as if this is not true and trying to figure out how to kind of do something and make career for themselves in this environment. I think he recognized that, but part of it is mathematics is a very unusual subject. Things really are wrong or right and you're
You absolutely cannot seriously make progress on the subject unless you recognize that. Mathematicians are also much more used to being wrong. One of my colleagues, John Morgan, likes to say that mathematics is the only subject he knows of where if two people
Disagree about something and they each think the other is wrong They'll go into a room and sit down and talk about it and then they'll emerge from the room with one of them having admitted He was wrong. The other one was right and that this is just not it's not a normal human behavior, but it's something that is part of the mathematical culture earlier I said speaking of Brian Green and what I meant was I had a conversation with Brian Green about
Almost a year ago now. And I mentioned, yeah, so Peter White has a potential toe Euclidean twister unification. And then he said, Oh, does he? Oh, I didn't know. He is in your university, not to put you on the spot. But why is that? Well, it said aloud, I don't think it's true by the professor of physics, mainly who studies string theory. Well, there's so many proposals for toes.
Yeah, there are proposals in your inbox, but there aren't serious proposals by other professors. There aren't that many serious proposals of things of everything, at least not on a monthly basis. Well, I mean, I mean, this is this really doesn't mean anything in particular to do with Brian, you could you could ask, you know, since, you know, people on this subject,
Yeah, in principle should be interested in this. There's I've gotten very little reaction from from physicists to this. And in some sense, it's kind of clear, clear why I mean, they're, you know, I wrote this, I wrote this paper, I've read about the blog, and you know, I've gotten no reaction in both cases, I don't have reaction from people writing, telling me that I've talked to about or saying, oh, you know, this is this
This is wrong, this can't work for this reason. I think this is very much the problem with the paper that I wrote about this. It uses some quite tricky understanding of how twisters work and twister geometry works, which is something that very few physicists have. So Brian
I'd be completely shocked if Brian actually really understood some of the things going on with twisters that I'm talking about. And the problem, I think, for anybody who then, if somebody comes to you and says, oh, I have this great idea, it involves these subtleties of twister theory, and you're like, well,
you know i'm really not in the mood to spend a week or so sitting down trying to understand as subtle as a twister theory so i think you know maybe i'll just nod my head politely and and and go on go on my way that's part of it and then part of it is also that a lot of you know this is very much expected at work in progress you know i'm seeing a lot of very interesting things happening here but i'm not um i in no sense have completely understood what's going on or or have the kind of uh you know
understanding of this where you can write this down and people really can follow exactly what's going on. It's not too surprising. I haven't got that much. I can see why I understand the typical reaction to this. Brian is somewhat of a special case because he also actually is very
I think I actually he actually a lot of his effort is as good as in recent years has gone into other things especially the I mean the World Science Foundation Festival I think is now more or less uh you know it's kind of most it's mostly brian green at this point yeah and then it's uh so he's anyway he's thinking about other things um and and I have very I don't have very little contact with people in the physics department I mean they're mostly thinking about very different things and
Here at Columbia, but it's true essentially everywhere else that the, you know, the mathematicians and physicists really don't talk to each other. They're really separate silos, separate languages, separate cultures and, you know, places where you have kind of mathematicians and physicists and kind of active and high level interaction with each other is very unusual. It doesn't happen very much.
I have a couple of questions again. I'll say two of them just so I don't forget them and then we can take them in whichever order you like. So one of the questions is how slash why did you get placed into the math department? Because that's one question. And then another one is you mentioned earlier that Witten has this power to survey a vast number of people and extract the ideas at great speed. And so a large part of that is raw IQ, like sheer intellect. But is there something else that he employs like a technique that you think others can emulate?
I imagine if Whitten was to read your paper, he would understand it. And I imagine that he would say, Oh, he would see the benefit of it. And maybe the application to string theory, or maybe it offshoots in its own direction. But anyhow, so those are two separate questions, one about Whitten, and then one about you and the department you're in. Okay, yeah, I've got the other two. But let me start.
Let me just say something quickly about Witten, just saying about having dealt with him over the years. One thing I find very interesting about him is just, he travels around a lot, but let's just say his way of socializing is to, if he's come to a department and he's at tea or whatever, and he's introduced anybody
He almost immediately will ask me, okay, well, what are you working on? Explain it to me. Anyway, that's a lot of what he's done over the years has just been trying to really be aware. Anyway, I've said what I've been doing and tried to get him interested. He's
Anyway, we'll see where that goes. Maybe I'll have more success with it with this new paper, maybe not. But he's responded though, or no? He has responded. But it's more that he's kind of looked at it. He actually the first version, he actually made some technical comments more about the beginning of it. But I think he didn't engage with most of what I was talking about. We're going to get back to the math question soon, the math department question. But do you think a part of that is because there's a sour taste
given your book? Yeah, yeah. I mean, I'm not, I mean, I'm, again, I've known him since I was an undergraduate. You know, I think, you know, he's, I think he's aware, you know, that this guy is not an idiot, but, but he's also, I'm also not his favorite person in terms of kind of, you know, the impact I've had on his, on his subject. And yeah. And I think, you know, he also, I think he understands it's not personal, but you know, it's not, it's very hard to deal with somebody who's kind of,
You know, been this kind of main figure, kind of telling the world that the thing that you think is your main accomplishment in life is wrong. So this is not, yeah. Anyway, I'm not his favorite guy, but anyway, I can, we're still, it's fine. Yeah. I think he's a very, you know, anyway, he's a very ethical and great. And I think when I complained a lot of, a lot of, most of the worst of what the kind of
and this kind of pushing of string theory in ways which really were completely indefensible. He's rarely been the worst offender in that. That's really more other people than him. But yeah, he's a true believer. He's really enthusiastic about it. So to get back to my own personal story, I got a postdoc at the Stony Brook Institute for Theoretical Physics in 84.
I was there for four years and that was in the Physics Institute. But the Physics Institute was right above, it's the same building as the math building. And the things I was interested in, I was trying to stay away from string theory and I was interested in some other things. And I was often talking and I was trying to learn a lot of mathematics. I was trying to learn more mathematics to see if I could make any progress on these other problems. So I spent a lot of time talking to the mathematicians in Stony Brook.
And some of them, you know, there are some really great geometers. There are some really great mathematicians and I learned a lot from them. And it was a, that was a great experience. But at the end of four years there, you know, I needed another job. I did set out some applications for postdocs and physics, but the, I would say that that was kind of the height of the excitement over string theory. And especially somebody like me saying, you know, I'm really interested in doing something about the mathematics and physics, about applying mathematics, physics, but I don't want to do string theory.
That was not going to get any kind of reasonable kind of job that way. That's just not going to happen. I ended up realizing, well, maybe the better thing, I'll have better luck in a math department. I ended up spending a year in Cambridge as an unpaid visitor at Harvard, partly, and I was also teaching calculus at Tufts.
so then i have some kind of credential okay well at least this guy can teach calculus and so and i and i applied for a one-year postdoc at uh the math institute in berkeley msri and i i got that and so i spent a year is that how you got to know edward um no no he wasn't uh that was before him yeah i mean he would have still been he would have been at harvard at a much more junior person yeah yeah yeah he came to berkeley later you know that that was like 80
88-89. But that was an amazing, that was actually a fascinating year because that was the year that Witten had come out, Witten had kind of dropped string theory for a while and was doing this topological quantum field theory stuff in Chern Simon's theory and he was doing the stuff which won him the Fields Medal and you know it was just
just mind-blowing bringing together of ideas about mathematics and quantum field theory and so most of the year was devoted to learning about that and thinking about that and you know Witten came and visited and Atiya was there and I actually had a lot of chance to talk to him which was wonderful and so that was a really fascinating year at MSRI but and partly because so much of this was going on you know
math departments were more interested in hiring somebody like me even though I didn't have the usual credentials because they felt this is somebody who actually understands this new subject which is having a lot of impact on our field. So Columbia hired me to this non-tenured track for your position and so I was to that I was teaching here and after a few years again I was getting the point okay well now I got to find another job but and they
So the department needed somebody to, they'd set up a position for somebody to teach a course and maintain the computer system. And I said, well, you know, I could probably do that and that's not a bad job. And so I ended up
uh, agreeing, agreeing to take on that position. And that's, that's, uh, that's always been kind of a renewable position. It's not tenured, but it's, um, essentially permanent, renewable. And I've gone through various kinds of titles of various kinds of versions of that since I've been since the nineties. And it's, it's worked out very well for me. I'm actually quite happy with how it's worked, but it's a very unusual career path. And it,
It has given me a lot of insulation from the normal kind of pressures to perform in certain ways and to do certain things allowed me to get away with all sorts of things if you like.
Like what? Well, like writing a book called Not Even Wrong explaining what's wrong with
How did that come about? So, for instance, this is going to be incorrect because I'm just making this up, but then correct it. For instance, you're walking along someday, you have this idea, maybe it's a splinter in your thumb for a different reason.
About string theory. So then you go to a publisher and you say it or you say to a journalist and then the journalist hears and they say you should write a book and you say, maybe then you think about it. You start writing a chapter, the nitty gritty details. How does that happen? How did it go from Peter White mathematics professor to then writing this popular book? Um, well, so, so yeah, throughout, let's say throughout the nineties, you know, I was very much, um, you know,
I was interested in the same kind of questions. Can you do different things in math and physics? I was trying to follow what's going on in physics. I've been trying to follow what's going on in string theory. And I was getting more and more frustrated throughout the late 90s that this, what I would see in the public and what I would see, or just to not reflect my own understanding of what actually was going on. And partly I kind of mentioned, you know, there's a, for instance, Brian's PBS special about
I mean it just that just seemed to me to be giving that just didn't really didn't agree at all with what I would actually saw going on and so I thought well somebody you know somebody should write this up and I would have hoped it would be somebody else but then as you go along with no one else is going to do this and you know I'm actually pretty well placed to do it for very reasons and started thinking about it and I think around 2001 I actually wrote kind of a short thing that's on the archive of kind of
you know a little bit of a kind of polemical several page thing you say look here here's the opposite side this right here's what's right this is really not working and here's why and that that was the beginning of it and like i got a lot of reaction reaction to that and and i started to more and more feel that you know you the right way to do this was to actually
You needed to write something kind of at book, sit down and at book length, explain exactly what's going on. And I also wanted to do something also more positive to try to explain some of the things that I was seeing about how mathematics, you know, there were some very positive things happening in the relationship between mathematics and physics, which has some connections to string theory, but we're also quite independent, like Wittenstern-Simon's theory, for instance. So I also wanted to also write about
I also wanted to write about the story of what's going on in this kind of physics and this kind of fundamental physics, but kind of informed by someone who's actually spent a lot of time in the math community and informed by a lot more mathematics than is usual in the
this thing. So there was kind of a positive. It's rarely noticed, but there are a bunch of chapters in this book, like on topological quantum field theory, nothing to do with string theory, which nobody really paid much attention to or understands. But anyways, I wrote this and I was, so I just said, well, I'll just write this thing. And I think around then I may have also had a friend who had done a book proposal and written a book. But by the time he'd actually
was writing the thing, you know, he was just kind of sick of it and he didn't really want me writing it, but somebody had given him in advance and he had to, so he had to write the book. So I thought, well, you know, I don't want to do that. I'm not going to go out and make a proposal to a publisher. I'm just going to write when I want to write and we'll see how it turns out. And, you know, I think we'll see if someone wants to publish it. Great. And so then I was getting to the end of this and somebody from Cambridge University of Press showed up.
He was just in my office going around asking people, you know, what are you working on? Is there some kind of book project we could work on? And I told him about what I was doing and he got very, very interested in it. And so it actually then became you know, Cambridge University Press was then considering it for a while and they sent it out to various
Reviews and the reviews were kind of fascinating. There were half the reviews said this is great. This is wonderful Somebody is finally saying this this is fantastic and the other half said oh, this is absolutely awful. This was this will destroy the reputation of Cambridge University Press. So Interesting and the problem with the University Press is you know, they're not um They're actually not really they're not really equipped to do content
to deal with
Yeah, so he definitely agreed with me about that. Now that you're in the math department, is that what allowed you to see the connections between Twister Theory and the Langlands program or is that something that existed before? The connection, not the Langlands program, obviously that goes back to Langlands.
Well, whether there is, I think it's still, whether there is any connection between Twister theory and the language program, that's a very, that's extremely speculative idea and fairly reasonable. I would say, yeah. Yeah. So that. What aspect of the Langlands program, like the local or geometric? Maybe to back up a little bit. I mean, so the language program is, anyway, this amazing story. I guess you heard a lot about it from Edward, but it's,
One reason I got into it is it became more and more clear to me that the right way to think about quantum mechanics and quantum field theory issues was in this language of representation theory. And then I started to say, okay, I should learn as much as possible about what mathematicians know about representation theory. And sooner or later you find out about the Langlands program, and the Langlands program is saying that
All of the basic structure of how the integers work and how numbers work and things is closely related to this representation theory of Lie groups in this amazing, amazing way. There's just an amazing set of ideas behind the Geometric Langlands program, which they have a lot of similar flavor to the things I was seeing in some of physics. It's just been a many, many years process of slowly learning more and more about that.
But that stuff never really had anything to do with twisters. The interesting relation to twisters is that I had actually written this paper, I'd given some talks about the twister stuff, and I'd pointed out that in this way of thinking about things,
There's this thing that I told you that a space-time point is supposed to be a complex plane. Actually, in Euclidean space, you can think of it as a complex plane, or you can mod out by the constants and use the real structure of Euclidean space, and you get something, a geometrical object corresponding to each point, which is called the twister P1.
It's basically a sphere, but you identify opposite end points of the sphere. And so I'd written about that in my paper and in some of the talks I was given, I kind of emphasize that. And then, so then I get an email one day from
Peter Schulze, who's one of the people who's making this really great progress in the Langlands program in number theory. And he's been coming up with some of these fantastic new ideas relating geometric Langlands and arithmetic Langlands. And he basically said, yeah, I was looking at this talk you gave and it's really nice about this geometry and seeing this Twister P1 going there. He said, what's amazing is this Twister P1 is exactly that same thing as showing up in my own work.
There's this work he was doing on the relation of geometric Langlands and if you specialize to what happens kind of at the infinite prime or at the real place, not at finite primes, the structure he was seeing was exactly the twister P1. So he kind of pointed this out to me and asked me some other questions about the
about this. I don't think I could tell them anything useful, but that did kind of blow my mind that, wait a minute, this thing that I'm looking at in physics, that exactly the same structure is showing up in this really new ideas about geometry of numbers. And so I then spent a few months kind of learning everything I could about that mathematics in Twister P1, and I'm still following it. But
I should say that to my mind it's just a completely fascinating thing that these new things that we're learning about the geometry of number theory and these speculative ideas about
about physics that you're seeing a same fundamental structure on both sides and and but but i have no i mean i have no understanding of how these are related i don't think anyone else does either yeah have you asked peter if he would like to collaborate well there's not is that like uncouth no but but but i think he and i just have very
Are you too incompatible? No. He's doing what he's doing. First of all, one thing to say is he's having such incredible success and doing such amazing stuff that interfering with that anyway and telling him why don't you stop doing what you're doing and do something I'm interested in seems to be a really bad idea.
Anyways, so yeah, he's doing extremely well doing what he's doing and most of what he's doing isn't related to this. I mean, he's, you know, he really, really understands in an amazing way what's going on with the geometry of the adic numbers and these things like this, which I don't understand at all. And so and he's just been revolution. He's been revolutionizing that subject. And it's something I can only kind of marvel at from a distance. The kinds of issues that where I'm kind of stuck that are kind of for me are are actually much more
They really have nothing to do with his expertise. I probably should be talking to more physicists or whatever. I think it's in the back of his mind, this stuff that I'm seeing, I should always often look and think about if I can understand the relation to physics. It's in the back of my mind, the stuff that I'm seeing physics, I should try to keep learning about that number 37 and see if I see anything.
But that's really all it is. But a lot of this is very new. I just heard from him a few weeks ago that he actually has some new idea about this particular problem from his point of view. And he was supposed to give a talk about it on last Thursday at this conference in Germany. And I'm hoping to get a report back of that. But this is all very active and very poorly understood stuff. But it's not.
But definitely the connection between math and physics here is very, very unclear. But if there is one, it will be mind blowing. And it's certainly kind of on my agenda in the future to try to learn more and look for such a thing. But I don't have anything positive to say about that, really. So I want to get to space time is not doomed. There's quite a few subjects I still have to get to. I want to be mindful of your time. But how about we talk about space time not being doomed?
It's something that's said now. I don't know if you know, but there's someone named Donald Hoffman who frequently cites this. He's not a physicist, but he cites it as evidence or support for his consciousness as fundamental view. And then there's Neema Arkhani Hamed, who's the popularizer of that term, though not the inventor. Yeah. So maybe to, I mean, I can kind of summarize that. Yeah. So I don't really have anything useful to say about Hoffman. I mean, he's interested in consciousness and other things. I don't really have too much
I don't really know much about it, but maybe to say what the…I mean this has become…I mean the reason I wrote that there's this article you're referring to about space-time is not due…I wrote it partly because I was getting frustrated at how this had become such kind of an ideology among people and working in physics and on quantum gravity, this idea that
And I think one way I would say it would say what's happened is that so when people first start thinking about how do you get quantized gravity and you kind of gravity so the initial one of the initial ideas as well you know we've learned that we have this incredible successful standard model so let's just use the same methods that work for the standard model and apply them to gravity and we'll do that and so it's going to be
Anyway, and you're thinking of space and time in this usual way and then there are these degrees of freedom that live in space and time which tell you about the metric and the geometry of space and time and you're trying to write a quantum theory of those things living in space and time.
And I think, you know, anyway, people tried to do this. There's lots of problems with doing it. It's an incredibly long story. String theory was partly reaction to the story. But even string theory was still a theory of strings moving around in space and time. So you weren't. Yeah, I mean, you were still starting with thinking, thinking in terms of the space and time. But but more recently, you know, as string theory hasn't really
Worked out the way people expected. There has been this ideology of, oh, well, let's just get rid of this space and time somehow, and then we will write some theory in some completely different kind, and in the low energy limit, we'll recover space and time as some kind of effective structure, which you only see at low energies.
And that's become almost an ideology, like Arkani Hamid likes to say, space-time is doomed, meaning the truly fundamental theory is going to be in some other variables and space-time variables. He has his own proposals for this about these geometrical structures he's using to study amplitudes. Anyway, the things that I'm doing
You actually do get a theory, it looks like gravity should fit into this and it will fit into this in a fairly standard way. This is standard space and time except in the twister geometry point of view on it and interesting things happening with spinners you didn't expect but it's still, there is a usual idea about space and time are there. My general feeling with the
But the problem with this whole kind of space time is doomed thing is you have to have a plausible proposal for what you're going to replace it with. It's all well and good to say that there's some completely different theory out there and the theory people used to is just an effective approximation. But first you got to convince me that your alternative proposal works. And the problem is that people are just doing this without any kind of
you know, without any kind of plausible or interesting proposal for what it is you're going to replace space time with. And often it even comes down to this crazy level of kind of this multiverse thing. I mean, we have this theory where everything happens. So fundamentally everything happens, but then effectively you only see space and time and it's kind of, you know, you can say words like that, but it's kind of meaningless. Why is it that they have to come up with a decent proposal or replacement? Why can't they just say, look, there are some
With our current two theories, there's an incompatibility that suggests that space time quote unquote breaks down at the plank level or maybe before. So for instance, Nima's argument that if you were to measure anything with classically, you have to put an infinite amount of information somewhere and then that creates a black hole. And then there's also something with the black hole entropy that suggests holography. But that doesn't mean space time is doomed. It's just a different space time. Yeah.
Yeah, but from my point of view, what has become the focus of that field a lot are actually quite tricky, very non-perturbative, very kind of strong field problems about what's going to happen to the theory when you've got black holes and black holes are decaying. And so you've kind of moved away from
But the problem with the inconsistency between quantum mechanics and general relativity is a different, that is normally the one everybody worries about, is normally a different problem. It's a very, very local problem. It's just that if you think of this in terms of the standard kind of variables like what's the
The metric variables and you use the Einstein-Hilbert action for the dynamics for these things. If you try and apply standard ideas of quantum field theory locally to that at short distances, you get these normalization problems and the theory becomes unpredictable.
That's always been considered the real problem. How do you deal with that? But instead of having a proposal to deal with that and having a real kind of a new idea about what's really going to happen, what are the right variables at these short distances that will not have this problem, what are you going to do? They kind of ignore that, decided to ignore that problem and say, well, maybe string theory solves that problem, who knows? And then to move on and to try to do
you know, something much, much harder, which is to resolve these issues about what happens in black hole backgrounds and stuff. And I don't, I know, but it seems to me kind of a separate issue. You can still have space time and have these issues about, you know, what's going to happen in black hole backgrounds and stuff, and you could still resolve them in different ways. But they're just,
It's a very frustrating subject, I think, to actually try to learn about. You see people making these statements, and then you say, okay, well, what exactly do they mean? I mean, it's all well and good to say these very vague things about this is doomed and what about infinite amount of information, blah, blah, blah. But write down, tell me what we're talking about here. And there really isn't...
It's almost a comically impossible to kind of pin people down on what is the, what are you talking, what theory are you talking about? And, and then finally, when you pin them down, you find out that what they're actually talking about is they've, they're talking about some very, very toy model. They're saying, well, we don't know what's going on in four dimensions. So let's try it in three dimensions and maybe two dimensions, maybe one dimension. And so they're talking about some comically trivial toy model, which
They kind of ended up studying because well you could study it and then maybe there's some analogous problem happening in there and and that all they have are these kind of toy models which which actually don't seem to have any of the actual real physics of four-dimensional general relativity in them and that's what they're that's what they're all studying these days. I see even Nima. He's somewhat different because he's coming at it from a different point of view. He's
Coming at it from this point of view of really trying to see, find new structures in the perturbative expansions for standard quantum field theories. So he's got kind of a specific program looking at, he's not studying toy models, he's studying real four-dimensional physical models, but they're not
but they're generally models like Yang-Mills theory where you know exactly where the theory is and it's not, this isn't solving the problem of quantum gravity or anything, it's well in theory, but I think maybe I should, I'm saying this a bit too quickly without thinking, but just to try to give a flavor of what I think he thinks he's doing, he's trying to take a theory that you do understand well like Yang-Mills theory and look at its
perturbation series Feynman diagrams, find new structures there and a new language, and then see if you can rebuild the theory in terms of these new structures. And then if you've got kind of a new way of thinking about quantum field theory in terms of these new different structures like his amplitude hydron or whatever, then maybe you can then apply
Once you've got a way of thinking in terms of new structures, you can go back to the problem of quantum gravity. I see, I see. I don't think he's not in any way, as far as I know, claiming to have actually gotten anywhere near there. This gives you a lot to do. There's a lot of interesting structure there. There's a lot to work on. He and his collaborators have done a huge amount of calculation with these things. At least to my mind, I don't see them coming up with what
I think that they hope to come up with which is a different geometric language for that that really works and is really powerful for that that's going to get you something new. Did you listen or watch Sean Carroll's podcast on the crisis in physics? Well, no, I skimmed through the transcript of it. I was kind of wanting to see what he was doing. This is certainly something I'm very interested in.
But yeah, I thought anyway, I thought the whole thing was actually quite strange because it's like four, four, four and a half hours long. And it's just him talking. So he's just. Anyway, I thought the whole thing was actually very odd, and it has something to do with kind of the odd nature of the response to the. To criticisms in the subject, and so I think it was another kind of weird example.
You know, there's, he's kind of wants to say something about this issue of, you know, that many people are now are now kind of very aware there is some kind of problem here and they're referring to it in the crisis in physics. But, um, you know, instead of, but, but, but, but just kind of talking about it for four hours and four and a half hours yourself is just kind of, kind of strange. Um, and, and, and, and, and especially since he's got a podcast, one of the obvious things to do is to invite somebody on who
you know thinks there is a crisis in physics if you don't and he doesn't think there's one it seems and well you could actually have an interesting discussion with this person for some time but instead of discussing some this it's like you know there's a controversy going on of two kinds and instead of inviting somebody on to discuss this controversy with you or two people you just go on for four hours about how your view your view that the other you know the other side is wrong it was very odd.
Also, it wasn't as if he was arguing with the people that were saying that there's a crisis in physics. So when people say there's a crisis in physics, they generally mean that there's a crisis in high energy physics, particularly with coming up with fundamental law. And so what he was then taking it on to mean is there's a crisis in physics as a whole, like cosmology or astrophysics. And then he's like, No, but look in solid state physics and the progress there. That's called a straw man where you're not actually taking on the argument you're taking on a diminished. Yeah.
Well, he was also often involved in these arguments over string theory with me and Lee in 2006. And it was often the same kind of thing that he's kind of... And the whole thing is just odd from beginning to end because he's actually not a string theorist. And this is another weird sociological thing I found is that you find non-string theorist physicists who somehow want to take a bit side in this and want to
and have a big opinion about it and get emotionally involved in it, even though they actually don't know, don't actually understand the issues that this is not what they do. This is not their expertise. So, and, um, so I know, I think some of this, you know, knowing, not knowing Sean and what he's trying to do, I think he's not the only one who you see this phenomenon that there are people who, you know,
They see what they want to do in the world is really to bring to the public an understanding of the power and the great things that the subject has accomplished. And so he, and even in his four hours, he spends a lot of time, you know, giving very, very good explanations of, you know, various parts of the story of the history of the physics, the history of this. And, you know, they kind of see them, their goal in life is to kind of convince this, um,
you know the rest of the world who doesn't actually understand these great ideas or doesn't really appreciate them or skeptical about them you know to bring them to them and and i think part of the whole reason is i think he was kind of doing doing this or does this is because you know having people out there on twitter or whatever saying oh you know physics sucks it's got all these problems it's all wrong blah blah blah that this is you know this is completely against
His whole goal in life is to stop this kind of thing and to really get people to appreciate the subject. I think in a misguided way then enters into this from the point of view of, oh, I have to stop people from saying things about a crisis in physics and get them to really appreciate that this really is a great subject and wonderful subject.
that goes too far and then starts defending things which really aren't defensible and things which he often doesn't really know much about. For instance? Just the details of string theory. The reason I wrote this book is that some of these problems of string theory, these questions, people will go on about ADS, CFT and this and blah, blah, blah. This is incredibly technical stuff. It's just
even understand exactly what these theories are that on both sides of the ADS-CFT thing, what is known about them? What is the real problem here? What can you calculate? What can you not calculate? What can you not find? What can you not find? What happens in other dimensions? It's horrendously technical and very few people actually really know it. But lots of people want to kind of get involved in discussions about it and argue about it without actually understanding actually what's going on. And part of the reason for writing the
not even on the book, but was to sit down and try to write about what was really going on, what the specific technical issues actually were, as much as possible in a somewhat non-technical venue. Anyway, so that's some of my reaction to this. In particular, he just starts off the whole thing by
He picked up on something from Twitter about somebody had found a paper from somebody written in 1970s complaining about how, you know, there was a crisis, there wasn't any progress in the field. And this was a time when there was great progress in the field. And this was a person who honestly, somebody completely ignorant wrote a completely paper no one ever paid attention to in the mid 1970s that was wrong about this. And he wanted to use that as to kind of bludgeon
the people who are making serious arguments about the problems today. I don't know. I thought it was kind of a weird performance, but I think this is a good thing to ask kind of people on this other side of this argument, why there's very little willingness to actually engage in technical discussions publicly with people they disagree with. I mean, you know,
Sean has never been invited by me to be on his podcast. He hasn't invited Sabina Hassenfelder. There is no appetite for that at all among people in this subject. And I think a lot of that is because they're well aware that there are really serious, difficult problems with this, whether you want to call it a crisis or whatever it is, there are real problems and they're just not very interested in acknowledging and publicizing that.
Well, I have a tremendous appetite for it and the people in the audience of everything do. So if ever you have someone who you feel like would be a great guest with the opposite view that is defending string theory or the state of high-energy physics, then please let me know and I will gladly host you both. I know we spoke about some people behind the scenes, some people who are likely to say yes and have a congenial conversation. Well, actually most people are.
Funny thing is actually early on in this, I was invited, a guy down at University in Florida invited me and Jim Gates to come and debate strength theory. I think we really disappointed this big audience by agreeing on almost everything. He's a well-known strength theorist. We actually found that
I think things would be interesting to do this again now, but this was almost 20 years ago, maybe a little bit less, 15 years ago. The way I would describe it then is that
If we started talking about the details, what our disagreements came down to, where it was kind of more, you know, should you be out, you know, we would agree about the state of current things, but what do you think, where do you think this stuff is going? Are you optimistic? I see a reason why this can't work. He would see reasons why this is actually best thing to do. He knows how to do, and this might work. And, and there, it's just that kind of, you know, disagreement about ideas, which is, is perfectly reasonable.
And actually Gates told me, I remember at the end of when we were talking after this thing, he said, yeah, you know, I was asked to like, you know, write a review of your book about it. And I thought, oh, well, I'll just, I'll pick up this book and I'll see, you know, the guy's got it all wrong about string theory, whatever. And then, you know, I read your book and I realized that, you know, a lot of what you were saying was the stuff about that importance of representation theory in physics and that
And I actually, you know, that that's actually exactly the way I see the what's important in physics. So I find myself agreeing with much of your point of view and the book. So I couldn't I didn't anyway. So that was, you know, anyway, at the level of these these ideas, I think, especially back then, I think there wasn't it's perfectly possible to have a reasonable discussion. I think I think it has become weirder now
20 years later, I think it was a lot more possible to reasonably be an optimist back 20 years ago and say, well, the LHC is about to turn on. We're just going to look for these super partners. Maybe they'll see super partners. We have all this stuff that might vindicate us, and we're all hoping for that. But now the LHC has
has looked, the stuff is not there. There's really not, um, and you know, that's one thing that's somewhat shocked me is people willing to, um, people who were often to me or in public saying, look, you know, the crucial thing is going to be the results from the LHC. You know, we believe that you're going to see, we're going to see the super partners and this is going to show that we're riding the right track. And then the results come in and you know, you're wrong and you just,
There's a comment on your blog that said the LHC is great for string theory because it divides in half the moduli space.
That was certainly my feeling a lot when I was writing the book, whatever, is that this was going to be a crucial thing, the LHC, because either the LHC was going to see something along the lines of what these guys were advertising and which they were often willing to actually bet money on, or it wouldn't, and then they would back down and start saying, okay, well, maybe the critics have a point. But no, it's just amazing that people would just completely ignore the experimental results and keep going. About representation theory,
For people who don't know what representation theory is, can you please give them a taste and then also explain why is it important? More so than say you want a group to act on something like, okay, yes, but how much more involved does it get than that? Well, anyway, so just to say that to give a flavor of what we're talking about, yeah, so
It's very common for people to talk about the importance in physics of symmetries. And when you say that it's important to study the symmetries of something, people often then just explain it in terms of a group. So mathematically, a group is just a set with a multiplication operation. You can multiply two elements and get another. But the interesting thing about
Symmetry is actually not so much the groups, but the things that groups can act on. So what are the things that can be... So the standard example is like the group of rotations. You can pick things up and rotate them in three-dimensional space, but what are all the things that you can kind of do rotations to? And those in some sense are the representations, or the representation theory is kind of the
The linear version of that theory and if you try to work with a group action on something that isn't nonlinear, you can look at the functions on it and turn it into a linear problem. But anyway, so group representation theory is really
It really is the study of symmetries. What are the possible symmetries of things? What are the possible things that can have symmetries? It's really fundamental both in physics and in mathematics. Large fractions of mathematics you can put in this language. There is some kind of group and it's acting on some things. What are the representations?
The amazing fact about the language program and number theory is how much of number theory you can formulate in that language. You can formulate a lot of geometry in this language. It's kind of a unifying language throughout mathematics at a very deep level. To me, the amazing thing is that if you start looking at the structure of quantum mechanics, if you look at what are the quantum mechanics is this weird conceptual structure that states are
state of the world is a vector in a complex vector space and you get information about it by self-adjoint operators acting on this thing. So from the, that looks like a very, very weird, like where did that come from? But if you
If you look at that formalism, it fits very, very naturally into the formalism of group representations. And this is kind of why I wrote this book, taught this course here and wrote a book about it, about quantum mechanics from that point of view. What's the book called? Quantum Theory Groups and Representations and Introduction. It's kind of a textbook. So that was the second book I wrote. That link will be in the description. Yeah, there's also a free version with kind of corrected
With errors that I know about corrected on my website, you can also link to that. No, we want people to pay. They have to pay for the errors. Or you can buy a copy from Springer if you'd like a hardcover book or whatever. One of the things that most fascinates me about quantum theory is that there is a way of thinking about that. It's not just some weird out of the blue
Mathematical conceptual structure that makes no intuitive sense. I mean, it really has a structure which is kind of deeply rooted in understanding representation, understanding certain fundamental symmetries. Have you heard of this theorem by Radon Moyes in differential geometry?
About the amount of differentiable structures that can be placed on different dimensions. So for dimension one, there's I think up to some up to diffeomorphism or up to differentiable structure. I forget the exact term. There's just one and then there's just two for dimension two or just one. There's a finite amount for every dimension except dimension four. Yeah, in which case there's not just an infinite amount. There's an uncountably infinite amount.
Yeah, but there's even... Yeah, but this is actually also one of the most famous open problems in topology, the smooth black-array conjecture, which says that is there... There you're thinking about specifically the four manifold. Yeah, so is there a... Now I forgot what I used to know about this, but yeah.
There are exotic. Well, the point is that dimension four is picked out. And so it would have been nice for physics if dimension four was picked out and finite or as the rest were infinite, because then it just means, well, it's nicer for us, but it's picked out and made more diverse and more mysterious. Yeah, but, but it's, how does this go? Um,
Anyway, four dimensions is very, very special. One dimensions and two dimensions, you can kind of pretty easily understand the story. The classification story is pretty simple. Three dimensions is harder, but especially with the solution of Poincare conjecture, you actually have a good three-dimensional classification. And then once you get above four dimensions, things
Basically, there are more ways to move things, so things simplify so you can actually understand above four dimensions what's going on.
Anyway, I've never actually seen any kind of clear idea about what this has to do with four-dimensional, with physics. The stuff that I've been doing very much crucially involves the fact that four dimensions is special because the way spinners work or if you like, the rotation group in
In every dimension is a simple group except in four dimensions. In four dimensions, the rotation group breaks up into two independent pieces. And that's at the core of what a lot of what I'm trying to exploit. But so four dimensional geometry is very, very special. And I don't know, speculative, very speculative. Maybe the weirdness about infinite numbers of topological structures under four dimensions that the fact that you've got the rotation group has two different pieces means that
is behind that, but I know, I know, I know, I know. Of course, of course. Yeah, it's interesting that the fact that it's semi-simple is a positive here. Like you mentioned, it breaks up into two. Yeah. Whereas usually in physics for the grand unified theories, what you want is simple. You don't want semi-simple. You want to unify into one large group. Yeah. Well, there's nothing really in terms of unification. It's just
Yeah, maybe it's maybe I should also say something about this about why what I'm trying to do, I think is quite different than the usual sort of unification that the and what the usual. Yeah. Yeah. And please explain Euclidean twister theory once more. Again, people who are still like, I've heard the term, I've heard him explain twisters, they somewhat understand twisters has to do with lines and points and planes. Okay. And spinner is something called spinners. I think I understand that.
One way of stating the problem is we go out and look at the world and we see gravity and we see
We see the electromagnetic interactions, and that's kind of based upon a U1 gauge theory. It's a circle. We see the weak interactions are based upon an SU2 gauge theory. That's a three sphere. And we see the strong interactions are based upon an SU3 gauge theory. So where in the world did this U1, did these three groups come from and the way quarks and other elementary particles behave under those groups? So it's a very small amount of group theoretical data.
Where did it come from? Why that? The standard answer to this very soon after the Standard Model came out was that, well, there's some big league group. You take the group of all unitary transformations of five complex dimensions or take the group of all orthogonal transformations of 10 dimensions, let's say SO10, and then you fit
that data and show that that data fits inside that bigger structure. Within that SO10 group, I can fit U1 and SU2 and SU3, you can get them in there. And I can put all of the known particles together with their transformation properties and put those together as a transformation property of SO10. So you can kind of put stuff,
This kind of package of algebraic data, we're trying to understand where it came from. You can put it together in a simple group and into a group where the problem is in terms of group theory, it's a package involving several different groups. And so you get several different simple groups. So you can put this together. But the problem with this is always is if you try and do this,
You can then write down your SU5 or SO10 theory, whatever, and it looks a lot nicer than the standard model. It's only got one term where you had a lot of terms before, but you have to then explain, but wait a minute, why don't we see that? Why do we see this more complicated thing and not that? For instance, the standard thing that grain unified theories do is you put the weak interactions and the strong interactions into the same structure.
You put the stuff together, all of a sudden it can interact with itself and it can do things which you know don't happen and protons don't decay.
So your problem, when you write down these theories, the problem is you haven't necessarily done anything. You've put the stuff together in something bigger, but you've just changed the problem from why these pieces to why did this bigger thing break into these pieces. You haven't actually solved
Until you have an explanation for that, you haven't actually solved anything and this is I think the fundamental problem with these great unified theories. The only way to make them break down into these other things is to introduce more Higgs particles and more complicated structure and more degrees and more numbers and you lose predictivity if you do that. You also find that they also don't look like what you see in the real world if you do experiments but most people who
have tried to come up with some unification, have done some version of that actually. I mean, so for instance, I mean, I don't want to really get into things like what Garrett Leasey is talking about. But they're all versions of this. They've all got their own version of this. And I think when you see people kind of dismissing theories of everything and green and white theories, and you see Sabina Hassenfelder saying, well, these people are lost in math,
then they're all really referring to the same problem that people are trying to get a deeper understanding of what's going on by putting things together into a bigger structure. And they're all kind of foundering on not having an answer as to why this breaks up. So the thing that I'm trying to do, why I'm much for
interested in these ideas about spinners and twisters is that I'm not actually, I mean, a lot of what I'm doing, as I said, I mean, the fact that there are these two SU-2s, that's an aspect of four dimensions. There really are, maybe the thing to say is that I'm not introducing kind of new
I'm not introducing lots of new degrees of freedom and then having to explain why you can't see them. I'm trying to write down something. I'm trying to write down a new geometrical package, which packages together the, um, the things we know about and doesn't, and doesn't actually have new, you know, doesn't actually have all sorts of new stuff. Penrose said this was his motivation as well for Twister theory. Yeah. Yeah. So Twister theory, so in some sense, Twister theory is a bigger structure, but it's not, um,
It doesn't contain anything really new. It contains the same spinors you had before and puts them in an interesting new relation so you can understand conformal invariants. Twister theory is not the things you knew about Twister theory. It's not spinors and vectors and the things you knew about plus some other completely unrelated stuff. It's the things you knew about in a new, more powerful conceptual framework. That's the sort of thing I'm trying to do.
The problem is that it's, I guess, a misnomer to really say this is a well-defined theory. It's more a speculative set of ideas about how to, but that's the crucial, I mean, probably I think the most important new idea here, which for this to be right has to be true and which is exactly this idea that
About about rotate that if you think about rotations in four dimensions in Euclidean space-time When you relate it to a Cassie space-time in the real world one of the s e2s can be treated as an internal symmetry and that and that could explain the weak interactions, that's Mm-hmm. That's kind of a crucial Yeah, that's why it's also referred to as gravel weak unification by you or by other people other people have have you know, I mean other people have noticed this and and actually it's interesting when you read the
This is a very chirally asymmetric view of the world, and a lot of people said, oh, well, that means maybe you should be able to understand. The weak interactions are chirally asymmetric, so maybe there's something here. But the Twister people, I think, never really had a version of this. There are various people who have tried to write down to do this. I mean, one is actually, there's a paper by
Stefan Alexander has worked on this and Lee Smolin, they actually had a paper intended to do this. What they're doing is significantly different than what I'm trying to do. In particular, they're staying in Minkowski space. This idea of going to Euclidean space to get this thing to behave like an internal symmetry is not something that
Jonathan Oppenheim, Stefan Alexander, and Neema Arkani Hamid.
all were graduate school peers at the same time as my brother in physics. Oh, okay. This interesting because then later on in my life, this was all in Canada. Yeah, yeah. So U of T Nima was at U of T University of Toronto with my brother, but then in graduate school, Oppenheim and Stefan Alexander, I spoke to Stefan on the podcast as well. Yeah, no, there have been very few physicists who've been encouraging about this.
He's one example. Yeah, he's extremely open to new ideas and playful. He's a playful person with ideas, much like with his music. I think that both qualities rub off on one another. And I think also in his own research, I think it's not so much that he's followed up on this grab-a-week stuff, but he is very interested in
You know, is there some way in which gravity, you know, that gravity actually is a chiral theory, there is some chiral asymmetry in gravity, and especially, you know, can you know, anyway, I mean, are there kind of astrophysical and cosmological thing, places you can go and look and see, you know, is gravity really chirally symmetric or not? And so I know that that's something that he's worked a lot on.
So he's working on experimental tests of the chirality of gravity, but that doesn't mean experimental tests of your theory, just your theory is a chiral theory of gravity. Yeah, it's a, it's a chiral theory, but it's not. It would be validation of your theory or a testation. No, I mean, it's kind of, I mean, first of all, again, I have to keep saying I don't really have it. I don't, I would love to say I would love to say I've written down a consistent proposal for a theory of quantum gravity based on my ideas, but I'm not
I'm not there yet. I think what he's doing is more, it doesn't involve, it doesn't have the structures I'm trying to exploit are not there in what he's doing. But I believe what he's doing is more important thing. You kind of add Chern-Simons kind of terms. You assume that maybe there's some Chern-Simons term in the theory and ask what the observational implications of that would be and try and go out and look for that. But I haven't really
Carefully looked at what he's doing, just because it's quite different than what I'm trying to do. Can you explain what turn Simon's theory is? So what it means to add a turn Simon's term? I know Stefan's worked on turn Simon modified gravity. And then there's something like turn Simon terms in the Lagrangian of particle physics. But I don't know if those two are related. Yeah, I don't. Yeah, I shouldn't try and talk about it as we're gonna I don't remember exactly what he was doing. But um,
Well, Trent, I mean, you're very hard. Actually, one funny thing is that I actually went to a, I don't know. So I actually started thinking about Trent. So maybe I can go back to how I first encountered them. So when I was doing my PhD thesis, my problem was I'm trying to understand, I got engaged on a computer.
I've got this version of gauge fields and they're described on links on a lattice and you can store them in a computer and manipulate them. I want to look at one of these configurations and say there's supposed to be some interesting topology in this engaged theory. This is what people are getting interested in the 70s and 80s. In particular, there's something called the
Let's say the instanton number. These gauge fields are supposed to have some integer and variant called the instanton number. If somebody hands you a gauge field on a compact manifold, you should be able to calculate its instanton number. If you could calculate these instanton numbers and see them, you could do interesting physics with it.
So the problem in some sense of my thesis was, you've got these gauge fields, what are their instanton numbers? Can you define them? And they're just integers? They're just integers, yeah. So they're invariants, but they're not invariants of the base manifold. You basically have a bundle with connection and they're invariants of the bundle. And if you know the connection, you're sensitive to this invariant. But the
The one way of looking at that though is if you look at the interval formula for this thing, it's a total derivative so that if you're trying to integrate it over a ball or a hypercube, the formula that's supposed to add up to this instanton number, you can write it as an interval over the boundary. It's the interval of D of something so it's
It's the interval of boundary. It's a total derivative. So the thing that it's a total derivative, the thing that lives on the boundary is the Chern-Simons form actually. So this is kind of the first way that people started seeing this thing in physics. And so one idea was, well, I could
If I could, instead of calculating these instanton numbers, if I try and do it in terms of their local contributions from each hypercube, I should, if I could just calculate the Chern-Simons, the Chern-Simons number, the contribution, you know, if I could calculate the, that thing, then I would be done. And so I spent a lot of time looking at the Chern-Simons formula and then I spent a lot of time trying to put that in the lattice and then
I kind of finally realized it's kind of gauge. The problem is that it's very gauge invariant. So any kind of idea you have about how to calculate or construct it tends to be just an artifact of some choices you're making because of gauge symmetry. So this though, that led to one of the great experiences of my life. When I was at MSRI,
At one point, Atiya and a bunch of people were talking in the blackboard and somebody was asking Atiya said, how would you calculate this Chern Simons network? Then Chern Simons had become incredibly important because of Whitten. Whitten had said,
You can get these wonderful non-invariants of three manifold of variance if you can do path integrals and that you should take the path integral to be e to the i times the Chern-Simons number, exactly that integral that I was talking about. But Witten now wants to integrate it over a whole three manifold and so people were asking, can we try and think about how can we actually do this calculation what we're doing?
And then Atiya for thinking for about five seconds comes up and says, ìOh, well, maybe you could calculate it this way, do this.î I was luckily standing there and since Atiya had thought about it for about 10 seconds, I thought about it for about three years. I could say, ìNo, no, no, that doesnít work. You canít do that because of this.î So that was one of the high points of my mathematical career.
Yeah, anyway, but I don't know that this is in any way answered any question, but that's that's one definition of it, but it's a very It's kind of an amazing Piece of information about you know about about gauge fields about connections and it tells you some very subtle things and it turns out to be useful for all describe all sorts of interesting and unexpected physical phenomena and
These speculative ideas of yours of gravel week unification, have they been sent to Penrose? Has Penrose commented on them? I haven't heard anything back from Penrose. Penrose is a little bit of a problem. Whatever email I had from him back when he was helping my book no longer works and other emails tend to bounce. You don't have mutual friends?
I've come this close to actually running into him and being at the same conference as something to him and having a chance to talk to him personally. I keep expecting, instead of making a further effort to get a manuscript to him, part of the problem you'll see if you don't know his email and you try and contact him, you end up getting a secretary who may or may not be bringing things to him. I was actually at Oxford last year.
From things that he said about this kind of thing, I think he's made it very clear that he
He has always explicitly followed the kind of thing Attiya did, the kind of Euclidean version of the theory, but he's always said very clearly that in his mind the Euclidean version of theory is not the theory. Theory is what's happening in the Kassian space. Anyway, whether I could convince him otherwise, I don't know, but I think he's kind of pretty clearly in his mind thought through, okay, there is this interesting Euclidean theory, but
That's actually not really the physical thing is Minkowski. So I don't actually believe you're going to that by working over there, you're going to actually tell me something important. But um, but it's why I would I think I'd have to get around that particular initial reaction from him. So forgive this fairly foolish question. But if both gr and the standard model can be formulated in terms of bundles, then why can't you just take a direct product of the groups? So for instance, you have
the standard model gauge groups and then you direct product with SL13 so that's the principle you make an associated frame bundle that's like just a projection of SL13 and then you say that's general relativity and the other ones is the other associated bundles the standard model and then you call that unification like is that unification what are the problems there? Well the problem is that general relativity is a different
Well, maybe the thing to say is, so gauge theory is really just what you have is a bundle and the fibers are some group. And you have connections and curvature on that. You write down the interesting Lagrangian is the norm squared of the curvature. And anyway, so gauge theory is a nice, pretty story. If you try and write general to be the same language, you can do it.
It's fine. You have a G bundle where G is SO31 or D Euclidean Ridge, whatever, and you have a connection, you have a curvature. But the problem is that you crucially have something else and you have other things specifically because you're not some arbitrary G bundle, you're the frame bundle. And the frame bundle has
It's a principal bundle for the group of just all changes of frame, but it also is, I mean, people use the term soldered or tie. It also knows about the base structure, so a point in the fiber of the frame bundle is not just an abstract group element, it's a frame.
It's a frame down on, you know, if you take vectors, you can predict on the base space and it's a frame for those vectors. So it's kind of soldered to the tangent space and so what this means in practice is it means that there's new variables which are part of the story, which are not just the
not just the SO31 connection and curvature. There's also, you know, so you've got this connection one form of curve. Soldering form? Yeah, it's called the soldering form or the tetrad or I mean, there are a lot of different different people names for it. But there's kind of, there's kind of a one form, you feed it the vector and you feed it a vector and it tells you and you know, since you're up on the frame bundle,
you've got a frame and this one form has components which tell you what the components of the vector are with respect to the frame. So it's a very kind of canonical object, but it's there, the space-time geometry depends upon it. So the space-time geometry doesn't just depend upon the connection of the curvature, it depends upon the connection and this
this canonical one-form. So the problem is that so you've got extra variables which you didn't have in that these just don't exist in the Yang-Mills case and you have to and so you can and with those variables you can write down a different lower order Lagrangian instead of taking the curvature squared you can take the curvature times
some of these guys, and you can get the Einstein-Hilbert Lagrangian. The fundamental Lagrangian of gravity is very different than the fundamental Lagrangian of Yang-Mills theory, and it's because you've got these extra gadgets to work with. I see, I see. So that's one way of saying it. You can't. But people have speculated a lot about why
Why not just try adding these higher curvature terms like you had in the Yang-Mills case, add those to gravity? Anyway, there's a long, long story about trying to mess with different, change the Lagrangian of gravity to try to make something better behave. Now, have you found any unification attempts that are between gravity and the standard model or gravity in any of the interactions that are improved if you don't view gravity as curvature but rather as torsion?
So for instance, this is something Einstein was working on later in his life. And then there's also non-matricity. Carton was working on that. Yeah. Yeah. So there are equivalent formulations of gravity, at least the torsion one. The gravity is actually not curvature. It's just torsion. Yeah. Yeah. So the... Well, one way to say it is, so now once you've got these
The two compatibility conditions to create the Levi-Civita connection, I believe it's called?
is that you have no torsion and that you have that the metric doesn't change with the covariant derivative. So if you take the covariant derivative on the metric, it's zero. If you don't have that, then you have non-metricity. In other words, along the parallel transport, the metric is preserved. Yeah. Okay. Yeah. I'm not so sure about that, but I can't say about torsion, but your problem is that if you
So if you just write down a theory with some, you put together a Lagrangian which is going to give you equivalent results to the Einstein-Hilbert, you put it together out of the curvature and the canonical one-form. Now your problem is that you've got, when you try to get the Euler-Lagrange equations, you can vary the canonical one-form and you can vary the connection. So you've got
And one of them, let's say, I guess it's if you vary the connection, then you end up, that gives you the torsion free condition. So you've got more variables, so you need more equations. So you recover gravity, but you recover, with the standard Lagrangian, you recover not the Einstein's equations and
As one equation, but also the torsion free condition as the other one. The standard simplest version of Einstein-Hilbert in that theory has no torsion again, but you can certainly write down more different Lagrangians in which torsion is not zero, but it has some kind of dynamics and does something. That might be interesting.
Yeah, I was watching a talk a few maybe a few weeks ago or a couple months ago about when trying to modify gravity, especially for explaining quote unquote dark matter that you can explain dark matter as a particle. But if you want to do modified gravity, it's useful to have torsion in your theory. Well, anyway, what I was thinking was, OK, if it's useful there, maybe it's not actually the case that that explains
dark matter, but maybe it would be more useful to try unification with torsion models of gravity than with the regular curvature model of gravity. Yeah, I should say one kind of funny thing about all this is that I've always, before I got involved in this particular thing, I tended to kind of stick to thinking, I mean, I spent a lot of time over the years trying to learn about quantum gravity and about these issues that we're talking about, but I never actually
I'm trying to understand what's going on in particle physics and the standard model. There are these groups of people who just think about quantum gravity and they're very smart. They've been doing this for 30 or 40 years and a lot of them aren't strength theorists.
I'm not seeing anything that they're doing that I could do better. They seem to be doing interesting things with torsion but they know more about torsion than I do.
Anyway, I kind of stayed away from more particle. Yeah, exactly. Yeah, that's why we're saying it. But I really stayed away from kind of going more in that direction, becoming more expert, a lot of these things, figuring. Yeah, I mean, until I see something that I could that I maybe I can do something with. I mean, if it's just a. It's interesting to see what the story is there, but there are really smart people have been banging away at the story for a long time and I can't help I'll stay away from it. But, um,
I've actually, partly because of this, had to learn a lot more about and get some remedial education on some of this stuff. I'm still, in some sense, the wrong person to talk to about theories of gravity.
Yeah, before we wrap up, there are a couple other proposed toes. So one with Lisi, like you mentioned, and then Eric Weinstein has geometric unity and Wolfram has Wolfram's physics project. I believe that's still the title. And Chiaro Marletto has a framework, not an actual toe, but constructor theory. So which of those have you delved even superficially into and what are your comments on them?
I should say I mean the Wolfram or the other one mentioned. So these ideas that you're going to start with some completely different starting point like Wolfram we're going to start and whatever you want to call whatever he's starting with. The fact that you're going to start from this kind of completely different thing that has nothing to do with any of the mathematics that we know of and that you're going to then reproduce the standard model whatever this
That seems to be highly implausible and anything I've ever looked at it and of his for briefly, you know, doesn't change that opinion. I just I just don't see how you get from. Anyway, I mean, you're telling me that you're going to go start and start way, way, way far away at something else and and make some progress right here. And I don't see how you're going to get you're ever going to get back. And so there's a lot of that. Lizzie's thing, I looked a bit
I know Garrett and Eric both fairly well. Garrett has slept on my couch like many people. Garrett I think had a fairly well defined proposal but to my mind it has exactly the same problems that I was telling you about. He wants to put
So these are the same problems you explicated about Grand Unified Theories earlier. Yeah, so he wants to put all these things together and he wants to put it together and have it live inside E8 and it's very nice except that he doesn't really have a, to my mind by doing that he hasn't actually solved the problem but he has to tell me why the E8 breaks down into the pieces that we know about and he doesn't have any, as far as I know, has no useful
I mean, Eric, you know, I've talked to a lot about this over the years. I've I don't know. I mean, he and I've looked a bit at, you know, paper that he finally put out. But I think again, it seems to me it has the same kind of problems. Again, he's trying to put he's trying to put everything together into this bigger geometric structure. And then but he doesn't, to my mind, have
I have any kind of plausible idea about how he's ever going to break that down and recover what, what, what we, uh, the real world that we see. And, and, and his, his, his is a lot harder to see exactly what he's doing or unless Lizzie is kind of following much more kind of a standard story. You can, you can see exactly what he's doing where it's harder to tell. But, but both of them, I think suffer from the same problem as guts as far as I know.
What about category theory? There's plenty of hype about category theory in physics but you're also in math and so you're much more close to category theory. Is there a hope that somehow higher categorical structures will elucidate how to make progress in high energy physics? I haven't seen any evidence for that. I mean the things people are doing with those are actually much more
I'm trying to understand, there's a lot of people actively trying to use some of that mathematics to understand classification of more kind of theories you would use in condensed matter systems. It's possible that the right way to
To understand gauge groups, the infinite dimensional group of all gauge transformations or maybe you can even think of the diffeomorphism group about how to think about representations of those groups. It may be that the higher categorical stuff has something useful to say about that because there the problem is that the standard notions of what a representation is don't really
The problem is when you're dealing with these influential groups, you really don't even know what… You can't just say representation. You have to put some more additional structure to make this well-defined and what the additional structure is unclear and maybe it would help with those. Anyway, I haven't really followed… I've spent some effort trying to follow that mathematics but I don't do that. Anyway, category theory in general is just a very, very general…
The problem is it's a very, very general idea. It's part of the way mathematicians think about every subject. It's very, very useful to think not about representations, but the category of all representations. That opens up all sorts of new ways of thinking and questions through that. It's just a very abstract language.
It can be used for many, many things. When I realized at some point, when I was a student, I thought the way to understand mathematics is to look at the mathematics they're teaching us and look for the more and more general structures and then just understand the most general structure and then you'll be able to derive the rest of the stuff. Then it looked like category theory was this thing which was the most general thing that people were using. I thought I should go learn category theory.
But then at some point I realized that what I was doing, what you're doing is that as you go to greater and greater generality, you're, you're, you're, you're saying what, what you're doing, you're talking about, you're saying something about more things, but you're saying less and less. And so in the limit, you're saying nothing about everything, which is really not, not actually useful limits. And that's the problem with just, you know, category theory as just a,
Now what if someone retorts about the polemics against string theory by saying, hey look, string theory has produced something much that's positive,
So for instance, the math is used in the fractional quantum Hall effect and many other condensed matter systems.
There was a comment that said, look, I'm a physicist and I'm not a string theorist, but we use string theory in the fractional quantum Hall effect. And that was a comment on the Ed Frankel video. Well, I think probably the problem is string theorists are happy to kind of claim
Anyway, they're kind of claiming that everything comes from a string theory and they're actually at this point, David Gross kind of argues that well, you have to shut up and stop arguing about string theory because string theory and quantum field theory are actually all one big thing and so you're arguing against quantum field theory so that's just a waste of time. Because string theory is supposed to be a generalization of quantum field theory?
Well, it's because, oh, you know, with these dualities and m-theory, whatever, we realize it's all the same. And so, anyway, so I don't know in this specific case, and I'm not an expert on that case, but I strongly suspect that the saying that this came from string theory is that it's really some fact that they learned from string theorists. And string theorists are happy to say this came from string theory, but it's not actually
And to make this whole thing even more frustrating, more complicated, is that no one actually can, at this point, has a definition of what string theory is. So people then start talking about what Groves is trying to do. He's trying to say, well, string theory and quantum field theory are all the same. So when I say string theory, I mean quantum field theory. And people just keep doing this. So unless you're really, really expert and you know exactly what
The story is about what string theory is and how it's related to quantum field theory. Another weird thing I found is that almost everyone believes that Ed Whitten wrote one Fields Medal for his work on string theory, which is just not true. The things that he won the Fields Medal for are these totally amazing
It's really hard to convince anyone of this. Even most mathematicians believe this if you go up and ask a mathematician,
So what's a fulfilling life for you, Peter? I'm quite happy. I think when my book came out, a lot of people, the ad hominem attack was, oh, here's this guy who was not a success and didn't really, and he's just embittered and unhappy. They didn't realize that I'm
I'm actually quite discussingly pleased with my life and very happy with myself. I've had a weird career here at Columbia, but I've been extremely well treated by the department and allowed pretty much to do, as I said, get away with doing whatever I want and treated well and paid well.
I had a very happy life. Meaningful. Yeah, and I'm actually proud of the books I've written and some of the things I've done. I'm actually quite excited about what I'm working on now. And this was always one of my great frustrations is that there were a lot of things that seemed to me that something interesting was going on, but I didn't understand enough to really be sure this is really something, I've really got something here.
and now I'm much more optimistic about that and so I'm trying to, I'm getting older though, I'm 66, I'm trying to figure out, I'm actually trying to negotiate with the department of the university some kind of exit strategy out of my current position to some different kind of situation here and I may or I might be doing less teaching and less and
and less involved and less taking care of the computers and get other people to do that. You take care of the computers? I told you about this. My official title is Senior Lecturer and the weird thing about this title is this is a title that the university gives to people who are in non-tenured positions but are teaching courses here and so I'm doing that but I'm also part of
The deal with the department has always been that I do relatively not that much teaching, but also make sure the department computer system runs, and so I actually do it on a day-to-day basis. I also make sure our computer system is going. You don't want to do that anymore? Well, let's just say I like to do it. Maybe a better way of saying it is I've actually kind of enjoyed that. Actually, that's always been in some ways fun.
There is an inconsistency I found between having the time and focus to work on making progress on the stuff I want to make progress on and also teaching a course and also having to deal off and on with computer problems and trying to fit all those together in a 40-hour week doesn't work so well. I've decided in my life
I definitely have to prioritize the working on these new ideas. I've got to start dumping some of the other things and change things, but we'll see.
I managed to find that specific comment that was referenced earlier and I sent it to Peter Royt over email. Here's the comment and then subsequently there'll be Peter's response. I am a physicist and I use string theory all the time in my research on the fractional quantum Hall effect. What Frenkel means here is that the expectation to find the standard model in the 90s by Calibri-Yau compactification of one of the super string theories turned out to be unfulfillable to this date. This does not harm the theory.
The prediction was just wrong, therefore the title of this video is misleading. String theory revolutionized the way we understand physics and math in general, and it continues to do so. By the way, it's the only consistent theory unifying quantum field theory and gravity. Peter's response is, Hi Kurt, in the podcast I misunderstood what you were telling me, that a condensed matter theorist was saying that they thought understanding the fractional quantum Hall effect used string theory.
I was speculating that they were misunderstanding some QFT explanation as a string theory explanation. It seems, though, that this is not a condensed matter theorist, but a string theorist. The quote-unquote string theory revolutionized the way we understand physics and math in general and continues to do so is just pure hype. It's the sort of thing you will ever hear from a string theorist devoted to that cause.
I was unaware that some string theorists have worked on embedding the fractional quantum hall effect system in a complicated string theory setup. I don't understand the details of this from long experience, think it's highly likely. This, like many string theory explains condensed matter physics claims, is just hype. String theory since the beginning has had a huge problem
and it continues to this day. The current tactic for dealing with the failure of string theory hype around particle physics is to double down with new hype about nuclear physics, condensed matter physics, and quantum information theory, etc, etc. Peter then quickly sent a follow-up email. Hey, I just read the thread. I'm guessing this is a string theory undergrad or graduate student. The claims about the fractional quantum Hall effect are based on relating it to Chern Simon's theory, which is a QFT story, so quantum field theoretic story.
Also, all those fans of David Hestein should know that I did ask Peter about geometric algebra, but he's not familiar enough to comment on it. OK, well, it was wonderful speaking with you and I hope we speak again. I hope we meet in person. Oh, sure. Let me know if you're ever in New York. Oh, yeah, I go quite frequently. So I'll let you know the next time I'm there and maybe I'll see you at perimeter if you ever come down this way. Yeah, I haven't haven't been there yet, but I would at some point like to like to like to go there.
I just signed up to participate via Zoom. They have a conference on quantum gravity at the end of the month, but it's mostly virtual. Anyway, I'll watch some of the talks on Zoom, but someday I'll actually get there physically.
The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked that like button, now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. You should also know that there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, disagree respectfully about theories and build as a community our own toes.
Links to both are in the description. Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc., it shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well.
Last but not least, you should know that this podcast is on iTunes, it's on Spotify, it's on every one of the audio platforms, just type in theories of everything and you'll find it. Often I gain from re-watching lectures and podcasts and I read that in the comments, hey, toll listeners also gain from replaying, so how about instead re-listening on those platforms?
Every dollar helps far more than you think. Either way, your viewership is generosity enough.
▶ View Full JSON Data (Word-Level Timestamps)
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"text": " The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze."
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"text": " Where senior editors argue through the news with world leaders and policy makers in twice weekly long format shows. Basically an extremely high quality podcast. Whether it's scientific innovation or shifting global politics, The Economist provides comprehensive coverage beyond headlines. As a toe listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount."
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"text": " You cannot play any games about this. You have to admit that this is wrong. I think especially for mathematicians to come in and see an environment where there's guiding ideas that people haven't really worked out and a lot of things are known do not work for known reasons but people are still acting as if this is not true and trying to figure out how to do something and make career for themselves."
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"text": " Peter Wojt is a theoretical physicist and a mathematician at Columbia University. He's been an influential figure in the ongoing debates surrounding string theory. His critiques, as articulated in his book, Not Even Wrong, strike at the heart of many popular assertions about this framework. Professor Wojt also has a widely read blog in the math and physics scene called Not Even Wrong, so it's the same name, and the links to all resources everything mentioned will be in the description as usual. We take meticulous timestamps and we take meticulous show notes."
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"text": " In one sense, the problem with string theory is the opposite of the problem of fossil fuels. With fossil fuel companies, you have a goal, let's say it's to wash your clothes, and you're able to achieve that goal, but you produce negative externalities. Whereas string theory has plenty of positive externalities, but arguably achieves little toward its initial goal. Professor White introduces a novel toe approach called Euclidean twister unification. You may recognize that term twister as it's primarily associated with Roger Penrose. Twisters provide an alternative to space-time descriptions in quantum physics."
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"text": " Peter's application of twisters is in the Euclidean setting, and he talks about how this significantly changes the playing field. It opens up a connection between gravity and the weak interaction, because space-time in this formulation is inherently chiral. We also talk about spinners and Michael Atiyah. You know how some people are Christian mystics or Muslim mystics? Well, Atiyah seems to be a spinner mystic."
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"text": " We alternate between technical and more intuitive discourse. If you're new to the Theories of Everything channel, this is Par for the Course, and my name is Kurt Jaimungal. Usually what we do is we interweave between rigorous, steep technicality, and then periods of explaining the intuition behind what was just said. In other words, you can think of it as high-intensity interval training for the mind. Recall the system here on Toe, which is if you have a question for any of the guests, whether this guest or from a different Toe podcast,"
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"text": " Welcome, Professor."
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"text": " Thank you so much. It's an honor to have you. I've been wanting to speak to you for almost two years since you came out with Euclidean Twister Theory or Euclidean Unification Theory, and well, here you are. Well, thanks. Thanks for having me on. I'm looking forward to the opportunity to be able to talk about some of these topics. I've certainly enjoyed some of your other programs. The one with my friend Edward Frankel recently was really spectacular."
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"text": " Thank you. That's all due to Ed, of course. What are you working on these days? What's your research interest? There's something very specific. I'm just in the middle of trying to finish a short paper about an idea which I'm not quite sure what it is. I guess I've for now entitled the"
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"text": " The draft of the paper is titled, Space Time is Right-Handed. There's a slight danger it'll change conventions. It'll end up being that space time is left-handed, but I think it will stay right-handed. It's related to the twister stuff that I've been working on for the last few years, which I'm still quite excited about. There's one kind of basic claim at the bottom of what I'm trying to do with the twisters, which is"
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"text": " I think to the standard way of thinking about particle physics and general relativity and spinners, it's initially not very plausible. I should say one reason that it took me a long time to get back to the Euclidian twister stuff from some early ideas years ago was that I didn't actually believe that this basic thing that I needed to happen could happen."
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"text": " I think lots of other people have had the same problem with this. The more I looked into the twister stuff, the more I became convinced that something like this had to work out. More recently, the last few months, I've come up with an understanding in much simpler terms, not involving twisters, just involving spinners, about the really unusual thing that's going on here. I think that I've"
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"text": " I've been trying to write up an explanation of the basic idea, and I think it's a fairly simple one. As I've been writing it up, I keep thinking, well, wait a minute, can this really work? There's no way this can actually really work. But the more I've been thinking about it, the more I've been convinced, yes, this actually does really work. I'm hoping within the next few days to have a"
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"text": " a final version of that paper. Well, not a final version, but a version of that paper I can at least send around to people and try to get comments on and also write about it publicly on my blog. I read the paper. Thank you for sending it. What you have is a very, it was very early draft of it, which made even less, hopefully the, I'll have something that will make more sense will be what all the public will see, but we'll see. Yeah. Do you think spinners are more simplified or easy to understand than twisters?"
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"text": " Oh, yeah. So spinors are really very basic, very, very basic things. I mean, every, you know, every elementary particle like electrons are just the way you describe them. They're spin would have nature is as spinors. You have to electron wave functions are spinors. And so they're in every, you know, every physics textbook or every if you do quantum mechanics, you do quantum field theory, you have to spend a fair amount of time to spinors. So"
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"text": " Spinners are very, very basic things. I spent a lot of my career thinking about them, trying to better understand them. I keep learning new things. In the last few months, I realized something about them, which I think is new, at least I'd never seen before. This is what I'm trying to write about. They're very fundamental objects. It's a little bit hard to"
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"text": " I can give you a whole lecture on spinners. I'm not sure how much of that you want or where you want to start with that. Right. Well, there's one view that we can understand them in quotes algebraically, but that doesn't mean we understand what spinners are. So that's the Michael Attia approach where he says it's like the letter I, the complex I, the imaginary I back in the fourteen hundreds or fifteen hundreds. It's only now or a couple hundred years later you realize what they are. And so, sure, we have many different ways of describing spinners mathematically."
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"text": " but it's still a mystery as to what they are. Do you feel like we understand what they are or there's much more to be understood more than the formalism?"
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"text": " If you try and do geometry of any kind or Riemannian geometry, expressing everything in terms of spinors instead of in terms of vectors and tensors gives you a very different and in some ways more powerful formalism but one that people are not that used to and it has some amazing properties. It's kind of deeply related to"
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"text": " the notions about topology and k-theory and the Dirac operator gets into it. So the thing that made Atiyah really most famous, his index there was Singer. It's basically saying everything comes down to a certain kind of fundamental case and that is the fundamental case of the Dirac operator and spinners. So he was seeing the spinners kind of at the"
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"text": " as this really kind of central thing to the most important thing that he'd worked on. And so there's a lot to say. So there's a lot known about spinners, but there's also a lot, it's a little bit mysterious where they come from. I think the new stuff that I've been more, so I've been thinking about that a lot over the years, but the new stuff that has gotten where I think there's something new that I see going on is"
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"text": " Not the general story about spinners, but a very, very specific story about spinners in four dimensions. So you have spinners in any dimension, any dimension you can write down spinners and they're useful. But in four dimensions, some very, very special things happen. And the other very, very special thing, interesting thing that's going on in four dimensions is that from the point of view of physics, there's two different"
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"text": " Signatures that you're interested in you're interested in either spinners in the usual kind of four dimensions where all four dimensions are the same and you're just trying to do Euclidean geometry in four dimensions, which I might sometimes call Euclidean spinners or you're interested in spinners of the sort that you actually observe in relativistic quantum field theories where the geometry is that of Minkowski space. So sometimes refer to those as Minkowski spinners. And so you have two different versions of four dimensions, one"
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"text": " What is it your"
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"text": " Understanding or your proposal that the world is actually Euclidean and it's been a mistake to do physics in a Minkowski way when we wick rotate, we see that as some mathematical trick and you're saying no, no, no, that's actually the real space. That's real quote unquote, even though there's something imaginary about it. And the Minkowski case was the mistake like an analogy would be we operate in USD and then for some calculations, it's easier to go into yen."
},
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"text": " And we think that the actual world is operating in the United States and the calculations are just something to make the numbers easier. And then you're saying, no, no, no, what's really happening is in Japan and it's been a mistake to go into the USD or the USD is just to make the math easier. So is that what you're saying or no? Well, so this goes back more to the Euclidean twister stuff. Yes. So there. Well, it's been well known in physics that you really kind of that"
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"index": 28,
"start_time": 723.899,
"text": " There's a problem in Minkowski's space-time. If you try and write down your theory in Minkowski's space-time, the simplest story about how a free particle evolves, you write down the formulas for what's a free particle going to do, what's its propagator, and you see that it's just ill-defined. You've written down a formula which mathematically is ill-defined. It needs more information in order to actually be a well-defined formula."
},
{
"end_time": 780.316,
"index": 29,
"start_time": 754.104,
"text": " and I mean technically if you look at any physics book you'll see they're saying well you know we're going to do the answer is this integral and you look at this integral and this integral is going straight through two poles poles and uh you know that's just ambiguous you don't know what how to define such an ambiguity is about how you define such intervals so the one they ask what you've always known you have to do something like rotation you have to do something you have to"
},
{
"end_time": 810.23,
"index": 30,
"start_time": 780.708,
"text": " get rid of those ambiguities. And one way of getting rid of those ambiguities is, you know, analytically continuing and making time a complex variable, analytically continuing it, analytically continuing maybe to Euclidean signature, and there the formulas are well defined. So it's um, yeah, I'm not sure. I'm very comfortable saying one of these is real and one of these is not. It's the same. It's the same formula. It's just, you have to realize that"
},
{
"end_time": 839.428,
"index": 31,
"start_time": 810.759,
"text": " To make sense of it, you have to kind of go into the complex plane in time and you can, if you things are analytic, if this is a holomorphic function in time, you can either evaluate what happens at a measuring time or you can make time real, but you have to take the limit in a certain way moving, like perhaps starting with a measuring time and then moving analytically continuing a certain direction to get"
},
{
"end_time": 868.097,
"index": 32,
"start_time": 839.889,
"text": " a real time. But that's a standard story. That's not me saying this. That's a standard story. And then there's a, how do you, what sense do you make of this? Is this just a mathematical trick? Which a lot of physicists will say, well, that's just some kind of weird mathematical trick. It's not, it has nothing to do with reality. Or do you take this more seriously? So what's always fascinated me is more, is that it's fairly clear what's going on if you just talk about"
},
{
"end_time": 893.336,
"index": 33,
"start_time": 868.677,
"text": " scalar fields. If you talk about particles with spin zero or fields that transform trivially under rotations, what happens when you go to imaginary time is quite interesting and in some ways tricky, but it's very well understood. But it's never actually been very well understood what happens when you have spinner fields. And this is the problem is that"
},
{
"end_time": 923.183,
"index": 34,
"start_time": 894.838,
"text": " The spinners in Euclidean signature and spinners in Kowski signature are quite different things. And so you can't just say, oh, I'm going to analytically continue from one to the other because they're not related. Anyway, it's very unclear how you're going to do that. And so there's also a similar story in twister theory. You can do twister theory in Kowski space time, which is what Penrose and his collaborators mostly did, or you can do it in Euclidean"
},
{
"end_time": 953.404,
"index": 35,
"start_time": 923.78,
"text": " Signature space time, which is what a Tia and a lot of other people and mathematicians have done and and and in principle the two are related by analytic continuation, but the way that works is quite um, you know, I think it's much it's much subtler than you expect and uh, and so and what i've been interested in, you know, most recently this this business about um, it really is a claim That the standard way of thinking about how you analytically continue between these two different kinds of spinners is um"
},
{
"end_time": 982.619,
"index": 36,
"start_time": 953.933,
"text": " you're making kind of a wrong choice when you do that and there's a good reason for the standard choice you're making when you normally when you do that but there is actually another choice you can make which is that instead of working with spinners which are kind of symmetric between there's two different kinds which by convention you can call right and left handed or positive and negative chirality and the standard set up treats this question"
},
{
"end_time": 999.411,
"index": 37,
"start_time": 984.616,
"text": " What I've realized recently is it looks like it's quite possible to make this setup completely asymmetric so that you"
},
{
"end_time": 1025.333,
"index": 38,
"start_time": 999.94,
"text": " You just described spinners using these right-handed or positive chirality spinners. You just don't use the left-handed ones at all in your construction of space-time. You can do that, it appears to be, and that's why this paper is called space-time is right-handed. Is it the case that you could have called it space-time is chiral and you could have equivalently described as left-handed or is there something specific about right-handedness?"
},
{
"end_time": 1054.565,
"index": 39,
"start_time": 1025.469,
"text": " No, it's a matter of convention. To say it a little bit more technically, the Lorentz symmetry group is this group called SL2C. It's two by two complex matrices, determinate one. What you realize is if you work in complex version of four dimensions,"
},
{
"end_time": 1076.749,
"index": 40,
"start_time": 1055.145,
"text": " The symmetry group is two copies of SL2C and you can call it a plus copy and a minus copy or you can call it a right copy and a left copy but there's two of them. And the standard convention in order to get analytic continuation to work out the way people expected has been to say that the physical Lorentz group"
},
{
"end_time": 1106.254,
"index": 41,
"start_time": 1077.5,
"text": " that we that corresponds to our real world is is not chirally symmetric it's it's kind of a diagonal which is you use both the right and left and you have to complex conjugate when you go from one side to the other but it kind of the lorenz group the sl2c lorenz group we know is supposed to sit as kind of a diagonal thing which is both right right and left but um what i'm kind of arguing is that no you can actually set things up so that the"
},
{
"end_time": 1132.927,
"index": 42,
"start_time": 1106.954,
"text": " The Lorentz group is just one of these two factors. It could have been the right factor, the left factor. You have to make a choice of convention. So it is very much a chiral setup. But the strange thing about this is you only really see this when you complexify. If you just look at Minkowski's space-time, you don't actually see this"
},
{
"end_time": 1162.244,
"index": 43,
"start_time": 1133.404,
"text": " Anyway, you don't see this problem or you don't see this ability to make this distinction. It's only when you go to Euclidean space-time where the rotation group really does split into two completely distinct right and left things, or if you go to complexified space-time where you have this two copies of SL2C, it's only in those contexts that you actually see that there is a difference between choosing the diagonal and choosing the right-handed side."
},
{
"end_time": 1192.637,
"index": 44,
"start_time": 1162.739,
"text": " So for SL2C, you call that the Lorentz group. Is that technically the double cover of the Lorentz group? Yeah, people use both terminology. If you're going to work with spinners, you have to use the double cover. But yes, it's also... Yeah, sometimes you might want to say that SL3-1 is the Lorentz group and this is the double cover. But mostly you're interested in working with spinners and then you have to use the double cover, really. Yes."
},
{
"end_time": 1216.869,
"index": 45,
"start_time": 1192.824,
"text": " So is there a reason that triple covers or quadruple covers aren't talked about much? Is it just because of experiment, there's nothing there? Well, it's more the mathematics that they don't. There is, I mean, there is, you know, any the rotation groups of any kind, you know, have this to have this twofold nature, there is this spin double cut, there is this heavy spin double covers."
},
{
"end_time": 1245.691,
"index": 46,
"start_time": 1217.875,
"text": " In many cases, one way of seeing this is just a basic topology. The topology of rotations has a plus and minus thing in it and you have to do something about that. So there aren't any kind of known mathematically interesting triple covers, etc. Now, in the standard model, the way that"
},
{
"end_time": 1268.063,
"index": 47,
"start_time": 1246.596,
"text": " It's written in bundle languages that it's a principal bundle, and then the gauge groups are the structure groups. And then for general relativity, you have a tangent bundle. And then some people say that the gauge group of GR is the diffeomorphism group. But is there a way of making that into a bundle, like a principal bundle with a diffeomorphism group? How is one supposed to understand that as a bundle construction?"
},
{
"end_time": 1294.497,
"index": 48,
"start_time": 1269.189,
"text": " Yeah, yeah. Anyway, there's a lot of different ways. There's several different ways of thinking about geometry and about Romanian geometry. Yeah, and this starts to get a complicated subject. Maybe the best way to... Well, thinking in terms of different morphism groups is something you can do."
},
{
"end_time": 1318.541,
"index": 49,
"start_time": 1295.009,
"text": " I it's actually not my favorite way of doing this kind of geometry and for for the reason is that it um well maybe let me just say something about about an alternate way of uh of thinking about geometry which which seems to be more powerful maybe actually to motivate this a little bit better sure if you just think about different morphism groups"
},
{
"end_time": 1348.729,
"index": 50,
"start_time": 1318.916,
"text": " It's very, very hard to understand what spinners are and where they come from. You really kind of can't see them at all if you're just thinking about the diffeomorphism group of a manifold. So the other formulation of geometry, going back to Cartan, which makes it much easy to see where spinners are going and is a lot more powerful in other respects, is to think not about"
},
{
"end_time": 1373.729,
"index": 51,
"start_time": 1349.309,
"text": " not about a manifold, but about a bigger space, which is a bundle that for each point in the manifold, you consider all possible bases for the tangent bundle. It's also called frames. And so this is sometimes called the frame bundle. And so it's kind of saying if you want to understand geometry, you should look at the points of space and time, but at the same point,"
},
{
"end_time": 1403.234,
"index": 52,
"start_time": 1374.445,
"text": " You also got to think about the tangent space and you should think about the possible bases of the tangent space and the so-called frames. So you should always kind of think, instead of bringing all your formulas in terms of local coordinates on the manifold, you should think about your problem as being a problem that lives up on the frame bundle and that you're not just at a point in space time, but you've also got a frame."
},
{
"end_time": 1431.51,
"index": 53,
"start_time": 1403.746,
"text": " But then you have to be careful to kind of work kind of equivalently that you have, you know, you can, you can change your choice of frame, you can rotate your frames. So you have, you kind of work up in the frame bundle, but equivalently with respect to rotations or whatever that, so that's a, that gives a lot more structure to the problem. In particular, it allows you to easily say what spinners are, which you couldn't if you just talk about it. So, um, so,"
},
{
"end_time": 1460.367,
"index": 54,
"start_time": 1432.449,
"text": " Anyway, there's a lot more we could say, but if you're more for some groups and that, but just in terms of the relation to the spinner stuff, maybe to forget about it, to say it that way. It's not that you have to do something quite different if you're going to talk about spinner. Right. OK, now the problem you were working on earlier that you said you weren't sure if it would have a solution and you're finding that it does. What was it in the early part of the conversation what you're working on your research interests?"
},
{
"end_time": 1480.725,
"index": 55,
"start_time": 1460.828,
"text": " Well, do you mean, right at the beginning where I'm still what I'm still confused about? Yeah. Okay. It seemed to me that you were saying you're solving the problem. Oh, yes. Yes. I think it could be solved. You're surprised. So this actually I mean, this was actually it goes back to when I was graduate student or postdoc of his first"
},
{
"end_time": 1504.974,
"index": 56,
"start_time": 1481.237,
"text": " Occurred to me look, you know, actually, maybe to kind of explain how this all came about. So I was a graduate student at Princeton and I was working on lattice gauge theory. So we're working on this kind of formulation of Yang-Mills theory on a lattice. And so you can actually do computer calculations of it. And so I was trying to understand, you know,"
},
{
"end_time": 1531.613,
"index": 57,
"start_time": 1505.367,
"text": " There's a lot of interest in topological effects in Yang-Mills theory, and I was trying to understand how to study those in the kind of numerical calculations on the lattice. And then, so I made some progress on that. But then the next thing that really occurred to me was exactly spinners came up. Besides having Yang-Mills theory on the lattice, we also want to put spinner fields on the lattice. So there's this really beautiful way of putting"
},
{
"end_time": 1560.708,
"index": 58,
"start_time": 1532.176,
"text": " gauge fields in the lattice, Yang-Mills theory, which kind of respects the geometric nature of the gauge fields very, very nicely. It's kind of the Wilson's lattice gauge theory. But there isn't, if you try and put spinors in the lattice, a lot of very mysterious things happen. And again, in some sense, the problem is that if you're just looking at this lattice that you've written down, it's clear kind of what the discrete analogs of vectors are and of planes and of"
},
{
"end_time": 1590.725,
"index": 59,
"start_time": 1561.664,
"text": " you know, of those things, but it's very, very unclear what the, you know, since you don't really have a good way of thinking about spinners in terms of kind of standard geometry of, you know, lines, planes, etc. You don't really know how to put the spinners and lattice in a way that respects their geometry. And if you try to write down the formulas or do anything, you run into a lot of weird problems. There's a lot of anyway, there's a long story about what happens if you spinners and lattice."
},
{
"end_time": 1619.121,
"index": 60,
"start_time": 1591.408,
"text": " Yeah, so there's one thing you find is that there's no consistent way to put a single kind of fermion in the lattice. That if you try and do it any way you know of doing it produces all these extra versions of the same thing and you have to somehow disentangle those. That's part of the problem. But that's when I started thinking about the geometry of spinners and"
},
{
"end_time": 1647.807,
"index": 61,
"start_time": 1619.599,
"text": " some ideas about putting them on the lattice. And then what I was seeing, I started to see that, wait a minute, you know, if you, so this is all happening in Euclidean space where the rotation group is a copy of two SU2s. There's again a left-handed one and a right-handed one, if you like. And what I was seeing really was that the, some of the choices, the geometry I was trying to use to put these things in the lattice gave me kind of"
},
{
"end_time": 1672.534,
"index": 62,
"start_time": 1649.189,
"text": " Things occurring and kind of multiplets that had the same SU2 structure as what you see in a generation of electroweak particles. So in a generation of electroweak particles, for instance, you have a neutrino and left-handed neutrinos and you have right-handed and left-handed electrons, for instance."
},
{
"end_time": 1701.647,
"index": 63,
"start_time": 1673.456,
"text": " And those have certain transformation properties under the SU2 and under a U1. And those were the same ones that I was seeing when I was trying to construct these spinners. So it seemed to me, if you can think of part of this rotation group, this SU2, as an internal symmetry, as the symmetry of the weak interactions of the Weinberg's law model, then you could actually"
},
{
"end_time": 1728.746,
"index": 64,
"start_time": 1702.892,
"text": " Anyway, you got all sorts of interesting things to happen, but the thing that this, but making this idea work really required that some explanation of why in Euclidean space, what you thought were space-time symmetries that really broke up into half space-time symmetries and half an internal, internal symmetries, which didn't affect space-time. So I never,"
},
{
"end_time": 1755.145,
"index": 65,
"start_time": 1729.258,
"text": " This is what, for many years after looking at this, I was like, well, this just can't work. I mean, you can't, if you just look at the whole formalism for how you've set this up and, you know, both of these SC2s have to be space-time symmetries. You can't, they're both going to affect space-time. You can't get away from that. Other people didn't see this as a problem? No, no, I think everybody saw this as a problem. I mean, I think anybody who ever looked at this idea of trying to get"
},
{
"end_time": 1781.613,
"index": 66,
"start_time": 1755.998,
"text": " you know one of the part of the four-dimensional rotation symmetry to be an internal symmetry has probably backed away backed away from it for the same reason saying well wait a minute this can't you know i just can't see how that could actually happen that that you have to you're telling me this should be an internal symmetry which doesn't affect space time but looks to me that you're rotating space time with it so you can't do that and so this so this is what um"
},
{
"end_time": 1810.811,
"index": 67,
"start_time": 1782.637,
"text": " many years kind of kept me from going back to those ideas. And as I learn more about quantum field theory, actually one motivation as I was teaching this course on quantum field theory and quantum field theory in the back of my mind is, okay, you know, as I go along and teach this course, I may not explain this to the students, but I'm going to very, very carefully look at the formalism and I'm going to understand exactly how this analytic continuation is working of these spinners. And I'm going to"
},
{
"end_time": 1838.456,
"index": 68,
"start_time": 1811.715,
"text": " and I'm going to see that it looks like this has to work and I'll finally understand why and then I can stop thinking about this. But as I was teaching this, as I was looking at this, I never actually saw the argument for why this has to be a space observatory. It looked like it had to, but you couldn't quite pin down why."
},
{
"end_time": 1868.712,
"index": 69,
"start_time": 1839.292,
"text": " Anyway, so then when I went back to the twister stuff, I became convinced that if you think about everything in terms of twisters, then the whole twister setup is naturally chirally asymmetric. From the twister point of view, this kind of thing looked a lot more plausible and I got more interested in it again. But it's only very recently, the last few weeks, the last couple of months that I've kind of"
},
{
"end_time": 1897.602,
"index": 70,
"start_time": 1870.06,
"text": " I have a very good understanding of exactly why it seemed that why I was right. This should be impossible. There is a standard assumption that you're making, which makes what I wanted to do impossible. But it's also possible to not make that assumption and do something else. And that assumption is? It's the symmetry between right and left. It's kind of when you go between Minkowski and Euclidean,"
},
{
"end_time": 1925.469,
"index": 71,
"start_time": 1898.626,
"text": " spinners you know the the setup that you use to analytically continue do you do that in a setup which is um which is right left symmetric and and if you want the setup to be holomorphic then you have to you have to use the right left symmetric one but what i saw so simultaneously i realized yes you can yeah yes i mean this in the standards"
},
{
"end_time": 1955.725,
"index": 72,
"start_time": 1925.947,
"text": " There was a very, very good reason that I and everyone is skeptical that this can make sense, but there also there actually is a way around it. You can just decide, OK, I'm going to I'm going to just use right handed spinners and I'm going to and you can get you can get a theory that makes sense. I don't know if I'm jumping ahead, but I recall in one of the lectures that I saw online of you and you were giving the lecture, I believe Cole Fury was in the audience. You're saying that what we have to use are hyper functions."
},
{
"end_time": 1981.783,
"index": 73,
"start_time": 1956.067,
"text": " Yeah. Am I jumping ahead because you're saying it's not going to be holomorphic? No, but actually hyper functions are really part of the holomorphic story. They're not. Hyper functions are really just saying, so what I was saying when I was trying to explain this business about, you know, why about WIC rotation and that things were"
},
{
"end_time": 2009.616,
"index": 74,
"start_time": 1982.944,
"text": " That if you write down the standard formulas, you end up with something in the Caskey space time, which is ill defined. Okay. And then you have to use, you have to define it via re-rotation or analytic continuation. There's just another way of saying that more with putting in a more interesting mathematical context is to say that the things that you're looking at him in Caskey space time are not actually normal functions there, or they really are"
},
{
"end_time": 2038.626,
"index": 75,
"start_time": 2010.776,
"text": " What they are best thought of as hyper functions. In this case, they're hyper functions which are just kind of boundary values of analytic things as you approach the real line. So the hyper function story is just kind of part of the standard. It's really part of the rotation story. This latest thing I'm trying to do actually gets away from analytic continuation."
},
{
"end_time": 2068.814,
"index": 76,
"start_time": 2039.206,
"text": " You really, I'm really, I'm still kind of, you know, trying to wrap my head around exactly what the implications of this are, but you are, you're not doing the standard sort of analytic continuation anymore. The standard sort of way of analytically continuing, which uses all four space time dimensions, that you're not doing that. You're doing something different and it's unclear."
},
{
"end_time": 2099.309,
"index": 77,
"start_time": 2069.343,
"text": " Yeah, anyway, I mean, if you start writing out formulas, you'll still get the same story with hyper functions. But what prompted you to then go look at twisters? And by the way, is it called a twister formalism or twister formulation? I don't know. Either one is I don't know if those are used interchangeably. I hear, for instance, that there's different quantum formalisms like Vigners or interaction or path or categorical. But then sometimes I hear, yeah, the categorical formulation of quantum mechanics. I'm like, OK, you get the idea."
},
{
"end_time": 2122.995,
"index": 78,
"start_time": 2099.599,
"text": " Well, the thing about twisters is they're not actually... Maybe a good thing to say about twisters is we don't actually know exactly what their relevance is to the real world. If you have a well-developed idea using twisters for describing the real world and you wanted to contrast it to other"
},
{
"end_time": 2148.183,
"index": 79,
"start_time": 2123.66,
"text": " similar descriptions you might want to say oh this is the twister formalism or maybe twister formulation i don't know but it's a little bit but either one is a little bit premature in terms of physics that we don't actually know what exactly how the twisters are related to the real world so it's not like you can translate a real world problem to twister formalism and then back well you can so maybe"
},
{
"end_time": 2177.244,
"index": 80,
"start_time": 2150.213,
"text": " Twisters are a bit like spinners. They have some of the mathematical properties of spinners, but they do something more interesting. They're kind of a higher dimensional thing. Maybe one of the best things to say about them is that they're very useful. If you want to understand Minkowski's space-time, this is what Einstein figured out. You can use"
},
{
"end_time": 2203.097,
"index": 81,
"start_time": 2177.449,
"text": " Minkowski's geometry, Minkowski metric, if you want to talk about vectors and metrics and tensors, or if you talk about Minkowski space-type spinors if you want, that's what I've been most interested in. But the other interesting thing about our theory is when we write them down in Minkowski space-time, theories of massless fields and things like Yang-Mills theory,"
},
{
"end_time": 2226.92,
"index": 82,
"start_time": 2203.797,
"text": " They have this bigger invariance group than just under rotations and translations, they're conformally invariant. So the geometry of Christos really comes into its own if you're trying to describe, to understand the properties of space-time under conformal transformations."
},
{
"end_time": 2248.831,
"index": 83,
"start_time": 2228.183,
"text": " Anyway, so that's kind of a motivation. So if you don't care about conformal transformations, you may not be very interested in spinners. But if you really want to understand, you know, what is, how do I write down my theories? And how do I have a version of you, of Mitkowski space time that where the conformal group acts"
},
{
"end_time": 2278.763,
"index": 84,
"start_time": 2249.65,
"text": " in a nice linear fashion where everything works out and the spinner, now you can call it a formalism or a formulation, but it's a way of doing conformal geometry. It really comes into its own. So spinners go, I mean, twisters go way back and this really was mainly Roger Penrose is doing in the 60s and he was very interested in using them to understand"
},
{
"end_time": 2301.664,
"index": 85,
"start_time": 2279.531,
"text": " You know, things happening in Minkowski's Space Time and especially the conformal invariance of these things. And so there's a huge amount of effort and a lot of beautiful things discovered during the 70s, especially by him and his collaborators in Minkowski's Space Time. And then Atiya realized that you could take this over and do some very, very interesting things in"
},
{
"end_time": 2326.766,
"index": 86,
"start_time": 2302.381,
"text": " Romani and geometry and Euclidean space time. Yeah, so I was you know, I kind of learned about this geometry the response that sentence could be said about a Tia in the most general form and then a Tia realized you could use this for underscore with geometry. Yeah. Yeah. Yeah. So it's but anyways, so I've been kind of aware about twisters for a long time, but I, you know, I didn't see"
},
{
"end_time": 2357.073,
"index": 87,
"start_time": 2327.722,
"text": " Anyway, I actually wrote a very speculative paper a long, long, long ago about this, and it mentioned the connection to twisters, but there's just a lot about them that I didn't understand back then. It took me many years to understand, and especially the relationship between Euclidean signature and Mancassi signature spinners, how they're related. That's quite a tricky story, which would take me a long time to understand. So you have the splinter in your"
},
{
"end_time": 2384.377,
"index": 88,
"start_time": 2357.295,
"text": " thumb for decades about the space-time symmetries and them acting not just on space-time. What happened in 2020 and 2021? One thing that happened in 2020 was COVID. In your mind, what happened in 2019 then? No, but this is actually relevant because actually in 2020, I was much more"
},
{
"end_time": 2410.538,
"index": 89,
"start_time": 2385.742,
"text": " And I was thinking of this stuff, but yeah, but yeah, but in 2020, all of a sudden, you're kind of, you know, you're at home, you're at home a lot that you're just sitting there and I office at home and I don't have a lot of all the usual distractions or whatever. And so and so that actually actually gave me some of the more time to kind of think peacefully about about some of this stuff and make some and make some progress. Yeah. So I'd have to, I mean, I,"
},
{
"end_time": 2439.599,
"index": 90,
"start_time": 2410.93,
"text": " How does it fit? Is there a way of explaining it? Maybe the best thing to say about Twister theory is that it really"
},
{
"end_time": 2470.282,
"index": 91,
"start_time": 2440.759,
"text": " It really kind of naturally wants to be a theory of complex space-time. And this is the thing, if you say I'm going to study four dimensional complex space-time and I'm interested in its conformal group and things like that, then the Twister story is actually very, very simple. You're basically just saying that there's a four complex dimensional space and a point in space-time is a complex two-plane in that four dimensional space. So points"
},
{
"end_time": 2498.712,
"index": 92,
"start_time": 2470.964,
"text": " Anyway, yeah, so instead of thinking of the way of normal thinking of some space with these points where you got to think about just think about the complex two planes and complex four dimensional space and and you know everything is kind of drops out of that and and that there is one there's a beautiful relation of that story to the theory of spinners is that and this is kind of the relationship between the theory of twistered and theory of spinners"
},
{
"end_time": 2528.695,
"index": 93,
"start_time": 2499.838,
"text": " In twister theory, a point in four-dimensional space-time is a complex two-plane. That's the definition of what a point is. But that complex two-plane, that kind of tautologically answers the question of where do these spinners come from? Because the space of spinners is a complex two-plane. So from the standard point of view,"
},
{
"end_time": 2555.913,
"index": 94,
"start_time": 2529.036,
"text": " As I was saying, if you just think about the diffeomorphism group, it's very, very hard to even say what a spinner is. So where are these weird complex two planes coming from? Well, from the point of view of twister theory, it's purely tautological. It's just, you know, the two plane is a point. So the spinner, the spin one half two plane, complex two plane, which is describing the spin of an electron is exactly"
},
{
"end_time": 2583.951,
"index": 95,
"start_time": 2557.5,
"text": " That's exactly what the definition of a point is. A point in twister space or a point in space-time? A point in space-time. Twister space is a four complex dimensional thing. The points in it correspond to various structures in space-time, but the complex two planes in it correspond to the points in space-time. That's one of the basic"
},
{
"end_time": 2605.572,
"index": 96,
"start_time": 2584.548,
"text": " Yeah, so then is the statement that the points in space time are the same as spinners or the points in space time or the structure of space time gives rise to the structure of spinners and vice versa or are none of those statements correct? I think both of them. I mean, it really is telling you twister theory is really telling you that it's a it's a way of thinking about space time in which"
},
{
"end_time": 2632.381,
"index": 97,
"start_time": 2606.067,
"text": " And sorry, this is four dimensional space-time. Four dimensional space-time, yeah. Yeah, yeah, yeah. It's a way of thinking about, yeah, so Twister theory is very, very special to four dimensions. It doesn't really work in other dimensions. But it really is, it's a way of thinking about space-time in which, you know, the occurrence of spinners and their properties are just completely tautological. They're just built into the very definitions. Sociologically, why do you think it is that Penrose's Twister program"
},
{
"end_time": 2660.623,
"index": 98,
"start_time": 2633.046,
"text": " Firstly has been allowed to continue because many other programs just die out if you're not loop or string or causal or asymptotic. Like there's just four as far as I can tell. Five with Penrose. So why is it alive? And then why hasn't it caught on? Well, for I mean, or maybe you disagree, it's not alive. No, no, no, it's very much it's very much alive. It's very much alive and still. But and so there's an interesting kind of history. But but a lot of it was really"
},
{
"end_time": 2687.466,
"index": 99,
"start_time": 2661.203,
"text": " So he had this idea and he's raised places to explain how he came up with it and he was very, very struck by this. And so he quite successfully at Oxford built up a group of people working on this. And so it was a good example of how normal science kind of works sociologically. Somebody comes up with a good idea and they actually build a group of people around them and"
},
{
"end_time": 2717.329,
"index": 100,
"start_time": 2687.875,
"text": " People do as people do more work, they learn more interesting things about this more people get interested. So, you know, he always, you know, throughout the 70s, I would say into the 80s, there always was a quite healthy group of people, you know, working on Penrose or people somehow having some relation to Penrose collaborators were working on this. So it was anyways, but perfectly normal science. It wasn't it wasn't so clear, though, how to get"
},
{
"end_time": 2741.288,
"index": 101,
"start_time": 2717.841,
"text": " Some things were very clear. Some things were clear that this was really a beautiful way of writing down conformally invariant wave equations and studying their properties. The beauty of the idea and the power to do certain things was known, but it didn't seem to be necessary or have any particular connection to specific problems in particle physics. Particle physicists would look at this and say, well, that's nice, but"
},
{
"end_time": 2770.265,
"index": 102,
"start_time": 2741.698,
"text": " You know, I don't, that doesn't actually tell me anything. You know, if I need, if I needed to do some conformally invariant calculations, I might be able to use that, but it's not actually telling me something really that, you know, really knew I can't get elsewhere. Um, and, and then, you know, and then in the eighties, you also had, uh, you know, a Tia got into the game and there's a lot, a lot of mathematicians got into it through the, um, the relations to the, on the Euclidean side. So, you know, it was, uh,"
},
{
"end_time": 2793.541,
"index": 103,
"start_time": 2770.845,
"text": " Especially among mathematicians, mathematical physicists, it remained a very active area and it still is to this day. A lot of it was based in Oxford but also a lot of other places. But in terms of its implications for physics, I would say the thing that"
},
{
"end_time": 2820.845,
"index": 104,
"start_time": 2794.36,
"text": " I think Penrose and his people trying to connect this to physics in an interesting way, they kind of ran out of new ideas or some things that they could do, but they couldn't actually get any kind of really killer app if you like. From my point of view, I don't know if I can, I think"
},
{
"end_time": 2845.896,
"index": 105,
"start_time": 2821.34,
"text": " Anyway, I don't know if I'll ever be able to convince them or what they think of it these days. But the problem was that they were thinking of connecting this to physics purely from the Minkowski spacetime side. So they're looking at Minkowski spacetime twisters, Minkowski spacetime spinners. And those, the twister theory just didn't, if you just look at Minkowski spacetime, you don't see"
},
{
"end_time": 2872.449,
"index": 106,
"start_time": 2847.551,
"text": " You don't see the sort of new things, which I'm finding interesting, which I think tell you something new about particle physics. You don't see this kind of internal, the fact that one of these factors can be an internal symmetry. You just can't see that in Mikowski's space time. And then there's some other more technical things about, better not get into that, but there's kind of a"
},
{
"end_time": 2902.944,
"index": 107,
"start_time": 2873.404,
"text": " Well, it's okay. The audience is generally extremely educated in physics and math. Yeah, I would actually, well, maybe to connect this to what I'm saying, right, is I think, you know, also the way people think about general relativity in, I mean, Caskey's signature, general relativity is not a chiral theory. It's supposed to be left right invariant, parity symmetric theory. So the problem with thinking about general relativity in terms of twisters"
},
{
"end_time": 2932.005,
"index": 108,
"start_time": 2903.336,
"text": " is that your setup is completely chiral. If you try and do gravity with it, you end up with something that's not quite the right theory of gravity. It's kind of a chiral version of gravity. Anyway, this is a very interesting story. I think Penrose always referred to this as the googly problem. Something about cricket. In cricket, there's something about how"
},
{
"end_time": 2954.172,
"index": 109,
"start_time": 2932.602,
"text": " You can see from my point of view that was always"
},
{
"end_time": 2982.415,
"index": 110,
"start_time": 2954.667,
"text": " That's evidence of exactly what I'm trying to say now that, well, space-time is right-handed. Yes. Yeah. So it's a related problem. So Penrose and the people around him, I think, put a lot of effort into trying to revamp twister theory into something chirally symmetric. Now, why would they want to do that if the standard model isn't? Well, they weren't really trying to describe the standard model. They never really have it."
},
{
"end_time": 3011.886,
"index": 111,
"start_time": 2982.995,
"text": " They thought twisters were a way of thinking about space-time, so they wanted to do general relativity. And general relativity is not a chiral theory. So they were trying to find kind of a, how do we get rid of all this chirality? And they never were really successful at that. So you're saying it's a pro, not a con. Yeah, exactly. It's a feature, not a bug. Yeah. Right, right. But one interesting, fun thing about the sociology, though, is that what..."
},
{
"end_time": 3038.814,
"index": 112,
"start_time": 3012.5,
"text": " The idea that you could use twisters to do general relativity and perhaps quantize it, that was always something which Penrose and his people were working on. But most physicists, I think, felt that wasn't really going anywhere. This wasn't going to work. And maybe Witten was an example of somebody, I think, who really could see the mathematical power of these ideas and how important they were as new ideas about geometry."
},
{
"end_time": 3066.118,
"index": 113,
"start_time": 3039.155,
"text": " Again, that's a general statement that can be said, and then Ed Witten saw the power of this mathematics, dot, dot, dot. Yeah. I'll say so he I think even going back to a postdoc, he had learned about twisters, he was trying to do some things with it. But um, but he never kind of but he that he that actually finally finally found something and this was about 20 years ago. And what became known as the twister string. So we actually became he found a way of kind of writing"
},
{
"end_time": 3096.732,
"index": 114,
"start_time": 3067.739,
"text": " Yeah, a different way of writing down the perturbed calculations in Yang-Mills in terms of a sort of string theory, except it's a very different kind of string theory than the one that's supposed to be the theory of everything. And it's a theory where the string lives in twister space. So Ritten wrote this really kind of beautiful, very, very beautiful paper about twister string theory. And so since Whitten is talking about twisters, of course, all of a sudden there's a lot of"
},
{
"end_time": 3117.841,
"index": 115,
"start_time": 3097.278,
"text": " Physicists who were never had anything good to say about twisters all of a sudden are rushing out to learn about twisters. There's been an ongoing story of this twister string story which is a lot of people have done a lot of things but again a lot of it hasn't really worked out the way people"
},
{
"end_time": 3148.558,
"index": 116,
"start_time": 3118.592,
"text": " Well, like, and for the same reason as Pender, that Pender's always had that the people are trying to find quantize a chirally version, a chirally symmetric version of general relativity using this thing. And that's not what it really wants to do. So anyway, but that's kind of that's sociologically very important about why most high energy physicists, you know, have more have heard about twisters and don't and often have nice things to say about them is because of the twister string."
},
{
"end_time": 3171.817,
"index": 117,
"start_time": 3149.07,
"text": " There are quite a few questions that I have. One is, the particle physicists' repudiation of twister theory or just distancing from it because it's not useful to them, is that something that they also slung at string theory or were they more embracing of it? Earlier you said that the particle physicists"
},
{
"end_time": 3195.196,
"index": 118,
"start_time": 3172.278,
"text": " weren't initially adopting string theory, sorry, twister theory, because it didn't provide them with anything that's new. You said, well, okay, if we need to do some conformally invariant calculation, we'll use twister theory. Yeah. But at the same time, string theory is known, or at least colloquially known for not producing what's useful to high energy physicists, but useful outside of high energy physics, like to mathematics, or maybe condensed matter physics."
},
{
"end_time": 3222.398,
"index": 119,
"start_time": 3195.52,
"text": " What I'm asking is around the same time when they were distancing themselves from twister theory, you're not using it. Were they then embracing of string theory or they gave the same critique? Well, okay, so we have to you should start talking about string theory. Yeah, that's a kind of a complex, this kind of complex story. And it has the whole story of particle physics and string theory. That that's pretty well pretty much completely disconnected from from twisters because"
},
{
"end_time": 3249.104,
"index": 120,
"start_time": 3223.353,
"text": " The issues about why people were doing string theory or why they might or might not want to do string theory really had nothing to do with twisters. Twisters is a speculative geometric framework, and then twisters make a small appearance due to Whitten at one point 20 years ago, but that's about it."
},
{
"end_time": 3280.435,
"index": 121,
"start_time": 3250.435,
"text": " Maybe we can start talking about the whole string theory and particle physics business, but I'm not twister. Anyway, just twisters. It seems like a bad place to start. I'm not trying to mix up twisters with it. What I just meant to say was it's interesting what gets accepted and what doesn't. Yeah. And so why was string theory accepted? Take us through the history of that. And also you could tell people who may have just heard the term, the name, sorry, Ed Whitten, but all they know about him is that he's a genius, but they don't realize that influence that he has."
},
{
"end_time": 3310.367,
"index": 122,
"start_time": 3281.92,
"text": " This is a good place to start. Witten is really central to this story. I think the short summary of the history of this subject of particle physics was that by 1973, you had this thing called the Standard Model, which was this incredibly successful way of talking about particle physics and capturing everything that you see in"
},
{
"end_time": 3339.497,
"index": 123,
"start_time": 3310.93,
"text": " When you do high energy physics experiments, and the story, you know, when I kind of came in, it feels like I went to start learning about, probably started reading books and things about what's happening in particle physics, probably right around the mid, late 70s, mid 70s. I went to college in 75 and I spent most of my college career, a lot of it learning about the standard model and this stuff. And then, so by, but by the time I left grad,"
},
{
"end_time": 3362.398,
"index": 124,
"start_time": 3339.735,
"text": " Grad school, by the time I left college, 1979, and I went to graduate school at Princeton, people were starting to get, people had now spent, let's say just six years, let's say, trying to figure out how to do better than the standard model. And one thing is how to find some kind of new"
},
{
"end_time": 3392.398,
"index": 125,
"start_time": 3363.422,
"text": " Anyway, how to do better the standard model as a theory of particle physics, but also but one thing is the standard model doesn't give you a quantum theory of gravity. So the other thing was, how do we get a quantum theory of gravity? So these were kind of the big problems are already in the air. And Witten, you know, so Witten is a genius and he had been a grad student at Princeton. He actually came to Harvard as a postdoc, I think in 77, 78. And I met him when he was actually was a postdoc."
},
{
"end_time": 3422.432,
"index": 126,
"start_time": 3393.217,
"text": " And he quickly started doing some really amazing things. I went to Princeton in 79. A year or two later, he went directly from a postdoc at Harvard to becoming a full professor at Princeton, becoming a professor at Princeton very quickly, and he was there. And so the years I was in Princeton as a graduate student were from 79 to 84, and those were years"
},
{
"end_time": 3451.886,
"index": 127,
"start_time": 3423.234,
"text": " People I think were getting more and more frustrated. There were lots of ideas coming up, but every idea that people kind of tried to do better than the standard model or maybe to quantize gravity really didn't quite work. And people were kind of cycling every six months through. There's some new idea, you'd work on it for six months or a year and people start to realize, well, this doesn't really do what we want to do, let's find something else. So there were a lot of new ideas, but nothing"
},
{
"end_time": 3479.701,
"index": 128,
"start_time": 3452.312,
"text": " There was this idea that was very unpopular, that very few people were working on, to try to quantize gravity and unify it with the particle physics through string theory. And so it was people like John Schwartz and Michael Green were working on this, but it was a very small group of people."
},
{
"end_time": 3507.91,
"index": 129,
"start_time": 3480.401,
"text": " There wasn't much attention being paid to that. But Winton was paying attention. I think one thing to say about him is that besides being very, very smart, he's also somebody who can read people's ideas or talk to them and absorb new ideas very, very quickly. So he was also spending a lot of time looking around trying to see what other ideas are either out there. And this was one that he got interested in."
},
{
"end_time": 3537.961,
"index": 130,
"start_time": 3508.695,
"text": " But for various reasons, technical reasons, he thought, you know, there's a technical reason, so-called anomaly calculations about why this is not going to work out. And what happened right in the fall of 84, I actually went to as a postdoc to Stony Brook. And right around that time, Green and Schwartz had done this calculation that showed that these anomalies canceled except"
},
{
"end_time": 3561.578,
"index": 131,
"start_time": 3538.677,
"text": " There's some specific case where these anomalies canceled. Witten then became very excited about the idea that you could use in that specific case of this so-called super string theory. Witten heard about this and said, the reason I had my mind why super string theory couldn't work as a unified theory"
},
{
"end_time": 3592.346,
"index": 132,
"start_time": 3562.483,
"text": " And now it looks like maybe you can get around that. So he kind of then started working full time on trying to, you know, come up with models or understand SuperStream models that you could use to do unification. And so throughout kind of, I was now at Stony Brook, but I was kind of hearing reports of what's going on at Princeton and throughout late 84, 85, 86, this was, you know, Witten and the people around him, this is what they were working on. And they were, you know,"
},
{
"end_time": 3624.07,
"index": 133,
"start_time": 3594.684,
"text": " They had a very specific picture in mind. It was that the super string only is consistent in 10 dimensions, so you can get rid of four of them by the so-called Calabi-Yau Compactification and hopefully there's only a few of these Calabi-Yau's and one of those is going to describe the real world and we're going to have this wonderful, beautiful, unified theory using this kind of six-dimensional geometry of Calabi-Yau's and we're going to have it within the next year or two. That was the way they were thinking."
},
{
"end_time": 3646.34,
"index": 134,
"start_time": 3624.582,
"text": " and you know a lot of the people you know friends and colleagues of mine who you know were doing kind of the thing that you would often do is go down and go you know when you're in Princeton go talk to Whitten and say here's here's what I'm working on you know can you what do you think about this and I got several of them reported back to me yeah you know I went down to Princeton I talked to Whitten and"
},
{
"end_time": 3673.985,
"index": 135,
"start_time": 3647.056,
"text": " he said well you know what you're working on that's all very nice well and good but you know you really should be working on string theory because that's actually you know where all the action is and that's really and you know we're almost going to have the theory of everything there and you kind of work on string theory so you know this just had a huge effect so and um and this was called the so-called first super string revolution and you know uh there's kind of there's a story over the next five or ten years of how you know"
},
{
"end_time": 3701.852,
"index": 136,
"start_time": 3674.872,
"text": " People were brought into this field and some people were always skeptical, but it gained more and more influence and became institutionalized during the decade after that. In some sense, the weird thing that's hard to understand in strength theory is why once it became clear these ideas really weren't working out, why didn't this just fall by the wayside and people go and do something else?"
},
{
"end_time": 3731.749,
"index": 137,
"start_time": 3702.159,
"text": " So what do you see as the main physics, physical problem or even mathematical problem of string theory? Do you see it as, well, how do we search this landscape or how do we find the right manifold, the six dimensional Taylor manifold? Yeah, I think that was always the thing that bothered me about it from the beginning, which I think is the fundamental problem."
},
{
"end_time": 3761.766,
"index": 138,
"start_time": 3732.329,
"text": " And it's a fundamental problem whenever you decide to use higher dimensional Riemannian geometry. I mean, this actually goes back to Einstein, Einstein and these Clutes of Klein models. People have often said, okay, well, we had this beautiful theory of four-dimensional geometry in Einstein's general relativity, and we had this particle physics stuff going on, which seems to have some interesting geometry to it, so let's just add some dimensions and"
},
{
"end_time": 3787.381,
"index": 139,
"start_time": 3762.261,
"text": " and write down a theory in five or seven or ten or whatever dimensions and then do geometry there and that's going to solve and that's going to be the unified theory so I mean this is sort of thing Einstein was thinking about but um if you start thinking about this the problem is you realize that these kind of internal dimensions that the the geometry of particle physics and the geometry of special relativity are quite different they're not um"
},
{
"end_time": 3815.06,
"index": 140,
"start_time": 3788.268,
"text": " You know, there are these metric degrees of freedom in four dimensions. And if you try and you don't really have those in like in the standard model, you just have things like that. So if you put those sort of dynamical variables into there, the ability for these for these other dimensions by the four went to all the you have a vast"
},
{
"end_time": 3842.108,
"index": 141,
"start_time": 3815.367,
"text": " You've hugely increased the number of degrees of freedom and you have a theory where you have to now explain why all this extra geometry which you've put in there and which you're only trying to get a kind of small kind of very rigid kind of couple pieces of information out. Why are all these infinite number of degrees of freedom? How can you just ignore them? You have to find the dynamics"
},
{
"end_time": 3873.08,
"index": 142,
"start_time": 3843.712,
"text": " Consistent dynamics for them and then you and that consistent dynamics has to explain why you don't see them Yeah, and and so that's always been the problem with like Kaluza Klein models and with Any kind of extradimensional models and and string theory just kind of has this problem in spades in here You know your instead of feel sort of point particles you have springs They have a huge number of new degrees of freedom You have to say that well the string vibrations are all happening at such high energy as we can't see them and"
},
{
"end_time": 3900.503,
"index": 143,
"start_time": 3873.592,
"text": " and then they're trying to use the fact that superstrings have very special properties in 10 dimensions and they're trying to use that to argue that our strings are moving in 10 dimensions and that 4 are the ones we see and 6 are going to be described particle physics. It becomes a very complicated theory you have to write down"
},
{
"end_time": 3928.439,
"index": 144,
"start_time": 3901.817,
"text": " in order to kind of make any of this work and make any of this look like physics. And from the beginning, there was kind of no story about why is anything that looks like the real world going to drop out of this? And why that? And that's still the case 40 years later. And the whole thing just suffers from this problem that you don't"
},
{
"end_time": 3958.763,
"index": 145,
"start_time": 3930.333,
"text": " You don't actually have the theory. When you say that you have a string theory and people say, oh, we have this mathematically elegant, well-defined, unique theory, they're talking about that's not a full theory. That's a perturbative limit of a theory. And so what they really need in order to answer the questions they want to answer is they need something more general, a non-perturbative kind of general version of string theory."
},
{
"end_time": 3987.654,
"index": 146,
"start_time": 3959.258,
"text": " Sometimes people, we all call it M theory. So if you want, we can call it M theory and they need an M theory and nobody knows what M theory is. No one has come up. You can write down a list of properties that, you know, M theory is supposed to be some theory with this list of properties, but you can't actually write down a theory. And so on the one hand, you don't actually have a real theory that you can nail down and say, this is a theory, we're going to solve it and look at the solutions and see if they look like the real world."
},
{
"end_time": 4017.125,
"index": 147,
"start_time": 3988.166,
"text": " So what you what people end up doing is saying, well, we don't really know what the theory is. Let's assume that but it seems that maybe there's one that has some properties that look like the real world. So let's work with that and and then try to constrain, see what constraints we can get out of it will tell us, you know, are we seeing something like the real world? And then they just end up finding that, no, there aren't really useful constraints that you can get almost anything out of it. So you get this landscape of all possibilities. Yes, yes."
},
{
"end_time": 4040.913,
"index": 148,
"start_time": 4017.381,
"text": " and then you know twenty years ago things got very weird when people just started say well you know instead of saying that normally if you have a theory it can't predict anything because you know almost everything is a solution to it you say okay well that was a bad idea and you move on but instead you saw people saying oh well that's it just means the real world is you know all of these possible things exist in the real world the multiverse and yeah and just for"
},
{
"end_time": 4065.725,
"index": 149,
"start_time": 4041.254,
"text": " You know, for anthropic reasons, we happen to live in this random one. And, you know, I mean, anyway, it's the fact that anyone ever took any of that seriously is just still kind of, I don't have any explanation for it. It's just, yeah. Okay. So to summarize, somewhere around, this is not a part of the story that was said, but somewhere around the 1960s, some amplitude called the Veneziano, I think, Veneziano. I don't know how to pronounce it. Just read it."
},
{
"end_time": 4093.78,
"index": 150,
"start_time": 4066.152,
"text": " That was the first inklings of string theory and it had to do was come up with because of the strong force. They were trying to solve something that it was forgotten about. And then around the 1980s, there were some other problems with string theory that were solved. And so this is the Green Shorts anomaly cancellation. Yeah. And then some people say that that was the first revolution. But it's also more accurate to say that that precipitated Ed Witten to take it seriously. And then that's what precipitated the first string revolution. Yeah."
},
{
"end_time": 4118.626,
"index": 151,
"start_time": 4094.087,
"text": " Okay, then from there, then you realize that there are different ways that something like five to the 100 or 10 to the 500 or some extreme amount that if you're to do some calculation, all those books behind you, the amount of words ever written, not just books ever published, words ever written, I think easily letters ever written, like single letters, it would be like saying find this one letter,"
},
{
"end_time": 4138.507,
"index": 152,
"start_time": 4119.582,
"text": " Well, that..."
},
{
"end_time": 4163.49,
"index": 153,
"start_time": 4138.763,
"text": " Actually, maybe go back to one thing and say, yeah, so this is one part of the story I didn't say is that your string theory had originally come out as a potential theory of the strong interactions. And that actually was one reason Winton, I think, was looking at it is that so one of the open problems that the standard model left open was, how do you solve the strong? We have this strong interaction theory, but how do you solve it? And it looked like maybe you could you could use the old ideas about strings to solve it and"
},
{
"end_time": 4192.722,
"index": 154,
"start_time": 4163.695,
"text": " I actually spent a lot of time learning about strings as a graduate student because of that and I was ready to win. But the problem with this kind of multiplicity of solutions of string theory is that it's not just that there are too many of them, it's just that you don't actually have a definition of the problem. This kind of drives me crazy. People often talk about, well, the problem is that we don't know how to put a measure on the space of solutions"
},
{
"end_time": 4220.947,
"index": 155,
"start_time": 4193.336,
"text": " a string theory. And if we could put a measure that we could figure out, you know, maybe it's concentrated someplace, right? And that would be great. But I keep pointing out that the problem is not that you don't have a measure of the space. The problem is that you have no idea what the space is. As I was saying, you know, to even define what a string theory solution is, requires knowing precisely what M theory is. You don't know it. There are no equations anyone could write down, which"
},
{
"end_time": 4250.691,
"index": 156,
"start_time": 4221.783,
"text": " If we were smart enough and could find all the solutions to this, these are all the solutions to string theory. You just don't have that. So all of the things that you do have, like you can go out and say, well, maybe it's these gadgets and you have 10 in the 500 of them or whatever. Those are all just kind of cooked together possible approximations to what you think might be a string theory solution."
},
{
"end_time": 4281.34,
"index": 157,
"start_time": 4251.561,
"text": " There are solutions to some equations you've written down, which are not the equations of string theory. There's something you wrote down and think maybe these things have something to do with string theory. So the problem is much worse than any of these practical problems of there's too many of these things. And now it's become kind of an industry that, well, let's apply machine learning techniques to this. You're just applying"
},
{
"end_time": 4310.93,
"index": 158,
"start_time": 4282.227,
"text": " Does this frustrate you? Yes. This data is garbage. You basically do not actually know what your problem is so you're cooking up something which you can feed to a computer but it actually is known to be garbage and you're doing processing on this and producing more garbage and getting grants to do this and going around telling people that you're looking for the"
},
{
"end_time": 4338.729,
"index": 159,
"start_time": 4311.664,
"text": " Or the universe. I mean, it's real. That's just utter nonsense. I'm sorry. Many people don't know because they don't know the history. But since 2010s, it's become somewhat cool to dunk on string theory, at least in the popular press. Maybe not inside academia. But you were alone. You and Lee Smolin were lone wolves. Early lone wolves. Yeah, yeah. Can you talk about that and talk about some of the flak you took? Maybe still take?"
},
{
"end_time": 4355.06,
"index": 160,
"start_time": 4340.06,
"text": " Yeah, anyway, it was certainly a very strange experience, a very strange time. But, you know, I think the thing to say is that, you know, throughout, you know, I was never, I was always fairly skeptical about string theory, but, you know, initially for many years, my attitude was, well, you know,"
},
{
"end_time": 4386.544,
"index": 161,
"start_time": 4356.647,
"text": " Who knows? It's certainly very smart. These people are going to, sooner or later, they'll figure out for themselves, either they'll figure out this works or they'll do something else. But then, just as time went by, years went by, and this was just not happening. You had more and more popular books. I have to confess, maybe in some sense, it's somewhat of a reaction to Brian Greene, who is my friend and colleague here at Columbia. He did a very, very good job with PBS specials convincing"
},
{
"end_time": 4407.944,
"index": 162,
"start_time": 4387.022,
"text": " the world that this was a successful, this was an idea on the way to success when it really wasn't. So I thought, okay, well, somebody should sit down and write a book about what the real situation here is. And it's not like when I talk to people privately about this,"
},
{
"end_time": 4437.363,
"index": 163,
"start_time": 4408.422,
"text": " You know, I would say that people who are not string theorists mostly would, would, would say, yeah, you know, yeah, you're probably right. This is not, this doesn't seem to be going anywhere, but you know, whatever. And then the, um, and people, and when I talked to string theorists, I have plenty of string theorist friends, they would often say, yeah, you know, yeah, there are a lot of huge problems and we, we just, we don't really know anything better to do right now. So we're going to keep doing this, but yeah, yeah. All these problems you're pointing out are really, uh, uh, yeah, they're real. And, um, so what's wrong with that?"
},
{
"end_time": 4467.961,
"index": 164,
"start_time": 4438.473,
"text": " Well, the weird thing I think was this disjunction between the private opinions of people, what people were saying to each other privately, and what you were saying in the popular press. One aspect of this was people not wanting to publicly criticize something."
},
{
"end_time": 4489.633,
"index": 165,
"start_time": 4468.985,
"text": " I think the subject became more and more ideological and the string theorists started to feel kind of in battle. They were very well aware that a lot of their colleagues thought what they were doing was not working. On the other hand, they became more defensive and a lot of people I think felt"
},
{
"end_time": 4513.541,
"index": 166,
"start_time": 4490.179,
"text": " would tell me, yeah, I agree with a lot of your saying, but yeah, but don't quote me on this publicly. I don't want to get involved in that mess and alienating a lot of my colleagues. Anyway, I have this weird status that I'm actually in a math department, not a physics department. I don't have a lot of the same reasons that you don't want to"
},
{
"end_time": 4543.49,
"index": 167,
"start_time": 4513.985,
"text": " I spent a lot of time thinking about this stuff. I started writing this in around 2002, 2003. The book was finally published. It was a long story, but it finally got published in 2006. In the meantime, Lee Smolin had been writing"
},
{
"end_time": 4567.295,
"index": 168,
"start_time": 4544.258,
"text": " a book. He was coming from a different direction. Trouble with physics? Yeah, the trouble with physics. And he had his own motivation. So it was trying to write something I think more general and sociological, but with this as an example. And I think the way he describes it, the example kind of took over the general theory. And so he ended up also writing a book about string theory. And the books ended up coming out at the same time, which I think"
},
{
"end_time": 4595.555,
"index": 169,
"start_time": 4568.2,
"text": " You know, it was kind of a force multiplier there that, you know, people, if one person is writing a book, which says, well, you know, a lot of the things you're hearing, you're hearing are not right. Or people say, well, that's just one person's opinion. But if two people do it, I think everybody's like, oh, you know, there must be something to this. And so I think that the combination of the two books, I think it did have a lot of effect on them. It did make a lot of people realize there was a problem here."
},
{
"end_time": 4625.469,
"index": 170,
"start_time": 4595.879,
"text": " It made a lot of the string theories much more defensive. It also caused a lot of young people thinking of doing string theory or people doing string theory to decide to move on to something else. People very often tell me about effects this book had on them or other people they knew in terms of their decisions about what to do with their research or their career. The book is called Not Even Wrong, the links to"
},
{
"end_time": 4655.384,
"index": 171,
"start_time": 4625.759,
"text": " All resources mentioned will be in the description, including this book. So you mentioned that your colleagues would talk to you privately and then they would say something else to the popular press. Now, when you say popular press, are you also including grant agencies with that, like just the public in general? Because it's not just a popular science issue. It's also a grant issue where the money goes. Yeah. So it's not just the popular press. And to be clear, I should say it's not that they would say one thing, one place. It's just,"
},
{
"end_time": 4682.176,
"index": 172,
"start_time": 4656.323,
"text": " they would carefully just not say, you know, that there are things that they would say in conversation with me or I think in conversations with other people, not just me, that they would just say, okay, this is not something that, okay, sin of commission versus omission. Yeah, it's not like they were going out and saying, oh, strength theory is going great. It's just that, you know, anyway, they were, they were, they were not kind of, they were not saying this is really appears to be a failure. But, uh,"
},
{
"end_time": 4703.046,
"index": 173,
"start_time": 4682.858,
"text": " Yeah, but you're right. This issue kind of occurs at all levels from the very, very popular press, from kind of television specials to more serious popular press, what gets into Scientific American, what gets into now we have"
},
{
"end_time": 4732.688,
"index": 174,
"start_time": 4703.609,
"text": " quantum magazine, which are more serious parts of the press aimed more at the public, all the way down to exactly what do you write in grant proposals, whatever, or if you're trying to explain to some kind of funding person or something about what's going on in your subject."
},
{
"end_time": 4762.125,
"index": 175,
"start_time": 4733.848,
"text": " What do you say about string theory? I think everybody, whatever you're working on, you're often forced by this business of getting your students a job or getting a grant to go right up to the boundary of what's defensible and being optimistic about what you're doing. That's what string theorists have certainly"
},
{
"end_time": 4781.493,
"index": 176,
"start_time": 4763.046,
"text": " always been always been doing you can argue you know in many cases it's not different than what other other scientists do but it's um i think the thing which i had i have to say i have found more and more disturbing the reaction of and and it started when my book came out and i think we smell it is some reaction the um."
},
{
"end_time": 4809.206,
"index": 177,
"start_time": 4785.128,
"text": " I think both of us were expecting a much more serious intellectual response to the issues we were raising. We were raising serious technical questions and we were getting back personal attacks. From people in the community or from the public? From people in the community."
},
{
"end_time": 4838.319,
"index": 178,
"start_time": 4810.776,
"text": " You know what you're getting from people who don't in the public don't know much about this year, you're getting some completely random combination of people who are annoyed because you're saying something different than what they heard and other people who become your fan because you're saying something different. And so you end up with a huge number of fans who you don't necessarily want as your fans. But anyway, the yeah, so both of us were expecting, you know, that, you know, we put a lot of effort into making a"
},
{
"end_time": 4865.265,
"index": 179,
"start_time": 4839.002,
"text": " You know a serious intellectual case about what these problems were and instead of getting a serious response we were getting You know, you know these kind of personal attacks of how dare you say this and so for instance, you know There's one prominent blogger who says who would write these endless blog entries about what's wrong with peter white and what he's doing and and at some point I was trying to respond to these and at some point I realized you know"
},
{
"end_time": 4893.217,
"index": 180,
"start_time": 4867.108,
"text": " What this guy's talking about is nothing to do with what I actually wrote in my book. And then he actually kind of publicly admitted that he refuses to read the book. So anyway, this kind of blew my mind. How can you be an academic and engaged in academic discussion, intellectual issues, and you're spending all this time arguing about a book and you're refusing to read it? I mean, how is this really crazy?"
},
{
"end_time": 4918.831,
"index": 181,
"start_time": 4893.558,
"text": " And that was a string theorist or just a colleague? A string theorist, yeah. Speaking of Brian Greene. Oh, sorry, continue please. Yeah, no, it wasn't Brian Greene. No, no, no. I didn't mean to suggest that. No, no, no. But anyway, that's just one example. And I think this is an ongoing, I think, disturbing situation that people are just not, people are kind of"
},
{
"end_time": 4946.92,
"index": 182,
"start_time": 4919.241,
"text": " defending that field and continued and researched there with just kind of refusing to acknowledge the problems or to have kind of serious discussions of it. I think you're on your last thing with Edward Frankel. I think it's kind of funny because I know him and I actually was out visiting him in Berkeley in June or something and we're talking about things and he told me, oh, Peter, I'm going to go to the strings conference and it's the first time I've been to a strings conference."
},
{
"end_time": 4967.739,
"index": 183,
"start_time": 4947.5,
"text": " He knows all these people and he knows a lot about the story and I think he knows me well enough."
},
{
"end_time": 4994.718,
"index": 184,
"start_time": 4968.456,
"text": " I'm not a complete fool and I have a somewhat serious point of view, but maybe I'm really a bit too extreme about this. But then he went to this conference and then after when it comes back, he gives me a call and says, Peter, I didn't realize how bad it really was. You're right. This really is as bad as you've been saying. So anyway. What was bad? The exuberance of the young people or the old people telling"
},
{
"end_time": 5023.131,
"index": 185,
"start_time": 4995.555,
"text": " misleading the younger people into a useless pit or like what was what was bad? Yes, it is as bad as you say. Well, I think what's what's bad is it is really just this kind of this kind of refusal to admit I mean, this is a field which influxes serious problems, things have not worked out, these ideas really have failed to work. And instead of admitting that some ideas have failed and moving on, people will just kind of"
},
{
"end_time": 5051.237,
"index": 186,
"start_time": 5023.763,
"text": " keep acting as if that's not true. Sorry to interrupt. I'm so sorry. So why would Edward expect an admittance of the failure of string theory at a strings conference? I think one thing to say, part of the story about him is he's a mathematician. So mathematicians, if you do mathematics, the one thing you have to be completely clear about is"
},
{
"end_time": 5077.585,
"index": 187,
"start_time": 5051.988,
"text": " What you understand and what you don't understand and what is a wrong idea and what is a right idea? You know, and if something doesn't work and is wrong you have to You can't play a game. You cannot play any games about this This is you know, you have to admit that this is wrong and so I think especially for mathematicians to come in and see an environment where there's you know The kind of guiding"
},
{
"end_time": 5108.114,
"index": 188,
"start_time": 5078.422,
"text": " ideas that people haven't really worked out and a lot of things are known, do not work for known reasons, but people are still kind of acting as if this is not true and trying to figure out how to kind of do something and make career for themselves in this environment. I think he recognized that, but part of it is mathematics is a very unusual subject. Things really are wrong or right and you're"
},
{
"end_time": 5131.869,
"index": 189,
"start_time": 5109.104,
"text": " You absolutely cannot seriously make progress on the subject unless you recognize that. Mathematicians are also much more used to being wrong. One of my colleagues, John Morgan, likes to say that mathematics is the only subject he knows of where if two people"
},
{
"end_time": 5156.954,
"index": 190,
"start_time": 5132.312,
"text": " Disagree about something and they each think the other is wrong They'll go into a room and sit down and talk about it and then they'll emerge from the room with one of them having admitted He was wrong. The other one was right and that this is just not it's not a normal human behavior, but it's something that is part of the mathematical culture earlier I said speaking of Brian Green and what I meant was I had a conversation with Brian Green about"
},
{
"end_time": 5182.329,
"index": 191,
"start_time": 5157.858,
"text": " Almost a year ago now. And I mentioned, yeah, so Peter White has a potential toe Euclidean twister unification. And then he said, Oh, does he? Oh, I didn't know. He is in your university, not to put you on the spot. But why is that? Well, it said aloud, I don't think it's true by the professor of physics, mainly who studies string theory. Well, there's so many proposals for toes."
},
{
"end_time": 5203.302,
"index": 192,
"start_time": 5182.944,
"text": " Yeah, there are proposals in your inbox, but there aren't serious proposals by other professors. There aren't that many serious proposals of things of everything, at least not on a monthly basis. Well, I mean, I mean, this is this really doesn't mean anything in particular to do with Brian, you could you could ask, you know, since, you know, people on this subject,"
},
{
"end_time": 5231.34,
"index": 193,
"start_time": 5203.797,
"text": " Yeah, in principle should be interested in this. There's I've gotten very little reaction from from physicists to this. And in some sense, it's kind of clear, clear why I mean, they're, you know, I wrote this, I wrote this paper, I've read about the blog, and you know, I've gotten no reaction in both cases, I don't have reaction from people writing, telling me that I've talked to about or saying, oh, you know, this is this"
},
{
"end_time": 5258.387,
"index": 194,
"start_time": 5232.022,
"text": " This is wrong, this can't work for this reason. I think this is very much the problem with the paper that I wrote about this. It uses some quite tricky understanding of how twisters work and twister geometry works, which is something that very few physicists have. So Brian"
},
{
"end_time": 5275.742,
"index": 195,
"start_time": 5258.746,
"text": " I'd be completely shocked if Brian actually really understood some of the things going on with twisters that I'm talking about. And the problem, I think, for anybody who then, if somebody comes to you and says, oh, I have this great idea, it involves these subtleties of twister theory, and you're like, well,"
},
{
"end_time": 5303.439,
"index": 196,
"start_time": 5276.391,
"text": " you know i'm really not in the mood to spend a week or so sitting down trying to understand as subtle as a twister theory so i think you know maybe i'll just nod my head politely and and and go on go on my way that's part of it and then part of it is also that a lot of you know this is very much expected at work in progress you know i'm seeing a lot of very interesting things happening here but i'm not um i in no sense have completely understood what's going on or or have the kind of uh you know"
},
{
"end_time": 5323.626,
"index": 197,
"start_time": 5303.797,
"text": " understanding of this where you can write this down and people really can follow exactly what's going on. It's not too surprising. I haven't got that much. I can see why I understand the typical reaction to this. Brian is somewhat of a special case because he also actually is very"
},
{
"end_time": 5353.916,
"index": 198,
"start_time": 5325.384,
"text": " I think I actually he actually a lot of his effort is as good as in recent years has gone into other things especially the I mean the World Science Foundation Festival I think is now more or less uh you know it's kind of most it's mostly brian green at this point yeah and then it's uh so he's anyway he's thinking about other things um and and I have very I don't have very little contact with people in the physics department I mean they're mostly thinking about very different things and"
},
{
"end_time": 5378.097,
"index": 199,
"start_time": 5354.206,
"text": " Here at Columbia, but it's true essentially everywhere else that the, you know, the mathematicians and physicists really don't talk to each other. They're really separate silos, separate languages, separate cultures and, you know, places where you have kind of mathematicians and physicists and kind of active and high level interaction with each other is very unusual. It doesn't happen very much."
},
{
"end_time": 5407.654,
"index": 200,
"start_time": 5378.763,
"text": " I have a couple of questions again. I'll say two of them just so I don't forget them and then we can take them in whichever order you like. So one of the questions is how slash why did you get placed into the math department? Because that's one question. And then another one is you mentioned earlier that Witten has this power to survey a vast number of people and extract the ideas at great speed. And so a large part of that is raw IQ, like sheer intellect. But is there something else that he employs like a technique that you think others can emulate?"
},
{
"end_time": 5428.029,
"index": 201,
"start_time": 5408.37,
"text": " I imagine if Whitten was to read your paper, he would understand it. And I imagine that he would say, Oh, he would see the benefit of it. And maybe the application to string theory, or maybe it offshoots in its own direction. But anyhow, so those are two separate questions, one about Whitten, and then one about you and the department you're in. Okay, yeah, I've got the other two. But let me start."
},
{
"end_time": 5455.384,
"index": 202,
"start_time": 5429.667,
"text": " Let me just say something quickly about Witten, just saying about having dealt with him over the years. One thing I find very interesting about him is just, he travels around a lot, but let's just say his way of socializing is to, if he's come to a department and he's at tea or whatever, and he's introduced anybody"
},
{
"end_time": 5477.602,
"index": 203,
"start_time": 5455.913,
"text": " He almost immediately will ask me, okay, well, what are you working on? Explain it to me. Anyway, that's a lot of what he's done over the years has just been trying to really be aware. Anyway, I've said what I've been doing and tried to get him interested. He's"
},
{
"end_time": 5507.858,
"index": 204,
"start_time": 5478.729,
"text": " Anyway, we'll see where that goes. Maybe I'll have more success with it with this new paper, maybe not. But he's responded though, or no? He has responded. But it's more that he's kind of looked at it. He actually the first version, he actually made some technical comments more about the beginning of it. But I think he didn't engage with most of what I was talking about. We're going to get back to the math question soon, the math department question. But do you think a part of that is because there's a sour taste"
},
{
"end_time": 5534.514,
"index": 205,
"start_time": 5508.2,
"text": " given your book? Yeah, yeah. I mean, I'm not, I mean, I'm, again, I've known him since I was an undergraduate. You know, I think, you know, he's, I think he's aware, you know, that this guy is not an idiot, but, but he's also, I'm also not his favorite person in terms of kind of, you know, the impact I've had on his, on his subject. And yeah. And I think, you know, he also, I think he understands it's not personal, but you know, it's not, it's very hard to deal with somebody who's kind of,"
},
{
"end_time": 5561.152,
"index": 206,
"start_time": 5535.196,
"text": " You know, been this kind of main figure, kind of telling the world that the thing that you think is your main accomplishment in life is wrong. So this is not, yeah. Anyway, I'm not his favorite guy, but anyway, I can, we're still, it's fine. Yeah. I think he's a very, you know, anyway, he's a very ethical and great. And I think when I complained a lot of, a lot of, most of the worst of what the kind of"
},
{
"end_time": 5590.384,
"index": 207,
"start_time": 5562.363,
"text": " and this kind of pushing of string theory in ways which really were completely indefensible. He's rarely been the worst offender in that. That's really more other people than him. But yeah, he's a true believer. He's really enthusiastic about it. So to get back to my own personal story, I got a postdoc at the Stony Brook Institute for Theoretical Physics in 84."
},
{
"end_time": 5618.097,
"index": 208,
"start_time": 5591.084,
"text": " I was there for four years and that was in the Physics Institute. But the Physics Institute was right above, it's the same building as the math building. And the things I was interested in, I was trying to stay away from string theory and I was interested in some other things. And I was often talking and I was trying to learn a lot of mathematics. I was trying to learn more mathematics to see if I could make any progress on these other problems. So I spent a lot of time talking to the mathematicians in Stony Brook."
},
{
"end_time": 5648.029,
"index": 209,
"start_time": 5618.558,
"text": " And some of them, you know, there are some really great geometers. There are some really great mathematicians and I learned a lot from them. And it was a, that was a great experience. But at the end of four years there, you know, I needed another job. I did set out some applications for postdocs and physics, but the, I would say that that was kind of the height of the excitement over string theory. And especially somebody like me saying, you know, I'm really interested in doing something about the mathematics and physics, about applying mathematics, physics, but I don't want to do string theory."
},
{
"end_time": 5676.254,
"index": 210,
"start_time": 5648.712,
"text": " That was not going to get any kind of reasonable kind of job that way. That's just not going to happen. I ended up realizing, well, maybe the better thing, I'll have better luck in a math department. I ended up spending a year in Cambridge as an unpaid visitor at Harvard, partly, and I was also teaching calculus at Tufts."
},
{
"end_time": 5705.23,
"index": 211,
"start_time": 5676.732,
"text": " so then i have some kind of credential okay well at least this guy can teach calculus and so and i and i applied for a one-year postdoc at uh the math institute in berkeley msri and i i got that and so i spent a year is that how you got to know edward um no no he wasn't uh that was before him yeah i mean he would have still been he would have been at harvard at a much more junior person yeah yeah yeah he came to berkeley later you know that that was like 80"
},
{
"end_time": 5724.445,
"index": 212,
"start_time": 5706.732,
"text": " 88-89. But that was an amazing, that was actually a fascinating year because that was the year that Witten had come out, Witten had kind of dropped string theory for a while and was doing this topological quantum field theory stuff in Chern Simon's theory and he was doing the stuff which won him the Fields Medal and you know it was just"
},
{
"end_time": 5751.374,
"index": 213,
"start_time": 5725.299,
"text": " just mind-blowing bringing together of ideas about mathematics and quantum field theory and so most of the year was devoted to learning about that and thinking about that and you know Witten came and visited and Atiya was there and I actually had a lot of chance to talk to him which was wonderful and so that was a really fascinating year at MSRI but and partly because so much of this was going on you know"
},
{
"end_time": 5780.009,
"index": 214,
"start_time": 5752.176,
"text": " math departments were more interested in hiring somebody like me even though I didn't have the usual credentials because they felt this is somebody who actually understands this new subject which is having a lot of impact on our field. So Columbia hired me to this non-tenured track for your position and so I was to that I was teaching here and after a few years again I was getting the point okay well now I got to find another job but and they"
},
{
"end_time": 5797.244,
"index": 215,
"start_time": 5780.384,
"text": " So the department needed somebody to, they'd set up a position for somebody to teach a course and maintain the computer system. And I said, well, you know, I could probably do that and that's not a bad job. And so I ended up"
},
{
"end_time": 5821.613,
"index": 216,
"start_time": 5797.91,
"text": " uh, agreeing, agreeing to take on that position. And that's, that's, uh, that's always been kind of a renewable position. It's not tenured, but it's, um, essentially permanent, renewable. And I've gone through various kinds of titles of various kinds of versions of that since I've been since the nineties. And it's, it's worked out very well for me. I'm actually quite happy with how it's worked, but it's a very unusual career path. And it,"
},
{
"end_time": 5839.087,
"index": 217,
"start_time": 5823.336,
"text": " It has given me a lot of insulation from the normal kind of pressures to perform in certain ways and to do certain things allowed me to get away with all sorts of things if you like."
},
{
"end_time": 5869.258,
"index": 218,
"start_time": 5843.507,
"text": " Like what? Well, like writing a book called Not Even Wrong explaining what's wrong with"
},
{
"end_time": 5881.578,
"index": 219,
"start_time": 5869.667,
"text": " How did that come about? So, for instance, this is going to be incorrect because I'm just making this up, but then correct it. For instance, you're walking along someday, you have this idea, maybe it's a splinter in your thumb for a different reason."
},
{
"end_time": 5911.101,
"index": 220,
"start_time": 5882.039,
"text": " About string theory. So then you go to a publisher and you say it or you say to a journalist and then the journalist hears and they say you should write a book and you say, maybe then you think about it. You start writing a chapter, the nitty gritty details. How does that happen? How did it go from Peter White mathematics professor to then writing this popular book? Um, well, so, so yeah, throughout, let's say throughout the nineties, you know, I was very much, um, you know,"
},
{
"end_time": 5939.172,
"index": 221,
"start_time": 5911.493,
"text": " I was interested in the same kind of questions. Can you do different things in math and physics? I was trying to follow what's going on in physics. I've been trying to follow what's going on in string theory. And I was getting more and more frustrated throughout the late 90s that this, what I would see in the public and what I would see, or just to not reflect my own understanding of what actually was going on. And partly I kind of mentioned, you know, there's a, for instance, Brian's PBS special about"
},
{
"end_time": 5968.319,
"index": 222,
"start_time": 5939.718,
"text": " I mean it just that just seemed to me to be giving that just didn't really didn't agree at all with what I would actually saw going on and so I thought well somebody you know somebody should write this up and I would have hoped it would be somebody else but then as you go along with no one else is going to do this and you know I'm actually pretty well placed to do it for very reasons and started thinking about it and I think around 2001 I actually wrote kind of a short thing that's on the archive of kind of"
},
{
"end_time": 5987.193,
"index": 223,
"start_time": 5969.36,
"text": " you know a little bit of a kind of polemical several page thing you say look here here's the opposite side this right here's what's right this is really not working and here's why and that that was the beginning of it and like i got a lot of reaction reaction to that and and i started to more and more feel that you know you the right way to do this was to actually"
},
{
"end_time": 6014.991,
"index": 224,
"start_time": 5988.456,
"text": " You needed to write something kind of at book, sit down and at book length, explain exactly what's going on. And I also wanted to do something also more positive to try to explain some of the things that I was seeing about how mathematics, you know, there were some very positive things happening in the relationship between mathematics and physics, which has some connections to string theory, but we're also quite independent, like Wittenstern-Simon's theory, for instance. So I also wanted to also write about"
},
{
"end_time": 6034.053,
"index": 225,
"start_time": 6016.101,
"text": " I also wanted to write about the story of what's going on in this kind of physics and this kind of fundamental physics, but kind of informed by someone who's actually spent a lot of time in the math community and informed by a lot more mathematics than is usual in the"
},
{
"end_time": 6060.828,
"index": 226,
"start_time": 6034.258,
"text": " this thing. So there was kind of a positive. It's rarely noticed, but there are a bunch of chapters in this book, like on topological quantum field theory, nothing to do with string theory, which nobody really paid much attention to or understands. But anyways, I wrote this and I was, so I just said, well, I'll just write this thing. And I think around then I may have also had a friend who had done a book proposal and written a book. But by the time he'd actually"
},
{
"end_time": 6089.821,
"index": 227,
"start_time": 6061.408,
"text": " was writing the thing, you know, he was just kind of sick of it and he didn't really want me writing it, but somebody had given him in advance and he had to, so he had to write the book. So I thought, well, you know, I don't want to do that. I'm not going to go out and make a proposal to a publisher. I'm just going to write when I want to write and we'll see how it turns out. And, you know, I think we'll see if someone wants to publish it. Great. And so then I was getting to the end of this and somebody from Cambridge University of Press showed up."
},
{
"end_time": 6112.125,
"index": 228,
"start_time": 6091.015,
"text": " He was just in my office going around asking people, you know, what are you working on? Is there some kind of book project we could work on? And I told him about what I was doing and he got very, very interested in it. And so it actually then became you know, Cambridge University Press was then considering it for a while and they sent it out to various"
},
{
"end_time": 6135.111,
"index": 229,
"start_time": 6112.927,
"text": " Reviews and the reviews were kind of fascinating. There were half the reviews said this is great. This is wonderful Somebody is finally saying this this is fantastic and the other half said oh, this is absolutely awful. This was this will destroy the reputation of Cambridge University Press. So Interesting and the problem with the University Press is you know, they're not um They're actually not really they're not really equipped to do content"
},
{
"end_time": 6165.469,
"index": 230,
"start_time": 6135.486,
"text": " to deal with"
},
{
"end_time": 6191.357,
"index": 231,
"start_time": 6165.913,
"text": " Yeah, so he definitely agreed with me about that. Now that you're in the math department, is that what allowed you to see the connections between Twister Theory and the Langlands program or is that something that existed before? The connection, not the Langlands program, obviously that goes back to Langlands."
},
{
"end_time": 6221.596,
"index": 232,
"start_time": 6191.698,
"text": " Well, whether there is, I think it's still, whether there is any connection between Twister theory and the language program, that's a very, that's extremely speculative idea and fairly reasonable. I would say, yeah. Yeah. So that. What aspect of the Langlands program, like the local or geometric? Maybe to back up a little bit. I mean, so the language program is, anyway, this amazing story. I guess you heard a lot about it from Edward, but it's,"
},
{
"end_time": 6248.848,
"index": 233,
"start_time": 6221.971,
"text": " One reason I got into it is it became more and more clear to me that the right way to think about quantum mechanics and quantum field theory issues was in this language of representation theory. And then I started to say, okay, I should learn as much as possible about what mathematicians know about representation theory. And sooner or later you find out about the Langlands program, and the Langlands program is saying that"
},
{
"end_time": 6278.763,
"index": 234,
"start_time": 6249.65,
"text": " All of the basic structure of how the integers work and how numbers work and things is closely related to this representation theory of Lie groups in this amazing, amazing way. There's just an amazing set of ideas behind the Geometric Langlands program, which they have a lot of similar flavor to the things I was seeing in some of physics. It's just been a many, many years process of slowly learning more and more about that."
},
{
"end_time": 6307.295,
"index": 235,
"start_time": 6279.206,
"text": " But that stuff never really had anything to do with twisters. The interesting relation to twisters is that I had actually written this paper, I'd given some talks about the twister stuff, and I'd pointed out that in this way of thinking about things,"
},
{
"end_time": 6335.862,
"index": 236,
"start_time": 6307.892,
"text": " There's this thing that I told you that a space-time point is supposed to be a complex plane. Actually, in Euclidean space, you can think of it as a complex plane, or you can mod out by the constants and use the real structure of Euclidean space, and you get something, a geometrical object corresponding to each point, which is called the twister P1."
},
{
"end_time": 6354.275,
"index": 237,
"start_time": 6336.391,
"text": " It's basically a sphere, but you identify opposite end points of the sphere. And so I'd written about that in my paper and in some of the talks I was given, I kind of emphasize that. And then, so then I get an email one day from"
},
{
"end_time": 6383.217,
"index": 238,
"start_time": 6354.753,
"text": " Peter Schulze, who's one of the people who's making this really great progress in the Langlands program in number theory. And he's been coming up with some of these fantastic new ideas relating geometric Langlands and arithmetic Langlands. And he basically said, yeah, I was looking at this talk you gave and it's really nice about this geometry and seeing this Twister P1 going there. He said, what's amazing is this Twister P1 is exactly that same thing as showing up in my own work."
},
{
"end_time": 6409.189,
"index": 239,
"start_time": 6383.712,
"text": " There's this work he was doing on the relation of geometric Langlands and if you specialize to what happens kind of at the infinite prime or at the real place, not at finite primes, the structure he was seeing was exactly the twister P1. So he kind of pointed this out to me and asked me some other questions about the"
},
{
"end_time": 6437.978,
"index": 240,
"start_time": 6409.531,
"text": " about this. I don't think I could tell them anything useful, but that did kind of blow my mind that, wait a minute, this thing that I'm looking at in physics, that exactly the same structure is showing up in this really new ideas about geometry of numbers. And so I then spent a few months kind of learning everything I could about that mathematics in Twister P1, and I'm still following it. But"
},
{
"end_time": 6451.118,
"index": 241,
"start_time": 6438.473,
"text": " I should say that to my mind it's just a completely fascinating thing that these new things that we're learning about the geometry of number theory and these speculative ideas about"
},
{
"end_time": 6473.063,
"index": 242,
"start_time": 6452.602,
"text": " about physics that you're seeing a same fundamental structure on both sides and and but but i have no i mean i have no understanding of how these are related i don't think anyone else does either yeah have you asked peter if he would like to collaborate well there's not is that like uncouth no but but but i think he and i just have very"
},
{
"end_time": 6501.8,
"index": 243,
"start_time": 6474.514,
"text": " Are you too incompatible? No. He's doing what he's doing. First of all, one thing to say is he's having such incredible success and doing such amazing stuff that interfering with that anyway and telling him why don't you stop doing what you're doing and do something I'm interested in seems to be a really bad idea."
},
{
"end_time": 6532.432,
"index": 244,
"start_time": 6502.927,
"text": " Anyways, so yeah, he's doing extremely well doing what he's doing and most of what he's doing isn't related to this. I mean, he's, you know, he really, really understands in an amazing way what's going on with the geometry of the adic numbers and these things like this, which I don't understand at all. And so and he's just been revolution. He's been revolutionizing that subject. And it's something I can only kind of marvel at from a distance. The kinds of issues that where I'm kind of stuck that are kind of for me are are actually much more"
},
{
"end_time": 6560.145,
"index": 245,
"start_time": 6533.626,
"text": " They really have nothing to do with his expertise. I probably should be talking to more physicists or whatever. I think it's in the back of his mind, this stuff that I'm seeing, I should always often look and think about if I can understand the relation to physics. It's in the back of my mind, the stuff that I'm seeing physics, I should try to keep learning about that number 37 and see if I see anything."
},
{
"end_time": 6590.401,
"index": 246,
"start_time": 6560.674,
"text": " But that's really all it is. But a lot of this is very new. I just heard from him a few weeks ago that he actually has some new idea about this particular problem from his point of view. And he was supposed to give a talk about it on last Thursday at this conference in Germany. And I'm hoping to get a report back of that. But this is all very active and very poorly understood stuff. But it's not."
},
{
"end_time": 6618.968,
"index": 247,
"start_time": 6590.725,
"text": " But definitely the connection between math and physics here is very, very unclear. But if there is one, it will be mind blowing. And it's certainly kind of on my agenda in the future to try to learn more and look for such a thing. But I don't have anything positive to say about that, really. So I want to get to space time is not doomed. There's quite a few subjects I still have to get to. I want to be mindful of your time. But how about we talk about space time not being doomed?"
},
{
"end_time": 6648.78,
"index": 248,
"start_time": 6619.497,
"text": " It's something that's said now. I don't know if you know, but there's someone named Donald Hoffman who frequently cites this. He's not a physicist, but he cites it as evidence or support for his consciousness as fundamental view. And then there's Neema Arkhani Hamed, who's the popularizer of that term, though not the inventor. Yeah. So maybe to, I mean, I can kind of summarize that. Yeah. So I don't really have anything useful to say about Hoffman. I mean, he's interested in consciousness and other things. I don't really have too much"
},
{
"end_time": 6675.316,
"index": 249,
"start_time": 6649.172,
"text": " I don't really know much about it, but maybe to say what the…I mean this has become…I mean the reason I wrote that there's this article you're referring to about space-time is not due…I wrote it partly because I was getting frustrated at how this had become such kind of an ideology among people and working in physics and on quantum gravity, this idea that"
},
{
"end_time": 6702.381,
"index": 250,
"start_time": 6676.374,
"text": " And I think one way I would say it would say what's happened is that so when people first start thinking about how do you get quantized gravity and you kind of gravity so the initial one of the initial ideas as well you know we've learned that we have this incredible successful standard model so let's just use the same methods that work for the standard model and apply them to gravity and we'll do that and so it's going to be"
},
{
"end_time": 6720.828,
"index": 251,
"start_time": 6704.053,
"text": " Anyway, and you're thinking of space and time in this usual way and then there are these degrees of freedom that live in space and time which tell you about the metric and the geometry of space and time and you're trying to write a quantum theory of those things living in space and time."
},
{
"end_time": 6747.961,
"index": 252,
"start_time": 6721.305,
"text": " And I think, you know, anyway, people tried to do this. There's lots of problems with doing it. It's an incredibly long story. String theory was partly reaction to the story. But even string theory was still a theory of strings moving around in space and time. So you weren't. Yeah, I mean, you were still starting with thinking, thinking in terms of the space and time. But but more recently, you know, as string theory hasn't really"
},
{
"end_time": 6770.23,
"index": 253,
"start_time": 6748.524,
"text": " Worked out the way people expected. There has been this ideology of, oh, well, let's just get rid of this space and time somehow, and then we will write some theory in some completely different kind, and in the low energy limit, we'll recover space and time as some kind of effective structure, which you only see at low energies."
},
{
"end_time": 6795.06,
"index": 254,
"start_time": 6771.442,
"text": " And that's become almost an ideology, like Arkani Hamid likes to say, space-time is doomed, meaning the truly fundamental theory is going to be in some other variables and space-time variables. He has his own proposals for this about these geometrical structures he's using to study amplitudes. Anyway, the things that I'm doing"
},
{
"end_time": 6821.681,
"index": 255,
"start_time": 6795.435,
"text": " You actually do get a theory, it looks like gravity should fit into this and it will fit into this in a fairly standard way. This is standard space and time except in the twister geometry point of view on it and interesting things happening with spinners you didn't expect but it's still, there is a usual idea about space and time are there. My general feeling with the"
},
{
"end_time": 6849.599,
"index": 256,
"start_time": 6823.217,
"text": " But the problem with this whole kind of space time is doomed thing is you have to have a plausible proposal for what you're going to replace it with. It's all well and good to say that there's some completely different theory out there and the theory people used to is just an effective approximation. But first you got to convince me that your alternative proposal works. And the problem is that people are just doing this without any kind of"
},
{
"end_time": 6880.145,
"index": 257,
"start_time": 6851.459,
"text": " you know, without any kind of plausible or interesting proposal for what it is you're going to replace space time with. And often it even comes down to this crazy level of kind of this multiverse thing. I mean, we have this theory where everything happens. So fundamentally everything happens, but then effectively you only see space and time and it's kind of, you know, you can say words like that, but it's kind of meaningless. Why is it that they have to come up with a decent proposal or replacement? Why can't they just say, look, there are some"
},
{
"end_time": 6908.166,
"index": 258,
"start_time": 6880.674,
"text": " With our current two theories, there's an incompatibility that suggests that space time quote unquote breaks down at the plank level or maybe before. So for instance, Nima's argument that if you were to measure anything with classically, you have to put an infinite amount of information somewhere and then that creates a black hole. And then there's also something with the black hole entropy that suggests holography. But that doesn't mean space time is doomed. It's just a different space time. Yeah."
},
{
"end_time": 6934.036,
"index": 259,
"start_time": 6908.951,
"text": " Yeah, but from my point of view, what has become the focus of that field a lot are actually quite tricky, very non-perturbative, very kind of strong field problems about what's going to happen to the theory when you've got black holes and black holes are decaying. And so you've kind of moved away from"
},
{
"end_time": 6958.626,
"index": 260,
"start_time": 6935.964,
"text": " But the problem with the inconsistency between quantum mechanics and general relativity is a different, that is normally the one everybody worries about, is normally a different problem. It's a very, very local problem. It's just that if you think of this in terms of the standard kind of variables like what's the"
},
{
"end_time": 6978.49,
"index": 261,
"start_time": 6959.633,
"text": " The metric variables and you use the Einstein-Hilbert action for the dynamics for these things. If you try and apply standard ideas of quantum field theory locally to that at short distances, you get these normalization problems and the theory becomes unpredictable."
},
{
"end_time": 7009.565,
"index": 262,
"start_time": 6981.852,
"text": " That's always been considered the real problem. How do you deal with that? But instead of having a proposal to deal with that and having a real kind of a new idea about what's really going to happen, what are the right variables at these short distances that will not have this problem, what are you going to do? They kind of ignore that, decided to ignore that problem and say, well, maybe string theory solves that problem, who knows? And then to move on and to try to do"
},
{
"end_time": 7039.172,
"index": 263,
"start_time": 7010.589,
"text": " you know, something much, much harder, which is to resolve these issues about what happens in black hole backgrounds and stuff. And I don't, I know, but it seems to me kind of a separate issue. You can still have space time and have these issues about, you know, what's going to happen in black hole backgrounds and stuff, and you could still resolve them in different ways. But they're just,"
},
{
"end_time": 7067.637,
"index": 264,
"start_time": 7039.974,
"text": " It's a very frustrating subject, I think, to actually try to learn about. You see people making these statements, and then you say, okay, well, what exactly do they mean? I mean, it's all well and good to say these very vague things about this is doomed and what about infinite amount of information, blah, blah, blah. But write down, tell me what we're talking about here. And there really isn't..."
},
{
"end_time": 7096.817,
"index": 265,
"start_time": 7068.37,
"text": " It's almost a comically impossible to kind of pin people down on what is the, what are you talking, what theory are you talking about? And, and then finally, when you pin them down, you find out that what they're actually talking about is they've, they're talking about some very, very toy model. They're saying, well, we don't know what's going on in four dimensions. So let's try it in three dimensions and maybe two dimensions, maybe one dimension. And so they're talking about some comically trivial toy model, which"
},
{
"end_time": 7124.394,
"index": 266,
"start_time": 7097.415,
"text": " They kind of ended up studying because well you could study it and then maybe there's some analogous problem happening in there and and that all they have are these kind of toy models which which actually don't seem to have any of the actual real physics of four-dimensional general relativity in them and that's what they're that's what they're all studying these days. I see even Nima. He's somewhat different because he's coming at it from a different point of view. He's"
},
{
"end_time": 7153.422,
"index": 267,
"start_time": 7124.872,
"text": " Coming at it from this point of view of really trying to see, find new structures in the perturbative expansions for standard quantum field theories. So he's got kind of a specific program looking at, he's not studying toy models, he's studying real four-dimensional physical models, but they're not"
},
{
"end_time": 7184.565,
"index": 268,
"start_time": 7155.145,
"text": " but they're generally models like Yang-Mills theory where you know exactly where the theory is and it's not, this isn't solving the problem of quantum gravity or anything, it's well in theory, but I think maybe I should, I'm saying this a bit too quickly without thinking, but just to try to give a flavor of what I think he thinks he's doing, he's trying to take a theory that you do understand well like Yang-Mills theory and look at its"
},
{
"end_time": 7210.213,
"index": 269,
"start_time": 7185.162,
"text": " perturbation series Feynman diagrams, find new structures there and a new language, and then see if you can rebuild the theory in terms of these new structures. And then if you've got kind of a new way of thinking about quantum field theory in terms of these new different structures like his amplitude hydron or whatever, then maybe you can then apply"
},
{
"end_time": 7240.418,
"index": 270,
"start_time": 7210.589,
"text": " Once you've got a way of thinking in terms of new structures, you can go back to the problem of quantum gravity. I see, I see. I don't think he's not in any way, as far as I know, claiming to have actually gotten anywhere near there. This gives you a lot to do. There's a lot of interesting structure there. There's a lot to work on. He and his collaborators have done a huge amount of calculation with these things. At least to my mind, I don't see them coming up with what"
},
{
"end_time": 7269.804,
"index": 271,
"start_time": 7240.862,
"text": " I think that they hope to come up with which is a different geometric language for that that really works and is really powerful for that that's going to get you something new. Did you listen or watch Sean Carroll's podcast on the crisis in physics? Well, no, I skimmed through the transcript of it. I was kind of wanting to see what he was doing. This is certainly something I'm very interested in."
},
{
"end_time": 7299.753,
"index": 272,
"start_time": 7270.503,
"text": " But yeah, I thought anyway, I thought the whole thing was actually quite strange because it's like four, four, four and a half hours long. And it's just him talking. So he's just. Anyway, I thought the whole thing was actually very odd, and it has something to do with kind of the odd nature of the response to the. To criticisms in the subject, and so I think it was another kind of weird example."
},
{
"end_time": 7328.473,
"index": 273,
"start_time": 7299.991,
"text": " You know, there's, he's kind of wants to say something about this issue of, you know, that many people are now are now kind of very aware there is some kind of problem here and they're referring to it in the crisis in physics. But, um, you know, instead of, but, but, but, but just kind of talking about it for four hours and four and a half hours yourself is just kind of, kind of strange. Um, and, and, and, and, and especially since he's got a podcast, one of the obvious things to do is to invite somebody on who"
},
{
"end_time": 7356.613,
"index": 274,
"start_time": 7328.899,
"text": " you know thinks there is a crisis in physics if you don't and he doesn't think there's one it seems and well you could actually have an interesting discussion with this person for some time but instead of discussing some this it's like you know there's a controversy going on of two kinds and instead of inviting somebody on to discuss this controversy with you or two people you just go on for four hours about how your view your view that the other you know the other side is wrong it was very odd."
},
{
"end_time": 7386.715,
"index": 275,
"start_time": 7357.073,
"text": " Also, it wasn't as if he was arguing with the people that were saying that there's a crisis in physics. So when people say there's a crisis in physics, they generally mean that there's a crisis in high energy physics, particularly with coming up with fundamental law. And so what he was then taking it on to mean is there's a crisis in physics as a whole, like cosmology or astrophysics. And then he's like, No, but look in solid state physics and the progress there. That's called a straw man where you're not actually taking on the argument you're taking on a diminished. Yeah."
},
{
"end_time": 7415.759,
"index": 276,
"start_time": 7387.056,
"text": " Well, he was also often involved in these arguments over string theory with me and Lee in 2006. And it was often the same kind of thing that he's kind of... And the whole thing is just odd from beginning to end because he's actually not a string theorist. And this is another weird sociological thing I found is that you find non-string theorist physicists who somehow want to take a bit side in this and want to"
},
{
"end_time": 7442.261,
"index": 277,
"start_time": 7416.92,
"text": " and have a big opinion about it and get emotionally involved in it, even though they actually don't know, don't actually understand the issues that this is not what they do. This is not their expertise. So, and, um, so I know, I think some of this, you know, knowing, not knowing Sean and what he's trying to do, I think he's not the only one who you see this phenomenon that there are people who, you know,"
},
{
"end_time": 7468.319,
"index": 278,
"start_time": 7443.353,
"text": " They see what they want to do in the world is really to bring to the public an understanding of the power and the great things that the subject has accomplished. And so he, and even in his four hours, he spends a lot of time, you know, giving very, very good explanations of, you know, various parts of the story of the history of the physics, the history of this. And, you know, they kind of see them, their goal in life is to kind of convince this, um,"
},
{
"end_time": 7496.681,
"index": 279,
"start_time": 7469.855,
"text": " you know the rest of the world who doesn't actually understand these great ideas or doesn't really appreciate them or skeptical about them you know to bring them to them and and i think part of the whole reason is i think he was kind of doing doing this or does this is because you know having people out there on twitter or whatever saying oh you know physics sucks it's got all these problems it's all wrong blah blah blah that this is you know this is completely against"
},
{
"end_time": 7519.906,
"index": 280,
"start_time": 7497.227,
"text": " His whole goal in life is to stop this kind of thing and to really get people to appreciate the subject. I think in a misguided way then enters into this from the point of view of, oh, I have to stop people from saying things about a crisis in physics and get them to really appreciate that this really is a great subject and wonderful subject."
},
{
"end_time": 7545.469,
"index": 281,
"start_time": 7520.52,
"text": " that goes too far and then starts defending things which really aren't defensible and things which he often doesn't really know much about. For instance? Just the details of string theory. The reason I wrote this book is that some of these problems of string theory, these questions, people will go on about ADS, CFT and this and blah, blah, blah. This is incredibly technical stuff. It's just"
},
{
"end_time": 7573.848,
"index": 282,
"start_time": 7546.271,
"text": " even understand exactly what these theories are that on both sides of the ADS-CFT thing, what is known about them? What is the real problem here? What can you calculate? What can you not calculate? What can you not find? What can you not find? What happens in other dimensions? It's horrendously technical and very few people actually really know it. But lots of people want to kind of get involved in discussions about it and argue about it without actually understanding actually what's going on. And part of the reason for writing the"
},
{
"end_time": 7601.476,
"index": 283,
"start_time": 7574.309,
"text": " not even on the book, but was to sit down and try to write about what was really going on, what the specific technical issues actually were, as much as possible in a somewhat non-technical venue. Anyway, so that's some of my reaction to this. In particular, he just starts off the whole thing by"
},
{
"end_time": 7630.35,
"index": 284,
"start_time": 7602.159,
"text": " He picked up on something from Twitter about somebody had found a paper from somebody written in 1970s complaining about how, you know, there was a crisis, there wasn't any progress in the field. And this was a time when there was great progress in the field. And this was a person who honestly, somebody completely ignorant wrote a completely paper no one ever paid attention to in the mid 1970s that was wrong about this. And he wanted to use that as to kind of bludgeon"
},
{
"end_time": 7657.637,
"index": 285,
"start_time": 7630.896,
"text": " the people who are making serious arguments about the problems today. I don't know. I thought it was kind of a weird performance, but I think this is a good thing to ask kind of people on this other side of this argument, why there's very little willingness to actually engage in technical discussions publicly with people they disagree with. I mean, you know,"
},
{
"end_time": 7686.169,
"index": 286,
"start_time": 7657.978,
"text": " Sean has never been invited by me to be on his podcast. He hasn't invited Sabina Hassenfelder. There is no appetite for that at all among people in this subject. And I think a lot of that is because they're well aware that there are really serious, difficult problems with this, whether you want to call it a crisis or whatever it is, there are real problems and they're just not very interested in acknowledging and publicizing that."
},
{
"end_time": 7715.998,
"index": 287,
"start_time": 7686.374,
"text": " Well, I have a tremendous appetite for it and the people in the audience of everything do. So if ever you have someone who you feel like would be a great guest with the opposite view that is defending string theory or the state of high-energy physics, then please let me know and I will gladly host you both. I know we spoke about some people behind the scenes, some people who are likely to say yes and have a congenial conversation. Well, actually most people are."
},
{
"end_time": 7743.012,
"index": 288,
"start_time": 7716.391,
"text": " Funny thing is actually early on in this, I was invited, a guy down at University in Florida invited me and Jim Gates to come and debate strength theory. I think we really disappointed this big audience by agreeing on almost everything. He's a well-known strength theorist. We actually found that"
},
{
"end_time": 7755.043,
"index": 289,
"start_time": 7744.019,
"text": " I think things would be interesting to do this again now, but this was almost 20 years ago, maybe a little bit less, 15 years ago. The way I would describe it then is that"
},
{
"end_time": 7784.923,
"index": 290,
"start_time": 7756.732,
"text": " If we started talking about the details, what our disagreements came down to, where it was kind of more, you know, should you be out, you know, we would agree about the state of current things, but what do you think, where do you think this stuff is going? Are you optimistic? I see a reason why this can't work. He would see reasons why this is actually best thing to do. He knows how to do, and this might work. And, and there, it's just that kind of, you know, disagreement about ideas, which is, is perfectly reasonable."
},
{
"end_time": 7812.858,
"index": 291,
"start_time": 7785.879,
"text": " And actually Gates told me, I remember at the end of when we were talking after this thing, he said, yeah, you know, I was asked to like, you know, write a review of your book about it. And I thought, oh, well, I'll just, I'll pick up this book and I'll see, you know, the guy's got it all wrong about string theory, whatever. And then, you know, I read your book and I realized that, you know, a lot of what you were saying was the stuff about that importance of representation theory in physics and that"
},
{
"end_time": 7841.63,
"index": 292,
"start_time": 7813.336,
"text": " And I actually, you know, that that's actually exactly the way I see the what's important in physics. So I find myself agreeing with much of your point of view and the book. So I couldn't I didn't anyway. So that was, you know, anyway, at the level of these these ideas, I think, especially back then, I think there wasn't it's perfectly possible to have a reasonable discussion. I think I think it has become weirder now"
},
{
"end_time": 7867.841,
"index": 293,
"start_time": 7842.466,
"text": " 20 years later, I think it was a lot more possible to reasonably be an optimist back 20 years ago and say, well, the LHC is about to turn on. We're just going to look for these super partners. Maybe they'll see super partners. We have all this stuff that might vindicate us, and we're all hoping for that. But now the LHC has"
},
{
"end_time": 7895.179,
"index": 294,
"start_time": 7869.258,
"text": " has looked, the stuff is not there. There's really not, um, and you know, that's one thing that's somewhat shocked me is people willing to, um, people who were often to me or in public saying, look, you know, the crucial thing is going to be the results from the LHC. You know, we believe that you're going to see, we're going to see the super partners and this is going to show that we're riding the right track. And then the results come in and you know, you're wrong and you just,"
},
{
"end_time": 7916.681,
"index": 295,
"start_time": 7896.203,
"text": " There's a comment on your blog that said the LHC is great for string theory because it divides in half the moduli space."
},
{
"end_time": 7947.517,
"index": 296,
"start_time": 7917.773,
"text": " That was certainly my feeling a lot when I was writing the book, whatever, is that this was going to be a crucial thing, the LHC, because either the LHC was going to see something along the lines of what these guys were advertising and which they were often willing to actually bet money on, or it wouldn't, and then they would back down and start saying, okay, well, maybe the critics have a point. But no, it's just amazing that people would just completely ignore the experimental results and keep going. About representation theory,"
},
{
"end_time": 7969.616,
"index": 297,
"start_time": 7947.841,
"text": " For people who don't know what representation theory is, can you please give them a taste and then also explain why is it important? More so than say you want a group to act on something like, okay, yes, but how much more involved does it get than that? Well, anyway, so just to say that to give a flavor of what we're talking about, yeah, so"
},
{
"end_time": 7999.821,
"index": 298,
"start_time": 7972.108,
"text": " It's very common for people to talk about the importance in physics of symmetries. And when you say that it's important to study the symmetries of something, people often then just explain it in terms of a group. So mathematically, a group is just a set with a multiplication operation. You can multiply two elements and get another. But the interesting thing about"
},
{
"end_time": 8028.422,
"index": 299,
"start_time": 8000.657,
"text": " Symmetry is actually not so much the groups, but the things that groups can act on. So what are the things that can be... So the standard example is like the group of rotations. You can pick things up and rotate them in three-dimensional space, but what are all the things that you can kind of do rotations to? And those in some sense are the representations, or the representation theory is kind of the"
},
{
"end_time": 8041.732,
"index": 300,
"start_time": 8029.309,
"text": " The linear version of that theory and if you try to work with a group action on something that isn't nonlinear, you can look at the functions on it and turn it into a linear problem. But anyway, so group representation theory is really"
},
{
"end_time": 8069.036,
"index": 301,
"start_time": 8043.217,
"text": " It really is the study of symmetries. What are the possible symmetries of things? What are the possible things that can have symmetries? It's really fundamental both in physics and in mathematics. Large fractions of mathematics you can put in this language. There is some kind of group and it's acting on some things. What are the representations?"
},
{
"end_time": 8097.602,
"index": 302,
"start_time": 8069.428,
"text": " The amazing fact about the language program and number theory is how much of number theory you can formulate in that language. You can formulate a lot of geometry in this language. It's kind of a unifying language throughout mathematics at a very deep level. To me, the amazing thing is that if you start looking at the structure of quantum mechanics, if you look at what are the quantum mechanics is this weird conceptual structure that states are"
},
{
"end_time": 8112.637,
"index": 303,
"start_time": 8098.029,
"text": " state of the world is a vector in a complex vector space and you get information about it by self-adjoint operators acting on this thing. So from the, that looks like a very, very weird, like where did that come from? But if you"
},
{
"end_time": 8142.176,
"index": 304,
"start_time": 8114.053,
"text": " If you look at that formalism, it fits very, very naturally into the formalism of group representations. And this is kind of why I wrote this book, taught this course here and wrote a book about it, about quantum mechanics from that point of view. What's the book called? Quantum Theory Groups and Representations and Introduction. It's kind of a textbook. So that was the second book I wrote. That link will be in the description. Yeah, there's also a free version with kind of corrected"
},
{
"end_time": 8169.411,
"index": 305,
"start_time": 8142.5,
"text": " With errors that I know about corrected on my website, you can also link to that. No, we want people to pay. They have to pay for the errors. Or you can buy a copy from Springer if you'd like a hardcover book or whatever. One of the things that most fascinates me about quantum theory is that there is a way of thinking about that. It's not just some weird out of the blue"
},
{
"end_time": 8187.244,
"index": 306,
"start_time": 8170.384,
"text": " Mathematical conceptual structure that makes no intuitive sense. I mean, it really has a structure which is kind of deeply rooted in understanding representation, understanding certain fundamental symmetries. Have you heard of this theorem by Radon Moyes in differential geometry?"
},
{
"end_time": 8209.855,
"index": 307,
"start_time": 8187.722,
"text": " About the amount of differentiable structures that can be placed on different dimensions. So for dimension one, there's I think up to some up to diffeomorphism or up to differentiable structure. I forget the exact term. There's just one and then there's just two for dimension two or just one. There's a finite amount for every dimension except dimension four. Yeah, in which case there's not just an infinite amount. There's an uncountably infinite amount."
},
{
"end_time": 8237.449,
"index": 308,
"start_time": 8212.773,
"text": " Yeah, but there's even... Yeah, but this is actually also one of the most famous open problems in topology, the smooth black-array conjecture, which says that is there... There you're thinking about specifically the four manifold. Yeah, so is there a... Now I forgot what I used to know about this, but yeah."
},
{
"end_time": 8262.261,
"index": 309,
"start_time": 8238.558,
"text": " There are exotic. Well, the point is that dimension four is picked out. And so it would have been nice for physics if dimension four was picked out and finite or as the rest were infinite, because then it just means, well, it's nicer for us, but it's picked out and made more diverse and more mysterious. Yeah, but, but it's, how does this go? Um,"
},
{
"end_time": 8292.056,
"index": 310,
"start_time": 8264.377,
"text": " Anyway, four dimensions is very, very special. One dimensions and two dimensions, you can kind of pretty easily understand the story. The classification story is pretty simple. Three dimensions is harder, but especially with the solution of Poincare conjecture, you actually have a good three-dimensional classification. And then once you get above four dimensions, things"
},
{
"end_time": 8308.865,
"index": 311,
"start_time": 8293.234,
"text": " Basically, there are more ways to move things, so things simplify so you can actually understand above four dimensions what's going on."
},
{
"end_time": 8338.148,
"index": 312,
"start_time": 8309.36,
"text": " Anyway, I've never actually seen any kind of clear idea about what this has to do with four-dimensional, with physics. The stuff that I've been doing very much crucially involves the fact that four dimensions is special because the way spinners work or if you like, the rotation group in"
},
{
"end_time": 8368.268,
"index": 313,
"start_time": 8338.558,
"text": " In every dimension is a simple group except in four dimensions. In four dimensions, the rotation group breaks up into two independent pieces. And that's at the core of what a lot of what I'm trying to exploit. But so four dimensional geometry is very, very special. And I don't know, speculative, very speculative. Maybe the weirdness about infinite numbers of topological structures under four dimensions that the fact that you've got the rotation group has two different pieces means that"
},
{
"end_time": 8395.725,
"index": 314,
"start_time": 8369.394,
"text": " is behind that, but I know, I know, I know, I know. Of course, of course. Yeah, it's interesting that the fact that it's semi-simple is a positive here. Like you mentioned, it breaks up into two. Yeah. Whereas usually in physics for the grand unified theories, what you want is simple. You don't want semi-simple. You want to unify into one large group. Yeah. Well, there's nothing really in terms of unification. It's just"
},
{
"end_time": 8423.66,
"index": 315,
"start_time": 8397.483,
"text": " Yeah, maybe it's maybe I should also say something about this about why what I'm trying to do, I think is quite different than the usual sort of unification that the and what the usual. Yeah. Yeah. And please explain Euclidean twister theory once more. Again, people who are still like, I've heard the term, I've heard him explain twisters, they somewhat understand twisters has to do with lines and points and planes. Okay. And spinner is something called spinners. I think I understand that."
},
{
"end_time": 8452.534,
"index": 316,
"start_time": 8424.036,
"text": " One way of stating the problem is we go out and look at the world and we see gravity and we see"
},
{
"end_time": 8483.148,
"index": 317,
"start_time": 8453.541,
"text": " We see the electromagnetic interactions, and that's kind of based upon a U1 gauge theory. It's a circle. We see the weak interactions are based upon an SU2 gauge theory. That's a three sphere. And we see the strong interactions are based upon an SU3 gauge theory. So where in the world did this U1, did these three groups come from and the way quarks and other elementary particles behave under those groups? So it's a very small amount of group theoretical data."
},
{
"end_time": 8511.459,
"index": 318,
"start_time": 8484.326,
"text": " Where did it come from? Why that? The standard answer to this very soon after the Standard Model came out was that, well, there's some big league group. You take the group of all unitary transformations of five complex dimensions or take the group of all orthogonal transformations of 10 dimensions, let's say SO10, and then you fit"
},
{
"end_time": 8540.998,
"index": 319,
"start_time": 8512.142,
"text": " that data and show that that data fits inside that bigger structure. Within that SO10 group, I can fit U1 and SU2 and SU3, you can get them in there. And I can put all of the known particles together with their transformation properties and put those together as a transformation property of SO10. So you can kind of put stuff,"
},
{
"end_time": 8569.36,
"index": 320,
"start_time": 8541.425,
"text": " This kind of package of algebraic data, we're trying to understand where it came from. You can put it together in a simple group and into a group where the problem is in terms of group theory, it's a package involving several different groups. And so you get several different simple groups. So you can put this together. But the problem with this is always is if you try and do this,"
},
{
"end_time": 8599.616,
"index": 321,
"start_time": 8570.503,
"text": " You can then write down your SU5 or SO10 theory, whatever, and it looks a lot nicer than the standard model. It's only got one term where you had a lot of terms before, but you have to then explain, but wait a minute, why don't we see that? Why do we see this more complicated thing and not that? For instance, the standard thing that grain unified theories do is you put the weak interactions and the strong interactions into the same structure."
},
{
"end_time": 8630.179,
"index": 322,
"start_time": 8600.247,
"text": " You put the stuff together, all of a sudden it can interact with itself and it can do things which you know don't happen and protons don't decay."
},
{
"end_time": 8654.48,
"index": 323,
"start_time": 8630.708,
"text": " So your problem, when you write down these theories, the problem is you haven't necessarily done anything. You've put the stuff together in something bigger, but you've just changed the problem from why these pieces to why did this bigger thing break into these pieces. You haven't actually solved"
},
{
"end_time": 8684.394,
"index": 324,
"start_time": 8654.906,
"text": " Until you have an explanation for that, you haven't actually solved anything and this is I think the fundamental problem with these great unified theories. The only way to make them break down into these other things is to introduce more Higgs particles and more complicated structure and more degrees and more numbers and you lose predictivity if you do that. You also find that they also don't look like what you see in the real world if you do experiments but most people who"
},
{
"end_time": 8714.309,
"index": 325,
"start_time": 8684.633,
"text": " have tried to come up with some unification, have done some version of that actually. I mean, so for instance, I mean, I don't want to really get into things like what Garrett Leasey is talking about. But they're all versions of this. They've all got their own version of this. And I think when you see people kind of dismissing theories of everything and green and white theories, and you see Sabina Hassenfelder saying, well, these people are lost in math,"
},
{
"end_time": 8743.029,
"index": 326,
"start_time": 8715.026,
"text": " then they're all really referring to the same problem that people are trying to get a deeper understanding of what's going on by putting things together into a bigger structure. And they're all kind of foundering on not having an answer as to why this breaks up. So the thing that I'm trying to do, why I'm much for"
},
{
"end_time": 8766.254,
"index": 327,
"start_time": 8744.206,
"text": " interested in these ideas about spinners and twisters is that I'm not actually, I mean, a lot of what I'm doing, as I said, I mean, the fact that there are these two SU-2s, that's an aspect of four dimensions. There really are, maybe the thing to say is that I'm not introducing kind of new"
},
{
"end_time": 8795.623,
"index": 328,
"start_time": 8767.551,
"text": " I'm not introducing lots of new degrees of freedom and then having to explain why you can't see them. I'm trying to write down something. I'm trying to write down a new geometrical package, which packages together the, um, the things we know about and doesn't, and doesn't actually have new, you know, doesn't actually have all sorts of new stuff. Penrose said this was his motivation as well for Twister theory. Yeah. Yeah. So Twister theory, so in some sense, Twister theory is a bigger structure, but it's not, um,"
},
{
"end_time": 8827.551,
"index": 329,
"start_time": 8797.671,
"text": " It doesn't contain anything really new. It contains the same spinors you had before and puts them in an interesting new relation so you can understand conformal invariants. Twister theory is not the things you knew about Twister theory. It's not spinors and vectors and the things you knew about plus some other completely unrelated stuff. It's the things you knew about in a new, more powerful conceptual framework. That's the sort of thing I'm trying to do."
},
{
"end_time": 8854.019,
"index": 330,
"start_time": 8829.531,
"text": " The problem is that it's, I guess, a misnomer to really say this is a well-defined theory. It's more a speculative set of ideas about how to, but that's the crucial, I mean, probably I think the most important new idea here, which for this to be right has to be true and which is exactly this idea that"
},
{
"end_time": 8884.155,
"index": 331,
"start_time": 8854.633,
"text": " About about rotate that if you think about rotations in four dimensions in Euclidean space-time When you relate it to a Cassie space-time in the real world one of the s e2s can be treated as an internal symmetry and that and that could explain the weak interactions, that's Mm-hmm. That's kind of a crucial Yeah, that's why it's also referred to as gravel weak unification by you or by other people other people have have you know, I mean other people have noticed this and and actually it's interesting when you read the"
},
{
"end_time": 8912.875,
"index": 332,
"start_time": 8884.633,
"text": " This is a very chirally asymmetric view of the world, and a lot of people said, oh, well, that means maybe you should be able to understand. The weak interactions are chirally asymmetric, so maybe there's something here. But the Twister people, I think, never really had a version of this. There are various people who have tried to write down to do this. I mean, one is actually, there's a paper by"
},
{
"end_time": 8941.613,
"index": 333,
"start_time": 8913.49,
"text": " Stefan Alexander has worked on this and Lee Smolin, they actually had a paper intended to do this. What they're doing is significantly different than what I'm trying to do. In particular, they're staying in Minkowski space. This idea of going to Euclidean space to get this thing to behave like an internal symmetry is not something that"
},
{
"end_time": 8953.148,
"index": 334,
"start_time": 8941.886,
"text": " Jonathan Oppenheim, Stefan Alexander, and Neema Arkani Hamid."
},
{
"end_time": 8980.128,
"index": 335,
"start_time": 8953.677,
"text": " all were graduate school peers at the same time as my brother in physics. Oh, okay. This interesting because then later on in my life, this was all in Canada. Yeah, yeah. So U of T Nima was at U of T University of Toronto with my brother, but then in graduate school, Oppenheim and Stefan Alexander, I spoke to Stefan on the podcast as well. Yeah, no, there have been very few physicists who've been encouraging about this."
},
{
"end_time": 9007.125,
"index": 336,
"start_time": 8980.64,
"text": " He's one example. Yeah, he's extremely open to new ideas and playful. He's a playful person with ideas, much like with his music. I think that both qualities rub off on one another. And I think also in his own research, I think it's not so much that he's followed up on this grab-a-week stuff, but he is very interested in"
},
{
"end_time": 9032.551,
"index": 337,
"start_time": 9008.524,
"text": " You know, is there some way in which gravity, you know, that gravity actually is a chiral theory, there is some chiral asymmetry in gravity, and especially, you know, can you know, anyway, I mean, are there kind of astrophysical and cosmological thing, places you can go and look and see, you know, is gravity really chirally symmetric or not? And so I know that that's something that he's worked a lot on."
},
{
"end_time": 9062.568,
"index": 338,
"start_time": 9032.824,
"text": " So he's working on experimental tests of the chirality of gravity, but that doesn't mean experimental tests of your theory, just your theory is a chiral theory of gravity. Yeah, it's a, it's a chiral theory, but it's not. It would be validation of your theory or a testation. No, I mean, it's kind of, I mean, first of all, again, I have to keep saying I don't really have it. I don't, I would love to say I would love to say I've written down a consistent proposal for a theory of quantum gravity based on my ideas, but I'm not"
},
{
"end_time": 9092.807,
"index": 339,
"start_time": 9063.029,
"text": " I'm not there yet. I think what he's doing is more, it doesn't involve, it doesn't have the structures I'm trying to exploit are not there in what he's doing. But I believe what he's doing is more important thing. You kind of add Chern-Simons kind of terms. You assume that maybe there's some Chern-Simons term in the theory and ask what the observational implications of that would be and try and go out and look for that. But I haven't really"
},
{
"end_time": 9120.657,
"index": 340,
"start_time": 9093.422,
"text": " Carefully looked at what he's doing, just because it's quite different than what I'm trying to do. Can you explain what turn Simon's theory is? So what it means to add a turn Simon's term? I know Stefan's worked on turn Simon modified gravity. And then there's something like turn Simon terms in the Lagrangian of particle physics. But I don't know if those two are related. Yeah, I don't. Yeah, I shouldn't try and talk about it as we're gonna I don't remember exactly what he was doing. But um,"
},
{
"end_time": 9146.988,
"index": 341,
"start_time": 9122.858,
"text": " Well, Trent, I mean, you're very hard. Actually, one funny thing is that I actually went to a, I don't know. So I actually started thinking about Trent. So maybe I can go back to how I first encountered them. So when I was doing my PhD thesis, my problem was I'm trying to understand, I got engaged on a computer."
},
{
"end_time": 9172.978,
"index": 342,
"start_time": 9148.37,
"text": " I've got this version of gauge fields and they're described on links on a lattice and you can store them in a computer and manipulate them. I want to look at one of these configurations and say there's supposed to be some interesting topology in this engaged theory. This is what people are getting interested in the 70s and 80s. In particular, there's something called the"
},
{
"end_time": 9199.019,
"index": 343,
"start_time": 9175.043,
"text": " Let's say the instanton number. These gauge fields are supposed to have some integer and variant called the instanton number. If somebody hands you a gauge field on a compact manifold, you should be able to calculate its instanton number. If you could calculate these instanton numbers and see them, you could do interesting physics with it."
},
{
"end_time": 9224.411,
"index": 344,
"start_time": 9199.411,
"text": " So the problem in some sense of my thesis was, you've got these gauge fields, what are their instanton numbers? Can you define them? And they're just integers? They're just integers, yeah. So they're invariants, but they're not invariants of the base manifold. You basically have a bundle with connection and they're invariants of the bundle. And if you know the connection, you're sensitive to this invariant. But the"
},
{
"end_time": 9253.695,
"index": 345,
"start_time": 9226.186,
"text": " The one way of looking at that though is if you look at the interval formula for this thing, it's a total derivative so that if you're trying to integrate it over a ball or a hypercube, the formula that's supposed to add up to this instanton number, you can write it as an interval over the boundary. It's the interval of D of something so it's"
},
{
"end_time": 9281.92,
"index": 346,
"start_time": 9254.053,
"text": " It's the interval of boundary. It's a total derivative. So the thing that it's a total derivative, the thing that lives on the boundary is the Chern-Simons form actually. So this is kind of the first way that people started seeing this thing in physics. And so one idea was, well, I could"
},
{
"end_time": 9312.756,
"index": 347,
"start_time": 9283.541,
"text": " If I could, instead of calculating these instanton numbers, if I try and do it in terms of their local contributions from each hypercube, I should, if I could just calculate the Chern-Simons, the Chern-Simons number, the contribution, you know, if I could calculate the, that thing, then I would be done. And so I spent a lot of time looking at the Chern-Simons formula and then I spent a lot of time trying to put that in the lattice and then"
},
{
"end_time": 9342.295,
"index": 348,
"start_time": 9313.148,
"text": " I kind of finally realized it's kind of gauge. The problem is that it's very gauge invariant. So any kind of idea you have about how to calculate or construct it tends to be just an artifact of some choices you're making because of gauge symmetry. So this though, that led to one of the great experiences of my life. When I was at MSRI,"
},
{
"end_time": 9363.729,
"index": 349,
"start_time": 9342.892,
"text": " At one point, Atiya and a bunch of people were talking in the blackboard and somebody was asking Atiya said, how would you calculate this Chern Simons network? Then Chern Simons had become incredibly important because of Whitten. Whitten had said,"
},
{
"end_time": 9387.534,
"index": 350,
"start_time": 9364.087,
"text": " You can get these wonderful non-invariants of three manifold of variance if you can do path integrals and that you should take the path integral to be e to the i times the Chern-Simons number, exactly that integral that I was talking about. But Witten now wants to integrate it over a whole three manifold and so people were asking, can we try and think about how can we actually do this calculation what we're doing?"
},
{
"end_time": 9411.613,
"index": 351,
"start_time": 9388.285,
"text": " And then Atiya for thinking for about five seconds comes up and says, ìOh, well, maybe you could calculate it this way, do this.î I was luckily standing there and since Atiya had thought about it for about 10 seconds, I thought about it for about three years. I could say, ìNo, no, no, that doesnít work. You canít do that because of this.î So that was one of the high points of my mathematical career."
},
{
"end_time": 9439.718,
"index": 352,
"start_time": 9411.613,
"text": " Yeah, anyway, but I don't know that this is in any way answered any question, but that's that's one definition of it, but it's a very It's kind of an amazing Piece of information about you know about about gauge fields about connections and it tells you some very subtle things and it turns out to be useful for all describe all sorts of interesting and unexpected physical phenomena and"
},
{
"end_time": 9469.991,
"index": 353,
"start_time": 9440.384,
"text": " These speculative ideas of yours of gravel week unification, have they been sent to Penrose? Has Penrose commented on them? I haven't heard anything back from Penrose. Penrose is a little bit of a problem. Whatever email I had from him back when he was helping my book no longer works and other emails tend to bounce. You don't have mutual friends?"
},
{
"end_time": 9499.206,
"index": 354,
"start_time": 9470.674,
"text": " I've come this close to actually running into him and being at the same conference as something to him and having a chance to talk to him personally. I keep expecting, instead of making a further effort to get a manuscript to him, part of the problem you'll see if you don't know his email and you try and contact him, you end up getting a secretary who may or may not be bringing things to him. I was actually at Oxford last year."
},
{
"end_time": 9525.947,
"index": 355,
"start_time": 9500.896,
"text": " From things that he said about this kind of thing, I think he's made it very clear that he"
},
{
"end_time": 9555.196,
"index": 356,
"start_time": 9526.544,
"text": " He has always explicitly followed the kind of thing Attiya did, the kind of Euclidean version of the theory, but he's always said very clearly that in his mind the Euclidean version of theory is not the theory. Theory is what's happening in the Kassian space. Anyway, whether I could convince him otherwise, I don't know, but I think he's kind of pretty clearly in his mind thought through, okay, there is this interesting Euclidean theory, but"
},
{
"end_time": 9585.401,
"index": 357,
"start_time": 9555.896,
"text": " That's actually not really the physical thing is Minkowski. So I don't actually believe you're going to that by working over there, you're going to actually tell me something important. But um, but it's why I would I think I'd have to get around that particular initial reaction from him. So forgive this fairly foolish question. But if both gr and the standard model can be formulated in terms of bundles, then why can't you just take a direct product of the groups? So for instance, you have"
},
{
"end_time": 9611.527,
"index": 358,
"start_time": 9585.725,
"text": " the standard model gauge groups and then you direct product with SL13 so that's the principle you make an associated frame bundle that's like just a projection of SL13 and then you say that's general relativity and the other ones is the other associated bundles the standard model and then you call that unification like is that unification what are the problems there? Well the problem is that general relativity is a different"
},
{
"end_time": 9637.142,
"index": 359,
"start_time": 9612.193,
"text": " Well, maybe the thing to say is, so gauge theory is really just what you have is a bundle and the fibers are some group. And you have connections and curvature on that. You write down the interesting Lagrangian is the norm squared of the curvature. And anyway, so gauge theory is a nice, pretty story. If you try and write general to be the same language, you can do it."
},
{
"end_time": 9664.292,
"index": 360,
"start_time": 9637.892,
"text": " It's fine. You have a G bundle where G is SO31 or D Euclidean Ridge, whatever, and you have a connection, you have a curvature. But the problem is that you crucially have something else and you have other things specifically because you're not some arbitrary G bundle, you're the frame bundle. And the frame bundle has"
},
{
"end_time": 9687.329,
"index": 361,
"start_time": 9665.111,
"text": " It's a principal bundle for the group of just all changes of frame, but it also is, I mean, people use the term soldered or tie. It also knows about the base structure, so a point in the fiber of the frame bundle is not just an abstract group element, it's a frame."
},
{
"end_time": 9715.196,
"index": 362,
"start_time": 9687.961,
"text": " It's a frame down on, you know, if you take vectors, you can predict on the base space and it's a frame for those vectors. So it's kind of soldered to the tangent space and so what this means in practice is it means that there's new variables which are part of the story, which are not just the"
},
{
"end_time": 9740.111,
"index": 363,
"start_time": 9715.759,
"text": " not just the SO31 connection and curvature. There's also, you know, so you've got this connection one form of curve. Soldering form? Yeah, it's called the soldering form or the tetrad or I mean, there are a lot of different different people names for it. But there's kind of, there's kind of a one form, you feed it the vector and you feed it a vector and it tells you and you know, since you're up on the frame bundle,"
},
{
"end_time": 9769.753,
"index": 364,
"start_time": 9740.759,
"text": " you've got a frame and this one form has components which tell you what the components of the vector are with respect to the frame. So it's a very kind of canonical object, but it's there, the space-time geometry depends upon it. So the space-time geometry doesn't just depend upon the connection of the curvature, it depends upon the connection and this"
},
{
"end_time": 9797.073,
"index": 365,
"start_time": 9770.179,
"text": " this canonical one-form. So the problem is that so you've got extra variables which you didn't have in that these just don't exist in the Yang-Mills case and you have to and so you can and with those variables you can write down a different lower order Lagrangian instead of taking the curvature squared you can take the curvature times"
},
{
"end_time": 9821.442,
"index": 366,
"start_time": 9797.449,
"text": " some of these guys, and you can get the Einstein-Hilbert Lagrangian. The fundamental Lagrangian of gravity is very different than the fundamental Lagrangian of Yang-Mills theory, and it's because you've got these extra gadgets to work with. I see, I see. So that's one way of saying it. You can't. But people have speculated a lot about why"
},
{
"end_time": 9850.35,
"index": 367,
"start_time": 9821.596,
"text": " Why not just try adding these higher curvature terms like you had in the Yang-Mills case, add those to gravity? Anyway, there's a long, long story about trying to mess with different, change the Lagrangian of gravity to try to make something better behave. Now, have you found any unification attempts that are between gravity and the standard model or gravity in any of the interactions that are improved if you don't view gravity as curvature but rather as torsion?"
},
{
"end_time": 9876.664,
"index": 368,
"start_time": 9851.049,
"text": " So for instance, this is something Einstein was working on later in his life. And then there's also non-matricity. Carton was working on that. Yeah. Yeah. So there are equivalent formulations of gravity, at least the torsion one. The gravity is actually not curvature. It's just torsion. Yeah. Yeah. So the... Well, one way to say it is, so now once you've got these"
},
{
"end_time": 9894.821,
"index": 369,
"start_time": 9878.404,
"text": " The two compatibility conditions to create the Levi-Civita connection, I believe it's called?"
},
{
"end_time": 9918.695,
"index": 370,
"start_time": 9895.316,
"text": " is that you have no torsion and that you have that the metric doesn't change with the covariant derivative. So if you take the covariant derivative on the metric, it's zero. If you don't have that, then you have non-metricity. In other words, along the parallel transport, the metric is preserved. Yeah. Okay. Yeah. I'm not so sure about that, but I can't say about torsion, but your problem is that if you"
},
{
"end_time": 9947.176,
"index": 371,
"start_time": 9919.36,
"text": " So if you just write down a theory with some, you put together a Lagrangian which is going to give you equivalent results to the Einstein-Hilbert, you put it together out of the curvature and the canonical one-form. Now your problem is that you've got, when you try to get the Euler-Lagrange equations, you can vary the canonical one-form and you can vary the connection. So you've got"
},
{
"end_time": 9973.712,
"index": 372,
"start_time": 9947.654,
"text": " And one of them, let's say, I guess it's if you vary the connection, then you end up, that gives you the torsion free condition. So you've got more variables, so you need more equations. So you recover gravity, but you recover, with the standard Lagrangian, you recover not the Einstein's equations and"
},
{
"end_time": 10001.834,
"index": 373,
"start_time": 9974.753,
"text": " As one equation, but also the torsion free condition as the other one. The standard simplest version of Einstein-Hilbert in that theory has no torsion again, but you can certainly write down more different Lagrangians in which torsion is not zero, but it has some kind of dynamics and does something. That might be interesting."
},
{
"end_time": 10027.466,
"index": 374,
"start_time": 10002.278,
"text": " Yeah, I was watching a talk a few maybe a few weeks ago or a couple months ago about when trying to modify gravity, especially for explaining quote unquote dark matter that you can explain dark matter as a particle. But if you want to do modified gravity, it's useful to have torsion in your theory. Well, anyway, what I was thinking was, OK, if it's useful there, maybe it's not actually the case that that explains"
},
{
"end_time": 10056.323,
"index": 375,
"start_time": 10027.927,
"text": " dark matter, but maybe it would be more useful to try unification with torsion models of gravity than with the regular curvature model of gravity. Yeah, I should say one kind of funny thing about all this is that I've always, before I got involved in this particular thing, I tended to kind of stick to thinking, I mean, I spent a lot of time over the years trying to learn about quantum gravity and about these issues that we're talking about, but I never actually"
},
{
"end_time": 10083.08,
"index": 376,
"start_time": 10058.114,
"text": " I'm trying to understand what's going on in particle physics and the standard model. There are these groups of people who just think about quantum gravity and they're very smart. They've been doing this for 30 or 40 years and a lot of them aren't strength theorists."
},
{
"end_time": 10099.94,
"index": 377,
"start_time": 10083.473,
"text": " I'm not seeing anything that they're doing that I could do better. They seem to be doing interesting things with torsion but they know more about torsion than I do."
},
{
"end_time": 10130.52,
"index": 378,
"start_time": 10102.824,
"text": " Anyway, I kind of stayed away from more particle. Yeah, exactly. Yeah, that's why we're saying it. But I really stayed away from kind of going more in that direction, becoming more expert, a lot of these things, figuring. Yeah, I mean, until I see something that I could that I maybe I can do something with. I mean, if it's just a. It's interesting to see what the story is there, but there are really smart people have been banging away at the story for a long time and I can't help I'll stay away from it. But, um,"
},
{
"end_time": 10145.572,
"index": 379,
"start_time": 10131.493,
"text": " I've actually, partly because of this, had to learn a lot more about and get some remedial education on some of this stuff. I'm still, in some sense, the wrong person to talk to about theories of gravity."
},
{
"end_time": 10171.852,
"index": 380,
"start_time": 10146.049,
"text": " Yeah, before we wrap up, there are a couple other proposed toes. So one with Lisi, like you mentioned, and then Eric Weinstein has geometric unity and Wolfram has Wolfram's physics project. I believe that's still the title. And Chiaro Marletto has a framework, not an actual toe, but constructor theory. So which of those have you delved even superficially into and what are your comments on them?"
},
{
"end_time": 10196.305,
"index": 381,
"start_time": 10172.568,
"text": " I should say I mean the Wolfram or the other one mentioned. So these ideas that you're going to start with some completely different starting point like Wolfram we're going to start and whatever you want to call whatever he's starting with. The fact that you're going to start from this kind of completely different thing that has nothing to do with any of the mathematics that we know of and that you're going to then reproduce the standard model whatever this"
},
{
"end_time": 10227.534,
"index": 382,
"start_time": 10197.927,
"text": " That seems to be highly implausible and anything I've ever looked at it and of his for briefly, you know, doesn't change that opinion. I just I just don't see how you get from. Anyway, I mean, you're telling me that you're going to go start and start way, way, way far away at something else and and make some progress right here. And I don't see how you're going to get you're ever going to get back. And so there's a lot of that. Lizzie's thing, I looked a bit"
},
{
"end_time": 10248.78,
"index": 383,
"start_time": 10228.166,
"text": " I know Garrett and Eric both fairly well. Garrett has slept on my couch like many people. Garrett I think had a fairly well defined proposal but to my mind it has exactly the same problems that I was telling you about. He wants to put"
},
{
"end_time": 10276.442,
"index": 384,
"start_time": 10249.428,
"text": " So these are the same problems you explicated about Grand Unified Theories earlier. Yeah, so he wants to put all these things together and he wants to put it together and have it live inside E8 and it's very nice except that he doesn't really have a, to my mind by doing that he hasn't actually solved the problem but he has to tell me why the E8 breaks down into the pieces that we know about and he doesn't have any, as far as I know, has no useful"
},
{
"end_time": 10305.606,
"index": 385,
"start_time": 10276.8,
"text": " I mean, Eric, you know, I've talked to a lot about this over the years. I've I don't know. I mean, he and I've looked a bit at, you know, paper that he finally put out. But I think again, it seems to me it has the same kind of problems. Again, he's trying to put he's trying to put everything together into this bigger geometric structure. And then but he doesn't, to my mind, have"
},
{
"end_time": 10334.121,
"index": 386,
"start_time": 10306.305,
"text": " I have any kind of plausible idea about how he's ever going to break that down and recover what, what, what we, uh, the real world that we see. And, and, and his, his, his is a lot harder to see exactly what he's doing or unless Lizzie is kind of following much more kind of a standard story. You can, you can see exactly what he's doing where it's harder to tell. But, but both of them, I think suffer from the same problem as guts as far as I know."
},
{
"end_time": 10359.804,
"index": 387,
"start_time": 10334.906,
"text": " What about category theory? There's plenty of hype about category theory in physics but you're also in math and so you're much more close to category theory. Is there a hope that somehow higher categorical structures will elucidate how to make progress in high energy physics? I haven't seen any evidence for that. I mean the things people are doing with those are actually much more"
},
{
"end_time": 10382.244,
"index": 388,
"start_time": 10361.305,
"text": " I'm trying to understand, there's a lot of people actively trying to use some of that mathematics to understand classification of more kind of theories you would use in condensed matter systems. It's possible that the right way to"
},
{
"end_time": 10409.838,
"index": 389,
"start_time": 10383.114,
"text": " To understand gauge groups, the infinite dimensional group of all gauge transformations or maybe you can even think of the diffeomorphism group about how to think about representations of those groups. It may be that the higher categorical stuff has something useful to say about that because there the problem is that the standard notions of what a representation is don't really"
},
{
"end_time": 10438.2,
"index": 390,
"start_time": 10412.261,
"text": " The problem is when you're dealing with these influential groups, you really don't even know what… You can't just say representation. You have to put some more additional structure to make this well-defined and what the additional structure is unclear and maybe it would help with those. Anyway, I haven't really followed… I've spent some effort trying to follow that mathematics but I don't do that. Anyway, category theory in general is just a very, very general…"
},
{
"end_time": 10465.691,
"index": 391,
"start_time": 10439.07,
"text": " The problem is it's a very, very general idea. It's part of the way mathematicians think about every subject. It's very, very useful to think not about representations, but the category of all representations. That opens up all sorts of new ways of thinking and questions through that. It's just a very abstract language."
},
{
"end_time": 10495.623,
"index": 392,
"start_time": 10466.101,
"text": " It can be used for many, many things. When I realized at some point, when I was a student, I thought the way to understand mathematics is to look at the mathematics they're teaching us and look for the more and more general structures and then just understand the most general structure and then you'll be able to derive the rest of the stuff. Then it looked like category theory was this thing which was the most general thing that people were using. I thought I should go learn category theory."
},
{
"end_time": 10524.275,
"index": 393,
"start_time": 10496.152,
"text": " But then at some point I realized that what I was doing, what you're doing is that as you go to greater and greater generality, you're, you're, you're, you're saying what, what you're doing, you're talking about, you're saying something about more things, but you're saying less and less. And so in the limit, you're saying nothing about everything, which is really not, not actually useful limits. And that's the problem with just, you know, category theory as just a,"
},
{
"end_time": 10549.036,
"index": 394,
"start_time": 10524.906,
"text": " Now what if someone retorts about the polemics against string theory by saying, hey look, string theory has produced something much that's positive,"
},
{
"end_time": 10564.309,
"index": 395,
"start_time": 10549.326,
"text": " So for instance, the math is used in the fractional quantum Hall effect and many other condensed matter systems."
},
{
"end_time": 10592.398,
"index": 396,
"start_time": 10564.957,
"text": " There was a comment that said, look, I'm a physicist and I'm not a string theorist, but we use string theory in the fractional quantum Hall effect. And that was a comment on the Ed Frankel video. Well, I think probably the problem is string theorists are happy to kind of claim"
},
{
"end_time": 10614.94,
"index": 397,
"start_time": 10593.575,
"text": " Anyway, they're kind of claiming that everything comes from a string theory and they're actually at this point, David Gross kind of argues that well, you have to shut up and stop arguing about string theory because string theory and quantum field theory are actually all one big thing and so you're arguing against quantum field theory so that's just a waste of time. Because string theory is supposed to be a generalization of quantum field theory?"
},
{
"end_time": 10644.309,
"index": 398,
"start_time": 10615.23,
"text": " Well, it's because, oh, you know, with these dualities and m-theory, whatever, we realize it's all the same. And so, anyway, so I don't know in this specific case, and I'm not an expert on that case, but I strongly suspect that the saying that this came from string theory is that it's really some fact that they learned from string theorists. And string theorists are happy to say this came from string theory, but it's not actually"
},
{
"end_time": 10674.872,
"index": 399,
"start_time": 10646.101,
"text": " And to make this whole thing even more frustrating, more complicated, is that no one actually can, at this point, has a definition of what string theory is. So people then start talking about what Groves is trying to do. He's trying to say, well, string theory and quantum field theory are all the same. So when I say string theory, I mean quantum field theory. And people just keep doing this. So unless you're really, really expert and you know exactly what"
},
{
"end_time": 10700.282,
"index": 400,
"start_time": 10675.52,
"text": " The story is about what string theory is and how it's related to quantum field theory. Another weird thing I found is that almost everyone believes that Ed Whitten wrote one Fields Medal for his work on string theory, which is just not true. The things that he won the Fields Medal for are these totally amazing"
},
{
"end_time": 10722.415,
"index": 401,
"start_time": 10700.691,
"text": " It's really hard to convince anyone of this. Even most mathematicians believe this if you go up and ask a mathematician,"
},
{
"end_time": 10752.193,
"index": 402,
"start_time": 10722.892,
"text": " So what's a fulfilling life for you, Peter? I'm quite happy. I think when my book came out, a lot of people, the ad hominem attack was, oh, here's this guy who was not a success and didn't really, and he's just embittered and unhappy. They didn't realize that I'm"
},
{
"end_time": 10776.493,
"index": 403,
"start_time": 10753.66,
"text": " I'm actually quite discussingly pleased with my life and very happy with myself. I've had a weird career here at Columbia, but I've been extremely well treated by the department and allowed pretty much to do, as I said, get away with doing whatever I want and treated well and paid well."
},
{
"end_time": 10802.329,
"index": 404,
"start_time": 10777.022,
"text": " I had a very happy life. Meaningful. Yeah, and I'm actually proud of the books I've written and some of the things I've done. I'm actually quite excited about what I'm working on now. And this was always one of my great frustrations is that there were a lot of things that seemed to me that something interesting was going on, but I didn't understand enough to really be sure this is really something, I've really got something here."
},
{
"end_time": 10826.937,
"index": 405,
"start_time": 10802.671,
"text": " and now I'm much more optimistic about that and so I'm trying to, I'm getting older though, I'm 66, I'm trying to figure out, I'm actually trying to negotiate with the department of the university some kind of exit strategy out of my current position to some different kind of situation here and I may or I might be doing less teaching and less and"
},
{
"end_time": 10854.087,
"index": 406,
"start_time": 10827.688,
"text": " and less involved and less taking care of the computers and get other people to do that. You take care of the computers? I told you about this. My official title is Senior Lecturer and the weird thing about this title is this is a title that the university gives to people who are in non-tenured positions but are teaching courses here and so I'm doing that but I'm also part of"
},
{
"end_time": 10884.735,
"index": 407,
"start_time": 10855.128,
"text": " The deal with the department has always been that I do relatively not that much teaching, but also make sure the department computer system runs, and so I actually do it on a day-to-day basis. I also make sure our computer system is going. You don't want to do that anymore? Well, let's just say I like to do it. Maybe a better way of saying it is I've actually kind of enjoyed that. Actually, that's always been in some ways fun."
},
{
"end_time": 10910.538,
"index": 408,
"start_time": 10885.657,
"text": " There is an inconsistency I found between having the time and focus to work on making progress on the stuff I want to make progress on and also teaching a course and also having to deal off and on with computer problems and trying to fit all those together in a 40-hour week doesn't work so well. I've decided in my life"
},
{
"end_time": 10918.643,
"index": 409,
"start_time": 10910.845,
"text": " I definitely have to prioritize the working on these new ideas. I've got to start dumping some of the other things and change things, but we'll see."
},
{
"end_time": 10946.886,
"index": 410,
"start_time": 10919.155,
"text": " I managed to find that specific comment that was referenced earlier and I sent it to Peter Royt over email. Here's the comment and then subsequently there'll be Peter's response. I am a physicist and I use string theory all the time in my research on the fractional quantum Hall effect. What Frenkel means here is that the expectation to find the standard model in the 90s by Calibri-Yau compactification of one of the super string theories turned out to be unfulfillable to this date. This does not harm the theory."
},
{
"end_time": 10971.015,
"index": 411,
"start_time": 10946.886,
"text": " The prediction was just wrong, therefore the title of this video is misleading. String theory revolutionized the way we understand physics and math in general, and it continues to do so. By the way, it's the only consistent theory unifying quantum field theory and gravity. Peter's response is, Hi Kurt, in the podcast I misunderstood what you were telling me, that a condensed matter theorist was saying that they thought understanding the fractional quantum Hall effect used string theory."
},
{
"end_time": 10990.418,
"index": 412,
"start_time": 10971.015,
"text": " I was speculating that they were misunderstanding some QFT explanation as a string theory explanation. It seems, though, that this is not a condensed matter theorist, but a string theorist. The quote-unquote string theory revolutionized the way we understand physics and math in general and continues to do so is just pure hype. It's the sort of thing you will ever hear from a string theorist devoted to that cause."
},
{
"end_time": 11009.855,
"index": 413,
"start_time": 10990.418,
"text": " I was unaware that some string theorists have worked on embedding the fractional quantum hall effect system in a complicated string theory setup. I don't understand the details of this from long experience, think it's highly likely. This, like many string theory explains condensed matter physics claims, is just hype. String theory since the beginning has had a huge problem"
},
{
"end_time": 11038.541,
"index": 414,
"start_time": 11010.145,
"text": " and it continues to this day. The current tactic for dealing with the failure of string theory hype around particle physics is to double down with new hype about nuclear physics, condensed matter physics, and quantum information theory, etc, etc. Peter then quickly sent a follow-up email. Hey, I just read the thread. I'm guessing this is a string theory undergrad or graduate student. The claims about the fractional quantum Hall effect are based on relating it to Chern Simon's theory, which is a QFT story, so quantum field theoretic story."
},
{
"end_time": 11068.046,
"index": 415,
"start_time": 11038.985,
"text": " Also, all those fans of David Hestein should know that I did ask Peter about geometric algebra, but he's not familiar enough to comment on it. OK, well, it was wonderful speaking with you and I hope we speak again. I hope we meet in person. Oh, sure. Let me know if you're ever in New York. Oh, yeah, I go quite frequently. So I'll let you know the next time I'm there and maybe I'll see you at perimeter if you ever come down this way. Yeah, I haven't haven't been there yet, but I would at some point like to like to like to go there."
},
{
"end_time": 11085.282,
"index": 416,
"start_time": 11068.626,
"text": " I just signed up to participate via Zoom. They have a conference on quantum gravity at the end of the month, but it's mostly virtual. Anyway, I'll watch some of the talks on Zoom, but someday I'll actually get there physically."
},
{
"end_time": 11114.616,
"index": 417,
"start_time": 11085.828,
"text": " The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked that like button, now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. You should also know that there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, disagree respectfully about theories and build as a community our own toes."
},
{
"end_time": 11132.688,
"index": 418,
"start_time": 11114.616,
"text": " Links to both are in the description. Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc., it shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well."
},
{
"end_time": 11153.507,
"index": 419,
"start_time": 11132.688,
"text": " Last but not least, you should know that this podcast is on iTunes, it's on Spotify, it's on every one of the audio platforms, just type in theories of everything and you'll find it. Often I gain from re-watching lectures and podcasts and I read that in the comments, hey, toll listeners also gain from replaying, so how about instead re-listening on those platforms?"
},
{
"end_time": 11182.773,
"index": 420,
"start_time": 11153.507,
"text": " Every dollar helps far more than you think. Either way, your viewership is generosity enough."
}
]
}No transcript available.