Theories of Everything with Curt Jaimungal - Peter Woit: A New Path to Unification (The Forgotten Geometry)

Episode Date: September 2, 2024

Peter Woit is a theoretical physicist and mathematician, currently a Senior Lecturer in the Department of Mathematics at Columbia University. Peter is known for his work in quantum field theory and representation theory, particularly for contributions to the understanding of gauge theories. In addition to his academic work, Woit is the author of "Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law," where he critically examines string theory while advocating for alternative approaches in the quest for a unified physical theory. Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) Join TOEmail at https://www.curtjaimungal.org Links: ⁠- Peter Woit’s first appearance on TOE: https://www.youtube.com/watch?v=9z3JYb_g2Qs - ⁠Peter Woit’s book on Quantum Theory and Representations: https://www.amazon.com/Quantum-Theory-Groups-Representations-Introduction/dp/3319646109 - Peter Woit’s Papers - https://inspirehep.net/literature?sort=mostrecent&size=25&page=1&q=a%20P.Woit.1 - Peter Woit’s Blog - https://www.math.columbia.edu/~woit/wordpress/ - Peter Woit’s book “Not Even Wrong”: https://amzn.to/3X8c1pS Timestamps: 00:00 - Introduction 01:31 - Overview of Unification in Physics and the Standard Model 05:11 - Historical Development of the Standard Model and its Success 07:00 - Introduction to General Relativity and its Challenges 09:32 - Unanswered Questions in the Standard Model (SU1, SU2, SU3) 13:12 - Technical Issues in Quantum Field Theory and General Relativity 17:24 - The Rise of Grand Unified Theories (GUTs) 21:07 - Challenges and Failures of GUTs (Proton Decay) 25:43 - Abandonment of GUTs and Introduction of Supersymmetry 26:45 - Basics of Supersymmetry and Its Predictions 31:28 - Failure of Supersymmetry (No Evidence for Superpartners) 32:08 - Supergravity, Kaluza-Klein Theories, and Extra Dimensions 35:52 - String Theory and the Unification Paradigm in the 1980s 39:00 - Experimental Failures and the Lack of Evidence for String Theory 41:00 - Ongoing Pursuit of Failed Theories and Resistance to New Ideas 47:09 - The Shift in Attitudes Towards Unification Efforts in Physics 48:13 - Introduction to Peter Woit's New Ideas on Unification 52:32 - The Role of Four-Dimensional Geometry and Spinors in Unification 58:11 - Wick Rotation and Differences Between Euclidean and Minkowski Space-Time 1:03:05 - Technical Challenges in Wick Rotation and Quantum Field Theory 1:09:01 - Unique Aspects of Spinors in Euclidean vs. Minkowski Space-Time 1:14:38 - The Dirac Operator and its Role in Space-Time Symmetry 1:18:02 - Relation to Supersymmetry and the Right-Handed Nature of Space-Time 1:22:04 - Connection to Gravity and Loop Quantum Gravity (Ashtakar Variables) 1:23:04 - Outro / Support TOE Support TOE: - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Crypto: https://tinyurl.com/cryptoTOE - PayPal: https://tinyurl.com/paypalTOE - TOE Merch: https://tinyurl.com/TOEmerch Follow TOE: - NEW Get my 'Top 10 TOEs' PDF + Weekly Personal Updates: https://www.curtjaimungal.org - Instagram: https://www.instagram.com/theoriesofeverythingpod - TikTok: https://www.tiktok.com/@theoriesofeverything_ - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Pandora: https://pdora.co/33b9lfP - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything Join this channel to get access to perks: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join #science #physics #stringtheory Learn more about your ad choices. Visit megaphone.fm/adchoices

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Ambition is on the inside. So that goal to beat your personal best? Keep chasing it. Drive your ambition. Mitsubishi Motors. The reason we don't see any extra dimensions is that there aren't any most serious people in the subject. Just stop working on the ideas that these things are failures. It's all about four dimensions. What if our quest for unification in physics has been fundamentally misguided? Since the 1980s, string theory promised a unified framework, but after 40 years, it's failed to deliver.

Now, a growing number of physicists are calling for a radical rethinking of our foundations. Enter Peter White from Columbia University, who earned his masters from Harvard and his PhD in particle physics from Princeton. Known for his incisive writings on not even wrong, his textbook quantum theory groups and representations, and a fresh approach to a theory of everything, White isn't just pointing out flaws in mainstream fundamental physics, he's proposing something disruptively new. In this episode, we'll dive into the standard model, explore the problems with supersymmetry, and uncover why Wojt believes that the solution

to unification lies in understanding imaginary time. At the core of his approach are spinners, which researchers like Roger Penrose and Michael Atiyah call the most mysterious objects in the world. Welcome Professor Peter White. It's an honor to have you back on the podcast again. It's your second round, I believe. Yes, that's right. Thanks.

Thanks. I'm glad to be back. Today, you have a talk prepared for this conference called Rethinking the Foundations of Physics and What is Unification is the theme of this year. So take it away. Okay. So we'll see. I mean, this is fairly sketchy.

I'll have to make some excuses for to really go into a lot of the things. I'd like to go into would take quite a while, but I thought this is what I could do that I think I could try to convey in a relatively reasonable amount of time. So let's just start with that. So what I wanted to do is first go over, you know,

what it is, at least to me, what unification is. What are the things that we're trying to unify? And then explain kind of what the kind of current paradigm for what this kind of unification might look like that we've been kind of living with for the last basically 50 years. And then I want to explain what that is. And then I want to say just a little bit about what I've been trying to do and what's gotten me very excited in the last

few years, which is what to me, I believe, is kind of a quite new idea about how to do unification or about how to do a substantial part of unification in a new way, which doesn't have the same kind of problems as the things that we've been living with for the last 50 years. same kind of problems as the things that we've been living with for the last 50 years. So that's just the outline. Okay, so to start, so I mean, this is, you never know how much to try to tell people about this. It's just kind of there's a standard outline of what's the standard model. But we have this incredibly successful theory called the standard model, and it's basically a fairly simple conceptually object. Once you get used to certain kind of

technical ideas about the mathematics and the physics, and it basically says that there are three forces in the world and they're due to these U1, SU2, and SU3 gauge fields, there's basically the electromagnetic, the weak and the strong force. Then the matter is spin one half fermions and there's some specific pattern of charges which are the couplings to these three different kinds of forces. I won't write out, there's a standard table of these. It's an intriguing pattern we won't write out, there's a standard table of these. It's an intriguing pattern we don't quite understand, but it's a pretty simple pattern. So that's forces, that's matter.

Then the one probably most mysterious part of it is the Higgs field. This Higgs field is this space-time scalar field which breaks the U1 and SU2 down to a U1 subgroup and that gives masses to the weak big, to the SU2 gauge bosons and to the matter. So that's pretty much all there is. And so if somebody just tells you that, knowing the basics of the geometry and how this is supposed to work, you could reconstruct the whole theory. You can reconstruct the whole theory once I tell you the charges and then there's going

to be a lot of undetermined parameters in the thing. Okay, so history. So this basically, we're kind of been over 50 years out from this. Ah, okay. So for here, just a quick clarification. See how it has U1 cross SU2, but then it goes down to just U1, and some people may be wondering, okay, you had electroweak unification,

but you still have electromagnetism plus the weak force. Where did the weak force go? You're saying, correct me if I'm incorrect, that U1 is the only unbroken symmetry left after the Higgs mechanism. Okay, understood. Okay. Okay. So the history of this, so this is pretty much, there's a long history of this, but it kind of came together pretty quickly in a few years. And, you know, in April 1973, you know, you could write down this theory and people started to realize that, you know, what they had, then it took them a while to really gather the experimental evidence to be convinced that

this was really the right thing, but it was there in April of 73. So now, the most amazing and bizarre aspect of this whole situation is that this relatively simple theory, there are basically all experimental results agree exactly with it. There's no such thing as some interesting experimental result, which you can't explain with this theory. And there's some technicalities about,

the first version of this story didn't have masses for the neutrinos, but it turns out you can throw in some right-handed neutrino fields and it all works exactly. As you expect so far, there isn't any data. The only data that people talk about that's, we're not sure what to do about often is

often more astrophysical data, things like dark matter and dark energy, and questions about cosmology, but just questions that you can kind of study in an accelerator or by looking at matter at a short distance scale. I mean, every experiment that we know how to do agrees exactly with this theory.

I see. Okay, so this is the problem of unification in some sense that we're used to historically having experimental results, which, you know, are, which disagree with our best theory and which tell you kind of what you should be doing instead. And we don't really have that. Okay. So now the other part of the story is general relativity.

And so this is a theory which says that space time is this three plus one dimensional pseudo-Romani manifold. It's a standard kind of curved manifold except one of the directions the metric is negative in one direction. Locally, it looks like the Kowski space-time. Then the gravitational force is described by the curvature of this space-time. There's this Einstein-Hilbert action or the Einstein equations which tell you about this. But this is a classical theory.

So we'll say more about this later on, but the standard model is a quantum theory. This is a classical theory. But again, the history of this is basically in place 1915, so we've had it for over a hundred years without changing. And it kind of has the same problem. It has that everything that we can do where we study the gravitational force agrees precisely with general relativity. We just don't have any kind of measurements or anything we see that disagrees with general relativity.

Okay. So what's the problem? Well, both of these theories, they're geometrical. There's a very basic symmetry story behind them. Once you understand the symmetry story, you can understand how to construct a theory largely. But the situation isn't quite satisfactory because there's some questions that these things don't answer. There's no evidence that there's anything wrong about either of these, but there's some kind of unanswered questions. Maybe the basic one about the standard model is why SU1, SU2, and SU3?

What's the explanation for why those three gauge groups and why those three forces? Then part of the story is that for each of these things, you have a free parameter, a coupling concept which describes the strength of the force. So there's three numbers that come out of this. One of them is the strength of the electromagnetic force. But why those numbers? So it would be nice. We'd certainly like to have a better theory which would tell you something about either tell you

why the values of each of those three numbers or tell you the ratios of them or some extra piece of information about where they come from. For people who don't understand this part but they see these symbols, it seems like it's quite ad hoc. Like you have a circle here

and you have a triangle and you have a square. It's like saying the universe is composed of that and then you wonder why is it a circle, triangle and square? Yeah, exactly. I mean, if you look at the, there's a long list of possible symmetry groups. So these groups, I mean, they're a little bit technical. U1 is basically just a circle.

It's just a circle on the complex plane. You can think of it as U2 is, you can think of it as, well, it's two by two unitary matrices with determinant one or you can, or it actually looks like a three-dimensional sphere. Right. SU3 is three by three unitary matrices of determinant one, but why those three groups? I mean, they're among, if you look at the possible symmetry groups,

Lie groups of this kind, these are three of the simplest possibilities. But why those three? Why not something else? Why not? Before we move on, the quick retort would be, well, no matter what it was, whether it was E8 or G2, we would still say, well,

why E8? Why G2? No? Well, sure. I'll get to this in a minute about, but what, you know, yeah, so one kind of unification is to say, and maybe say something about this is that, so we'll see that, anyway, maybe let me give me a minute to get to that next, to grant unification, and we'll say a bit about that. Wonderful.

But this kind of is the problem, I mean, so one, anyway, this is the general version of the problem. And then the, with the matter problem. I mean, so one, anyway, this is the general version of the problem. And then with the matter particles, so one question is why are these things spin one half? Why are they fermions? Why do they spin one half? And then why do they have this specific pattern of charges?

Are these short list of numbers which tell you how, they're integers which tell you how they couple to the U1, SU2, and SU3, and why that pattern of charges. And then they come in three generations, they're kind of three, it's a pattern,

you see the same pattern copied three times. Why all of this? So it's a small of small and manageable amount of kind of discrete structure, but you know, where does it come from? It's not, it looks like there should be some explanation for it. The other thing is about the Higgs field.

So the Higgs field is this scalar field and you've chosen its potential energy so that it has a minimum away from zero so it breaks the symmetry. Where did this kind of potential energy function for the Higgs field come from and why the Higgs field? The Higgs field is a complex doublet that transforms under SU2 and what's that about and then why this potential energy function.

And then the matter fields are all getting their masses from the strength of their coupling to the Higgs field. These are called Yukawa couplings. Why does each different matter field seem to couple to the Higgs field without some different parameter and where do all those parameters come from or what's going on with that? So those are some of the questions that you have just looking at this theory that, you know,

why it looks like there should be a better theory which explains these things. And then maybe a couple of other things to say about why we're not quite happy yet. So one question that's something that's actually not mentioned very often is that there's a technical problem. We still, it's still has never really been sorted out, is that when you write down this quantum field theory

of the standard model, you mostly do computations and perturbation theory using Feynman diagrams. And that's kind of an approximate calculation method. We know how to make that. That works fine. But we also know that that only works in the limit of extremely small coupling. That for larger couplings, you need

a definition of the theory, which works for any coupling. And for SU3 and U1, well, for the SU3, we think we know how to do that. It's done using lattice gauge theory. You can write down this lattice discretization of the theory and you can very explicitly say here's how you would put it on a computer and you do this computation, take a limit, that defines the theory. And if you start trying to put the matter particles in with that, that leads to some confusing and complicated things, but there are ways to make it work.

But there still is no known way to really completely make this work for, well, for what are called chiral gauge theories in general, but specifically for this SU-2. The SU-2 couples differently to, we'll talk later about left-handed and right-handed spinners, but the SU, unlike the U-1 and the SU-3, the SU-2 couples differently to left-handed,

right-handed spinners. And how do, if you try and do that, if you try and discretize that and put it on a lattice, or if you try to find some other way of defining that non-perturbatively, it's still not known exactly how to do that. There's some pretty complicated proposals for what something it might work,

but that's an open problem that's never really been resolved. Okay. And it's not often mentioned. Okay, and the problem that does, has been resolved. Hmm, okay. And it's not often mentioned, okay. And the problem that has gotten all the attention is that the general relativity looks fine as a classical theory, but if you try to quantize it in the using kind of standard methods,

you find this renormalizability problem, you find kind of infinities which you can't be handled in a standard way. Any way you try to handle them just is going to introduce an infinite number of new constants into the theory or something. Nobody really has a – well, there's maybe two ways to say this. Nobody has a really completely consistent non-perturbative definition of quantum gravity either by itself or coupled to the standard model in the sense of something that really you can show this is always going to give consistent answers and that you can calculate

anything you want. That's one way of saying it, but another way of saying it is that there are plenty of people who claim that, okay, they have an idea. Here's the idea. Here's a way to solve quantum gravity, whether it's string theory or loop quantum gravity or a hundred other proposals. Many people claim to have at least a plausibility argument that they've got a way to handle the problems of general relativity.

So depending on how seriously you take these claims of people, you could say either there's no such thing or there's actually a huge number of them. So we have in some sense, if you believe everything that a lot of the string theorists would like to be true, they would like to say that string theory gives you such a thing, but it may give you an exponentially larger numbers of such a thing depending upon these questions about string vacua, et cetera. There's maybe two ways to say the problem. One is that this problem, there is no solution at all. The other is to say that the world is full of claimed solutions, but none of them really seem to actually explain very much

or have any way to test them or are satisfactory. Okay, so now I wanna kind of start on what has been happening since April, 1973. When it became clear that what these problems were was more or less immediately obvious. So the first thing that happened is a few months later, Howard Georgia and Shelley Glashow came up with what's called, the first example was called the Grand Unified Theory. And so they were kind of addressing, I think, the kind of thing you were starting to ask about, which is, you know, what happened? So they were trying to address this problem,

what about these three groups with three constants? Maybe we can at least improve the situation by fitting them together as subgroups of one larger group, and either like something that was typically SU5 or SO10 they were talking about. So you only had this one group and one thing that's very good about this is instead of having three coupling constants, you've got one coupling constant. So this kind of, if you do this, you end up with relations between three coupling constants. And so then anyway, so you have to do that. You have to do that. The other thing you have to do is.

Oh, just a moment. Sorry. Can you explain that you get a relation between the three coupling constants from the one larger Lie group? Well, there's only one. Yeah. I mean, anyway, if you write down the theory for one, or write down the theory for the bigger Lie group, it's just got one couplet constant in it.

Then what you have to do is you have to explain, why do we see three couplet constants? But maybe I was going to come a little bit more to this later. This is the problem. The problem is that if there just was an SU5 theory, there just would be one number that determined everything. The problem is that we're saying three things and three numbers. If there just wasn't SU5 theory, there just would be one number that determined everything. The problem is that we're seeing three things

and three numbers. So you have to first explain why are we seeing three things, not just that one thing. And then once you have a model for why we're seeing the three things, that model has to explain, you know, how you go from getting that one number to getting three numbers.

I see. Does it give you a relation between those three numbers? Yeah. Like some bound or some inequality? No, I mean, it, it, so, so, so very precisely the way that this works is you, um, you set this up with a new kind of Higgs mechanism, and the new kind of Higgs mechanism is such that if you go above a certain energy scale, the so-called gut energy scale, which is like 10 to the 15th GeV, then you're going to see the full SU5 theory. It just looks like the SU5 theory, you're above.

Anyway, there's some kind of new symmetry breaking scale you had to introduce. Above that symmetry breaking scale, you do just have one theory. You just have one theory, you have one coupling constant. Everything about the theory above 10 to the 15th GeV is written down in terms of these SU5 gauge bosons and one coupling constant. But then you have to introduce the symmetry breaking at this so-called gut scale. Then once you introduce the symmetry breaking at this so-called gut scale. And then once you introduce the symmetry breaking by a new set of Higgs or something, then you have to kind of evolve down to lower energies

and say, what are we going to see at our energy scale? And you find that the U1 and the SU2 and the SU3 couplings evolve differently as you change energy. So you often see this graph of these three coupling constants. things evolve differently as you change energy. So you often see this graph of these three coupling constants, and then they kind of come together at a point, which is the point where they unify it at this higher, where they unify it. Okay, but then the next thing you have to do is you have to say something about matter.

So a technical way of saying it, when I said you had a certain list of charges, that was another way of saying that technically is that you've written down a list of the irreducible representations of U1, SU2, SU3 that all your matter fields are fitting into and how they transform into those symmetries. And so you have to kind of do this, you have to explain how all those things, those numbers you get from the subgroups fit

together into one thing, how all those matter things fit together into a representation of the bigger group. So in some sense you have a generalized notion of charge for SU5, and you have to pick the SU5 charge of your basic particles and then look at, and make sure that it gives you, when you look at the U1, SU2, and SU3 subgroups, that it gives you the correct list of charges that we know about. Anyway, so that's just a technical thing you have to do.

But you can do both of these very nice, and it actually works out quite nicely for SO10. You can, all the known particles fit together into one nice representation of SO10, the spinner representation. But then here's the problem is that you also have to introduce new Higgs. So you have to explain why we don't see this big group of symmetries, why we see the smaller group of symmetries. So you have to, just as I always said that was said that, you know, we know that SU2 cross U1

breaks down at that the energy that the vacuum is only invariant under U1. You have to, we know that the vacuum is, it can't be invariant under SU5 or SO10. So you have to introduce some more dynamics that's going to break it down to this. And later you're going to break it down again to the U1. Great summary. Okay, so now there's initial, I know that George Anglashaw got very excited about this, a lot of people, because this not only gave you

a little bit of a pretty pattern of an explanation of some patterns and some of these numbers, but it also gave you some new predictions of some new physics. Specifically, because you're putting this SU2 with the weak force and the SU3, the strong force together, quarks can decay into leptons. Protons in particular are not going to be stable, that the quarks inside a proton or inside a neutron, let's say quarks inside a proton, are going to sooner or later at some point decay into another quark and a couple leptons.

And you had a nice calculation of exactly how fast that should happen. The initial numbers that they got were that, this should happen but very, very slowly. It was perfectly consistent with the fact that we don't observe protons decay. People then started going out and doing experiments, looking for this, looking for proton decay at the rates that these things predicted.

Then the problem was, and the basic problem since then has been that, well, it turns out protons don't decay. People have kept building bigger and bigger detectors and looking more and more carefully for this, but there's just no, this just doesn't happen. Protons don't decay. And any of the kind of characteristic new physics you would expect from this, from having this larger group of symmetries, you just can't see any of it. You don't see any of it. So it's not that we found proton decay is just smaller than the rate expected,

it's that we haven't found any evidence for proton decay. expected is that we haven't found any evidence for proton decay. Yeah. And so, I mean, so these initial SU5SO10 theories actually had kind of a very rough estimate of what proton. I mean, the problem is the exact rate depends like on how you do the Higgs breaking and various other things. But the, yeah, so the initial kind of predicted rate, you by now the back, I don't know, I forget the numbers, but by now it's 10,000 or a hundred thousand times.

Anyway, the bound is way above that. So this is definitely wrong. And I know that, so one thing that's true and interesting about George Ryan Glashow is that they actually did give up. I mean, part of the problem with this subject is people don't give up on these ideas they actually did give up. I mean, part of the problem with this subject is people don't give up on these ideas. They did give up and they stopped working on this.

And if you go and talk to them these days, they'll say, yeah, well, this was a pretty idea. We were very excited, but it really didn't work. And we've given up on it. Interesting. Yeah, and I believe Georgi or Glashow is working on the un-particle now, correct? I know that Georgi, Georgi.

Georgi is the one with the un-particles. But anyway, they've done a lot of different things, but I forget exactly when, on a time scale of 10 or 15 years after this, when the experimental results came in, they said, okay, well, we were wrong. This is just a bad idea, it doesn't work. That's one part of this.

But maybe the thing to say to me, the more disturbing situation is you can go and open a lot of kind of basic textbooks that we teach graduate students with and they'll tell them the story. They'll tell them, oh, you know, there's this great wonderful idea about unification and here it is.

And they don't really mention very clearly that it doesn't work. Okay, then supersymmetry was another part of our standard paradigm that we've been living with. And it also in the earliest, this standard model is written down in April, by December people were writing down these supersymmetric extensions of the standard model. So let me explain what those are. This can get quite technical, but one way of saying the basic idea

is to – if you understand there's this crucial relation between spinners and vectors that – spinners in some sense are a square root of vectors. They're mathematical objects that if you take the product, the tensor product of these – of two of them, you They're mathematical objects that if you take the product, the tensor product of two of them, you get a vector. And if you think of vectors as being corresponding to translations, we know that the world has this, world is locally looks like a certain vector space

of four dimensions and you can translate in any four directions and you get corresponding momentum or energy operators. There's also rotations. But what supersymmetry says is, well, you should extend your standard story about momentum and angular momentum and how it fits together into this Poincare-Aigh algebra and you get these generators, you should add some new generators which correspond to the spinner direction, which correspond to the spinners. And they're going to be anti-commuting unlike the usual, the ones you know about, but they're anti-commutator.

The fact that the tensor product of these spinors as a vector will correspond to the fact that the anti-commutator of two of these operators will be a translation operator. So that's the basic idea of super-centering. It is a beautiful idea. And so what you do then is you, what people did starting in 74 was you take the standard model and you just kind of add, you add some fields to it and things

which then allow you to define this extended symmetry and define these new spinner generators, these cues, these supersymmetry generators. And you can do that with the standard model. You could also play the same game with one of these grand unified theories. You could take your favorite grand unified theory and turn it into a supersymmetric grand unified

theory. OK, and again, so there's a lot of enthusiasm about this. I mean, a lot of it was also driven by just the beauty of the idea. This is a really beautiful idea. If you try and do this, you find that these Qs commute with all of the Z1, because Z1, SU2, SU3 commutes with these Qs.

So you find what a Q is going to do is it's going to take any particle that you know about with certain charges, and it's going to turn it into a super partner. It's gonna produce a different kind of particle, which has exactly all of the same standard model charges, but it has spin differing by a half because it has a spinner nature.

So it has this prediction that, okay, well, and maybe I shouldn't say that completely this wasn't completely enthusiasm. What you would have really liked to have happened was to look at the list of particles that you know about the standard model and find two of them that are related by one of these supersymmetry generators. If you had two particles that differed by spin half and that had the same standard model charges, that would be a good candidate.

You would identify them as super partners. Yeah, you'd have two super partners. And anyway, in some sense, I think the problem is you don't see this. So you've had this beautiful new symmetry, but the problem is it doesn't relate any two known things. It relates everything you know to something you've never seen before. I see.

So, I mean, technically, it's this symmetry acts trivially on everything you know about. And so, okay, but you can then say, okay, well, this gives us a prediction of, you know, we've only seen half the particles in the world, that there's every particle we know about is going to have a super partner. That's what you say. Some people, I guess, would take this enthusiastically, oh great, there's all these new particles in the world. I think I and many people were also a little bit, wait a minute, this is a little bit implausible that this doesn't.

Anyway, there's this new symmetry, but we haven't seen any of its effects its effects but anyways so then this is the supersymmetry there's a long story but it goes into the LHC is now given you has a very very strong limits on this there are no there are no super there are there really are no super partners and there's just zero evidence for any of this okay so then you can do another part of the unification paradigm is supergravity and Kaluza-Klein.

And again, these are things that were developed a little bit later, but within a few years after the standard model. And supergravity is basically, you turn supersymmetry into a gauge theory and it gives you an extension of general relativity. The Gravitino is a partner to the Graviton and you have a theory which you could hope when you quantize it would have, it seems to have fewer renormalizability problems. That's a whole

long story. But anyway, we had the super gravity theories. Then you also going way back to early days of general relativity, people had been looking at what happens if you have more than four space-time dimensions. Can you explain, one thing you might try to do is explain where does U1, SC2, SC3 come from by postulating more than four space-time dimensions and it's these other so-called kind of internal dimensions which explain

everything. And that had been an idea that was wrong for a long time, but it became kind of a big part of this paradigm that people were looking at. I have a quick question. So supersymmetry can be formulated at the classical level, correct? Yeah. Okay, so if you're putting supersymmetry on GR, then do you have a gravitino?

Like you don't have a graviton at the classical level? Well, you don't have, yeah. So this would be, you have a gravitino in the quantum version. But yeah, but you've got... Like does the classical version of supersymmetric general relativity have any properties that are wanted or that are studied? Or do people

only care about it because it allows something interesting when you quantize it? Well, the problem is that you've it's a problem with all supersymmetric theories when you there is a there is a classical version of them. but the problem is that you've extended your standard kind of variables with these, to get frame arounds, you've extended your standard variables with these anti-commuting variables. So it's kind of a weird, so classically it's kind of a weird subject. So you have non-commuting classical variables. Yeah, it's noncommuting classical variables. So you can write down such a theory. You can look at it, but it doesn't correspond to any.

All of our intuitions about what's going on in classical physics, it doesn't really correspond to any of... You've got all these new degrees of freedom, which are different weird algebraic things which aren't what you're used to thinking about. I see. So. Now, someone like Elaine Konis, would he be comfortable with classical non-commutativity?

Or does he only study quantum non-commutativity? Well, I mean, he's more interested, I mean, it's non-commutativity, but of a very specific sort. It's just, it's It's just what is sometimes called Z2-graded commutativity or super commutativity. It's like things don't commute, but the extent to which they don't commute is just something very minor.

Certain things pick up minus signs when you interchange them. So I think someone like Alan Conner, people are talking about non-commutative geometry, that they're often generally, it generally means something much more seriously non-commutative, where there's, it's not just, yeah, anyway, this is often, some mathematicians often call this super-commutative and it's, and actually, you know, the people who do kind of standard, standard commutative geometry, they're used to having these little algebraic gadgets in it, which square root of zero and which anti-commute,

that's also part of their story. So some mathematicians would claim it's really just part of commutative geometry. It's not the non-commutative geometry that Al-Ankhan wants. So now this is actually getting into the period when I actually remember. So I was a undergraduate starting in 75, and I was taking quantum field theory courses starting in 76, 77,

and starting to try to pay attention to what was going on. And so I remember a lot of, that this was kind of what people were talking about as the answer to these unification problems at that time when I first got into this. And like one example is Hawking gave his kind of initial lecture for his professorship called, you know, is the end in sight for theoretical physics? And he basically was saying, well, you know, this, we've got this super gravity in this Kaluza-Klein version and it looks like, you know, that, that may get, looks like it should give us a quantum theory which everything fits into and which is going to explain everything.

But anyway, there's the basic problem that none of this kind of worked out in the sense that we've never seen any extra mentions, we've never seen anything besides four dimensions. So there's really never been anything giving an indication that the Kaluza-Klein idea goes somewhere. Well, there's no Gravitinos and maybe that's a little bit unfair because it's hard enough to see gravitons. You're probably not going to see Gravitinos either, but there's really kind of nothing. These ideas kind of never led to anything which you could go out and go out and check

it anyway, or if you went out and right check it, it wasn't there. Okay. Or if you went out and write, check it wasn't there. Okay, so then that was kind of the situation in the early 80s. And then people had been also studying these string theories. And that's a long history we don't want to really talk about here. But maybe one interesting thing is that the first super string theory, the idea that it could describe gravity, that you could describe gravity using a super string theory that would, the idea that it could describe gravity, that you could describe gravity using the super string was, first paper about that was like a month after

the standard model was in place. Anyway, but that kind of exploded in 1984 when Witten got into the subject and there was a very serious interest in doing unification this way. And the basic idea there, anyway, there are a lot of things to say about it, but one idea is instead of thinking about a point, particles at a point, and fields based on those point particles, you think about your basic objects

of your theory are one-dimensional extended objects. And then the idea of the super string theories then was to bring together all these things. So they had an E8 gut, they had super gravity as a low energy limit, they had extra dimensions, a Kaluza-Klein going on, so they had everything. So this was kind of, I think one reason this appealed to everybody is there were all these ideas which hadn't really worked out, but now we can, we spent all this time studying them.

Now we can put them all together into this big new idea, which is gonna explain everything. Anyway, and so people thought, okay, we got a theory of everything. I mean, Witten, who is an amazing genius and done amazing things, was very excited and telling everybody that this is the way the future is going to go. So that was 1984.

Again, now, 40 years later, there's no evidence for any of the components of this, or including for the strings. It just really hasn't. To stick to just experimental statements, there's absolutely zero, nothing anyone has seen of any kind which indicates any connection to this stuff. Maybe I just want to reason for going through all this is partly,

I think, physicists working in this area just don't make clear the extent to which this just has not worked out. But I think if you look at all of this stuff, you see the same kind of generic problems. They're taking something which is incredibly successful, works perfectly, and they're embedding it in a larger structure of some kind, whether it's a larger gauge group, or it's anyway more and more dimensions, whatever. But the problem is that they're doing this for various reasons because it's some larger thing which they can compute, maybe there'll be some new symmetries and some new things you can do.

But there's no evidence at all for any of the components of this new structure. Then the problem is that once you've got this larger structure, you say, okay, it's got all these great properties, it's got these great symmetries, it's got supersymmetry, it's got larger gauge group, it's got all the stuff. But the problem is you then have to then explain, wait, why don't we see any of that stuff?

You have this theory with all this new stuff in it, but we don't see any yet. So then you have to make the stuff go away. You have to break all these symmetries. You have to, anyway, you have to make all your dimensions so small you can't see them. You have to make all your super partners so massive you can't see them. You just kind of have to, yeah.

And so all this business about the elegant universe and all these elegant wonderful new ideas rapidly turns into something, really truly ugly because it was all very elegant wonderful new ideas, rapidly turns into something really truly ugly because it was all very elegant until you realize it didn't actually look like the real world and you then have to start turning the cranks and adding in various layers of ugliness to explain why you haven't seen any of this stuff.

And I think this is a very conventional way in which a theory fails. You know, you have some great new idea and you think it's wonderful, but then when people go out and don't see the things that this new idea predicts, you then have to, you know, one thing you can do is you can be like George I. and Gladshow

and say, okay, we were wrong, I give up, I go home, I'll do something else. But it's also very tempting to say, okay, well, there's a little bit more complicated version idea. I can add this structure into this theory or do something in this theory that's gonna explain why you don't see that. Right. And then you end up, but as people do more experiments,

you just keep on having to make the theory uglier and uglier purely just to avoid making a wrong prediction. At what point does it become more ugly than the beast you were trying to replace? Well, I would argue pretty quickly. And I think the truly amazing thing about our history so far is that we've gone through 50 years of people being willing to make things just spectacularly ugly and unpredictable and not behaving like George Anglashow and just not saying, okay, this just doesn't work.

No, let's just face the obvious. I mean, the obvious conclusion is that this was just the wrong idea. And how hard it is to get people to even admit that this is a sensible interpretation of what's happened in the last 50 years, is why I'm going through all this. Okay, and anyway, so this was just more of what I wanted to say on this. And I think what's actually happened is, you know, most, you know, lots of people were

kind of keep trying to push through these old ideas that don't work. But you know, I think many people and the most serious people in the subject just stopped working on these. They don't go out and say, okay, these things are failures, but they just stop working on them. If you ask them about it, they say, well, I just don't see how to push this any farther.

I still think it's a beautiful idea. And I don't want to put words into Witt in his mouth, but I think if you would ask him about some of this, I think he would say, well, I still think it's a great idea. I still think it's the best possible idea we have about how to get answers for unification. But unless some experiment comes along and tells us some new hint as

to how to make these things work, it looks kind of hopeless. And so I've kind of stopped thinking about it every day. And so I think the kind of new ideology is kind of turning into, well, let's not admit that this thing failed, but let's just kind of say that it's now thinking about unification is now no longer something a serious person should do because it's just hopeless until somebody has a really brilliant new idea or until we see some new, until the experimentalists help us out, we're just not going to be able to move forward with this. help us out, we're just not going to be able to move forward with this. This is something I see a lot talking to theorists and seeing where they say that they really,

the idea of thinking about unification is becoming something that they, is kind of a crank activity in a sense that this is something that only a crank would do now. Only you have to be some kind of amateur or crankers or not really know what you're doing to realize that look, the smartest people worked for 50 years on this and this was the best possible way of doing this that they found and they haven't been able to push it and make it work. So it's just, what are you going to do? Well, you mean to say unification attempts outside of string theory or to not even consider

string theory a unification attempts outside of string theory or to not even consider string theory a unification? Well, I mean, string theory then becomes a complicated. The question is what would you mean by string theory? But I guess one way to say, maybe a better way than specifically going on about string theory is to think of string theory, guts, supersymmetry. I really want extra dimensions. This really is kind of a,

that has been the paradigm that we've had for 50 years. And so the question, and I think the problem with anybody who's trying to say, okay, well that, what you guys have been doing for 50 years is just completely doesn't work. You have to do something completely different. I'm gonna tell you about it. I mean, that's a hard sell, I think,

because people have said, well, wait a minute. We're 50 years, for 50 years, this is geniuses have been working on this and these are all great ideas and this is wonderful. How can you tell us that this is all just wrong? You must, why, that's the kind of, it's like these crackpots who tell us that, Einstein must be wrong.

So it's always been a hard sell to say, look, everything you've been doing for all this time, I mean, you should forget about it. I want to tell you about something quite different. That's always been a hard sell, but it's still a hard sell. I think it would become less of a hard sell if people would actually admit that,

wait a minute, this was all just wrong. You really have to look at very different things. But I don't think that you're really seeing that kind of case made that, yeah, we have to look at, like, we have to go all the way back to 1973 and look at different things, not the things that we started looking at back then. So on the one hand, you put, and look at different things, not the things that we started looking at back then.

So on the one hand, you put something into the oven and it needs some cooking. There's the fear that if you take it out too soon and you prematurely dismiss it, like perhaps SU5 was a great idea, you don't dismiss it after the first year, you investigate it some more. But then there is the opposite phenomenon of overcooking. And you have to admit when something has become burnt, maybe it's been burnt after 50 years in the oven. Yeah.

Yeah, so that's always a question. At what point do you give up an idea? And in some sense, my argument with the string theory is always was from the beginning that my judgment of what's going on is you really have to give up. This is something which hasn't worked out. Their argument was, well, we still think it's the best thing we know how to do. We still think it's worth pushing forward.

So it's kind of hard to argue about that. But I think things have changed over the last 20 years. It's just as it's become clearer and clearer that this stuff just doesn't work. And this argument that we have, and it's gone from like, oh, we want to keep working on it. No, maybe within five or 10 years,

we'll have something new and we'll have made progress. And now you ask people talk about, well, you know, it may take 500 years for us to make any progress on this. Right. This is taking longer than I thought. Okay, okay, so anyway. No, no, take your time, take your time. Firstly, just for people who have gotten this far

into this talk, this is the quickest recapitulation of the standard model and the state of affairs of physics that probably exists online. It's been 40 minutes or so, and we've gone, and you've gone through the state of physics since 1915 to the 1970s and then to the present day. Well, but I haven't really explained a lot about it, but, and the bottom line is I think more depressing that you shouldn't actually study any of it.

Anyway, the post 73 stuff, you shouldn't just study it, you should try to find something else to do. Okay, so now there's a much shorter and much sketchier part, which is to end about what I've been trying to do. So let me start about this. So maybe the thing to say about this is, actually when I was a graduate student, let me go back, I worked on doing

these lattice calculations of using SU3 gauge theory, and the calculations just used the gauge fields, you didn't use the matter particles. And so there's a really beautiful way of putting gauge theory, of discretizing and putting out a lattice. And so I really worked a lot on that, and I thought that was great. And so then I thought, well, wait a minute, what about the matter particles? What happens when I put them on the lattice? And I started to realize that, wait a minute,

matter particles are these spin one half, the spin geometry is really weird. It's a very, it's not at all obvious how to capture that geometry and how to preserve any of that geometry when you discretize things. And there's a long story about people trying to put spinner fields on the lattice, and you end up with all sorts of interesting problems. And that's where I first started thinking about some of these things now.

And I had some kind of vague, very, very vague version of the idea I'll be talking about, one little piece of it, and thought about that for quite a while. But at some point I gave up on it. I decided that this wasn't giving up because there's no experimental evidence, but I just gave up on it thinking, okay, everything that I know about the subject says that this just is not going to work. This is implausible. You can't make that happen. It's just that. Everything you know about the subject forbids you putting fermions on the lattice?

No, no, we'll see. I'm gonna make a certain claim about that symmetries do something very odd you didn't expect. And I'm just saying that I had that very vague idea that maybe that should be possible, but at some point I convinced myself that, yeah, the way space-time symmetries work is clear enough that you just kind of can't have,

what I now believe happens, I had convinced myself could not possibly happen. And so- Interesting. Anyway, just some history of my own personal history. And it's within the last three or four years that I finally, thinking about this some more, and also a lot that I've learned actually by teaching courses on quantum mechanics and QFT and kind of writing a book about that and starting to understand, you know, very

precisely exactly how the symmetries work. I started to realize, I'd always assume that, you know, if you, there was some simple explanation for why for something that you would see once you wrote down the details of how these symmetries worked. And then what I just found as I started writing down the details and learning more about it is that just wasn't there. It really wasn't there.

And then I finally started thinking about it in different ways. I started to see that, wait a minute, this actually looks, there's a perfectly coherent way of thinking about what I thought couldn't possibly happen. There's now perfectly good reasons to believe that it could happen. Sorry, and that occurred to you while you were writing the book on quantum theory and representations? Yeah, more later after that was done.

Yeah. Which book are you referring to that you were writing and it elucidated ideas to you? Well, no, it was more, it was kind of after writing that book, but I've also taught that course several times. So it's, I've, when I say writing, I keep thinking, okay, I should improve that book and produce some more things, but it's never really got written down, but. I see.

I should say that. And I've also, yeah, anyway, so maybe that's a better way of saying it. But that was the first, writing that book first got me, and actually it was one motivation in the back of my own motivation for writing that book was to kind of get the story of these space-time symmetries written down very clearly, and so that I could,

some things which I never understood exactly how they happened exactly, to get it all written down. And as I exactly to get it all written down. And as I started to get it all written down, I realized, wait a minute, I'm not kind of seeing the thing which I was convinced would have to be there that would explain why that would make clear why this couldn't work. All right. So let's get to the approach that seems promising promising as this is the hugest tease that we just Yeah, sorry. I just kept asking you questions. That's my fault. Oh, that's my audience hanging

Yeah, but yeah, I'm sorry You're not gonna get a detailed and answered this anyway because but what you'll see but but first of all Maybe it just to say what why what I'm to put this the context of what I was talking about already is to say that This is very have about four dimensions. So no extra dimensions four dimensions Maybe just to say why would I'm, to put this in the context of what I was talking about already is to say that this is Ray, how about four dimensions? So no extra dimensions, four dimensions. And it, what I'm, the idea is that there are no, there aren't, the reason we don't see any extra mentions

is that there aren't any, it's all about four dimensions. And you should look very carefully at four dimensions and ask what is very, very special about four dimensional geometry? What are, there's a lot of very interesting things that happen only in four dimensions and ask, what is very, very special about four dimensional geometry? There's a lot of very interesting things that happen only in four dimensions. Can we use those? Especially the geometry of spinners and twisters.

I won't really get into twisters, but twisters are a very beautiful idea to understand conformal geometry in four dimensions. They're very, very tied to four dimensional geometry. They really are. So it's an idea of Roger Penrose's. And there's part of the whole story of the spinners. But the other thing which I'm trying to use, which hasn't really been used very much, I think one thing to say about all of this, all the story that I told you, if you go and

look at any of those books about any of those, these guts or supersymmetry or super gravity or string theory, you'll find one strange thing if you start to dig into the technicalities that our space time has this so-called Minkowski metric that you put a minus sign on the distance squared in time. And if you try and write down these theories in any legitimate way, you find that there are technical problems if you try to do it in this indefinite Minkowski signature. So what you do is

you assume that you look at this case as if all four dimensions were the same, as if there was no distinguished time. And then you write the theory there and you do something called Wick rotation to recover what happens in Bukowski's space time. I think, you know, if you look at all of the literature on all of the theories I've been talking about, there's really, in every case, it always is like kind of a technical problem,

but wait a minute, you know, don't we need to do this in Euclidean signature? Are we doing it? How is it gonna go from one to the other? And it's kind of a technical problem, which was there for all of these theories, but nope, but people just kind of tried to avoid thinking about it.

There was always a feeling, okay, this is some technicality, maybe some mathematician will figure it out, we don't care, we're just gonna write down formulas and hope for the best. But this is something that really struck me that you really, this relationship between Euclidean and Cauchy's teacher was a really interesting topic. It was indicative of something? Well, it was something we really didn't understand.

I mean, in my mind, I mean, we had the standard theory, there are parts of it that I look at it and say, I understand that perfectly. It's beautiful. It's all comes from a simple symmetry argument. There's no technicalities are easy. That's done, cooked, that's it. There are other parts of the subject which,

where you look at something and say, wait a minute, you know, something I don't, there isn't a clear explanation for exactly what's going on here. And that, that's, this that's, this WIC rotation was a place that was, that happens in the standard model. So anyway, so the main new idea is to say, what I'm trying to do is to claim that this WIC rotation, you know, if you think about your geometry

in terms of spinners, it changes the geometry, the spinners in terms of spinors, it changes the geometry of the spinors in a very fundamental way. That the geometry of spinors in Euclidean signature and the geometry of spinors in Caskey's spinature is actually quite different. And the basic idea, this is the idea that I had going way back which I didn't think could work,

but which I'm now convinced does, is that you, in the four-dimensional rotation group, I'll say more about it, but it breaks up into two, that's your two factors. And the idea is that when you wick rotate to Mieczewski spacetime, one of those two factors is going to be a spacetime symmetry. The other one is going to be an internal symmetry. Ah, right, right. Interesting.

And this provides kind of a new unification of internal and space time symmetry. So these things get unified on the Euclidean side. And it just involves the degrees of freedom that we know about. There's no extra, nothing extra. But the new thing is to say, wait a minute, is to say, look, you really should think about what's going on in the E Euclidean signature and you should realize that there's a very important subtlety when you try to make spinners go back and forth between these and cascade

Euclidean. So, let me see if I can do a quick summary. There's the Pythagorean theorem, it's a squared plus b squared equals c squared and that's for two dimensions. And then if you want to do something in three dimensions, it's like a squared plus b squared plus c squared equals the, the hypotenuse or whatever you're trying to measure. You have to take a square root. But the point is that you have something plus something else,

plus something else. Now in Einstein's theory, you have something plus something plus something minus something else. And that minus causes some issues. For instance, with the Feynman path integral, it creates an oscillation. So sometimes you have to, you want to do something called wick rotating, which means that you take that minus sign, which is technically an imaginary for technical reasons into something that's a positive, into something that's a real number.

So then you have something plus something plus something plus something, and that's a much nicer space to be in. Additionally, you have this low dimensional coincidence with spin 4 being akin to spin, sorry, being akin to SU2 cross SU2 more than akin, they're equivalent or isomorphic to it. So I thought you're going to use SU4. Okay, actually, maybe let me, yeah, let me go on that. So it's more so formatted,

but I was gonna say a bit more. Let me specifically answer some of that. Cause I, yeah, I'll try to explain. This was just kind of an overall. And let me see how much I can do with that. Okay, so let me just first, yeah. So this is, so wick rotation. So another way of getting this minus sign on the square

is to change from, you know, put in a factor of the square root of minus one. So what this is, so what quotation is supposed to be doing is you've got a theory, a time variable, and it's saying, okay, you can make the time variable complex and then look at a theory where your time has become purely imaginary. And then that minus sign there, which is going to, when you multiply this by itself, the two factors of i are going to cancel that minus sign and everything is going to be plus. So the idea is that there's also, so sometimes I refer to this as going from Minkowski, which is real time, to Euclidean, which is imaginary time. So I'll go back and forth between saying Minkowski and Euclidean are real time and imaginary

time. But you can do this even for the simplest quantum mechanical models. You can start thinking about what happens if I make time imaginary. And that's simplest version of liquid rotation. Here's the problem when you try and do this in quantum field theory. So how are you going to do this? So this starts to get a bit technical, but a quantum field theory, you've got these field operators, and they depend on time. Now if you say, I'm going to make them depend on a complex time, so then what happens is that the, anyway, these fields in this Heisenberg picture, if you change time on them, you're

conjugating by the Hamiltonian operator. That's the Heisenberg picture. So what this is saying is that if you try to go to imaginary time, if you make imaginary time non-zero, you're going to conjugate by this operator, the exponential of the imaginary time times the Hamiltonian. But now, here's your problem. The Hamiltonian, its eigenvalues are the energy.

So it's an operator that has a spectrum, which is all at positive energy, which goes off to infinity in the cases we're interested in. So, you know, a typical theory of even a simple particle, it's got, it can have, it has to have positive energy, but it can have an arbitrarily high positive energy. So now your problem is that, you know, you've got these two operators,

e to the tau times h and e to the minus tau times h. If tau is positive, this one is going to make sense because it's e to the minus something positive times something positive, whereas this one's going to be a problem. This one is just going to become exponentially large. Whereas if tau is negative, then it's going to be the opposite. one is just going to become exponentially large. Whereas if tau is negative, then it's going to be the opposite. So there's just a fundamental issue in it, which everything we know about quantum field theories and the operator formalism, you can't analytically continue the theory. You can't make time complex and have it behave the way you want because you're going to, anyway, you're going to immediately have the rules for how, for

what's going to happen to the field. Just don't know, don't make any sense. You can't do it. And so that's what happens in the operator formalism. But the other formalism you have for writing down quantum field theories has the opposite behavior. If you write the data as path integrals, if you go to imaginary time, it's Euclidean space time, then the path integrals are e to the minus

something positive and large, and they make perfect sense. So you're integrating some kind of Gaussian thing or something that falls off at infinity very nicely. But if you try and do this in Minkowski space time or real time, then what you find is that you're trying to integrate over some infinite dimensional space e to the i times something. So you're integrating this wildly varying phase over an infinite dimensional space. It actually just doesn't make sense in any sense as a measure or as a real integral. Okay. So these two kind of formalisms we like to use to do path,

to do quantum field theory, they have opposite. People will talk about them as if you can use them to go between imaginary and real-time, but you can't. I mean, one of them works well in real-time and is kind of a formal object. In imaginary time, the other one is the opposite. I'm confused. Are you saying that wick rotation is defined in the Feynman case, but not the operator formalism? Because if those formalisms are physically equivalent and you can translate between them, why would it work in one but not the other?

Well, I mean, I'm saying you can't work rotate either one. I'm saying these two are two main formalisms for how we know how to write down a quantum field theory have, you know, one works in one case and doesn't really work in the other case and the other was the opposite. So if you tell me I wanna understand how to go back and forth, you know,

we don't have a theory that does that. I see. Okay. Yeah. So, there is no such... This took me a long while to realize that there is no such thing as any kind of full theory and formalism, which depends upon complex time analytically and allows you to analytically continue between time and imaginary time. There just is no such thing. Now is that problem in both directions? That is if you start with the Euclidean and then you try to get Minkowski versus

the opposite? Yeah, because only one of these works depending where you start. You've only got one that really works and but if you try to you start with either one and get to the other, you can't. Yes. Okay. I got it. It just doesn't work. So, and, okay. But now, but there is something you can do. So, what you can't analytically continue the theory. So you can't take your operators, states, measures, all these things and analytically continue them.

But what you can do, there are things that do analytically continue. So you can define these things called Whiteman functions. They're just vacuum expectation values of operators. So you take a product or two operators at two different space-time points, you multiply and you apply them, you hit the vacuum with them, you get another state,

and then you take the inner product of that state with a vacuum again. And anyway, and you get things dependent upon x and y. These kind of carry most of the information about the theory in them. So if you have an operator theory, you can compute these objects and you can characterize the theory, a lot of the theory by these objects. And they're kind of, I mean, the operators don't commute. So this thing is not symmetric in X and Y. If you interchange X and Y,

you're gonna get something different. They're also technically, these are distributions, they're not functions. These are things more like delta functions. You can't, they don't make sense as actual functions, but you can kind of take convolution of them with functions and get something that makes sense. That's what you can do in real time and operate your formalism.

And then in the imaginary time and the pathological formalism, you can take similar things which are moments of these. Anyway, similar pathological rules are kind of moments of these measures. And anyway, they correspond in a one-to-one way with the Whiteman things, except that they're symmetric. But it's a very different kind of theory. It's the calculation you're doing and the whole theoretical setup.

I mean, there's no states. There's no operators. There's just these measures and these integrals. And they look a lot more like what you do in statistical mechanics. And actually, they're really kind of one of the amazing things about this whole story is that if you take your imaginary time to have a finite extent of size beta and you do this calculation, it's precisely a statistical mechanical calculation at a temperature given by beta is equal to 1 over k times the time.

So it's a very different, the path integral formalism really is much more like a statistical mechanical system. It's very different than the operator formalism. But the output of it are some functions, the Schringer functions, which can be analytically continued to the Whiteman functions, which can be analytically continued to the Whiteman functions. Okay, now let's get to SO4. I'm interested how you break it to Lorentz.

Okay, so by the philosophy I'm pursuing, what you're supposed to do, what I believe is that the theory really makes most, you should think about the theory in Euclidean space time or in imaginary time, and then you can compute the Schwinger functions, but now if you want to have states and operators and the whole operator formalism, you have to do something which is often called, you have to kind of reconstruct the real-time theory from the imaginary time theory.

You can't just analytic continue. And sorry, this is where I'm rapidly kind of getting into talking about complicated things which I can't tell you anything about. But you can do this. One thing you have to do is in four dimensions, you do have to pick one direction, say that's the imaginary time, and you have to have an operator which just kind of reflects you in that direction. That's called the Ostrobothel-Schrotter reflection.

You can use that to reconstruct the real time theory from the imaginary time theory. I'm not telling you how to do it, but you can. But maybe just something to notice is that, so if you construct operators and states in real time, there's no distinguished direction of time in real time. And you've got positive and negative time like cones, but the whole, the construction of operators and states

and everything you do in real time doesn't have a distinguished direction. So maybe this is what it took me a long time to realize it, that this was, and this is when I started to realize that what I was, had to think about years ago could work is that Euclidean space time is quite different because in Euclidean space time and in the imaginary time, you have to pick, you have to break the SO4

for metral symmetry and pick a distinguished direction. Yes. You have to do that. Yeah, it sounds like your theory is introducing another problem of time. There are many problems of time. There's one about how is GR different than QM and how is... It's a different direct...

There's the Wojtyn problem of time. Well, these are imaginary times, so that's a different thing. But this is what it took me a long time to realize and what was kind of the, maybe it was first kind of breakthrough when I realized that this was going to work is that Euclidean theory has no operators or states. If you want to have operators and states and you want to get back your physics, you have to choose, you have to break the SO47 tree and pick an imaginary time direction. And this turns out that this is known. But the problem is really what happens for spinners. So it's kind of known, and you can read about this

a lot of ways for scalar field theories, for theories that don't involve spinners. But what happens when you try and do this for spinners has always been mysterious, and there isn't really any kind of convincing, well, anyway, there's some early papers on it, but there's really, a lot of people have tried to figure this out, but anyway,

not much to say, but my basic proposal now is that something really unexpected happens right here, that what was a space-time symmetry in the Euclidean QFT becomes an internal symmetry in the mid-Cassoc QFT exactly because of what you have to do when you try and do this reconstruction procedure and you introduce this ulcerative colorectal reflection operator when you do it with spinors.

That's the basic, one basic thing I'm saying now. Okay. And now, let me, here's just a couple of minutes on spinors before I do that. But maybe the one reason, this is, I kind of said this before, that spinors are really different in Minkowski and Euclidean space time. But the basic idea is that in Euclidean spacetime, the rotation group, SO4, has this double cover, which is two copies of SU2, which we'll call left and right.

And the matter particles are these vial spinners that are either, they're these C2, represent just the SU2 acting on C2, either the left-handed one or the right-handed one. And the standard story about Euclidean spacetime is that if you want vectors, you take the tensor product of the left-handed ones and the right-handed ones.

Anyway, so this is the story. And in Mikowski spacetime, you've got spin three one, you have this different treatment of one direction, but that's a very different group. It's not SU2 cross SU2, it's SL2C, it's two by two complex inverto matrices with determinant one. And so there's only one kind of a spinner in some sense then. There's only one two-dimensional group, it's acting also on a C2. So you have one kind of spinner I'll call S. But now you can also look at the complex conjugate.

And the complex conjugate B. Anyway, so the complex conjugate is a somewhat different thing. It's not true for SU2. And Minkowski spacetime vectors are tensor products of two kind of spinners, but they're the vial spinors times their conjugates. So the point is these are just two completely different things. Now, this is where I'm starting to run out of steam here, but maybe just a last important thing to explain,

which it also took me a while to realize is that is about the Dirac operator that maybe it's important to realize that the Dirac operator really is a vector. You know, when you write down the Dirac operator, people write it down, you know, using these kind of upper lowered indices of normally you make Lorentzian-Brayon things by putting together a vector and a dual vector and you contract and you get a something which is a scalar so when people write down the formula for the Dirac operator they use that formalism and they make it look what's what they're doing but that's just not true I mean the the Dirac operator is not a scale it's not a

Lorentz scalar the Dirac operator is not the Lorentz invariant. The Dirac operator transforms like a vector. It transforms like a vector under Lorentz transformations. And if you- Wait, can you go back? Can you explain what is the common account? What do people ordinarily say about the Dirac operator? And what is it that is the truth about it? Well, I mean, people don't say something directly wrong, but I would just say,

take any kind of physics book that explains relativistic quantum mechanics of the Dirac operator and look at the discussion of how does the Dirac operator behave under Lorenz transformations? I mean, they're writing down formulas so you'll see that there's a nontrivial transformation formula, they'll write it down. But people will have very confusing things about what the meaning of that transformation formula is.

I'm just saying the meaning of that transformation is very simple, that the Dirac operator is not what the notation makes it look like, which makes it look like a scalar, it's a vector. And if you understand the relationship between vectors and spinors, it's just a vector. And it's maybe a little bit easier if, anyway, it's so Dirac writers is just a vector. And that's rarely, if anywhere, said, though, that the form of those people writing down, just, they say that, but it's not the way people think.

This is, now, finally getting to the, maybe to the last, to the end of this, where this will become completely incomprehensible. But, so if you try and think about what is rick rotation, you try and think about what is Ric rotation, you try and think about it as analytic continuation from Minkowski to Euclidean spacetime. The standard way of doing that is thinking about complex spacetime,

making not just time complex, but all of space and time complex. And then there's a complex four vector. And then you look at the rotation group or spin group in four complex dimensions, you realize it breaks up into these two SL2Cs. And these complex four vectors, again, are just, it's just like in the Euclidean case,

they're just a product of a spin representation of one SL2C and spin representation of the other SL2C. Now the standard story is that this is all supposed to be a holomorphic or analytic story. Everything is supposed to depend. And I can't, anyway, everything is supposed to be analytic and all your complex variables are holomorphic. And so work rotations then this analytic continuation

in this complex space time. So now the new story I'm trying to tell is basically that one way of saying it technically is that if I'm going to do a WIC rotation, I'm not going to do WIC rotation by this analytic continuation, that that actually doesn't work or doesn't do what I want to do. But I am going to do WIC rotation starting with the Euclidean story and doing this reconstruction of the real time theory. And I need an appropriate Osterwalder-Schrater reflection for spinner fields.

And this is what I'm, anyway, I'm kind of in the middle of trying to get this written down carefully, but what I can see happening is that when you do this, the new thing you have in your Euclidean spacetime is you have a distinguished time, imaginary time direction. And that means you're going to have a distinguished Clifford algebra element, gamma zero, which is going to be, anyway, you get distinguished elements or gamma matrices, if you like, in the physicist language corresponding to the different directions.

Well, there is a distinguished gamma matrix corresponding to the imaginary time direction. And that interchanges left and right. If you hit a left-handed spinner with it, it gives you a right-handed spinner. And exactly because it's a spacetime vector, exactly. So it takes one to the other. And so what gets RIC rotated in Caissi spacetime is not this tensor product of left and right-handed spinners in Euclidean space, which is the vector of space, but something where you've hit one of them with a gamma zero. So you're actually looking at... So vectors in Minkowski spacetime are really should be thought of as tensor products of two right-handed spinners.

And so the geometry in Minkowski spacetime is not what you thought it was. It's not the analytic continuation you thought it was. It's something different. That looks spinorial, like making an analogy back to the beginning, where you said that spinners can be thought of as the square root of vectors Yeah, well all of these statements about vectors being different tensor products of different kinds of spinners Those are all the kind of thing that goes into discussions of the supersymmetry It's I mean I'm doing something a bit different that they people then and some of the things that I'm talking about

They always appeared It's very interesting if you go look at the literature of supersymmetry and you ask, wait a minute, what happens to supersymmetry under Wick rotation? You'll find that, anyway, you'll find a very, very confusing literature, let's just say. Yes.

But anyway, so this is just to explain that the bottom, so this is actually, we're at the end, I just wanted to explain my, the slogan and the last paper I wrote was a short paper trying to emphasize this, but from a different point of view. And it just, the slogan is that space-time is right-handed, that what, you know, when you're in Euclidean space-time, you've got vectors. Interesting, interesting. Vectors are attentional products of left and right, but when you do wick rotation, you just have right times right.

And so these left-handed spinners really are an internal symmetry. You can still think about them once you've wick rotated, but they're not space-time symmetries anymore. Anyway, and so the slogan is, yeah, that as far as space-time symmetry is concerned, you've just got right-handed, you're just dealing with right-handed spinners. These left-handed spinners that you had before you wick-rotated,

they have nothing to do with space-time. They have to do with the internal SU2 symmetry of the weak interactions. Was there an element of chance like in your theory or in your mind? Was there, firstly, wonderful talk, wonderful talk. Put in some applause. Okay, thank you. Wonderful. Okay, was there some degree of chance to what made space-time right-handed versus left-handed? Oh no, that's just a matter of convention. So, I mean, what I call left and right is a matter of convention.

I mean, the one thing which, one interesting thing to say about this, and one reason for thinking about twisters, so I haven't actually gotten into the relation of twisters, is that if you just think about the standard formalism that's in the QFT books, where you have gamma matrices, whatever, that standard formalism that's in the QFT books where you have gamma matrices whatever that standard formalism that formalism is kind of left right symmetric and and and it's

actually set up to work very nicely when you've got parity invariant theories which theories which you can interchange left and right um so you have to kind of add some things into that formalism to kind of project out whenever you have, yeah, so anyway, so, but yeah, but the thing which is different, and I haven't talked about twisters at all, twisters are a different part of the story, but the twister geometry is very, very much asymmetric. So twisters, when you write down twisters, you say that points in spacetime basically are spinners, but they're spinners of one kind. Again, they're just the right-handed spinners.

So twister geometry also has this kind of, in an interesting way, the same kind of aspect that it's left right asymmetric and you can you have to take one of them as fun as a fundamental thing it's telling you what the points are and um but I'm doing something different than the the usual twister story because I'm treating vectors differently than then okay that then what's going on vectors? My next two questions may be related. So where is gravity in this?

Sure we have space-time, but we've been dealing with flat space-time. So that's one question. And then the second one is what happened to Euclidean twister unification? Is that related to this? Okay. So this is just a part of, well, maybe let me try to answer them in order first. So first, we know how to write down general relativity as a gauge theory of formalism. And that SU2 right, so you can write down gravity.

And this is something which, if you look at the people who do loop quantum gravity, and they talk about things called Ashtakar variables. Well, so gravity written in terms of Ashtakar variables is written down in this very asymmetric way. And it starts to become a very, very, very, very, very, is written down in this very asymmetric way. And it starts to become a long story, but one way of saying it is that I had these two SU2s,

SU2 left and SU2 right. SU2 left is an internal symmetry. That's the theory of the weak interactions. SU2 right is a space-time symmetry. And gauging that is part of the, is basically how you get general relativity. You gauge that and, but then you also have to tell me

what you're gonna do with the vectors. But if you tell me how you're gonna, what you're gonna do with vectors and you gauge that SU2 right symmetry, you have general, you can get general relativity that way. It's general relativity, Ash to Kar variables. I see. Well, for people who want to delve more into the details,

we'll leave the links to your papers on screen. We'll show them currently. They're on screen. And then also, you and I, Peter, we have a podcast on theories of everything. I think it was two hours or three hours long. We went quite in depth into these theories. Although, space time is right handed. It came a few weeks or a couple of months afterward. two hours or three hours long, we went quite in depth into these theories. Although space

time is right handed, it came up a few weeks or a couple months afterward, but the Euclidean Twister Unification, I believe. So people can watch that if they're interested. Maybe something I should make clear is that, so the, I mean, I've written various things about this and the Euclidean Twister Unification is kind of part of, maybe a good way to say it is that this is, there were a lot of things about this Euclidean twister unification proposal, places where I really did, I specifically said, look,

I don't understand what's going on here. What I'm saying here is much more of an answer to parts of that story. There are parts of that story which were, I thought, you know, I can see here's some things that are going on that look like you can really do something with them, but there's a lot that I don't understand and this is more of an explanation

of things that I didn't understand there. So how to, so you have to then go back and see how I can use that there. The other thing to say is that this is really just kind of an ongoing program. I mean, I keep trying to write up a better version of the stuff I've done in the past for this. And when I write it up, I start to understand

something much better and see it from a different point of view. And so I stop writing and start doing some of it. So it's some. Oh, I see. It's an ongoing process. And so sooner or later, I'll, I mean, I or later, there are no technical details here. And what's on this slide here? You're not going to find anything

that I've written down that explains the details of that. It's still something that I'm working out the details for myself and have to. It's clear something like this is going on, but the exact details are still not in place. This is a point of view I've been thinking about a lot in the last couple, month or two, and it really seems to come together really nicely,

but it's very, very much not written up. So, and if I try and write it up, I may find that this isn't quite the right thing to do either. And now it'll be something different, but we'll see. Thank you, Professor. We'll also link your blog on screen. And that's something that I recommend. Yeah. And one thing, since I'm having trouble getting some of the stuff written up, one thing I keep thinking about is to try to use the blog to kind of, as I understand pieces of this story, to write up something about those pieces there. So it avoids being kind of a formal, completely coherent paper, but at least if I say, okay,

now I understand. Many people are reluctant to do that because they feel like their ideas make it swiped. Well, yeah, that was, I think, I guess I started to realize, I should say maybe when a lot of the stuff first occurred to me, I thought, OK, this is really cool. This is a great idea. The more I think about it, the more this works. I'll just start telling people about this, people.

And people complain, you know, there's no good ideas. They don't know what to do. You know, lots and lots of people are going to get interested in this. And what I found is that nobody really seems to understand what I'm talking about or be getting very interested. So the last thing I'm worried about at this point is people coming in and swiping my ideas.

I'll be very glad. You'd be glad, yeah. Wonderful. I hope if anybody who wants to kind of try to swipe any of the ideas and who's interested in doing something with them, please, yeah, please go ahead. Right, right. At least they care.

Okay. Yeah, yeah. So I actually want to get some of these things, figure out how to get some of these things out there and get people to understand some of the things I'm seeing. And I hope that some of them will then appreciate some of what I'm seeing here and start kind of help pushing it forward. Well, thank you for appearing on this series on Rethinking the Foundations of Physics. Sorry about that.

I thought it would be half an hour, but I guess not. That's perfect. Also, thank you to our partner, The Economist. Firstly, thank you for watching. Thank you to our partner, The Economist. Firstly, thank you for watching, thank you for listening. There's now a website, curtjymongle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service. Now a direct mailing list ensures that I have an untrammeled communication with you.

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