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Peter Woit: A New Path to Unification (The Forgotten Geometry)
September 2, 2024
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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,
Voigt 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 Voigt 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 for 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, and we'll see, I mean, this is fairly sketchy. I'll have to make some excuses for the, um,
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 it in a relatively reasonable amount of time. So let's just start with that. So what I wanted to do is first go over 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, you know, about how to do unification or about how to do a substantial part of
Of the occasion 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. So that that's that's just the outline. Okay, so to start. So I mean, this is you never know kind of how much to try to tell people about this is just kind of there's a standard outline of what's the standard model. But you know, we have this incredibly successful theory called the standard model and it has it's basically a fairly simple
Conceptually object and once you get used to certain kind of technical ideas about the mathematics and the physics and and it basically says that you know for there are three forces in the world and they're they're they're due to these um You won su2 and su3 Gauge gauge fields. There's a the basically the electromagnetic the weak and the strong force and then and then the matter, you know is
spin one-half fermions and there's some specific pattern of charges which are the you know the couplings to these three different kinds of forces and I won't write out there's kind of a standard table of these it's kind of an intriguing pattern we don't quite understand but it's it's a pretty simple pattern so that's forces that's matter and then the one probably most mysterious part of it is the Higgs field and then and so 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, 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
Knowing the basics of the geometry and how this is supposed to work, 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 a bit 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, um,
There's a long history of this, but it came together pretty quickly in a few years. In April 1973, you could write down this theory and people started to realize what they had. It took them a while to gather the experimental evidence to be convinced that this was really the right thing, but it was there in April 1973. The most amazing and bizarre aspect of this whole situation is that this relatively
Relatively simple theory. 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. 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
You know, as you expect so far, there isn't any data. The only kind of data that people talk about that we're not sure what to do about often is often more kind of 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.
So this is the problem of unification in some sense that we're used to historically having experimental results 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-Romagna manifold. It's a kind of a
Standard kind of curved manifold except one of the directions, the metric is kind of negative in one direction, and locally it looks like the Kowski spacetime. And then the gravitational force is described by the curvature of this spacetime, and 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 in 1915, so we've had it for over 100 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 any kind of anything we see that disagrees with general relativity. Okay, so what's the problem?
Both of these theories are 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. The situation isn't quite satisfactory because there are some questions that these things don't answer. There's no evidence that there's anything wrong about either of these, but there are some unanswered questions.
Basically, what about the standard model is, you know, why SU1, SU2 and SU3? I mean, what's the explanation for why those three gauge groups and why those three forces? And then part of the story is that for each of these things, you have kind of a free parameter, a coupling concept which describes the strength of the force. And so there's three kind of numbers that come out of this and one of them is the strength of the electromagnetic force.
but why those numbers? And so we don't, 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, some extra piece of information about where they come from. Okay. 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. Um, so these groups, I mean, they're a little bit technical. U one is basically just a circle. It's just a circle on the complex plane. You can think of it. SU two 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 but why why those three groups i mean they're among if you look at the possible symmetry groups lead groups of this kind these are kind of three of the simplest possibilities but why
Why those three? Why not something else? Why not? Extra value meals are back. That means 10 tender juicy McNuggets and medium fries and a drink are just $8. Only at McDonald's. For limited time only. Prices and participation may vary. Prices may be higher in Hawaii, Alaska and California and for delivery.
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. But 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 like this is that
So we'll, we'll see that anyway, maybe let me give me a minute to get to that next to grant unification. And we'll, we'll say a bit about that. But, but this kind of set is the problem. I mean, so one, anyway, this is the general version of the problem. And then the, with the matter particles, I mean, so one question is kind of, you know, why are these things spin one half? You know, why are there these, why are they fermions? Why they spend one half? And then why do they have this, um,
specific pattern of charges and these, you know, these, the short list of kind of numbers, which tell you how they're, they're integers, which tell you how they couple to the U1, SU2 and SU3 and why, why that pattern of charges. And then they, they come in kind of three generations or kind of three cuts. It's a pattern. You see the same pattern copied three times. Why all of this? It's a kind of small and manageable amount of kind of discrete structure, but you know, where,
Where does it come from? It looks like there should be some explanation for it. The other thing is about the Higgs field. 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 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 is there why this potential energy function and then it the matter fields are all getting their masses from the strength of their coupling to the Higgs field. These are called Yukawa couplings. You know, 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 the one question that that's something that's actually not mentioned very often is that there's a technical problem. We still is still has never really been sorted out is that, um, you know, when you write down this quantum field theory of the standard model,
It's if you mostly do computations in perturbation theory using Feynman diagrams and that that's kind of a an approximate calculation method. We've know how to make that that works fine. But do we? We also know that you know you. That only works in the limit of kind of extremely small coupling that for for larger couplings, you need a definition of the theory, which is isn't which 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, you'll get 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 unlike the U-1 and the SU-3, the SU-2 couples differently to left and 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 something that might work, but that's an open problem that's never really been resolved. It's not often mentioned. 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 using standard methods, you find this renormalizability problem, you find infinities which you can't be handled in a standard way, and any way you try to handle them just
Is it going to introduce an infinite number of new constants into the theory or something? 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.
But that's one way of saying it. But another way of saying it is that there are plenty of people who claim that, OK, 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. And 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 is 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 string they would like to say the string theory gives you such a thing but yeah, but it may give you kind of an exponentially large numbers of such a thing as depending upon these questions about string vacua, etc. So and every there's
There's maybe two ways to say the problem. One is that 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. Now I want to start on what
has been happening since April 1973, when it became clear that what these problems were was more or less immediately obvious. And 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 is 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. And then, 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 the 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. Anyway, if you write down the theory for the bigger Lie group, it's just got one coupling constant in it.
And then what you have to do is you have to explain what, why do we see, okay, but why do we see the three, three coupling constants? But, but maybe I was going to come a little bit more to this in later. I mean, this is kind of the problem. The problem is that you have to, if there just wasn't SU five theory, there just would be one number that determined everything. The problem is that we're saying three things and three numbers. So you have to first explain why are we saying 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, what, how you go from getting that one number to getting three numbers. I see. Does it give you a relation between those three numbers, like some bound or some inequality? 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 SU-5 theory and it just looks like the SU-5 theory. There's some kind of new symmetry breaking scale you had to introduce and above that symmetry breaking scale, you do just have one theory, you have one coupling constant. So 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. And then once you introduce the symmetry breaking by a new set of Higgs or something, then you have to 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
You evolve differently as you change energy. Okay. So you often see this graph of these three coupling constants, right? And then, you know, they kind of come together at a point, which is the point where they unify it at this higher, um, what they unified as you file. 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, 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. You have to explain how all 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. 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. Just as I always said, we know that SU2 cross U1 breaks down, that the vacuum is only invariant under U1. We know that the vacuum 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 so there's initial I think I know that Georgia and Glashow got very excited about this a lot of people because you know this not only was um 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 some new predictions of some new physics and in
In specifically, because you're putting this SU2 with the weak force and the SU3, the strong force together, quarks can decay into leptons. And so 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. And the initial numbers that they got were that this should happen, but very, very slowly. So it was perfectly consistent with the fact that we don't observe protons decay. And so people then started going out and doing experiments looking for this, looking for proton decay at the kind of rates that
at these things predicted. But then the problem was, and the basic problem since then has been that, well, it turns out protons don't decay. I mean, 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, 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 know, by now, I don't know, I forget the numbers, but it's,
By now, it's 10,000 or 100,000 times. Anyway, the bound is way above that. Got it. This is definitely wrong. I know that one thing that's true and interesting about Georgia and Glashow is that they actually did give up. Part of the problem with the 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 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,
ten or fifteen years after this, when the expounders 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 you know and they don't really mention very clearly that it doesn't work. Okay then supersymmetry was another another kind of part of our kind of standard paradigm that we've been living with and it also in the earliest standard models written down in April by December people were writing down these supersymmetric extensions of the standard model so let me explain what those are. I mean 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, you know, spinners in some sense are a square root of vectors. 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 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. And then 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-Ali 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 produce spinors is 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 Qs, 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. Okay. And again, so there's a lot of enthusiasm at this. I mean this, a lot of it was also kind of driven by just the beauty of the idea. This, this is a really beautiful idea. If you look at, if you try and do this, you find that these, these cues commute with all of the, um,
All these does you one cause is you one issue to SU three commutes with these cues. So you find what a cue 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, um, a super partner. It's going to produce a different kind of particle, which has exactly all of the same, um, standard model charges, but it, but it, it has spin differing by a half because, because the, cause it, cause it's, 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 by spin half and that had the same standard model charges you would
That would be a good candidate. You would identify them as super partners. Yeah, you'd have two super partners. Anyway, in some sense, I think the problem is you don't see this. 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. Technically, 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 that's kind of what you say. And some people, I guess, would take this enthusiastically. Oh, great. You know, there's all these new particles in the world. I think I and many people were also a little bit. Wait, wait, wait a minute. This is really this is a little bit implausible that this doesn't
Anyway, that there's this new symmetry, but we haven't kind of seen any of 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 know, it 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 super gravity includes a client.
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 less
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. One thing you might try to do is explain where does that U1, SC2, SC3 come from by
postulating more that more for more than four space-time dimensions and it's these other so-called you know kind of internal internal dimensions which explain everything and that was 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 yet. 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 there is a classical version of them.
But the problem is that it's you've you've extended that your standard kind of variables with these these to get very much. You've extended your standard variables with these anti commuting variables. So it's kind of a weird. So classically is kind of a weird subject. It's so you have non commuting classical variables. Yeah, you're not. It's not commuting class. So you can write down such a theory. You can you can look at it, but it doesn't kind of correspond to
And I mean, 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, which just had different products, which are kind of different, weird algebraic things, which aren't what you're used to thinking about. I see. So, um, now someone like Elaine Conus, would he be comfortable with classical non-commutativity or does he only study quantum non-commutativity? Well, he, I mean, he's, he's more interested. I mean, it's,
It's non-community activity, but of a very specific sort. It's just a, it's what we, 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, is just something very, very minor that they, they, they pick up my certain things, pick up minus signs when you interchange them. So it's, I think someone like Alan Connor, people do when their people are talking about non-community of geometry,
They generally mean something much more seriously non-commutative. Some mathematicians often call this super-commutative. The people who do standard commutative geometry, they're used to having these little algebraic gadgets in it which square to zero and which anti-commute. That's also part of their story. Some mathematicians would claim it's really just part of commutative geometry.
What like the non-commutative geometry that Alan Khan 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, you know,
We've never seen any extra dimensions. We've never seen anything besides four dimensions. 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 tried to check it, 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 can don't really talk about here but maybe one interesting thing is that the first super string theory that would that the idea that it could describe gravity that you could describe gravity using the super string was um first paper about that was like a month after the
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 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, it was to bring together all of these things. So they had, they had an E eight gut. They had super gravity as a low energy limit. They had extra dimensions of Calootsa Klein going on. And so that they, they had everything. So, I mean, this was kind of, I think one, one reason this appealed to everybody is, you know, 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's gonna go. So that was 1984.
And again, I mean, now 40 years later, there's kind of no, no evidence for any of the components of this or for including for the strings. And it just really hasn't to stick to just kind of experimental statements that there's absolutely kind of zero, nothing anyone has seen of any kind, which, you know, kind of indicates any connection to this stuff. Okay. So, so now maybe I just want to kind of reason for going through all this is partly, you know, 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, whether it's, anyway, more and more dimensions, whatever. But the problem is that they're doing this for various
reasons because that you know that it's some larger thing which they can compute maybe there'll be some new symmetries and some new things you can can do but there's no evidence at all for any of the components of this new structure and 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 super symmetry 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 where do you know
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 and you have to break all these symmetries. 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 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 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 Georgia and Glashow 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 this theory that's going to make them 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.
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At what point does it become more ugly than the beast you were trying to replace? Well, I would argue pretty quickly, but 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, you know, refute 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. But, um,
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 kind of why I'm going through all this. Okay. And anyway, and yeah, so this was just more of what I wanted to say on this. And I think what's actually happened is, 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 kind of the most serious people in the subject
You know, just kind of stopped working on these. They don't go out and say, okay, these things are failures, but they just kind of stop working on them. And if you ask them about it, they say, well, you know, I just don't see how to push this any farther. I still think it's a beautiful idea. I mean, I don't want to put words into it 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 a lot no longer something a serious person should do because it's it's just hopeless until somebody has a really brilliant new idea until we see some new until the experimentalists help help us out. We're just not going to be able to move forward with this. And this is something I see a lot talking to the theorists and seeing what they say. 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 that they fact this was the best possible way of doing this that they found and and you know they haven't been able to push it make it work so you know it's just uh
What are you going to do? Well, you mean to say unification attempts outside of string theory or to not even consider string theory unification? Well, I mean, the string theory then becomes a complicated question. What would you mean by string theory? But I guess one way to 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 is, 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 going to tell you about it. I mean, that that's a hard sell. I think because people say, well, wait a minute, you know, 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? It's like these crackpots who tell us that Einstein must be wrong. It's always been a hard sell to say, look, everything you've been doing for all this time, 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 we have to go all the way back to 1973 and look at different things, not the things that we started looking at back
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 SU five 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, yeah, no. So that's always a question. Yeah. At what point do you, um,
Yeah, did you give up an idea? Did you say it? And in some sense, I mean, my argument with the string theorist always was from the beginning that, you know, my judgment of what's going on is you guys, you know, this is a good, you really have to give up. This is something which hasn't worked out. Their argument was, well, you know, we still think it's the best thing we know how to do. We still think it's worth pushing forward. So it was kind of a, you know, it's kind of hard to argue about that. But, um,
I think things have changed over the last 20 years. It's just become clearer and clearer that this stuff just doesn't work. 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. Now you ask people talk about, well, it may take 500 years for us to make any progress on this.
This is taking longer than I thought. 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 you've gone through the state of physics since 1915 to the 1970s and then to the present day.
I haven't really explained a lot about it. 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. OK, so now there's a much shorter and much sketchier part, which is to kind of 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.
You know, I worked on doing these lattice calculations of using SU3 gauge theory and the calculations just use 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, you know,
Matter particles are these spin one half, the spin geometry is really weird. It's a very, it's not at all obvious, you know, how to capture that geometry and, you know, while how to preserve any of that geometry when you discretize things. And, you know, 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, 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 this subject says that this just is not going to work. This is implausible. You can't make that happen.
Everything you know about the subject forbids you putting fermions on the lattice? No, no, we'll see. I'm going to make a certain claim 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 the way spacetime and symmetries work is clear enough that you just can't have
What I'm going to, what I'm going to, I now believe happens. I had convinced myself could not possibly happen. And so, anyway, just some history of my own personal history. And it's within the last three or four years though, that I finally, you know, thinking about this some more and also a lot that I've learned actually by teaching, 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
These 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 that you would see once you wrote down the details of Of how these symmetries worked and then what I just found is I started writing down the details and learning more is that just wasn't there You know, it really wasn't wasn't there and um, and then I finally Started thinking about it in very 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 was there's now perfectly good reasons to believe that it that it could happen Sorry, and that occurred to you while you were writing the book on quantum theory and representations. Um, yeah more later after that was done and and yeah, but but yeah So 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 but 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. 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 mind, 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,
Let's get to the approach that seems promising.
As this is the hugest tease that I just kept asking you questions. That's my fault. You left the audience hanging. I'm sorry, you're not going to get a detailed answer to this anyway, but you'll see. First of all, to put this in the context of what I was talking about already, is to say that this has about four dimensions. No extra dimensions, four dimensions. The idea is that there are no extra dimensions.
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? There's a lot of very interesting things that happen only in four dimensions. And can we use those? And 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. And they're very, very tied to four-dimensional geometry. They really are.
Roger Penrose has been, but, and there's, there's part of the whole story of the spinner. Yes. But so, so that's, but the, the other thing which I'm trying to use, which, which hasn't really been used very much. I think one thing to say about all of this, all the, there's a story that I told you, if you go and look at any of those books about any, any of those, these guts or super symmetry or super gravity or string theory, um,
You'll find one strange thing if you start to dig into the technicalities. Our space-time has this so-called Minkowski metric. You put a minus sign on the distance squared in time. 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. What you do is you
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 if you look at all the literature on all the theories I've been talking about, there's really, in every case, it always is like kind of a technical problem about, wait a minute, don't we need to do this in Euclidean signature? Are we doing it? How is it going to go from one to the other? And it's kind of a technical problem, which was,
There for all of these theories, but no, but people just kind of tried to avoid thinking about it. There was always a feeling, okay, this is some technicality, you know, maybe some mathematician will figure it out. We don't care. We're just going to write down formulas and hope for the best. But I was, this is something that it really struck me that you really, this relationship between Euclidean and Caustic exchanger was a really interesting topic. It was indicative of something.
Well it was something it was something we really don't understand i mean it always in my mind i mean there's we had the standard theory there are parts of it that i look at it 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 this this wick rotation was
a place that was at that happens in the standard model. So anyway, so the main, the main new idea is to say what I'm trying to do is, is to claim that this, that this wick rotation, you know, if you think about your geometry in terms of spinners, it changes the geometry, the spinners in a very fundamental way that the geometry of spinners and Euclidean signature and the geometry of spinners and Caskey's signature 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 Minkowski 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 space time chemistry. 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 it but it's the new thing is to say wait a minute is to say look you really should think about what's going on and add the 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 um, okay 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,
create an oscillation.
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 four 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 let me go on.
This was just kind of an overall. And let me see how much I can do with that. OK, so let me just first. Yeah, so this is so we're quotation. So another way of getting this minus sign on the square is to change from, you know, put in a factor of the score to minus one. So what this is. So we're quotations, but what you're supposed to be doing is you've got.
a time variable and it's saying okay you can you can make the time variable complex and then look at look at look at a theory where that your time has become purely imaginary okay and then that minus sign there which is is going to when you multiply this by itself the two factors of i are going to are going to cancel that minus sign and you're going to everything is going to be plus so there's so the idea is that there's also is so i 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 the simplest version of liquid rotation.
Here's the problem when you try and do this in quantum field theory. How are you going to do this? This starts to get a bit technical, but in 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, then what happens is that the
These fields in this Heisenberg picture, if you change time on them, you're conjugating by the Hamiltonian operator. That's the Heisenberg picture. What this is saying is that if you try to go to imaginary time, if you make imaginary time on zero, you're going to conjugate by this operator the exponential of the imaginary time times the Hamiltonian.
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, but which goes off to infinity at 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, either the
Tau times h and e to the minus tau times h and if tau is positive this one is going to make sense because it's e to the minus something positive times something positive whereas 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 so there's just a fundamental issue in it which everything we know about quantum field theories and the operator formalism you can't
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 what's going to happen to the field just don't make any sense. You can't do it. 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 them down as path integrals, if you go to imaginary time, this 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 the
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. So these two kind of formalisms we like to use to do quantum field theory, they have opposite. People will talk about them as if you can use them to go between imaginary
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?
Our 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 want to understand how to get, how to go back and forth, you know, we don't have a theory that does that. I see. Yeah. So we, we don't, there, 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
where you can, 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. But if you try to, you start with either one and get to the other,
You can't, it just doesn't work. But there is something you can do. So you can't analytically continue the theory. So you can't take your operators, states, measures, and 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 of two operators at two different spacetime 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, things dependent on X and Y and, and they're these kind of carry most of the information about the theory in them. So if you have an operator theory, you can, you can compute these objects and you can characterize the theory, a lot of the theory by these objects. And they're kind of,
Mean the operators don't commute. So this, this thing is not symmetric and X and Y. If you interchange X and Y, you're going to get something different. They're, they're also technically these are distributions or 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 an operator formalism.
And then in the imaginary time and the pathological formalism, you can take similar things, which are moments of these. Anyway, similar pathologicals are kind of moments of these measures. 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.
These measures and these integrals and they they look a lot more like what you do in statistical mechanics and and actually they're really kind of one of the amazing things about this whole story is that if you 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 you know given by beta is equal to one over a k times the time so it's a very different
The path integral formalism really is much more like a 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. Okay, now let's get to SO4. I'm interested how you break it to Lorentz.
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 Schringer 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 without telling, which I can't tell you anything about, but you can do this. And 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 kind of, which just kind of reflects you in that direction. And that's called the Osterwalder Schrader reflection. And, and you could, you can, 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,
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 formational symmetry and pick a distinguished direction. 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 weight. There's the Wojtyn problem of time. Well, these are imaginary times, so it's a different thing. But this is what it took me a long time to realize and what was kind of the maybe the 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 in 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 a there's some early papers on it but there's really a lot of people have tried to figure this out, but Anyway, not what to say but but I my basic proposal now is it's something really unexpected happens right here that um what was a space-time symmetry in the Euclidean QFT becomes an internal simply in the classical QFT exactly because of the
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 Kavsky and Euclidean space-time. But the basic idea is that in Euclidean space-time,
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 spinors that are either, they're these C2, 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 then 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 made, 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 SU-2. And Minkowski's spacetime vectors are tensor products of two kinds of spinors, but they're the vial spinors times their conjugates. So the point is these are just two kind of completely different things. And now just to
This is where I'm starting to run out of steam here, but maybe just kind of a last kind of important thing to explain which people, 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 Lorentz Iberian things by putting together a vector
and a dual vector, and you contract and you get 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 they're doing, but that's just not true. I mean, the Dirac operator is not a scalar. 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.
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
Draca operator behave under Lorentz transformations. I mean, you know, they're writing down formulas. So they're, you'll see that there's a non-trivial transformation formula. They'll write it down. But the, um, if you try and people that 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 Draca operator is not what the notation makes it look like, which is, which, which just makes it look like a scalar. It's a vector. And if you understand,
and spinners. It's just a vector and it's maybe a little bit easier if, anyway, it's so the rock writer is just a vector. And that's rarely, if anywhere, said though, that the formulas people are writing down just, they say that, but it's not the way people think. This is, now I'm 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 it as analytic continuation from Minkowski to Euclidean space time. You would, the standard way of doing that is thinking about complex space time, making not just time complex, but all of space and time complex. And then you say, so it'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 SL two C's.
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 rotation is 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 work rotation, I'm not going to do work 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 wick rotation starting with the Euclidean story and doing this reconstruction of the real time theory. And I need an appropriate Osterwalder Schrader reflection for spinner fields. 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's language corresponding to the different directions. Well, there is a distinguished gamma matrix corresponding to the imaginary time direction and that interchanges left and left and right.
If you hit a left-handed spinner with it, it gives you a right-handed spinner. Exactly, because it's a space-time vector. Exactly. So it takes one to the other. And so what gets RIC-rotated in quasi-space-time is not this tensor product of left and right-handed spinners in
Euclidean space, but something where you've hit one of them with a gamma zero. So vectors in Minkowski's spacetime are really should be thought of as tensor products of two right-handed spitters. So the geometry in Minkowski's spacetime is not what you thought it was. It's not the analytic
continuation you thought it was, it's something different.
Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal. Rankings based on root, metrics, root, square, report data to 1H2025. Your results may vary. Must provide a post-paid consumer mobile bill dated within the past 45 days. Bill must be in the same name as the person who made the deal. Additional terms apply. 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. I mean, I'm doing something a bit different. 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? Anyway, you'll find a very, very confusing literature, let's just say.
But anyway, so this is just to explain that the body so this is actually we're at the 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 um you know when you're in Euclidean space-time you've got vectors interesting vectors are tensor products of left and right but when you do wick rotation
You just have right times right. 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. The slogan is that as far as space-time symmetry is concerned, 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 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? That's just a matter of convention. So, I mean,
What I call left and right is a matter of convention. The 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 or whatever, that standard formalism is kind of left-right symmetric 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, you have to kind of add some things into that formalism to kind of project out whenever you have. Yeah. So anyway, so, but, but yeah, but, but, 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 space-time basically are spinners, but they're spinners of one kind. Again, they're just the right-handed spinners. Twister geometry also has this, in an interesting way, the same kind of aspect that it's left-right asymmetric and you have to take one of them as a fundamental thing. It's telling you what the points are.
But I'm doing something different than the usual twister story because I'm treating vectors differently than what's going on in a picture. 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? 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 kind of 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, they, um, so, so gravity written in terms of Ashtakar variables is written down in this very asymmetric way. And the, and it's starts to become a long story, but, but one, 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 basically how you get general relativity. You gauge that, but then you also have to tell me what you're going to do with the vectors, but if you tell me what you're going to do with vectors and you gauge that SU2,
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
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 just to say it is that this is there there are a lot of things about
about this Euclidean Twister Unification Proposal thing, 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 are going on that are, 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've, I keep trying to write up a better version of the, 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 stopped writing and start doing some of it. So it's, it's, um, I see it's an, it's an ongoing process. And so, so sooner or later I'll,
There are no technical details here. 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 at the details for myself. 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 month or two.
It seems to come together really nicely, but it's very, very much not written up. And if I try and write it up, I may find that this isn't quite the right thing to do either. 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 this 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, which so it's it's avoids being kind of a formal Completely coherent paper, but at least 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 I think I guess I've started to realize I should say maybe when a lot of the stuff first occurred to me I thought okay. This is really cool. This is I
The more I think about it, the more this works.
Nobody really seems to understand what I'm talking about or, or be getting very interested. So, uh, the, the last thing I'm worried about at this point is people coming in and swiping my ideas. I'll be, uh, I'd be very glad if anybody who wants to kind of try to swipe into the ideas and, and it was interested in doing something with them, please, yeah, please go ahead. Right, right. At least they care. Okay. Yeah. So when I, yeah, I actually want, uh,
Also thank you to our partner, The Economist.
Firstly, thank you for watching, thank you for listening. There's now a website, kurtjymungle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service.
Now a direct mailing list ensures that I have an untrammeled communication with you. Plus, soon I'll be releasing a one-page PDF of my top ten toes. It's not as Quentin Tarantino as it sounds like. Secondly, if you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself
Plus, it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm, which means that whenever you share on Twitter, say on Facebook or even on Reddit, etc., it shows YouTube, hey, people are talking about this content outside of YouTube.
which in turn greatly aids the distribution on YouTube. Thirdly, there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, they disagree respectfully about theories and build as a community our own toe. Links to both are in the description. Fourthly, you should know this podcast is on iTunes. It's on Spotify. It's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from rewatching lectures and podcasts.
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▶ View Full JSON Data (Word-Level Timestamps)
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"text": " 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,"
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"text": " Voigt 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 Voigt 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."
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"text": " 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 for 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, and we'll see, I mean, this is fairly sketchy. I'll have to make some excuses for the, um,"
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"text": " 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 it in a relatively reasonable amount of time. So let's just start with that. So what I wanted to do is first go over 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"
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"text": " 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, you know, about how to do unification or about how to do a substantial part of"
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"text": " Of the occasion 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. So that that's that's just the outline. Okay, so to start. So I mean, this is you never know kind of how much to try to tell people about this is just kind of there's a standard outline of what's the standard model. But you know, we have this incredibly successful theory called the standard model and it has it's basically a fairly simple"
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"text": " Conceptually object and once you get used to certain kind of technical ideas about the mathematics and the physics and and it basically says that you know for there are three forces in the world and they're they're they're due to these um You won su2 and su3 Gauge gauge fields. There's a the basically the electromagnetic the weak and the strong force and then and then the matter, you know is"
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"text": " spin one-half fermions and there's some specific pattern of charges which are the you know the couplings to these three different kinds of forces and I won't write out there's kind of a standard table of these it's kind of an intriguing pattern we don't quite understand but it's it's a pretty simple pattern so that's forces that's matter and then the one probably most mysterious part of it is the Higgs field and then and so this Higgs field is this"
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"text": " Space time scalar field which breaks the U1 and SU2 down to a U1 subgroup and that gives masses to the weak, 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"
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"text": " Knowing the basics of the geometry and how this is supposed to work, 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 a bit over 50 years out from this."
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"text": " 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, um,"
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"text": " There's a long history of this, but it came together pretty quickly in a few years. In April 1973, you could write down this theory and people started to realize what they had. It took them a while to gather the experimental evidence to be convinced that this was really the right thing, but it was there in April 1973. The most amazing and bizarre aspect of this whole situation is that this relatively"
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"text": " Relatively simple theory. 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. 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"
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"text": " You know, as you expect so far, there isn't any data. The only kind of data that people talk about that we're not sure what to do about often is often more kind of 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."
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"text": " So this is the problem of unification in some sense that we're used to historically having experimental results 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-Romagna manifold. It's a kind of a"
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"text": " Standard kind of curved manifold except one of the directions, the metric is kind of negative in one direction, and locally it looks like the Kowski spacetime. And then the gravitational force is described by the curvature of this spacetime, and 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."
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"text": " But again, the history of this is basically in place in 1915, so we've had it for over 100 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 any kind of anything we see that disagrees with general relativity. Okay, so what's the problem?"
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"text": " Both of these theories are 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. The situation isn't quite satisfactory because there are some questions that these things don't answer. There's no evidence that there's anything wrong about either of these, but there are some unanswered questions."
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"text": " Basically, what about the standard model is, you know, why SU1, SU2 and SU3? I mean, what's the explanation for why those three gauge groups and why those three forces? And then part of the story is that for each of these things, you have kind of a free parameter, a coupling concept which describes the strength of the force. And so there's three kind of numbers that come out of this and one of them is the strength of the electromagnetic force."
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"text": " but why those numbers? And so we don't, 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, some extra piece of information about where they come from. Okay. 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."
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"text": " 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. Um, so these groups, I mean, they're a little bit technical. U one is basically just a circle. It's just a circle on the complex plane. You can think of it. SU two is, you can think of it as, well, it's two by two unitary"
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"text": " 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 but why why those three groups i mean they're among if you look at the possible symmetry groups lead groups of this kind these are kind of three of the simplest possibilities but why"
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"text": " 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. But 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 like this is that"
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"text": " So we'll, we'll see that anyway, maybe let me give me a minute to get to that next to grant unification. And we'll, we'll say a bit about that. But, but this kind of set is the problem. I mean, so one, anyway, this is the general version of the problem. And then the, with the matter particles, I mean, so one question is kind of, you know, why are these things spin one half? You know, why are there these, why are they fermions? Why they spend one half? And then why do they have this, um,"
},
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"text": " specific pattern of charges and these, you know, these, the short list of kind of numbers, which tell you how they're, they're integers, which tell you how they couple to the U1, SU2 and SU3 and why, why that pattern of charges. And then they, they come in kind of three generations or kind of three cuts. It's a pattern. You see the same pattern copied three times. Why all of this? It's a kind of small and manageable amount of kind of discrete structure, but you know, where,"
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"text": " Where does it come from? It looks like there should be some explanation for it. The other thing is about the Higgs field. 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 potential energy function for the Higgs field come from and why the Higgs field? The Higgs field is a"
},
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"end_time": 879.889,
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"start_time": 851.357,
"text": " Complex doublet that transforms under SU2 and what's that about and then why is there why this potential energy function and then it the matter fields are all getting their masses from the strength of their coupling to the Higgs field. These are called Yukawa couplings. You know, 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"
},
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"end_time": 906.425,
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"start_time": 880.93,
"text": " 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 the one question that that's something that's actually not mentioned very often is that there's a technical problem. We still is still has never really been sorted out is that, um, you know, when you write down this quantum field theory of the standard model,"
},
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"end_time": 936.493,
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"start_time": 906.886,
"text": " It's if you mostly do computations in perturbation theory using Feynman diagrams and that that's kind of a an approximate calculation method. We've know how to make that that works fine. But do we? We also know that you know you. That only works in the limit of kind of extremely small coupling that for for larger couplings, you need a definition of the theory, which is isn't which which works for any coupling and for"
},
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"index": 35,
"start_time": 936.766,
"text": " 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, you'll get that defines the theory. And if you start trying to put the matter particles in with that, that leads to"
},
{
"end_time": 996.118,
"index": 36,
"start_time": 966.954,
"text": " 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 unlike the U-1 and the SU-3, the SU-2 couples differently to left and right-handed spinners. And how do"
},
{
"end_time": 1024.155,
"index": 37,
"start_time": 996.476,
"text": " 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 something that might work, but that's an open problem that's never really been resolved. It's not often mentioned. The problem that has gotten all the attention is that the"
},
{
"end_time": 1044.104,
"index": 38,
"start_time": 1024.599,
"text": " General relativity looks fine as a classical theory, but if you try to quantize it using standard methods, you find this renormalizability problem, you find infinities which you can't be handled in a standard way, and any way you try to handle them just"
},
{
"end_time": 1073.012,
"index": 39,
"start_time": 1045.026,
"text": " Is it going to introduce an infinite number of new constants into the theory or something? 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."
},
{
"end_time": 1103.404,
"index": 40,
"start_time": 1073.473,
"text": " But that's one way of saying it. But another way of saying it is that there are plenty of people who claim that, OK, 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. And 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"
},
{
"end_time": 1133.404,
"index": 41,
"start_time": 1103.763,
"text": " Seriously you take these claims of people you could say either there is 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 string they would like to say the string theory gives you such a thing but yeah, but it may give you kind of an exponentially large numbers of such a thing as depending upon these questions about string vacua, etc. So and every there's"
},
{
"end_time": 1154.36,
"index": 42,
"start_time": 1133.575,
"text": " There's maybe two ways to say the problem. One is that 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. Now I want to start on what"
},
{
"end_time": 1184.053,
"index": 43,
"start_time": 1154.667,
"text": " has been happening since April 1973, when it became clear that what these problems were was more or less immediately obvious. And 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 is 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"
},
{
"end_time": 1213.336,
"index": 44,
"start_time": 1184.309,
"text": " 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. And then, 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"
},
{
"end_time": 1240.845,
"index": 45,
"start_time": 1214.855,
"text": " If you do this, you end up with relations between the 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. Anyway, if you write down the theory for the bigger Lie group, it's just got one coupling constant in it."
},
{
"end_time": 1269.718,
"index": 46,
"start_time": 1241.203,
"text": " And then what you have to do is you have to explain what, why do we see, okay, but why do we see the three, three coupling constants? But, but maybe I was going to come a little bit more to this in later. I mean, this is kind of the problem. The problem is that you have to, if there just wasn't SU five theory, there just would be one number that determined everything. The problem is that we're saying three things and three numbers. So you have to first explain why are we saying three things, not just that one thing. And then once you,"
},
{
"end_time": 1297.193,
"index": 47,
"start_time": 1270.486,
"text": " have a model for why we're seeing the three things that model has to explain, you know, what, how you go from getting that one number to getting three numbers. I see. Does it give you a relation between those three numbers, like some bound or some inequality? 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,"
},
{
"end_time": 1327.449,
"index": 48,
"start_time": 1297.722,
"text": " the so-called gut energy scale, which is like 10 to the 15th GeV, then you're going to see the full SU-5 theory and it just looks like the SU-5 theory. There's some kind of new symmetry breaking scale you had to introduce and above that symmetry breaking scale, you do just have one theory, you have one coupling constant. So everything about the theory above 10 to the 15th GeV is written down in terms of"
},
{
"end_time": 1355.759,
"index": 49,
"start_time": 1327.91,
"text": " These SU5 gauge bosons and one coupling constant. But then you have to 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 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"
},
{
"end_time": 1382.91,
"index": 50,
"start_time": 1356.254,
"text": " You evolve differently as you change energy. Okay. So you often see this graph of these three coupling constants, right? And then, you know, they kind of come together at a point, which is the point where they unify it at this higher, um, what they unified as you file. 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, saying it, when I said you had a certain list of charges that was,"
},
{
"end_time": 1412.739,
"index": 51,
"start_time": 1383.677,
"text": " 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. You have to explain how all 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."
},
{
"end_time": 1441.749,
"index": 52,
"start_time": 1413.183,
"text": " 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. All the known particles fit together into one"
},
{
"end_time": 1472.227,
"index": 53,
"start_time": 1442.381,
"text": " 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. Just as I always said, we know that SU2 cross U1 breaks down, that the vacuum is only invariant under U1. We know that the vacuum can't be invariant under SU5 or SO10, so you have to"
},
{
"end_time": 1502.108,
"index": 54,
"start_time": 1472.398,
"text": " 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 so there's initial I think I know that Georgia and Glashow got very excited about this a lot of people because you know this not only was um 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 some new predictions of some new physics and in"
},
{
"end_time": 1532.619,
"index": 55,
"start_time": 1502.961,
"text": " In specifically, because you're putting this SU2 with the weak force and the SU3, the strong force together, quarks can decay into leptons. And so 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."
},
{
"end_time": 1562.534,
"index": 56,
"start_time": 1533.968,
"text": " And you had a nice calculation of exactly how fast that should happen. And the initial numbers that they got were that this should happen, but very, very slowly. So it was perfectly consistent with the fact that we don't observe protons decay. And so people then started going out and doing experiments looking for this, looking for proton decay at the kind of rates that"
},
{
"end_time": 1590.418,
"index": 57,
"start_time": 1563.046,
"text": " at these things predicted. But then the problem was, and the basic problem since then has been that, well, it turns out protons don't decay. I mean, 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."
},
{
"end_time": 1620.896,
"index": 58,
"start_time": 1590.998,
"text": " So it's not that we found proton decay is just smaller than the rate 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 know, by now, I don't know, I forget the numbers, but it's,"
},
{
"end_time": 1641.749,
"index": 59,
"start_time": 1621.288,
"text": " By now, it's 10,000 or 100,000 times. Anyway, the bound is way above that. Got it. This is definitely wrong. I know that one thing that's true and interesting about Georgia and Glashow is that they actually did give up. Part of the problem with the subject is people don't give up on these ideas."
},
{
"end_time": 1670.794,
"index": 60,
"start_time": 1641.886,
"text": " 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 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,"
},
{
"end_time": 1697.858,
"index": 61,
"start_time": 1671.237,
"text": " ten or fifteen years after this, when the expounders 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."
},
{
"end_time": 1727.995,
"index": 62,
"start_time": 1698.319,
"text": " and you know and they don't really mention very clearly that it doesn't work. Okay then supersymmetry was another another kind of part of our kind of standard paradigm that we've been living with and it also in the earliest standard models written down in April by December people were writing down these supersymmetric extensions of the standard model so let me explain what those are. I mean this can get quite technical but one way of saying the basic idea is to"
},
{
"end_time": 1757.875,
"index": 63,
"start_time": 1728.746,
"text": " If you understand, there's this crucial relation between spinners and vectors that, you know, spinners in some sense are a square root of vectors. 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 is locally looks like a certain vector space of four dimensions and you can translate in any four directions."
},
{
"end_time": 1787.602,
"index": 64,
"start_time": 1758.166,
"text": " and you get corresponding momentum or energy operators. And then 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-Ali algebra. And you get these generators. You should add some new generators which correspond to the spinner direction, which correspond to the spinners."
},
{
"end_time": 1813.575,
"index": 65,
"start_time": 1787.961,
"text": " 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 produce spinors is 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."
},
{
"end_time": 1842.602,
"index": 66,
"start_time": 1813.951,
"text": " 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 Qs, these supersymmetry generators. And you can do that with the standard model. You could also play the same game"
},
{
"end_time": 1864.906,
"index": 67,
"start_time": 1842.927,
"text": " With one of these grand unified theories, you could take your favorite grand unified theory and turn it into a supersymmetric grand unified theory. Okay. And again, so there's a lot of enthusiasm at this. I mean this, a lot of it was also kind of driven by just the beauty of the idea. This, this is a really beautiful idea. If you look at, if you try and do this, you find that these, these cues commute with all of the, um,"
},
{
"end_time": 1894.599,
"index": 68,
"start_time": 1866.152,
"text": " All these does you one cause is you one issue to SU three commutes with these cues. So you find what a cue 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, um, a super partner. It's going to produce a different kind of particle, which has exactly all of the same, um, standard model charges, but it, but it, it has spin differing by a half because, because the, cause it, cause it's, it has a spinner nature."
},
{
"end_time": 1919.087,
"index": 69,
"start_time": 1894.872,
"text": " 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 by spin half and that had the same standard model charges you would"
},
{
"end_time": 1949.172,
"index": 70,
"start_time": 1919.753,
"text": " That would be a good candidate. You would identify them as super partners. Yeah, you'd have two super partners. Anyway, in some sense, I think the problem is you don't see this. 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. Technically, this symmetry acts trivially on everything you know about."
},
{
"end_time": 1976.34,
"index": 71,
"start_time": 1949.667,
"text": " 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 that's kind of what you say. And some people, I guess, would take this enthusiastically. Oh, great. You know, there's all these new particles in the world. I think I and many people were also a little bit. Wait, wait, wait a minute. This is really this is a little bit implausible that this doesn't"
},
{
"end_time": 2004.224,
"index": 72,
"start_time": 1977.312,
"text": " Anyway, that there's this new symmetry, but we haven't kind of seen any of 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 know, it 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 super gravity includes a client."
},
{
"end_time": 2032.483,
"index": 73,
"start_time": 2004.599,
"text": " 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 less"
},
{
"end_time": 2058.439,
"index": 74,
"start_time": 2032.927,
"text": " 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. One thing you might try to do is explain where does that U1, SC2, SC3 come from by"
},
{
"end_time": 2087.398,
"index": 75,
"start_time": 2058.865,
"text": " postulating more that more for more than four space-time dimensions and it's these other so-called you know kind of internal internal dimensions which explain everything and that was 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"
},
{
"end_time": 2116.869,
"index": 76,
"start_time": 2088.097,
"text": " Like you don't have a Graviton at the classical level. Well, you don't have yet. 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 there is a classical version of them."
},
{
"end_time": 2146.476,
"index": 77,
"start_time": 2117.671,
"text": " But the problem is that it's you've you've extended that your standard kind of variables with these these to get very much. You've extended your standard variables with these anti commuting variables. So it's kind of a weird. So classically is kind of a weird subject. It's so you have non commuting classical variables. Yeah, you're not. It's not commuting class. So you can write down such a theory. You can you can look at it, but it doesn't kind of correspond to"
},
{
"end_time": 2174.548,
"index": 78,
"start_time": 2146.749,
"text": " And I mean, 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, which just had different products, which are kind of different, weird algebraic things, which aren't what you're used to thinking about. I see. So, um, now someone like Elaine Conus, would he be comfortable with classical non-commutativity or does he only study quantum non-commutativity? Well, he, I mean, he's, he's more interested. I mean, it's,"
},
{
"end_time": 2204.855,
"index": 79,
"start_time": 2175.742,
"text": " It's non-community activity, but of a very specific sort. It's just a, it's what we, 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, is just something very, very minor that they, they, they pick up my certain things, pick up minus signs when you interchange them. So it's, I think someone like Alan Connor, people do when their people are talking about non-community of geometry,"
},
{
"end_time": 2234.787,
"index": 80,
"start_time": 2205.23,
"text": " They generally mean something much more seriously non-commutative. Some mathematicians often call this super-commutative. The people who do standard commutative geometry, they're used to having these little algebraic gadgets in it which square to zero and which anti-commute. That's also part of their story. Some mathematicians would claim it's really just part of commutative geometry."
},
{
"end_time": 2260.179,
"index": 81,
"start_time": 2235.282,
"text": " What like the non-commutative geometry that Alan Khan 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."
},
{
"end_time": 2289.241,
"index": 82,
"start_time": 2260.674,
"text": " 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, you know,"
},
{
"end_time": 2318.217,
"index": 83,
"start_time": 2289.753,
"text": " We've never seen any extra dimensions. We've never seen anything besides four dimensions. 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 tried to check it, it wasn't there."
},
{
"end_time": 2346.032,
"index": 84,
"start_time": 2318.609,
"text": " 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 can don't really talk about here but maybe one interesting thing is that the first super string theory that would that the idea that it could describe gravity that you could describe gravity using the super string was um first paper about that was like a month after the"
},
{
"end_time": 2374.838,
"index": 85,
"start_time": 2346.527,
"text": " 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 particles at a point and fields based on those point particles, you think about"
},
{
"end_time": 2402.466,
"index": 86,
"start_time": 2375.247,
"text": " Your basic objects of your theory are one dimensional extended objects. And then the idea of the super string theories then was to, it was to bring together all of these things. So they had, they had an E eight gut. They had super gravity as a low energy limit. They had extra dimensions of Calootsa Klein going on. And so that they, they had everything. So, I mean, this was kind of, I think one, one reason this appealed to everybody is, you know, there were all these ideas, which"
},
{
"end_time": 2429.855,
"index": 87,
"start_time": 2403.592,
"text": " 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's gonna go. So that was 1984."
},
{
"end_time": 2455.418,
"index": 88,
"start_time": 2430.026,
"text": " And again, I mean, now 40 years later, there's kind of no, no evidence for any of the components of this or for including for the strings. And it just really hasn't to stick to just kind of experimental statements that there's absolutely kind of zero, nothing anyone has seen of any kind, which, you know, kind of indicates any connection to this stuff. Okay. So, so now maybe I just want to kind of reason for going through all this is partly, you know, I think"
},
{
"end_time": 2483.712,
"index": 89,
"start_time": 2456.032,
"text": " 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, whether it's, anyway, more and more dimensions, whatever. But the problem is that they're doing this for various"
},
{
"end_time": 2511.493,
"index": 90,
"start_time": 2483.933,
"text": " reasons because that you know that it's some larger thing which they can compute maybe there'll be some new symmetries and some new things you can can do but there's no evidence at all for any of the components of this new structure and 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 super symmetry 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 where do you know"
},
{
"end_time": 2531.613,
"index": 91,
"start_time": 2512.09,
"text": " 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 and you have to break all these symmetries. 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"
},
{
"end_time": 2561.118,
"index": 92,
"start_time": 2532.125,
"text": " 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 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"
},
{
"end_time": 2587.244,
"index": 93,
"start_time": 2561.357,
"text": " A theory fails. 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 Georgia and Glashow 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"
},
{
"end_time": 2603.558,
"index": 94,
"start_time": 2587.739,
"text": " structure into this theory or do something this theory that's going to make them 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."
},
{
"end_time": 2633.166,
"index": 95,
"start_time": 2604.462,
"text": " This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state."
},
{
"end_time": 2662.329,
"index": 96,
"start_time": 2633.916,
"text": " At what point does it become more ugly than the beast you were trying to replace? Well, I would argue pretty quickly, but 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, you know, refute 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. But, um,"
},
{
"end_time": 2692.432,
"index": 97,
"start_time": 2662.688,
"text": " 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 kind of why I'm going through all this. Okay. And anyway, and yeah, so this was just more of what I wanted to say on this. And I think what's actually happened is, 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 kind of the most serious people in the subject"
},
{
"end_time": 2721.186,
"index": 98,
"start_time": 2692.841,
"text": " You know, just kind of stopped working on these. They don't go out and say, okay, these things are failures, but they just kind of stop working on them. And if you ask them about it, they say, well, you know, I just don't see how to push this any farther. I still think it's a beautiful idea. I mean, I don't want to put words into it 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"
},
{
"end_time": 2750.623,
"index": 99,
"start_time": 2721.886,
"text": " 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"
},
{
"end_time": 2775.538,
"index": 100,
"start_time": 2751.101,
"text": " Say that it's now thinking about unification is now a lot no longer something a serious person should do because it's it's just hopeless until somebody has a really brilliant new idea until we see some new until the experimentalists help help us out. We're just not going to be able to move forward with this. And this is something I see a lot talking to the theorists and seeing what they say. They really"
},
{
"end_time": 2802.381,
"index": 101,
"start_time": 2776.186,
"text": " 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 that they fact this was the best possible way of doing this that they found and and you know they haven't been able to push it make it work so you know it's just uh"
},
{
"end_time": 2830.06,
"index": 102,
"start_time": 2802.978,
"text": " What are you going to do? Well, you mean to say unification attempts outside of string theory or to not even consider string theory unification? Well, I mean, the string theory then becomes a complicated question. What would you mean by string theory? But I guess one way to 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"
},
{
"end_time": 2855.623,
"index": 103,
"start_time": 2830.623,
"text": " That has been the paradigm that we've had for 50 years. And so the question is, 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 going to tell you about it. I mean, that that's a hard sell. I think because people say, well, wait a minute, you know, we're 50 years for 50 years. This is,"
},
{
"end_time": 2883.763,
"index": 104,
"start_time": 2856.049,
"text": " 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? It's like these crackpots who tell us that Einstein must be wrong. It's always been a hard sell to say, look, everything you've been doing for all this time, 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."
},
{
"end_time": 2910.282,
"index": 105,
"start_time": 2884.138,
"text": " 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 we have to go all the way back to 1973 and look at different things, not the things that we started looking at back"
},
{
"end_time": 2939.906,
"index": 106,
"start_time": 2912.193,
"text": " 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 SU five 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, yeah, no. So that's always a question. Yeah. At what point do you, um,"
},
{
"end_time": 2967.432,
"index": 107,
"start_time": 2940.333,
"text": " Yeah, did you give up an idea? Did you say it? And in some sense, I mean, my argument with the string theorist always was from the beginning that, you know, my judgment of what's going on is you guys, you know, this is a good, you really have to give up. This is something which hasn't worked out. Their argument was, well, you know, we still think it's the best thing we know how to do. We still think it's worth pushing forward. So it was kind of a, you know, it's kind of hard to argue about that. But, um,"
},
{
"end_time": 2992.432,
"index": 108,
"start_time": 2967.995,
"text": " I think things have changed over the last 20 years. It's just become clearer and clearer that this stuff just doesn't work. 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. Now you ask people talk about, well, it may take 500 years for us to make any progress on this."
},
{
"end_time": 3016.664,
"index": 109,
"start_time": 2992.688,
"text": " This is taking longer than I thought. 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 you've gone through the state of physics since 1915 to the 1970s and then to the present day."
},
{
"end_time": 3046.254,
"index": 110,
"start_time": 3017.346,
"text": " I haven't really explained a lot about it. 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. OK, so now there's a much shorter and much sketchier part, which is to kind of 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."
},
{
"end_time": 3075.179,
"index": 111,
"start_time": 3046.903,
"text": " You know, I worked on doing these lattice calculations of using SU3 gauge theory and the calculations just use 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, you know,"
},
{
"end_time": 3104.667,
"index": 112,
"start_time": 3075.674,
"text": " Matter particles are these spin one half, the spin geometry is really weird. It's a very, it's not at all obvious, you know, how to capture that geometry and, you know, while how to preserve any of that geometry when you discretize things. And, you know, 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, and I had some kind of vague, very, very vague version of the idea I'll be talking about."
},
{
"end_time": 3127.381,
"index": 113,
"start_time": 3105.333,
"text": " 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 this subject says that this just is not going to work. This is implausible. You can't make that happen."
},
{
"end_time": 3154.804,
"index": 114,
"start_time": 3127.978,
"text": " Everything you know about the subject forbids you putting fermions on the lattice? No, no, we'll see. I'm going to make a certain claim 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 the way spacetime and symmetries work is clear enough that you just can't have"
},
{
"end_time": 3181.732,
"index": 115,
"start_time": 3155.35,
"text": " What I'm going to, what I'm going to, I now believe happens. I had convinced myself could not possibly happen. And so, anyway, just some history of my own personal history. And it's within the last three or four years though, that I finally, you know, thinking about this some more and also a lot that I've learned actually by teaching, 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"
},
{
"end_time": 3209.94,
"index": 116,
"start_time": 3182.432,
"text": " These 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 that you would see once you wrote down the details of Of how these symmetries worked and then what I just found is I started writing down the details and learning more is that just wasn't there You know, it really wasn't wasn't there and um, and then I finally Started thinking about it in very in different ways. I started to see that. Wait a minute. This actually looks there's a perfectly"
},
{
"end_time": 3238.951,
"index": 117,
"start_time": 3210.282,
"text": " Coherent way of thinking about what I thought couldn't possibly happen. There was there's now perfectly good reasons to believe that it that it could happen Sorry, and that occurred to you while you were writing the book on quantum theory and representations. Um, yeah more later after that was done and and yeah, but but yeah So 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 but but I've also taught that course several times so it's I've"
},
{
"end_time": 3268.916,
"index": 118,
"start_time": 3239.599,
"text": " 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. 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 mind, 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,"
},
{
"end_time": 3289.718,
"index": 119,
"start_time": 3269.445,
"text": " Let's get to the approach that seems promising."
},
{
"end_time": 3319.65,
"index": 120,
"start_time": 3290.077,
"text": " As this is the hugest tease that I just kept asking you questions. That's my fault. You left the audience hanging. I'm sorry, you're not going to get a detailed answer to this anyway, but you'll see. First of all, to put this in the context of what I was talking about already, is to say that this has about four dimensions. No extra dimensions, four dimensions. The idea is that there are no extra dimensions."
},
{
"end_time": 3349.531,
"index": 121,
"start_time": 3319.838,
"text": " 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? There's a lot of very interesting things that happen only in four dimensions. And can we use those? And 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. And they're very, very tied to four-dimensional geometry. They really are."
},
{
"end_time": 3376.118,
"index": 122,
"start_time": 3349.787,
"text": " Roger Penrose has been, but, and there's, there's part of the whole story of the spinner. Yes. But so, so that's, but the, the other thing which I'm trying to use, which, which hasn't really been used very much. I think one thing to say about all of this, all the, there's a story that I told you, if you go and look at any of those books about any, any of those, these guts or super symmetry or super gravity or string theory, um,"
},
{
"end_time": 3404.172,
"index": 123,
"start_time": 3376.561,
"text": " You'll find one strange thing if you start to dig into the technicalities. Our space-time has this so-called Minkowski metric. You put a minus sign on the distance squared in time. 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. What you do is you"
},
{
"end_time": 3435.299,
"index": 124,
"start_time": 3405.35,
"text": " 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 if you look at all the literature on all the theories I've been talking about, there's really, in every case, it always is like kind of a technical problem about, wait a minute, don't we need to do this in Euclidean signature? Are we doing it? How is it going to go from one to the other? And it's kind of a technical problem, which was,"
},
{
"end_time": 3463.029,
"index": 125,
"start_time": 3436.032,
"text": " There for all of these theories, but no, but people just kind of tried to avoid thinking about it. There was always a feeling, okay, this is some technicality, you know, maybe some mathematician will figure it out. We don't care. We're just going to write down formulas and hope for the best. But I was, this is something that it really struck me that you really, this relationship between Euclidean and Caustic exchanger was a really interesting topic. It was indicative of something."
},
{
"end_time": 3492.961,
"index": 126,
"start_time": 3463.2,
"text": " Well it was something it was something we really don't understand i mean it always in my mind i mean there's we had the standard theory there are parts of it that i look at it 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 this this wick rotation was"
},
{
"end_time": 3518.677,
"index": 127,
"start_time": 3493.831,
"text": " a place that was at that happens in the standard model. So anyway, so the main, the main new idea is to say what I'm trying to do is, is to claim that this, that this wick rotation, you know, if you think about your geometry in terms of spinners, it changes the geometry, the spinners in a very fundamental way that the geometry of spinners and Euclidean signature and the geometry of spinners and Caskey's signature is actually quite different."
},
{
"end_time": 3549.241,
"index": 128,
"start_time": 3519.599,
"text": " 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 Minkowski 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"
},
{
"end_time": 3579.684,
"index": 129,
"start_time": 3549.684,
"text": " Unification of internal and space space time chemistry. 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 it but it's the new thing is to say wait a minute is to say look you really should think about what's going on and add the 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 um, okay and cascade Euclidean"
},
{
"end_time": 3609.991,
"index": 130,
"start_time": 3580.111,
"text": " 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,"
},
{
"end_time": 3620.811,
"index": 131,
"start_time": 3610.572,
"text": " create an oscillation."
},
{
"end_time": 3647.244,
"index": 132,
"start_time": 3621.118,
"text": " 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 four 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 let me go on."
},
{
"end_time": 3677.056,
"index": 133,
"start_time": 3648.336,
"text": " This was just kind of an overall. And let me see how much I can do with that. OK, so let me just first. Yeah, so this is so we're quotation. So another way of getting this minus sign on the square is to change from, you know, put in a factor of the score to minus one. So what this is. So we're quotations, but what you're supposed to be doing is you've got."
},
{
"end_time": 3707.841,
"index": 134,
"start_time": 3678.08,
"text": " a time variable and it's saying okay you can you can make the time variable complex and then look at look at look at a theory where that your time has become purely imaginary okay and then that minus sign there which is is going to when you multiply this by itself the two factors of i are going to are going to cancel that minus sign and you're going to everything is going to be plus so there's so the idea is that there's also is so i sometimes i refer to this as"
},
{
"end_time": 3729.224,
"index": 135,
"start_time": 3708.422,
"text": " 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 the simplest version of liquid rotation."
},
{
"end_time": 3754.633,
"index": 136,
"start_time": 3729.343,
"text": " Here's the problem when you try and do this in quantum field theory. How are you going to do this? This starts to get a bit technical, but in 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, then what happens is that the"
},
{
"end_time": 3781.732,
"index": 137,
"start_time": 3755.657,
"text": " These fields in this Heisenberg picture, if you change time on them, you're conjugating by the Hamiltonian operator. That's the Heisenberg picture. What this is saying is that if you try to go to imaginary time, if you make imaginary time on zero, you're going to conjugate by this operator the exponential of the imaginary time times the Hamiltonian."
},
{
"end_time": 3808.029,
"index": 138,
"start_time": 3782.244,
"text": " 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, but which goes off to infinity at 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, either the"
},
{
"end_time": 3837.261,
"index": 139,
"start_time": 3809.036,
"text": " Tau times h and e to the minus tau times h and if tau is positive this one is going to make sense because it's e to the minus something positive times something positive whereas 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 so there's just a fundamental issue in it which everything we know about quantum field theories and the operator formalism you can't"
},
{
"end_time": 3862.722,
"index": 140,
"start_time": 3837.807,
"text": " 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 what's going to happen to the field just don't make any sense. You can't do it. So that's what happens in the operator formalism. But the other formalism you have for writing down"
},
{
"end_time": 3893.575,
"index": 141,
"start_time": 3863.66,
"text": " Quantum field theories has the opposite behavior. If you write them down as path integrals, if you go to imaginary time, this 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 the"
},
{
"end_time": 3922.005,
"index": 142,
"start_time": 3894.411,
"text": " 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. So these two kind of formalisms we like to use to do quantum field theory, they have opposite. People will talk about them as if you can use them to go between imaginary"
},
{
"end_time": 3952.227,
"index": 143,
"start_time": 3922.432,
"text": " 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?"
},
{
"end_time": 3982.176,
"index": 144,
"start_time": 3953.473,
"text": " Our 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 want to understand how to get, how to go back and forth, you know, we don't have a theory that does that. I see. Yeah. So we, we don't, there, 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"
},
{
"end_time": 4009.804,
"index": 145,
"start_time": 3982.927,
"text": " where you can, 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. But if you try to, you start with either one and get to the other,"
},
{
"end_time": 4040.179,
"index": 146,
"start_time": 4010.606,
"text": " You can't, it just doesn't work. But there is something you can do. So you can't analytically continue the theory. So you can't take your operators, states, measures, and 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 of two operators at two different spacetime points."
},
{
"end_time": 4069.275,
"index": 147,
"start_time": 4040.64,
"text": " 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, things dependent on X and Y and, and they're these kind of carry most of the information about the theory in them. So if you have an operator theory, you can, you can compute these objects and you can characterize the theory, a lot of the theory by these objects. And they're kind of,"
},
{
"end_time": 4095.043,
"index": 148,
"start_time": 4069.65,
"text": " Mean the operators don't commute. So this, this thing is not symmetric and X and Y. If you interchange X and Y, you're going to get something different. They're, they're also technically these are distributions or 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 an operator formalism."
},
{
"end_time": 4125.009,
"index": 149,
"start_time": 4095.35,
"text": " And then in the imaginary time and the pathological formalism, you can take similar things, which are moments of these. Anyway, similar pathologicals are kind of moments of these measures. 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."
},
{
"end_time": 4154.957,
"index": 150,
"start_time": 4125.452,
"text": " These measures and these integrals and they they look a lot more like what you do in statistical mechanics and and actually they're really kind of one of the amazing things about this whole story is that if you 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 you know given by beta is equal to one over a k times the time so it's a very different"
},
{
"end_time": 4177.073,
"index": 151,
"start_time": 4155.64,
"text": " The path integral formalism really is much more like a 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. Okay, now let's get to SO4. I'm interested how you break it to Lorentz."
},
{
"end_time": 4207.705,
"index": 152,
"start_time": 4177.824,
"text": " 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 Schringer 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"
},
{
"end_time": 4235.282,
"index": 153,
"start_time": 4208.097,
"text": " complicated things without telling, which I can't tell you anything about, but you can do this. And 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 kind of, which just kind of reflects you in that direction. And that's called the Osterwalder Schrader reflection. And, and you could, you can, 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."
},
{
"end_time": 4264.565,
"index": 154,
"start_time": 4235.657,
"text": " 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,"
},
{
"end_time": 4283.763,
"index": 155,
"start_time": 4264.821,
"text": " 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 formational symmetry and pick a distinguished direction. You have to do that."
},
{
"end_time": 4311.391,
"index": 156,
"start_time": 4284.121,
"text": " 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 weight. There's the Wojtyn problem of time. Well, these are imaginary times, so it's a different thing. But this is what it took me a long time to realize and what was kind of the maybe the 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"
},
{
"end_time": 4339.36,
"index": 157,
"start_time": 4311.681,
"text": " have operators in 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"
},
{
"end_time": 4362.449,
"index": 158,
"start_time": 4339.974,
"text": " Mysterious and there isn't really any kind of convincing. Well, anyway, there's a there's some early papers on it but there's really a lot of people have tried to figure this out, but Anyway, not what to say but but I my basic proposal now is it's something really unexpected happens right here that um what was a space-time symmetry in the Euclidean QFT becomes an internal simply in the classical QFT exactly because of the"
},
{
"end_time": 4392.278,
"index": 159,
"start_time": 4362.858,
"text": " 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 Kavsky and Euclidean space-time. But the basic idea is that in Euclidean space-time,"
},
{
"end_time": 4422.312,
"index": 160,
"start_time": 4392.944,
"text": " 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 spinors that are either, they're these C2, 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."
},
{
"end_time": 4451.852,
"index": 161,
"start_time": 4423.814,
"text": " And then 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 made, 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"
},
{
"end_time": 4478.865,
"index": 162,
"start_time": 4452.108,
"text": " 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 SU-2. And Minkowski's spacetime vectors are tensor products of two kinds of spinors, but they're the vial spinors times their conjugates. So the point is these are just two kind of completely different things. And now just to"
},
{
"end_time": 4509.462,
"index": 163,
"start_time": 4479.548,
"text": " This is where I'm starting to run out of steam here, but maybe just kind of a last kind of important thing to explain which people, 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 Lorentz Iberian things by putting together a vector"
},
{
"end_time": 4538.183,
"index": 164,
"start_time": 4509.94,
"text": " and a dual vector, and you contract and you get 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 they're doing, but that's just not true. I mean, the Dirac operator is not a scalar. 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."
},
{
"end_time": 4567.671,
"index": 165,
"start_time": 4538.695,
"text": " 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"
},
{
"end_time": 4597.654,
"index": 166,
"start_time": 4568.08,
"text": " Draca operator behave under Lorentz transformations. I mean, you know, they're writing down formulas. So they're, you'll see that there's a non-trivial transformation formula. They'll write it down. But the, um, if you try and people that 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 Draca operator is not what the notation makes it look like, which is, which, which just makes it look like a scalar. It's a vector. And if you understand,"
},
{
"end_time": 4627.176,
"index": 167,
"start_time": 4597.875,
"text": " and spinners. It's just a vector and it's maybe a little bit easier if, anyway, it's so the rock writer is just a vector. And that's rarely, if anywhere, said though, that the formulas people are writing down just, they say that, but it's not the way people think. This is, now I'm finally getting to the, maybe to the last, to the end of this, where this will become completely incomprehensible, but"
},
{
"end_time": 4656.101,
"index": 168,
"start_time": 4627.637,
"text": " So if you try and think about what is Rick rotation, you try and think about it as analytic continuation from Minkowski to Euclidean space time. You would, the standard way of doing that is thinking about complex space time, making not just time complex, but all of space and time complex. And then you say, so it'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 SL two C's."
},
{
"end_time": 4686.118,
"index": 169,
"start_time": 4657.022,
"text": " 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 rotation is then this analytic continuation in this complex space time."
},
{
"end_time": 4699.753,
"index": 170,
"start_time": 4686.63,
"text": " 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 work rotation, I'm not going to do work rotation by this analytic continuation that that actually"
},
{
"end_time": 4727.415,
"index": 171,
"start_time": 4701.084,
"text": " doesn't work or doesn't do what I want to do. But I am going to do wick rotation starting with the Euclidean story and doing this reconstruction of the real time theory. And I need an appropriate Osterwalder Schrader reflection for spinner fields. 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,"
},
{
"end_time": 4754.923,
"index": 172,
"start_time": 4727.927,
"text": " 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's language corresponding to the different directions. Well, there is a distinguished gamma matrix corresponding to the imaginary time direction and that interchanges left and left and right."
},
{
"end_time": 4774.94,
"index": 173,
"start_time": 4755.162,
"text": " If you hit a left-handed spinner with it, it gives you a right-handed spinner. Exactly, because it's a space-time vector. Exactly. So it takes one to the other. And so what gets RIC-rotated in quasi-space-time is not this tensor product of left and right-handed spinners in"
},
{
"end_time": 4801.22,
"index": 174,
"start_time": 4775.247,
"text": " Euclidean space, but something where you've hit one of them with a gamma zero. So vectors in Minkowski's spacetime are really should be thought of as tensor products of two right-handed spitters. So the geometry in Minkowski's spacetime is not what you thought it was. It's not the analytic"
},
{
"end_time": 4816.186,
"index": 175,
"start_time": 4801.476,
"text": " continuation you thought it was, it's something different."
},
{
"end_time": 4845.879,
"index": 176,
"start_time": 4816.647,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal. Rankings based on root, metrics, root, square, report data to 1H2025. Your results may vary. Must provide a post-paid consumer mobile bill dated within the past 45 days. Bill must be in the same name as the person who made the deal. Additional terms apply. 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"
},
{
"end_time": 4875.828,
"index": 177,
"start_time": 4846.032,
"text": " tensor products of different kinds of spinners. Those are all the kind of thing that goes into discussions of the supersymmetry. I mean, I'm doing something a bit different. 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? Anyway, you'll find a very, very confusing literature, let's just say."
},
{
"end_time": 4904.94,
"index": 178,
"start_time": 4876.357,
"text": " But anyway, so this is just to explain that the body so this is actually we're at the 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 um you know when you're in Euclidean space-time you've got vectors interesting vectors are tensor products of left and right but when you do wick rotation"
},
{
"end_time": 4932.295,
"index": 179,
"start_time": 4905.742,
"text": " You just have right times right. 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. The slogan is that as far as space-time symmetry is concerned, you're just dealing with right-handed spinners. These left-handed spinners that you had before you wick-rotated"
},
{
"end_time": 4960.657,
"index": 180,
"start_time": 4932.927,
"text": " 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 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? That's just a matter of convention. So, I mean,"
},
{
"end_time": 4990.52,
"index": 181,
"start_time": 4961.067,
"text": " What I call left and right is a matter of convention. The 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 or whatever, that standard formalism is kind of left-right symmetric and it's actually set up to work very nicely"
},
{
"end_time": 5019.684,
"index": 182,
"start_time": 4991.067,
"text": " When you've got parity invariant theories, which theories, which you can interchange left and right. Um, so you, you have to kind of add some things into that formalism to kind of project out whenever you have. Yeah. So anyway, so, but, but yeah, but, but, 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."
},
{
"end_time": 5049.053,
"index": 183,
"start_time": 5020.162,
"text": " When you write down twisters, you say that points in space-time basically are spinners, but they're spinners of one kind. Again, they're just the right-handed spinners. Twister geometry also has this, in an interesting way, the same kind of aspect that it's left-right asymmetric and you have to take one of them as a fundamental thing. It's telling you what the points are."
},
{
"end_time": 5077.278,
"index": 184,
"start_time": 5050.196,
"text": " But I'm doing something different than the usual twister story because I'm treating vectors differently than what's going on in a picture. 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? So this is just a part of"
},
{
"end_time": 5103.2,
"index": 185,
"start_time": 5077.739,
"text": " Well, maybe let me try to answer them in order first. So first, we know how to write down general relativity as kind of a gauge theory of formalism. And that SU2 right, so you can write down gravity. And this is something which"
},
{
"end_time": 5133.439,
"index": 186,
"start_time": 5104.087,
"text": " If you look at the people who do loop quantum gravity and they talk about things called Ashtakar variables. Well, they, um, so, so gravity written in terms of Ashtakar variables is written down in this very asymmetric way. And the, and it's starts to become a long story, but, but one, one way of saying it is that I had these two SU2s, SU2 left and SU2 right. SU2 left."
},
{
"end_time": 5153.507,
"index": 187,
"start_time": 5133.797,
"text": " is an internal symmetry. That's the theory of the weak interactions. SU2 right is a space-time symmetry and gauging that is basically how you get general relativity. You gauge that, but then you also have to tell me what you're going to do with the vectors, but if you tell me what you're going to do with vectors and you gauge that SU2,"
},
{
"end_time": 5177.91,
"index": 188,
"start_time": 5154.121,
"text": " 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"
},
{
"end_time": 5203.37,
"index": 189,
"start_time": 5178.387,
"text": " 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 just to say it is that this is there there are a lot of things about"
},
{
"end_time": 5233.49,
"index": 190,
"start_time": 5204.326,
"text": " about this Euclidean Twister Unification Proposal thing, 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 are going on that are, 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,"
},
{
"end_time": 5261.049,
"index": 191,
"start_time": 5233.797,
"text": " 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've, I keep trying to write up a better version of the, 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 stopped writing and start doing some of it. So it's, it's, um, I see it's an, it's an ongoing process. And so, so sooner or later I'll,"
},
{
"end_time": 5290.418,
"index": 192,
"start_time": 5261.783,
"text": " There are no technical details here. 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 at the details for myself. 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 month or two."
},
{
"end_time": 5320.913,
"index": 193,
"start_time": 5291.374,
"text": " It seems to come together really nicely, but it's very, very much not written up. And if I try and write it up, I may find that this isn't quite the right thing to do either. 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 this 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,"
},
{
"end_time": 5348.951,
"index": 194,
"start_time": 5321.186,
"text": " To write up something about those pieces there, which so it's it's avoids being kind of a formal Completely coherent paper, but at least 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 I think I guess I've started to realize I should say maybe when a lot of the stuff first occurred to me I thought okay. This is really cool. This is I"
},
{
"end_time": 5361.425,
"index": 195,
"start_time": 5349.172,
"text": " The more I think about it, the more this works."
},
{
"end_time": 5389.65,
"index": 196,
"start_time": 5361.817,
"text": " Nobody really seems to understand what I'm talking about or, or be getting very interested. So, uh, the, the last thing I'm worried about at this point is people coming in and swiping my ideas. I'll be, uh, I'd be very glad if anybody who wants to kind of try to swipe into the ideas and, and it was interested in doing something with them, please, yeah, please go ahead. Right, right. At least they care. Okay. Yeah. So when I, yeah, I actually want, uh,"
},
{
"end_time": 5417.722,
"index": 197,
"start_time": 5390.213,
"text": " Also thank you to our partner, The Economist."
},
{
"end_time": 5437.073,
"index": 198,
"start_time": 5419.974,
"text": " Firstly, thank you for watching, thank you for listening. There's now a website, kurtjymungle.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."
},
{
"end_time": 5461.391,
"index": 199,
"start_time": 5437.261,
"text": " Now a direct mailing list ensures that I have an untrammeled communication with you. Plus, soon I'll be releasing a one-page PDF of my top ten toes. It's not as Quentin Tarantino as it sounds like. Secondly, if you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself"
},
{
"end_time": 5478.712,
"index": 200,
"start_time": 5461.391,
"text": " Plus, it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm, which means that whenever you share on Twitter, say on Facebook or even on Reddit, etc., it shows YouTube, hey, people are talking about this content outside of YouTube."
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{
"end_time": 5508.131,
"index": 201,
"start_time": 5478.899,
"text": " which in turn greatly aids the distribution on YouTube. Thirdly, there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, they disagree respectfully about theories and build as a community our own toe. Links to both are in the description. Fourthly, you should know this podcast is on iTunes. It's on Spotify. It's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from rewatching lectures and podcasts."
},
{
"end_time": 5528.063,
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"start_time": 5508.131,
"text": " I also read in the comments"
},
{
"end_time": 5551.544,
"index": 203,
"start_time": 5528.063,
"text": " and donating with whatever you like there's also paypal there's also crypto there's also just joining on youtube again keep in mind it's support from the sponsors and you that allow me to work on toe full time you also get early access to ad free episodes whether it's audio or video it's audio in the case of patreon video in the case of youtube for instance this episode that you're listening to right now was released a few days earlier"
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{
"end_time": 5558.131,
"index": 204,
"start_time": 5551.544,
"text": " Every dollar helps far more than you think either way your viewership is generosity enough. Thank you so much"
}
]
}No transcript available.