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Stephon Alexander on The Autodidactic Universe, String Theory, Matrix Models & Cherns-Simons Gravity
January 19, 2022
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
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Where senior editors argue through the news with world leaders and policy makers in twice weekly long format shows. Basically an extremely high quality podcast. Whether it's scientific innovation or shifting global politics, The Economist provides comprehensive coverage beyond headlines. As a toe listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount.
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If you're merely listening to this podcast on Spotify, iTunes, etc., then you'll miss out on the equations being written, so see the link in the description for the YouTube video.
While you're clicking there, it would be great if you left a review, as I didn't find out until recently. Reviews radically help the promulgation of the podcast. Thank you in advance. Now for an extra quick note. Quick note before the podcast begins. What I found is that people who criticize string theory generally aren't physicists who have looked at the derivations of the equations of string theory, and thus they're simply parroting their criticisms from others by calling it quote unquote disconnected from reality and quote unquote a theory based on pure beauty.
The beauty of string theory is evident when one studies it. And it's also false to say that string theory hasn't produced any physics. String theory is a true contender for a theory of everything, much more so than even loop QG, which is merely a theory of quantum gravity. This year, I'll be exploring the flavors of string theory, such as type 2a, type 2b, with acute depth to give a sense of the naturalness of the equations. Personally, I think the word natural is more fitting than the word beautiful. Now onto the podcast introduction.
Professor Stefan Alexander is a theoretical physicist and a cosmologist at Brown's University, in addition to being a prolific musician. In this episode, we cover his theory of everything called the autodidactic universe, a model he developed in conjunction with Lee Smolin, as well as a few other luminaries listed here. The laws of physics can be approximated by matrix models, we talk about this, and machine learning deals well with matrix models, so a natural question arises, is there a relationship between the two?
Can the universe learn its own laws in a manner analogous to unsupervised learning, let's say, of a restricted Boltzmann machine? Click on the timestamp in the description if you'd like to skip this intro. For those new to this channel, my name is Kurt Geimungel. I'm a filmmaker with a background in mathematical physics, interested in explicating what are called theories of everything from a theoretical physics perspective,
but as well as delineating the possible connection consciousness has to the fundamental laws of the universe, provided these laws exist at all and are knowable to us. Generally, conversations on physics and consciousness tend to stay at a cosmetic level, not going past or rarely moving past even the double slit experiment or the Stern-Gerlach experiment. In these podcasts we tend to delve into intricacies, into equations,
Sometimes into meticulous technicalities and so forth because number one it's tedious to hear about the measurement problem for the 25th time Number two because it seems like the language or large part of the language at which the universe expresses itself is Mathematical then if one wants to understand the most profound enigmas of the universe some mathematical facility is necessary and number three because you can handle it and
Most of the time, I find that the public purveyors of science simplify overly so, because they're still assuming that you're the average passive listener of, say, cable news. But what I found is that there's not only a hunger for in-depth specialized conversation on these seemingly abstruse topics, but that the intelligence of the average listener, perhaps even the average person, has been
vastly underestimated. That is, there's a thirst, so that's like curiosity, and then there's the ability to quench that thirst, and that's something like intelligence or astuteness. Mainly, people have focused on the curiosity aspect while neglecting the brightness of you. If you'd like the notes from this podcast in PDF form, then check the description. There's also links to the Discord where conversations occur on psychology, consciousness, and physics. And there's a link to the Patreon, that is patreon.com slash Kurt Jaimungal,
If you'd like to support this channel, there would be almost no way for me to have conversations of this fidelity on the topics of consciousness, theoretical physics, string theory, loop, even geometric unity, which I'll tackle at some point. If I wasn't able to do this full time, the sponsors and the patrons are what allow for that. So thank you so much. Again, that's patreon.com slash Kurt Jaimungal C-U-R-T-J-A-I-M-U-N-G-A-L.
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Thank you and enjoy this conversation with Stefan Alexander. I've been looking forward to this for quite some time. Same here. So Brian told me that I should look into you and at first I just thought you were not interested in theories of everything, just a physicist working in some particular field of physics. But it turns out that what you're interested in is almost exactly what this channel is interested in, namely theories of everything. You also surmise about consciousness, but that's more in your book.
So we'll talk about the autodidactic universe. We'll touch on some of Chern Simon's modified gravity. I went back and read one of your seminal papers, Inflation Brain Annihilation from around 2001. Oh, yeah. My little strength theory days. Yep. And then quantum cosmological constant. I only got to skim that briefly. Okay. Do you have any questions for me before we get started?
Let's dive in. The way that this is meant to be treated is as if you have an imbecile across from you in office hours, who's extremely curious. So I'm going to be asking you, can you define this term, this term, this term? Office hours, forget about an external audience. Okay, gotcha. Okay, that sounds like that sounds like the problem is that I'm probably going to be the imbecile, but that's okay. Okay, well, why don't you give the audience an overview of your autodidactic universe theory?
Sure. Well, the theory was started by, for a couple of years of conversations between, it starts roots with independent conversation that Lee Smolin and my friend, colleague Jaron Lanier, the virtual reality pioneer, we've been, all three of us have been friends for a long time. So we, as with
We have our side chats. We talk over the years about things, about matters that are scientific or not scientific. And over the years, our conversation all coalesce into this thing about whether or not, well, first of all, Lee and John has over the years had their own side conversations about
whether physical laws can learn, physical systems could learn their own laws, that type of idea, and use an idea, some evolutionary theory. I kind of came in at it with Jarron and also Lee separately, thinking about fundamental theories, like theories of quantum gravity or unified theories, and just looking at them structurally, that the observation is that
You know, one interesting fact is that if you look at, for example, string theory and you look at loop quantum gravity and you look at other approaches to quantum gravity, even the original ideas of super membrane theory, the idea that the fundamental degree of freedom is really a membrane, not a string. And when people tried to quantize this membrane, they ran into problems and they found out that
Oh, look at this. This membrane theory could be properly quantized if you turn it into a matrix theory. So at the end of the day, all these approaches of quantum gravity pointed to matrix theories. And what do I mean by matrix theories? I'm sure you might want to know that.
So as far as I understand, I'll just tell you and then you can correct me because it helps me learn. Especially because I put myself on the line, my ego on the line, and I learn better. Okay, so as far as I understand with the matrix models, you just mentioned that it solves a particular issue, but another issue is created in that they're finite dimensional and what you want to do is take n to infinity. Is that correct? One of the things you can do to make contact with the continuum, for example,
Yang-Mills like theories, which are, is that, yes, right, when you take n, where n is the rank of the matrix, so if n is two, I have a two by two matrix. So when n goes to infinity, the rank goes to infinity, that it does reduce back to known theories like Yang-Mills theories, for example.
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That's a good question. It's similar to when you
You do a Fourier series, you take that sum and you look at basically the sum of sines and cosines, and then when you take basically n in that sum to infinity, that becomes the integral sign. So it's similar to the continuum hypothesis. I see. Okay, continue. Yeah, no pun intended. Yeah, so
So in a nutshell, the observation that I made with Lee Smolin and Lee made with me is that how interesting matrix models seem to underlie a couple of what we thought to be disparate approaches to quantum gravity or unification. Strain theory, loop quantum gravity, and other ways, you know, random matrix models, they all kind of seem like membrane theory.
They all pointed these matrix models. So maybe we should take more seriously that the matrix models themselves might actually be, well, not actually be, I mean, Banks, Fischler, Schenker and Susskind, so-called BFSS, and I think IKKT named after some Japanese theorists, actually conjectured that M theory, which is supposed to be the unification of all string theories,
m theory, or the so-called non-perturbative definition of string theory, it was hypothesized to be a matrix theory. So we weren't saying anything new there, but to maybe extend that, extend it beyond even m theory, to say that other approaches of quantum gravity might also have this. So that was one observation. The second observation that me, Jarn, and Lee made was that if you look at the equations of a matrix model,
It has a semblance to artificial neural network. It might be useful for me to write something.
And I'm going to be very schematic here, because I'm writing from memory. So just recall that an artificial neural network basically tells me that if I have a simple two-layered, if I have an input, so here's my x. So x is a vector. It's an n-tuplet, right?
I can, you know, that think of each point here, each dot is a neuron that could be connected, you know, in a forward way, right? I can have connection to, let me call this thing. Right. Right. So, oops, my bad. I don't know why it's doing that. Are you able to hear anywhere it sounds? Yep. No, no, no. Okay. I just want to get right here. So the equation says that if I, if I, there's some output
y, right? And there's a weight matrix that determines how correlated, how connected these neurons are. So, for example, x1, right? If I have x1 and then I have y1, for example, right? This wij will denote basically this is xj and this is yi.
Right. So this basically tells me how every neuron is connected. You know, the output is connected to the input. Right. And then, of course, there's some bias term here that basically helps out with to further basically, you know, to help with bias and these connections. All right. So that's there's a long story here about neural networks.
This is very similar to statistical inference. If I basically have in this case a line and I tell you the slope of the line, I can adjust the slope of the line basically to fit some data. Given an input
The output will basically sort of maximize or the slope will basically maximize. In this case, if you try to get the best standard mean, you can basically use this. This is a multi-dimensional version of statistical inference. I see. I see. OK. OK.
The matrix, so what I'm going to take notice of here is that mathematically, I'm basically performing some kind of linear transformation from one vector to another vector. And the weights basically is this transformation matrix. That's one way I like to think about it, right? Okay. Okay. So in a matrix model, what we have is something similar
Not similar, but what we have is a situation where we have... So the analogy, first of all, let me spell out the analogy. The analogy is instead of having neurons that are represented by vectors, the idea here is that we have matrices
which are basically tensor products of vectors. So in other words, I can, for example, I could take the tensor product of say two vectors, Xi, tensor Xj, right? And then I can have a matrix Xij, right? So likewise, I can have some correspondence where the equation of an artificial neural network, which is mapping the idea of a perceptron or an artificial neuron, is represented as a vector.
The idea here is that the matrices, right, there's a sense in which I can isolate some components of this matrix and I could freeze and this freezing procedure again is spelled out in the paper and it's a long story, but I just want to spell out the basic idea. I can basically isolate vectors in this thing, in this matrix model. What do you mean when you say you can isolate them?
Okay, so let me let me say another thing here. You mean like how they can be decomposed and then you just pull out one of them? Yeah, yeah. So let me let's so in the matrix models, what we have is basically is let me actually write down one of these matrices. Okay. X. So it's x, a seven, x, i, m, n. So okay, what is this thing, right? So basically,
It's basically, let's say that I runs from one to three for now, right? So this would be X1, X2, X3, and then I'll still have MN here. Right? So, so one thing I could do here is assume that MN is, say, completely diagonal, right? So I can basically
make some approximation and collapse this MN, right, into some X. So in other words, here's X MN, right. And what I now want to do is basically only look at these components here, the diagonal components. Okay. I can play with that for now. And then, you know, just look only at the diagonal components of this MN matrix. And there's something that allows you to say that it's diagonalizable.
Yes, there's something that allows me to say that. Right. Um, and so that's, that's, that's one, that's one thing you can do, but there are other, you know, one of the things that we are currently working on as we speak in the follower paper is exactly how to turn this thing into a, you know, um, into a bona fide, um,
into a bonafide learning architecture, similar to artificial neural network. But the upshot is that if you look at the equation that I wrote,
Okay, those matrices from when I was reading your paper, if I understand correctly, it's something like the BFSS matrix models. But then what I was wondering is, and this is my rudimentary knowledge that the more general form of BFSS is BMN. And it takes into account a turn Simon's term and so on. And it also is not in Minkowski space, it's in PP wave, which to me sounds as if it's more general. So I'm curious, why didn't you use the BMN model? Why did you choose to use BFSS?
Good question. I mean, right now we're not choosing, in fact, we're not even choosing, we are just trying to figure out, okay, the idea is that there are all these matrix models, as you said, BMN, BFSS, IKKT. What we're really focusing on is to actually liberate ourselves and really, we really want to use that as a motivation, but not yet commit ourselves to any one of those models, actually.
So the matrix model that we actually did commit ourselves to is something called a cubic matrix model. And that was actually authored by, you know, motivated by Lee Smolin. So the idea would be in this cubic matrix model is that you have, you know, you have a Lagrangian, okay, that has a matrix, let me call this thing,
a matrix X. And so now, but this matrix actually has a kinetic term, X dot square. Now I'm suppressing the MN indices here. So it has, okay, I'm suppressing it. So it has kinetic energy and then it will have a potential that depends on X, except this potential is cubic in X. So it's cubic in a sense because it's a matrix, it's a commutator, right?
Like this. Because matrices remember their matrix value, so the products will be commutators. And as a result, the equations of motion of these matrices, you know, the dynamics of these matrices classically will be something that looks like X dot, right, is there's some there's probably some coupling here and we call it lambda.
is going to be lambda you know x comma x because I have to take a derivative with respect to x and if you look at this thing here right the idea is that you know if you look at this here this is like I want to now think of this x dot as my y right okay and and somehow this you know this um x x commutator
could be massaged into something that looks like Y times a component of X. That's the analogy here. Now we're not there yet. So the idea is that somehow the dynamics of a matrix model is similar to the dynamics of basically how a neural network is able to learn
maybe in a supervised way. So in other words, if I present the theory with an output or something known, so like a known solution, the idea is that can the theory maybe spit out new solutions? Okay. Or for example, here's one thing we're playing with. Imagine that these matrix models could spit out realizations of the standard model. So in other words, because they're n by n matrices,
You know, so therefore it might correspond to a group S-U-N, special unitary group N, then you can imagine that basically S-U-3 times S-U-2 cross U-1 may pop out as solutions of this theory. Okay. And the idea would be like, given that we know that this is a solution, right, you think of that as the output. The same way we present a picture of a cat or a dog and have the neural network learn that,
the same way we were using a matrix model and the dynamics of the matrix model itself, right, as a learning architecture. So there's nothing external to the system. It's sort of like, you know, it's part of the system itself via its dynamics, its equations of motion. And the idea here is if you're in a one-to-one correspondence between a learning architecture via neural networks and the dynamics of the matrix model,
If we're able to make this correspondence between X and this correspondence. So let me see if I can make this a cleaner statement here. So on one side I have an artificial neural network and it has dynamics, Y maps, input goes to output. And then what happens is that, what's going on here? The weights then get adjusted.
So the weights are the things that actually get adjusted in this learning, right? The weights get optimized. Likewise, if I have a matrix model and then there's something like the standard model as a solution, can we use the dynamics? Can we use, let me see, hold on a second.
In the paper, did you focus or restrict yourself to restricted Boltzmann machines, or did you try out others? So far, we restricted ourselves to hop-feel-like models, which in some cases can have a semblance of RBMs, restricted Boltzmann machines. I see. And the reason for that is just simplicity?
The reason for that is generality and simplicity at the moment. But we're definitely keeping an eye out for other ways. So the idea here is that this correspondence here is instead of input-output via the artificial neural network, the matrix model, the input now would be the dynamic, like the equations of motion.
So we use the equation of motion itself as a learning mechanism. And the idea now is that what are the weights? How are the weights being adjusted? And the idea here is that the things that get adjusted might be the parameters of the standard model. Because one of the big unresolved things in theories of everything and like string theory or even grand unified theories is that you can spit out solutions or realizations of the standard model.
But as you know, because of this issue of the landscape, it's hard to tune those parameters. So we're saying, okay, embrace that. But really what's going on? Maybe it's that the universe is actually learning and it somehow finds a solution. If the solution is stable in some sense, stable meaning that it's because these weights are being adjusted. And the idea could be that these weights
You know, while you work with Lee, Lee has this idea of evolutionary black holes and that in the genesis of each black hole is another universe with differently tuned constants and it's predictive in the sense that
If we're in the typical member of the space of universes, we should see certain formations of black holes be maximal because the universe is constantly trying to maximize the amount of black holes it creates. Now, is that similar to this? Was this spawned by it? Can that be derived from this? Is it distinct? Yeah. I mean, so Lee, to my memory, you know, was the person that came up with the landscape.
idea in that picture of black holes spawning and being used as a mechanism to determine, not to determine, but to populate this landscape with different parameters of our standard model, for example, so of the coupling constants. So I would say this is in that spirit for sure, because obviously for many years I've been talking with Lee about
How do we get around the issues of how theories might determine the values of the standard model and what mechanisms exist? So one of the things I paid a lot of attention to when I worked in string phenomenology, which is how string theory can give us back the real world, was basically, yeah, this was a big question. And one way out, of course, is that if string theory gave you something like
like eternal inflation, then the idea there was that the different parts of the universe that are inflated would populate the stamp, you know, the different parameters and we happen to be living in one of them. So that's one, you hit the jackpot type of idea. The other one, so, but you know, I've always kept an open mind about
Other alternative ways of thinking about maybe there's something about the theory itself that's determined in this. And so the idea here is to really simply put a learn to think that maybe there's some kind of learning in the sense of artificial neural network.
But instead of it being a neural network is the degrees of freedom. Instead of being a neural network, it's actually the matrices, which are now the fundamental degrees of freedom, that are playing the role of the perceptron. And then the weights are being adjusted. The hope is that it's going to be the parameters of the standard model. That's it. Interesting. One out I would say, to give myself an out here, is that a quote from Albert Einstein, you know,
If we knew what we were talking about, we wouldn't call it research. So there's a part of me that was still confused about a couple of things, which is why it's great talking to smart people like yourself. As I just read the title of the paper before I actually read the abstract of the paper before diving into it, I thought perhaps it was something like, okay, the weights change and the weights change in such a manner that if you follow them, they look like particles along a trajectory. That's interesting. Tell me more about that. That's interesting.
With each pass, there's obviously a changing of the weights. Can this changing of the weights be seen as a trajectory? And then if so, can that trajectory map onto what we think the particle's trajectory should be? That's a great idea. No, no, no, that's a really good idea. That's a really good idea. And let me think about it. I'll get back to you. That's a really good idea, actually. Yeah.
In a sense, you know, a way that you're right, you know, because if you think about this, let me say one thing about that. Sure. So let me get back to this. This share thing. So one one way to think about matrix theory. So, you know, to give some because there is abstract matrix. Now, let me imagine that I'm in three dimensions.
So I have z, x, y. And now I'm going to put a particle in three dimensions. So I'm going to call this the location of this particle. I'm going to give it some vector x from the origin. And obviously, I can look at the components of this vector. So there's some component of the vector.
I'm going to take that vector sign off and label a component xi, where i goes from 1 to 3. So x1 is x, x2 is y, x3 is z. So now I'm going to now think about this particle confined to live on a sphere. And now the sphere has some basic area, unit area.
Now the picture in string theory is that actually these matrices correspond to the configuration of a particle in string theory called a D0 brain. So actually this will be a zero dimensional particle but it's fuzzy. So what happens is that in
smooth continuous space times, Xi is just some vector that will denote any position on my surface. But the fact that Xi and Xj, for example, don't commute, it corresponds to these d0 brains. So the idea is I have these d0 brains sitting around here, and their strings are basically attached to these d0 brains. So that when they cross each other, you know, brain one, the d0 particle
This is a D0 brain, right? D corresponds to a Dirichlet, meaning that a string ends on it with a Dirichlet boundary condition, and it ends at a point, right? So then you can now focus on the point particle, but a difference from an ordinary point particle in that it doesn't commute. The same way x and p don't commute in quantum mechanics. In this case, x1 and x2 is not going to commute.
So what that corresponds to this thing called... Can I make a quick aside for the audience? Please, please. Whenever you have a DP brain, so PM is an integer, that means the spatial dimension. So if you ever hear D6 brains, it means it's a seven dimension because you have to plus one for time. So right now D0 essentially means point, but you could still have world lines, which is what I believe is captured in the BFSS model. Very nice. So like what you just said, this will be a D2 brain and that will be a membrane.
For example, it helps clarify sometimes these small terms I know when I was learning, which by the way, just so you know, as a confession Stefan, I try my best to study for each interview assiduously. And this one, there was a personal family matter that I had to get to. And so I put a monkey wrench in my studying for this. And for the past 10 days or so, I knew nothing. I knew no turn simons. I knew no patriajan. I don't even know how to pronounce that.
I basically had to learn all of this and I still know a modicum of it just to prep for this. So even before this, I didn't know what a D zero brain was. So I'm saying this because these are questions I had and I'm sure the audience as they're watching would have similar questions. Wonderful. Right. So that's a correctly pointed D and a D one, a D one brain would be a string. That's right. And therefore a D zero brain would be a point particle. And,
So the idea here is that the matrix that I just talked about, matrix theory, corresponds to the position of a D0 brain in a non-commutative or so-called fuzzy space-time. So that's a nice picture to have in your mind when we're thinking about matrix theories, what they could describe. They're describing the motions of these D0 brains
but in a space time that's not commutative. Now, we're not, it's not only describing that. That's just one limit of the theory where it's doing that, but it's a useful thing to think about. And another way you can think about it too is the membrane, for example, you can think of it basically as a collection of these zero brains that come together to form the membrane. So the basic building blocks in this matrix theory are these zero brains and the things they can do. And why is that interesting for the insight that you had there?
Because when I think about the interaction of these zero brains, for example, it corresponds to the commutator, XI, XJ. And if this is in some correspondence to WIJ, the weight matrices of a learner that you're talking about, then you remember a potential energy determines basically the trajectory
You know, sometimes I say that it's, it's often useful for people who watch this podcast to watch it once and be befuddled and not understand. And it's basically in the second passing that you get the true understanding. The way that I like to think about it is that one is thirsty, like, they're curious, they're inquisitive,
and so they want to drink but often it's it's best
Often it's not always the best to try and drink from the fire holes, not because you're going to fail drinking from the fire holes, but at least the point is to get wet. I think Wheeler said that people are trying to drink, but the point is to get wet. So how about I'm going to take a couple sentences from your paper with this abstruse, unfathomable language for most people. Then we're going to break them down term by term so that afterwards people can go through and decipher it and understand what was meant.
Sure. Okay, so I believe this is just the abstract of the churn simons modified GR. So churn simons modified gravity is an effective extension of general relativity that captures leading order gravitational parity violation. So first of all, there's churn simons, we're going to explain that effective extension going to explain leading order going to explain and gravitational parity violation. So what is churn simons? Very good.
His name after, of course, the authors, someone who I consider a friend and a mentor, Jim Simons, mathematician and billionaire, philanthropist, and polymath, and overall great guy. He's one of actually, he's one of the most humorous, funniest people, people I know.
He just, he's, he makes me, anyway, so Jim is one of the architects of, yeah, it makes me laugh. And of course, his, his collaborator, Churn. So Churn Simonsley is based on this piece of math, which is a magical piece of math. And that basically has to do with something called
So if I give you a manifold, can I characterize properties of this manifold, in some cases topological properties of the manifold? For example, if you have a donut, you can characterize how many holes a manifold can have, no matter how much you deform the manifold locally,
There's an invariant, which is the number of holes that it has. An invariant because no matter how I change coordinates, whatever I do smoothly to this manifold, this thing's going to be. So is there a way to mathematically measure these types of topological things? And what Jim and Simon and Churns discovered was a new way, a new characteristic class called the Churn-Simon's, a new invariant called the Churn-Simon's invariant. And what's special about it for physicists
If you know the degrees of freedom already, like of our gauge theory, for example. So now let me get down to earth here. So if I give you a gauge theory, the gauge theory is described like electromagnetism or Yang or the standard model by a connection, right? So our gauge potential or the photon field, right? The photon field is this thing called a mu, right? And the turn Simon's theory says that if I give you, can you see this?
No. All right, so I'm not going to share screen. Hear that sound.
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We're informed that if I give you an electromagnetism A mu, when mu runs from zero to four, this is the grant of X, right? It's a four-dimensional object, right? So the zero component of this is some scalar quantity, and then the X, Y, and Z will be the spatial part, I. So this is a zero, and this will be a I. So that'll be four dimensions. Now, this thing is actually
In electromagnetism, I can use this basically to determine basically the electric and the magnetic fields, right? But all the information of the electric and magnetic field is contained in AME, which is a connection. They call it the connection because if I take covariant derivatives of this connection, or if I move this around, this connection around some
In a gauge theory, in other words, and I could define curvature. That's weird. Okay. So I'm going to start again. You can define this so-called field strength tensor. I know this is review for a lot of people, but just to be for completion. And basically by taking derivatives of
where this is partial derivative with respect to zero, x, y, and z. I could define this object. So here's a beautiful thing about turn assignments. Turn assignments theory tells you that if I know F mu nu and I can get it from A mu, I could define this invariant in three dimensions, which is just A, let me say, tensor F.
And when I mean by this tensor, it's really an anti-symmetric tensor product. So the churned Simons invariant, let me call it the wedge product. Okay, very good. It is a wedge. So I didn't want to mystify people, but it's what we call a wedge. That's right. So A wedge F is in fact proportional to this churned Simons invariant. And this thing, A wedge F,
They appear to be local quantities. They are, when I say local quantities, they're not topological, right? But when I take the wedge product, right, and I integrate this over, like say, if I have four dimensions and I take a three dimensional boundary, M3, that basically this thing is going to be, this thing is an invariant, right?
It's going to measure some kind of topological, it's going to measure a topological invariant. Okay. And when you say it's an invariant, do you mean it doesn't matter which M3 you take, you'll get the same value or what? Like what exactly is being invariant here? The value of this? Over what? So if this thing is some, yeah, if this thing is, you know, this thing is some, let me see.
It's some integer modulo something, which I'm not remembering right now. But basically this integer modulo something, which I forget what it is, is the invariant. So that's now that's the math side of it. And I'm by no means a differential geometer. I'm just a physicist. I can just now tell you. So that's what that is mathematically.
But there's a lot to it in the math literature, right? And it's all right. It was a great math. It was a tremendous mathematical discovery. But the thing that's amazing is that Turing-Simons theory has found itself at home in Nobel Prize winning discoveries in physics. Like when Jim and Turing were coming up, they had no idea it would actually be applied. They just made this mathematical discovery.
And now, like, you know, anywhere from the fractional quantum Hall effect, it's, it's, you know, it's found there in the standard model. It's a key, it plays a key role in establishing anomalies and anomaly cancellation. In fact, the churn Simon's term, I can say something even cool about this in the standard model, the churn Simon's form was called a churn sign form, which is, as I said,
A wedge F, right? That's for a certain dimension, correct? It's like one dimension for this or... So in this case, this is in three dimensions, yeah. I see, I see. Let's be in three dimensions. It could be also in four dimensions, three or four dimensions, right? Ah, I didn't know. So A wedge F, right? So this A wedge F here, and it turns out that
is proportional to a current. So in the standard model, we have currents, right? You know, the electromagnetic current. And one of the most important things in the standard model is that these currents are conserved. So for example, I look at, you know, current going in is equal to current coming out, which is a statement that D mu of the current, J mu, right, is zero. Right.
But, you know, this comes from Maxwell's equation that says that, you know, this is basically coming from the statement that d mu, f mu nu, right, is j nu. Right? So if I take another derivative of this thing, then by definition, you see it comes from Maxwell's equations. So what's important here? It turns out that this is no longer the case in the standard model when I turn on quantum corrections.
This is a major, this is so-called the ABJ anomaly, but actually this can be, when I turn on quantum corrections, this is proportional to D of the turned Simons. I'm being schematic here, okay? Yeah, and when you say when you turn on quantum corrections, what do you mean by that? When you add a turned Simons term? Very good. To me, to say when I say turn on quantum corrections, is that if I look at basically
say the interaction of in quantum electrodynamics. If I say I look at a photon that basically, you know, I can take an electron and it could scatter off and, you know, of a photon, right? This is like an electron E prime. I can imagine like doing things like having another photon like here, right? That will be a quantum effect. And this is now sort of looking like something called, well,
But you can have other quantum effects, so-called loop diagrams. And there's one special one called a triangle diagram like this, where I have an electron loop, for example, going around and then photons coming in like this. So I can have basically this type of quantum effect. This quantum effect, if you go and calculate it using Feynman's, you know,
Um, rules will give you this thing here. I see. And this is the famous result of Adela, Bell, and Jaquiv. Um, the ABJ anomaly. So it turns out the standard model will do this and this is not good. Yeah. And this is not good. Why? It's not good because
The big deal there is that it actually violates the fundamental principle of quantum mechanics, which is it violates unitarity, the conservation of probability. So you can probably see where this is coming from, because if you can now think about this loosely as the probability current, then this is no longer zero. And in quantum mechanics, the probability
Current, probability current has to be conserved. So it turns out that Chern-Simon's theory is a part of the Standard Model. And it just so happens though that the Standard Model, all the contributions of all the currents correspond to all the different forces, completely cancel. So when I sum over all the currents,
Okay. Some of all the anomalies, it turns out that they, it vanishes in a standard model. So that's what makes our standard model quite unique, actually, mathematically, that it cancels anomalies. So that's another place Chern-Simons theory shows up. Okay. And then the other place that shows up is actually in string theory. In string theory, the Chern-Simons theory shows up to actually
In a magical way, it also plays a role in canceling the anomalies in string theory as well. It's called a Green-Schwartz mechanism. Right, right, right. Turn Simon's gravity now is another place that I played a role in pushing over my career as a way of thinking about gravity that has the turn Simon's term in it.
Can we go back
What an anomaly is, is when there's a violation of the conserved current. But I'm unsure, is that all that anomalies are? Are there other types of anomalies other than quantum anomalies? In other words, whenever someone says there's an anomaly, are they always referring to that the right hand side is no longer zero? Very good. So let me, good question. So let me just say another in general, if I, this is a general statement I'm making about anomalies. Okay. For any current that is conserved,
That is conserved. I'm going to put on the right hand side the letter A. If it's not equal to zero and there's an A, that A is called the anomaly. That's literally what it is. So when A is zero, then the current is conserved. And the question you're asking is, can an anomaly arise in a non-quantum way? That's a good question.
So one thing, the calculations that are done to determine the anomaly, to my knowledge, are all quantum considerations. But I see no reason why you can't, in some theory, which I can't recall right now, generate an anomaly classically. Okay, so another question that
Especially undergrads as I know I had is let's say you have the Klein-Gordon and they say, well, it's not unitary. It doesn't conserve probability across time. Well, what's the big deal about that? Because so what if you add some extra, let's say lumps on the probability distribution, why can't you just simply constantly reweight it down to normalize it? So why can't you normalize it at every given infinitesimal moment?
Is my question making sense? Do you understand or should I restate it? You could always that's right. You can always re normalize. That's what we call re normalize. And that's you know, you can always re normalize. But if you find yourself in a situation that even when you re normalize, it still gets violated, then you're in trouble. I see. I see. Yeah. Is there a way of determining a priori whether that a on the right hand side at the bottom equation is re normalizable? Or is that some large
Very good. That's right. So the A that's generated actually has a divergence as well. And that divergence, when I say divergence, I mean, there's an infinity when I actually, you know, take
When I integrate out, when I integrate to, you know, to high, high momentum, right? And this, because remember this A is coming from the internal legs. And that notice, I would say that that's getting into, you know, notice, this is a question, the question that I think this is pointed to is, what is it about the anomaly?
that's leading you to deduce that the theory is not unitary. And this has to do with something called award identities. And the minute you have these anomalies, you can show that these award identities, which are identities having to do the unitarity of the theory, is violated. I need to think more about that. I don't have an intuition for it.
Sure, and then also looking at this middle equation, the one that has the sum with the D and the CS, why is it a difficult problem to get rid of an anomaly when it seems like, well, if my understanding is correct, you add a certain term to a Lagrangian, if it's as simple as that, in some cases it is. So you add a certain, in this case, a turnsimus term, perhaps then an interaction term with the turnsimus term, but you add a term nonetheless, then you go through this
No, we do have these anomaly canceling conditions in the standard model. And what that boils down to is
For the anomalies to cancel in the standard model, the charge assignments, the way you identify the charges of the quarks, the leptons and the quarks and the leptons, and the color of the quarks, and the gauge groups. That's what I mean by the color, the isospin as well as the charges. The charges, the assignments, the fact that the quarks have one fractional charge,
is precisely because when I add up the anomalies from all the other interactions, so those charge assignments are the things that actually are allowing this anomaly to cancel. I see. Interesting.
I want to know, what do you consider to be a theory of everything? The reason I ask this is when I asked, well, some people say, well, it needs to incorporate consciousness or needs to explain the origins of the universe. Some people just say, unify gravity in the standard model. What does the theory of everything mean to you? It's a really good question. Well, I mean, I have my ambitions now are
I would say that, for example, if string theory was able to provide as a solution that meets the standard of what a solution is in string theory, that gives us back, say, something like, at the very least, an early universe scenario that is consistent with observation.
Maybe it's inflation, maybe it's an alternative to inflation. I would literally say that string theory, therefore, modulo its difficulty and tell me why that solution is preferred over other solutions would be a fear of everything. All right.
And then I would add about the more like the questions of like, okay, higher level organizational properties of matter, including life and including consciousness. I have some thoughts about that too, but I would say that, you know, at this level, I would call that a theory of everything.
So it sounds like that's been a common thread throughout your entire career because around 2000, 2001 or so, but you've been working at it probably in 2000, you had the inflation of the D brain, D brain annihilation. And that seemed at least seem to produce something that looks akin to the big bang. And I believe you use some data to show, I'm not sure if you, if you made a prediction and you showed how it matches with prediction, I'm not sure about that, but either way, that sounds like a through line. Yeah. So, um,
I was trained as a string cosmologist, meaning that someone that knows both string theory and enough cosmology, enough of each, but certainly not a master of either. Because back then, this was the year 2000, 1999, 2000, the call was, can we... Some people felt string theory wasn't developed enough. Some of us felt it was developed enough to then ask questions of
Can we reproduce something like cosmic inflation? So I went to my first postdoc trying to do that. And that was my take on how to do that. So I guess the fact that it was published meant that it met some standards. But one of the things it did do was it opened the floodgates for other string theorists. And I certainly wasn't the first and the only one. But anyway, open the floodgates for others to then
improve or develop different ideas, but similar ideas, you know, with string theory, that somehow these D-brains are playing some role in describing the early universe and four dimensions out of 10 dimensions. Did you do that work at UBC? Very good. I spent a lot of my time thinking about the idea when I was at UBC as a grad student. But then I
really did it when I was a postdoc at Imperial College in London. I remember the first time we talked, I think the only time we talked about a year ago, that's how long this podcast has been in the making. You said, oh, Jai Mungo, Jai Mungo, wait, I went to school with your brother. Okay. Do you mind telling me a story about my brother? I think he's a genius. I remember when I, okay, so
First of all, one thing I think is interesting to note is that, you know, my parents immigrated from Trinidad when I was a kid to New York City and, you know, all throughout my growing up and I kind of was, I was alone. I was the only one, you know, there were lots of other really bright people around me, but I felt like, okay, I'm this immigrant guy from the Bronx and there weren't really many people I saw that looked like me or that was from a similar cultural background.
And maybe you take that in as a young person and maybe, well, maybe I'm not meant to be as good as I want. And let me just speak it as a younger person when I was a teenager and, you know, into college. So when I went to UBC and I met this guy, Sebastian Jaimungal, who was at the Blackboard, like, like completely destroying it. I mean, he was like, you know, me and Damien, the other grad students,
We looked at this guy like, you know, this guy is like, you know, this guy is like a total badass. He just kind of knew everything. And he was also, you know, one of the things that I realized I was so, had left an impression on me, actually, he actually inspired this in me. So if there's something I say I owe Sebastian, it was
that he was not only somebody that was highly versed in quantum field theory and string theory, I mean, he got a postdoc to go to Princeton, right, the top place in the world at that time, one of the top places for theoretical physics. So he not only did that, I mean, was that good, right, that he got the top postdoc in the world, but he was versed also in condensed matter theory. He was, you know, so he was one of these people that he was
verse in all these branches of theoretical physics. And that really was the thing that allowed me to break the chains of the disciplinary boundaries that we create for ourselves. He was somebody that really inspired that. So, and so anyway, meeting him also gave me a confidence booster because I was like, oh, wait a minute, look at this, you know, this other like, you know, I guess he's from Trinidad, Canadian Trinidadian, right?
He was born in Trinidad. From my background, he was one of the top grad students in the world in theoretical physics. That gave me a real confidence booster. We also spoke a lot. We talked a lot of physics and I learned a lot from him. He actually was the one that taught me wedge products when I was a grad student. Give Sebastian a big hug for me. I will, man. Tell him to come visit me.
Did you have doubts about your own mathematical ability or your own bet? If whether or not you could, not that you wanted to, maybe I'm sure you had doubts. Should I go into this? But could you, did you have the ability? So did you ever doubt your own ability? Big time, big time. Yeah. Big time. And I remember I, um, in fact, I remember when I was a graduate student, I knew I was deeply interested in the big questions and I, but I actually was going to settle for less. And,
Because internally I didn't feel I had what it took. And everybody else was just really mathematical and really knew things that I didn't know and I felt was going to be such a learning curve. And I remember one time that we had this visitor that had come visit Brown's physics department.
He was one of the most brilliant string theorists. And he carried himself as if he was some kind of guru. I remember he used to walk. I was like, is this guy some kind of yogi or something? And his name was Sumit Das. And he used to come visit the string theorists at Brown. And he'd be there on weekends. And one day I was hanging out, and he started talking to me. And I was like, why is this string theorist talking to me?
And then I asked him, I said, I felt comfortable. I was like, is that something that like, you know, if you want to do strength theory, how good do you, do you need to do this? He goes, no, no, no. All you have to do is be passionate about it and just go for it. And somehow the way he said it to me made me feel like, well, maybe I can do this. Right. So I definitely, I owe, I definitely want to give, I owe it to submit Das, you know, for, for kind of playing that role, just saying, Hey, you can do this.
But, you know, that still lives at me. That still lives at me. I still feel like I, yeah, I, you know, my strengths are not with, you know, knowing a whole bunch of math. Although I love math and I love learning from mathematicians and I, you know, you know, there's a place where we play, we have to play on our strengths and know what they are. In my case, I'm, you know, kind of intuitive. I have pictures. I play with thought experiments.
It's important to talk to people, to have soundboards, and one of the things that's very important to me is actually having soundboards that are not always experts in my field. So I find things like this to be very useful also to my research, like conversations like this. You're doing a service to physics research. Thank you, thank you. So what age was that when you met with that guy Sumit, I believe his name is Sumit Das?
Yes, Sumit Das. I was a first year graduate student and I was actually trying to be an experimentalist at the time. Not because it wasn't experimental work is as hard or even harder than theory work. That's the asterisk for Brian Keating. Yes, exactly. But I guess what I'm saying was that it was a time where what my real interests were, I was suppressing it.
Yeah, what advice do you have? Because there are quite a few people who are watching this who don't have a background in university. Maybe they have some training in mathematics, but that's it. Maybe some rudimentary physics that they've seen from an MIT OpenCourseWare video. But they want to understand string theory, M theory, well,
Yeah, I would say, you know, like if you can't basically
Yeah, that's a really good one. I mean, it depends on, you know, whether or not you can maybe go back to some kind of school. But there are lots of, you know, online presence now, information online, like I'm thinking about even things like Lenny Susskind's course. But even like one thing I find really interesting is that the Permit Institute has online, they have made
They've made their online seminar series. Jump in, listen to these seminars, go online. The other thing is there are some really good books now. So, for example, like Lenny Suskin has a book called Theoretical Minimum, which I endorse. I mean, they're really good. I read them, actually. It's a good place to kind of build some foundation and then actually go online and pull out some problem sets.
and try playing and working with these problem sets and get up, you know, join a group of friends and work for these problem sets together. I mean, in practicing problems, the reason why you want to practice things like problems that have been solved already is that you're building arsenal of solved problems and they can be used as a launch pad to solve unsolved problems, right? So kind of getting a sense of what's been solved out there.
And then I actually recommend one of the reasons why actually, and this is not an advertisement, I literally wrote my second book precisely because I wanted to fill a vacuum in terms of
how people can start thinking about research problem. What are the cutting edge things that we're thinking about now? And it was written very much in the spirit of Richard Feynman's character of physical law and a brief history of time to kind of carve some space out exactly for that person who wants to get a sense of what's out there. What are people thinking about? And what are the unsolved problems? And what are the directions that people are afraid of or is holding the field back?
from again from the opinion of a you know so in other words imagine i'm somebody's thesis advisor right um like a phd thesis or a master's thesis advisor and i and i had to disappear for a year i would leave this book with with that thesis thesis student right so those are three things three three concrete things i'll get your book get what's the book the name of the book and do you have it right in front of you i don't have the
I just gave my book away to a student of mine. The book is called Fear of a Black Universe, An Outsider's Guide to the Future of Physics. That's the subtitle. Now when I hear that, to me it sounds like a book about race and science. Is it a book about that or exclusively about that or minorly about that? Minorly about that. I'll say 10% of the book is about
is about identity in science. Of course, we can include race in that, but we can include personality, different modes of ways of thinking. But the title was also a play, it was a nod to one of my favorite rap bands when I was in college called Public Enemy.
That's something you and I also have in common. Not only are we from Trinidad, but we used to rap, although I think you used to do the beatboxing. I was more of a beatbox and a beat maker. I wish I could rap, so one of these days we might have to do something together. That'd be great, wouldn't it? Yeah, yeah. Okay, getting... Okay, you know what, first of all, about Brian Keating. Brian Keating's your friend, correct? He's my best friend, yeah. Yeah, I'm gonna prove to you that he's not your friend. Okay, see this? Yeah. Okay, hold on.
See that? See that thumbnail? Yeah. Yeah. No friend. No friend would leave your thumbnail like that. That's the worst thumbnail I've ever seen of anyone. I'm I'm going to tell Brian to change. Yeah, you gotta tell him. Okay, that's a good one. I'm just that's a joke. I'm just kidding around but still. No, I don't. I don't. I actually. Yeah. Caught him in the middle of a sneeze and then you chose that. Right, right, right. I'm going to I'm going to get on him. I will get on him about that.
Okay, how has the process of learning for you changed now that you're older? What would if let's imagine you could advise your young self practices to keep practices to drop practices to adopt? You're advising your 20 maybe even 2530 year old self.
About what though? About learning something like string theory or learning something like... Oh, yes, yes, yes, yes. I think it's important to combine practice with play. So rather than, you know, if I, you know, if I'm learning something like the equations of motion coming from varying the string world sheet action, for example,
It's important that I not only know how to correctly vary the Euler-Lagrange, how to obtain the Euler-Lagrange equations, and why the calculus of variation that applied for a point particle would also apply for a string world sheet action.
But it's important that once I get this that I play with those equations. I literally play with them. I move them around. I play with the rules of the math. I break the you know, I actually break the rules and see what happens like the same way a kid plays with a toy. What would be an example of trying to break the rule? Just making a mistake or what or making a purposeful mistake and seeing where it leads? Yeah, make it literally make a purposeful mistake and see where it leads. Exactly. That's interesting. Yeah. So I'm one for
playing with breaking the equations. Well, you know, kids don't try it at home, but this is definitely something you can try at home. And you might learn something, but when you go out and you give a talk or you try to write a paper, you're obviously not going to put that mistake there. But you do those things just to see. Again, that's kind of like
Yeah, that to me is just like, you know, the idea of playing with things. What would be an example of a time that you played? You purposefully did something incorrect in order to see where it lead. What would be the time that that led to an insight? Can you give me? Well, I think the paper that I wrote with Michael Peskin and Shaheen Sheikh Jabari on leptogenesis or the origin of matter over antimatter, we
proposed that this can take place during the period of early universe called Cosmic Inflation. And that actually came from putting a place filler in. So how do you create matter over antimatter? Well, you need to exactly have an anomaly. And then what I was doing was I didn't know what the answer would be, but I put the answer I needed to be in there.
clearly violated the Einstein equations, right? And then after like, you know, whatever, I mean, thinking about talking about it, having sound boards, it's important to have sound boards, you know, to have people that you can talk with who will not judge you, but actually take something dumb that you've said and throw back to you in some meaningful, more meaningful way. So Michael Peskin, my postdoc advisor was that guy, and Shaheen was that guy. So
And then next thing you know it takes form and next thing we discover, well actually the real story about that was that we were thinking that it maybe was torsion, this idea of torsion that would source the baryony symmetry, that turned out to not work but again the torsion thing had a tensorial structure meaning the way the indices are moving around and when I went to Caltech that year and I visited Mark Kamenig, the great cosmologist Mark Kamenigkowski
And then I was telling Mark the idea, and Mark goes, oh, you should take a look at this paper I wrote. It might be useful. And then when I look at the paper, it had actually, for other reasons, it had this Charm Simon's thing. When I came back to Stanford, we started playing with that and it turned out to work. So that's an example of like,
So I don't know if that was like deliberately making a mistake, but it was sort of like, yeah, I think that in this case you put a place filler in. You're fudging. You're literally fudging. It's what Einstein did. He put a fudge factor in to make it work. Right. For dark energy. In this case, there was no anomaly, but you needed there to be an anomaly because there is an asymmetry. We needed it to be a harmless anomaly. Okay. So for the people listening, when there's that J in the current
J isn't always current as in electric charge current. Yes. It can be other types of conserved quantities or quantities that need to be conserved. Yes. Okay. So what would, so in that example, it would look like D mu and then J mu at the top. What would that J represent for assuming? Okay.
So this will be the current associated with leptons. So the electron is a lepton, the neutrinos are leptons, right? So these are the leptons and there's a quantity called a lepton, the lepton number, right? The same way you have like an electric charge is actually a leptonic charge. And that leptonic charge, it can be violated by an anomaly. And that one is fine because it's so-called global anomaly. It doesn't depend on space time.
And those anomalies, sorry, I want to make sure what you, I don't want to lose. Okay. So you said that the lepton charge can be violated by an anomaly. You mean to what do you mean when you say it can be violated by anomaly? It's not just because the way that I see it is that you have your theory and then you find out, Oh, it's anomalous. It's not that, Oh, I can make this anomalous because I feel like I can make any theory anomalous. Very good. So the left and it's standard model, the lepton, it turns out that the lepton current is not anomalous.
With exception, and this is where the exception is, if you turn gravity on, there's a gravitational anomaly. And the thing that's doing that is the gravitational churn Simon's term. And it turns out that if you have a gravitational configuration, meaning in a gravitational field, that gives you a non-vanishing churn Simon's gravitational term, it could source lepton number.
I want to talk about something that sounds like it's not inspirational, but it is. There are certain no-go theorems in physics and in math, but let's talk about physics. What are some examples of no-go theorems that turned out to be a go theorem, like you could find your way around it?
Firstly, you should explain to the audience what a no-go theorem is. Very good. A no-go theorem is a statement, so I'll give you an example of a no-go theorem, and maybe I can... Actually, let me... So a no-go theorem is Weinberg's no-go theorem about any adjustment mechanism for the cosmological constant. So the statement says that
You can't use, say, in this case, a scalar field with a potential to relax, to relax the cosmological concept. And then he went and like actually did some calculations and showed that actually if you had such a theory that you cannot use that to cancel out the cosmological concept. All right. And that is true. But in that theorem. Hear that sound?
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Go to Shopify.com slash theories now to grow your business no matter what stage you're in Shopify.com slash theories. That theorem there were some axioms or some assumptions about in this case that if that scalar field relaxes to a back a ground state remember the field is can roll and then when it gets to its ground state or to its minimum the minimum of its potential if that ground state
is Poincare invariant, then what Weinberg said is true. But if the vacuum state is not Poincare invariant, then that assumption, that no-go theorem doesn't apply because you've relaxed that assumption. So now you have a loophole. So then people realize that by now constructing so-called P of X theories.
These are theories where the scalar field is actually has a non-trivial kinetic term. And those theories have ground states where the kinetic energy is still non-vanishing, right? And it's not a Poincare invariant vacuum. So recent manifestations of trying to solve the cosmological constant problem have, by really good people, have used those
those types of relaxation mechanisms that evade Weinberg's no-go theorem or evades one of the assumptions of that no-go theorem. The reason I said that... Yeah, yeah, it's actually inspirational. And the reason is that it seems clear. Oh, you have a no-go. Someone said there is no way. Look, this is math. This is physics. There is no way around it. But then you realize, well, there are hidden assumptions. You mentioned axioms. I call them anthem memes, which are just
unstated assumptions embedded in your question or embedded in your statement. And one of my favorite ones is, is Witten, I think it was just Witten, but though it could be Witten in Weinberg in 1980, where he said, okay, if you want a spin half larger than spin half particle, and it has a conserved a Lorentz covariant current, it can't exist if it's massless. And then same with it can't exist greater than one and be massless and have a conserved stress energy tensor.
The assumption that was made was so implicit that they never made it explicit and they didn't realize, I don't know if they realized, until someone else, I don't know, maybe it's Juan Maldicino came along and said, well, okay, that's right.
It cannot exist in this space time, but it can exist in another space time. And I believe that's part of the origin of the holographic principle. No, that's very good. That's very good. I think excellent point. Now, I don't remember, but I think, though, that the Weinberg-Witten theorem does make an assumption about the online space sign. And I can see how anti-dissidia space, which is the space sign ADS-CFT is based on, holography,
that version, I could see how that could avoid the Weinberg-Witten theorem exactly because in ADS-CFT, that's right, it's beautiful in the sense that the, let me just for the audience to say that it basically is a theory that says that in gravity in one higher dimension, so let's say I had a four-dimensional gravity theory, it's completely encoded in a non-gravitational theory living at the boundary of that four-dimensional
theory with no gravity and that theory that has no gravity is related to Yang-Mills theory where there's no gravity and the idea here is that where does gravity, how does gravity emerge and one I think simple minor idea is that in the Yang-Mills theory you can have condensates or degrees of freedom that emerge that come together collectively right to then form the graviton which would be a version of this Weinberg. If I need to get a graviton in the space time, I have to build it out of the
Can you explain why is it that the Graviton is said to have spin-2 when, for people who are just learning about this for the first time, it seems arbitrary. Well, why are you saying the Graviton has spin-2? Why are you saying that there's a particle associated at all with gravity? Because gravity, we've been told since we've been teenagers, it's not a force, it's the curvature of time and space, space-time and so on.
So firstly, why does there have to be a particle associated with gravity in the same way there are particles associated with other interactions? And second, why does it have to be spin two? Yeah, so the spin will correspond in this case to the helicity of the particle. And just like engage, I mean, if you look at a gauge field, a mu, the index mu now becomes basically related to the
If I have an electromagnetic wave propagating, the polarization tensor, E mu, is carrying the information about the spin, about all the helicity in this case, meaning the momentum projected onto how the particle is spinning. That's the helicity. So you can trace that back to the fact that this gauge field has one tensorial vector index, space-time index.
So if I now have a spin two particle out, I have two of these indices now. And that's exactly the tensorial form of the transverse traceless gravitational perturbation. However, to say it's a quantum particle would spin to is an extra, I would say, thing. General relativity doesn't tell you anything about, you know, that if I look at general relativity, it's a classical theory. But if I go through and make the same procedure,
and say, oh, look, the same way I do quantum field theory, I work in Minkowski space, there's a procedure, right? Perturb the field, the gravitational field, there's a tiny perturbation, and then define some kind of state that in some sort of modes, you know, oscillations with creation and annihilation operators. That's where you're going to start seeing the spin two quantum numbers come pop out. But from where I stand, that is in a that's not, you know, that's not part of
That's an extra assumption of doing quantum field theory in a weakly curved space. I'm sure you've heard Weinstein say that maybe we shouldn't be quantizing gravity, that we should be geometrizing the quantum. Have you taken a look at geometric unity? I have. I have taken a deep look at it, yes. Okay, what are your thoughts?
Well, I think, well, the mathematics is definitely very advanced. I think it's a beautiful idea, actually. I think it's a really nice idea. I don't know what the word is, but you start off with four dimensions, a Lorentz group, and then you do this, you think of all the components, all the ten components in this four-dimensional world,
You let that vary. So therefore you have a bundle structure like a fiber and all these components are now a fiber, a fiber over this four dimensional space. And that somehow then gives you something that starts looking like a grand unified group. Maybe it's SO10 or something like that. So the 10 components of this fiber is like M4 fiber over SO10 maybe.
Again, I'm bastardizing Eric's idea, but I like this idea that somehow you just start with that data and then the mathematics just naturally gives you this extra gauge structure that seems to have embedded in the standalone. Now the devil's in the details and I know that there's some criticisms that need to be ironed out, but I think that's kind of what we do when we do good theory. You put it out, you give it your best shot,
And especially if you're doing it alone, I think that then others jump in and then they improve it or they find a mistake. That's actually what the refereeing process is anyway. Any paper that I write, well, the first thing is I write the paper or I work it out, I do something, I get far enough where I feel confident I have something, but there's always places where I have blind spots, I give a seminar,
And the seminar is usually where I get feedback before I put the paper out. Then I put the paper out, and then I put up a publication. And then usually the referees further help me understand what's going on, actually. And if they find a bad, that it's not publishable, fine, I learn something new, I move on. That's happened to me many times. So I think that, you know, that component is missing.
I think that component is missing precisely because, you know, Eric is, you know, sort of going at a lot of this alone. And I encourage him, he put it out and I think that people should read it and take it very seriously and play with it and scrutinize it. And I think that there might be some gems in there. OK, even if it's not, it doesn't turn out to pan out to be correct in, you know,
in terms of what it's trying to solve, which is unifying the standard model with general relativity in this new way. At the very least, for me at least, I'm reading it or I've read it so that I can learn some things. I've definitely learned some interesting things. And it got me thinking about unification in different ways now. So it's valuable. We should have more of that. Have you read Wolfram's paper or Wolfram's physics project?
A little bit. The answer is I intend to. I intend to when I have some time. I do know that it is related to some ideas in graph theory. I also think that, again, it's some nice ideas out there. It may strike some resonance with other things like matrix theories and other approaches. But I'm all one for let's populate
the theory landscape with ideas and let's scrutinize it and learn from it. The reason I ask that is that there is a direct quote from you, I believe in your autodidactic universe paper about how there's how reality works. And then there's how we model it. And our models are somewhat like approximations, but then they get closer and closer to the real world. And then you start to wonder how much of the real world is these computational techniques underneath?
I don't have the exact line, but it reminds me of almost verbatim. That's what Wolfram thinks. He thinks because computers are so powerful. This is not exactly what he thinks or why he thinks and I'm just paraphrasing, but computers are so powerful and the computation under his models are so general and so powerful and so predictive in a certain sense that perhaps that is what the universe is. It's computation underneath. That's beautiful.
Okay, I know I don't want to take up too much more of your time I can keep honestly I keep talking to you for
I would like to. I also wanted to bring to the forefront, because there are quite a few mathematicians and physicists who watch this podcast, and for the physicists in particular, I'm interested in unification. That's the name of the channel, Theories of Everything. It's been proposed for quite some time now, almost 20 years now.
that geometric algebra should be seen as the standard force for unification or the standard language of unification. David Hastings, I believe. He's agreed to be on the show, I just have to book a date with him. Categorical, category theory as well. So categorical unification, whatever that means. That was proposed by quite a few people, James Weatherwall comes to mind and Elaine Landry had a book on quantum, sorry, on category theory for philosophers but had a few sections on category theory as applied
to physics for the purpose of unification so i'm extremely interested in that and bring a bit more attention to that there are there's coal furry have you heard of coal coal furry yeah yeah yeah yeah yeah so i want to have her on i've just yeah she's she's doing very cool stuff yeah yeah i i i love her little her mini youtube series on the quaternion and then ciara marledo i want to have on however i don't know she's like
ghosting me. It doesn't matter how many times I send her an email, she will not respond. And I don't know why. I don't know if she has. What's her name? Chiara Marledo. It's the student of David Joyce. Oh, yeah, I don't know her at all. Yeah, I don't know her at all.
You got to get going. I got to maybe half the questions. No, no, but let's reschedule and continue. We can do that. Yeah, let's do that. I'm around, so I just literally just got set up today. So now that I got the system going, just let me know and I'm happy to continue talking. Great. And I'm also like a little bit tired and frazzled. I think the next time you get me, now that I know kind of your style, I'll be able to do some better stuff here.
Sure. All right. Well, you did great. Oh, thanks, man. Whatever is better, it will be accepted. Yeah. And yeah, and seriously, tell, tell Sebastian, so what's up? I will, I will. The field, the field messenger, but I'm sure he's but I'll actually I'd like to get some advice from him about some because I'm also thinking I'm not between you and me. I'm actually looking at my options outside of physics, he says. Oh, yeah. Yeah. Yeah. So he's in math, finance. I don't know if you know.
Exactly. So I'm actually thinking about that direction myself, because I'm friends with Jim Simons. So why not, you know, because I kind of want to talk with him and get some, you know, talk with him, you know. Yeah. So let me know if he's ever interested.
The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash C-U-R-T-J-A-I-M-U-N-G-A-L. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you.
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"text": " If you're merely listening to this podcast on Spotify, iTunes, etc., then you'll miss out on the equations being written, so see the link in the description for the YouTube video."
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"text": " While you're clicking there, it would be great if you left a review, as I didn't find out until recently. Reviews radically help the promulgation of the podcast. Thank you in advance. Now for an extra quick note. Quick note before the podcast begins. What I found is that people who criticize string theory generally aren't physicists who have looked at the derivations of the equations of string theory, and thus they're simply parroting their criticisms from others by calling it quote unquote disconnected from reality and quote unquote a theory based on pure beauty."
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"text": " The beauty of string theory is evident when one studies it. And it's also false to say that string theory hasn't produced any physics. String theory is a true contender for a theory of everything, much more so than even loop QG, which is merely a theory of quantum gravity. This year, I'll be exploring the flavors of string theory, such as type 2a, type 2b, with acute depth to give a sense of the naturalness of the equations. Personally, I think the word natural is more fitting than the word beautiful. Now onto the podcast introduction."
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"text": " Professor Stefan Alexander is a theoretical physicist and a cosmologist at Brown's University, in addition to being a prolific musician. In this episode, we cover his theory of everything called the autodidactic universe, a model he developed in conjunction with Lee Smolin, as well as a few other luminaries listed here. The laws of physics can be approximated by matrix models, we talk about this, and machine learning deals well with matrix models, so a natural question arises, is there a relationship between the two?"
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"text": " Can the universe learn its own laws in a manner analogous to unsupervised learning, let's say, of a restricted Boltzmann machine? Click on the timestamp in the description if you'd like to skip this intro. For those new to this channel, my name is Kurt Geimungel. I'm a filmmaker with a background in mathematical physics, interested in explicating what are called theories of everything from a theoretical physics perspective,"
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"text": " but as well as delineating the possible connection consciousness has to the fundamental laws of the universe, provided these laws exist at all and are knowable to us. Generally, conversations on physics and consciousness tend to stay at a cosmetic level, not going past or rarely moving past even the double slit experiment or the Stern-Gerlach experiment. In these podcasts we tend to delve into intricacies, into equations,"
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"text": " Sometimes into meticulous technicalities and so forth because number one it's tedious to hear about the measurement problem for the 25th time Number two because it seems like the language or large part of the language at which the universe expresses itself is Mathematical then if one wants to understand the most profound enigmas of the universe some mathematical facility is necessary and number three because you can handle it and"
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"text": " vastly underestimated. That is, there's a thirst, so that's like curiosity, and then there's the ability to quench that thirst, and that's something like intelligence or astuteness. Mainly, people have focused on the curiosity aspect while neglecting the brightness of you. If you'd like the notes from this podcast in PDF form, then check the description. There's also links to the Discord where conversations occur on psychology, consciousness, and physics. And there's a link to the Patreon, that is patreon.com slash Kurt Jaimungal,"
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"text": " If you'd like to support this channel, there would be almost no way for me to have conversations of this fidelity on the topics of consciousness, theoretical physics, string theory, loop, even geometric unity, which I'll tackle at some point. If I wasn't able to do this full time, the sponsors and the patrons are what allow for that. So thank you so much. Again, that's patreon.com slash Kurt Jaimungal C-U-R-T-J-A-I-M-U-N-G-A-L."
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"text": " Headed by a bright individual by the name of Amjad Hussein, who's been a huge supporter of this podcast since nearly its inception. The second sponsor is Brilliant. Brilliant illuminates the soul of math, science and engineering through bite-sized interactive learning experiences. You can even learn group theory, which is what's being referenced when you hear that the standard model is predicated on U1 cross SU2 cross SU3. Those are called Lie groups."
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"text": " Visit Brilliant.org slash Toe to get 20% off the annual subscription and don't stop before four lessons, at least that's what I found. The third sponsor is CuriosityStream and they're joining us for the first time. There's something approximately like the Netflix for nerds or the Hulu for history buffs or the Disney Plus for the scientist in you. Go to curiositystream.com slash Toe, T-O-E, for unlimited access to the world's top documentaries and nonfiction series. More on them later."
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"text": " Thank you and enjoy this conversation with Stefan Alexander. I've been looking forward to this for quite some time. Same here. So Brian told me that I should look into you and at first I just thought you were not interested in theories of everything, just a physicist working in some particular field of physics. But it turns out that what you're interested in is almost exactly what this channel is interested in, namely theories of everything. You also surmise about consciousness, but that's more in your book."
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"text": " So we'll talk about the autodidactic universe. We'll touch on some of Chern Simon's modified gravity. I went back and read one of your seminal papers, Inflation Brain Annihilation from around 2001. Oh, yeah. My little strength theory days. Yep. And then quantum cosmological constant. I only got to skim that briefly. Okay. Do you have any questions for me before we get started?"
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"text": " Let's dive in. The way that this is meant to be treated is as if you have an imbecile across from you in office hours, who's extremely curious. So I'm going to be asking you, can you define this term, this term, this term? Office hours, forget about an external audience. Okay, gotcha. Okay, that sounds like that sounds like the problem is that I'm probably going to be the imbecile, but that's okay. Okay, well, why don't you give the audience an overview of your autodidactic universe theory?"
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"text": " Sure. Well, the theory was started by, for a couple of years of conversations between, it starts roots with independent conversation that Lee Smolin and my friend, colleague Jaron Lanier, the virtual reality pioneer, we've been, all three of us have been friends for a long time. So we, as with"
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"text": " We have our side chats. We talk over the years about things, about matters that are scientific or not scientific. And over the years, our conversation all coalesce into this thing about whether or not, well, first of all, Lee and John has over the years had their own side conversations about"
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"text": " whether physical laws can learn, physical systems could learn their own laws, that type of idea, and use an idea, some evolutionary theory. I kind of came in at it with Jarron and also Lee separately, thinking about fundamental theories, like theories of quantum gravity or unified theories, and just looking at them structurally, that the observation is that"
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"text": " You know, one interesting fact is that if you look at, for example, string theory and you look at loop quantum gravity and you look at other approaches to quantum gravity, even the original ideas of super membrane theory, the idea that the fundamental degree of freedom is really a membrane, not a string. And when people tried to quantize this membrane, they ran into problems and they found out that"
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"text": " Oh, look at this. This membrane theory could be properly quantized if you turn it into a matrix theory. So at the end of the day, all these approaches of quantum gravity pointed to matrix theories. And what do I mean by matrix theories? I'm sure you might want to know that."
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"text": " So as far as I understand, I'll just tell you and then you can correct me because it helps me learn. Especially because I put myself on the line, my ego on the line, and I learn better. Okay, so as far as I understand with the matrix models, you just mentioned that it solves a particular issue, but another issue is created in that they're finite dimensional and what you want to do is take n to infinity. Is that correct? One of the things you can do to make contact with the continuum, for example,"
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"text": " Yang-Mills like theories, which are, is that, yes, right, when you take n, where n is the rank of the matrix, so if n is two, I have a two by two matrix. So when n goes to infinity, the rank goes to infinity, that it does reduce back to known theories like Yang-Mills theories, for example."
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"text": " That's a good question. It's similar to when you"
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"text": " You do a Fourier series, you take that sum and you look at basically the sum of sines and cosines, and then when you take basically n in that sum to infinity, that becomes the integral sign. So it's similar to the continuum hypothesis. I see. Okay, continue. Yeah, no pun intended. Yeah, so"
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"text": " So in a nutshell, the observation that I made with Lee Smolin and Lee made with me is that how interesting matrix models seem to underlie a couple of what we thought to be disparate approaches to quantum gravity or unification. Strain theory, loop quantum gravity, and other ways, you know, random matrix models, they all kind of seem like membrane theory."
},
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"text": " They all pointed these matrix models. So maybe we should take more seriously that the matrix models themselves might actually be, well, not actually be, I mean, Banks, Fischler, Schenker and Susskind, so-called BFSS, and I think IKKT named after some Japanese theorists, actually conjectured that M theory, which is supposed to be the unification of all string theories,"
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"text": " m theory, or the so-called non-perturbative definition of string theory, it was hypothesized to be a matrix theory. So we weren't saying anything new there, but to maybe extend that, extend it beyond even m theory, to say that other approaches of quantum gravity might also have this. So that was one observation. The second observation that me, Jarn, and Lee made was that if you look at the equations of a matrix model,"
},
{
"end_time": 937.108,
"index": 37,
"start_time": 913.541,
"text": " It has a semblance to artificial neural network. It might be useful for me to write something."
},
{
"end_time": 962.5,
"index": 38,
"start_time": 937.5,
"text": " And I'm going to be very schematic here, because I'm writing from memory. So just recall that an artificial neural network basically tells me that if I have a simple two-layered, if I have an input, so here's my x. So x is a vector. It's an n-tuplet, right?"
},
{
"end_time": 991.169,
"index": 39,
"start_time": 962.79,
"text": " I can, you know, that think of each point here, each dot is a neuron that could be connected, you know, in a forward way, right? I can have connection to, let me call this thing. Right. Right. So, oops, my bad. I don't know why it's doing that. Are you able to hear anywhere it sounds? Yep. No, no, no. Okay. I just want to get right here. So the equation says that if I, if I, there's some output"
},
{
"end_time": 1021.544,
"index": 40,
"start_time": 992.142,
"text": " y, right? And there's a weight matrix that determines how correlated, how connected these neurons are. So, for example, x1, right? If I have x1 and then I have y1, for example, right? This wij will denote basically this is xj and this is yi."
},
{
"end_time": 1051.8,
"index": 41,
"start_time": 1021.834,
"text": " Right. So this basically tells me how every neuron is connected. You know, the output is connected to the input. Right. And then, of course, there's some bias term here that basically helps out with to further basically, you know, to help with bias and these connections. All right. So that's there's a long story here about neural networks."
},
{
"end_time": 1074.445,
"index": 42,
"start_time": 1052.261,
"text": " This is very similar to statistical inference. If I basically have in this case a line and I tell you the slope of the line, I can adjust the slope of the line basically to fit some data. Given an input"
},
{
"end_time": 1101.288,
"index": 43,
"start_time": 1074.821,
"text": " The output will basically sort of maximize or the slope will basically maximize. In this case, if you try to get the best standard mean, you can basically use this. This is a multi-dimensional version of statistical inference. I see. I see. OK. OK."
},
{
"end_time": 1131.766,
"index": 44,
"start_time": 1102.159,
"text": " The matrix, so what I'm going to take notice of here is that mathematically, I'm basically performing some kind of linear transformation from one vector to another vector. And the weights basically is this transformation matrix. That's one way I like to think about it, right? Okay. Okay. So in a matrix model, what we have is something similar"
},
{
"end_time": 1162.005,
"index": 45,
"start_time": 1132.466,
"text": " Not similar, but what we have is a situation where we have... So the analogy, first of all, let me spell out the analogy. The analogy is instead of having neurons that are represented by vectors, the idea here is that we have matrices"
},
{
"end_time": 1191.886,
"index": 46,
"start_time": 1162.432,
"text": " which are basically tensor products of vectors. So in other words, I can, for example, I could take the tensor product of say two vectors, Xi, tensor Xj, right? And then I can have a matrix Xij, right? So likewise, I can have some correspondence where the equation of an artificial neural network, which is mapping the idea of a perceptron or an artificial neuron, is represented as a vector."
},
{
"end_time": 1220.776,
"index": 47,
"start_time": 1192.312,
"text": " The idea here is that the matrices, right, there's a sense in which I can isolate some components of this matrix and I could freeze and this freezing procedure again is spelled out in the paper and it's a long story, but I just want to spell out the basic idea. I can basically isolate vectors in this thing, in this matrix model. What do you mean when you say you can isolate them?"
},
{
"end_time": 1249.599,
"index": 48,
"start_time": 1221.886,
"text": " Okay, so let me let me say another thing here. You mean like how they can be decomposed and then you just pull out one of them? Yeah, yeah. So let me let's so in the matrix models, what we have is basically is let me actually write down one of these matrices. Okay. X. So it's x, a seven, x, i, m, n. So okay, what is this thing, right? So basically,"
},
{
"end_time": 1277.875,
"index": 49,
"start_time": 1249.889,
"text": " It's basically, let's say that I runs from one to three for now, right? So this would be X1, X2, X3, and then I'll still have MN here. Right? So, so one thing I could do here is assume that MN is, say, completely diagonal, right? So I can basically"
},
{
"end_time": 1307.415,
"index": 50,
"start_time": 1278.404,
"text": " make some approximation and collapse this MN, right, into some X. So in other words, here's X MN, right. And what I now want to do is basically only look at these components here, the diagonal components. Okay. I can play with that for now. And then, you know, just look only at the diagonal components of this MN matrix. And there's something that allows you to say that it's diagonalizable."
},
{
"end_time": 1334.735,
"index": 51,
"start_time": 1308.387,
"text": " Yes, there's something that allows me to say that. Right. Um, and so that's, that's, that's one, that's one thing you can do, but there are other, you know, one of the things that we are currently working on as we speak in the follower paper is exactly how to turn this thing into a, you know, um, into a bona fide, um,"
},
{
"end_time": 1349.65,
"index": 52,
"start_time": 1336.374,
"text": " into a bonafide learning architecture, similar to artificial neural network. But the upshot is that if you look at the equation that I wrote,"
},
{
"end_time": 1380.606,
"index": 53,
"start_time": 1350.657,
"text": " Okay, those matrices from when I was reading your paper, if I understand correctly, it's something like the BFSS matrix models. But then what I was wondering is, and this is my rudimentary knowledge that the more general form of BFSS is BMN. And it takes into account a turn Simon's term and so on. And it also is not in Minkowski space, it's in PP wave, which to me sounds as if it's more general. So I'm curious, why didn't you use the BMN model? Why did you choose to use BFSS?"
},
{
"end_time": 1410.128,
"index": 54,
"start_time": 1381.391,
"text": " Good question. I mean, right now we're not choosing, in fact, we're not even choosing, we are just trying to figure out, okay, the idea is that there are all these matrix models, as you said, BMN, BFSS, IKKT. What we're really focusing on is to actually liberate ourselves and really, we really want to use that as a motivation, but not yet commit ourselves to any one of those models, actually."
},
{
"end_time": 1440.794,
"index": 55,
"start_time": 1411.271,
"text": " So the matrix model that we actually did commit ourselves to is something called a cubic matrix model. And that was actually authored by, you know, motivated by Lee Smolin. So the idea would be in this cubic matrix model is that you have, you know, you have a Lagrangian, okay, that has a matrix, let me call this thing,"
},
{
"end_time": 1469.394,
"index": 56,
"start_time": 1441.237,
"text": " a matrix X. And so now, but this matrix actually has a kinetic term, X dot square. Now I'm suppressing the MN indices here. So it has, okay, I'm suppressing it. So it has kinetic energy and then it will have a potential that depends on X, except this potential is cubic in X. So it's cubic in a sense because it's a matrix, it's a commutator, right?"
},
{
"end_time": 1494.48,
"index": 57,
"start_time": 1471.715,
"text": " Like this. Because matrices remember their matrix value, so the products will be commutators. And as a result, the equations of motion of these matrices, you know, the dynamics of these matrices classically will be something that looks like X dot, right, is there's some there's probably some coupling here and we call it lambda."
},
{
"end_time": 1524.787,
"index": 58,
"start_time": 1494.821,
"text": " is going to be lambda you know x comma x because I have to take a derivative with respect to x and if you look at this thing here right the idea is that you know if you look at this here this is like I want to now think of this x dot as my y right okay and and somehow this you know this um x x commutator"
},
{
"end_time": 1552.705,
"index": 59,
"start_time": 1525.247,
"text": " could be massaged into something that looks like Y times a component of X. That's the analogy here. Now we're not there yet. So the idea is that somehow the dynamics of a matrix model is similar to the dynamics of basically how a neural network is able to learn"
},
{
"end_time": 1578.729,
"index": 60,
"start_time": 1553.319,
"text": " maybe in a supervised way. So in other words, if I present the theory with an output or something known, so like a known solution, the idea is that can the theory maybe spit out new solutions? Okay. Or for example, here's one thing we're playing with. Imagine that these matrix models could spit out realizations of the standard model. So in other words, because they're n by n matrices,"
},
{
"end_time": 1608.422,
"index": 61,
"start_time": 1579.309,
"text": " You know, so therefore it might correspond to a group S-U-N, special unitary group N, then you can imagine that basically S-U-3 times S-U-2 cross U-1 may pop out as solutions of this theory. Okay. And the idea would be like, given that we know that this is a solution, right, you think of that as the output. The same way we present a picture of a cat or a dog and have the neural network learn that,"
},
{
"end_time": 1637.551,
"index": 62,
"start_time": 1608.968,
"text": " the same way we were using a matrix model and the dynamics of the matrix model itself, right, as a learning architecture. So there's nothing external to the system. It's sort of like, you know, it's part of the system itself via its dynamics, its equations of motion. And the idea here is if you're in a one-to-one correspondence between a learning architecture via neural networks and the dynamics of the matrix model,"
},
{
"end_time": 1667.5,
"index": 63,
"start_time": 1638.422,
"text": " If we're able to make this correspondence between X and this correspondence. So let me see if I can make this a cleaner statement here. So on one side I have an artificial neural network and it has dynamics, Y maps, input goes to output. And then what happens is that, what's going on here? The weights then get adjusted."
},
{
"end_time": 1691.886,
"index": 64,
"start_time": 1667.739,
"text": " So the weights are the things that actually get adjusted in this learning, right? The weights get optimized. Likewise, if I have a matrix model and then there's something like the standard model as a solution, can we use the dynamics? Can we use, let me see, hold on a second."
},
{
"end_time": 1720.742,
"index": 65,
"start_time": 1693.609,
"text": " In the paper, did you focus or restrict yourself to restricted Boltzmann machines, or did you try out others? So far, we restricted ourselves to hop-feel-like models, which in some cases can have a semblance of RBMs, restricted Boltzmann machines. I see. And the reason for that is just simplicity?"
},
{
"end_time": 1749.991,
"index": 66,
"start_time": 1721.783,
"text": " The reason for that is generality and simplicity at the moment. But we're definitely keeping an eye out for other ways. So the idea here is that this correspondence here is instead of input-output via the artificial neural network, the matrix model, the input now would be the dynamic, like the equations of motion."
},
{
"end_time": 1780.623,
"index": 67,
"start_time": 1752.312,
"text": " So we use the equation of motion itself as a learning mechanism. And the idea now is that what are the weights? How are the weights being adjusted? And the idea here is that the things that get adjusted might be the parameters of the standard model. Because one of the big unresolved things in theories of everything and like string theory or even grand unified theories is that you can spit out solutions or realizations of the standard model."
},
{
"end_time": 1810.162,
"index": 68,
"start_time": 1781.015,
"text": " But as you know, because of this issue of the landscape, it's hard to tune those parameters. So we're saying, okay, embrace that. But really what's going on? Maybe it's that the universe is actually learning and it somehow finds a solution. If the solution is stable in some sense, stable meaning that it's because these weights are being adjusted. And the idea could be that these weights"
},
{
"end_time": 1834.548,
"index": 69,
"start_time": 1811.101,
"text": " You know, while you work with Lee, Lee has this idea of evolutionary black holes and that in the genesis of each black hole is another universe with differently tuned constants and it's predictive in the sense that"
},
{
"end_time": 1859.07,
"index": 70,
"start_time": 1834.923,
"text": " If we're in the typical member of the space of universes, we should see certain formations of black holes be maximal because the universe is constantly trying to maximize the amount of black holes it creates. Now, is that similar to this? Was this spawned by it? Can that be derived from this? Is it distinct? Yeah. I mean, so Lee, to my memory, you know, was the person that came up with the landscape."
},
{
"end_time": 1888.729,
"index": 71,
"start_time": 1859.462,
"text": " idea in that picture of black holes spawning and being used as a mechanism to determine, not to determine, but to populate this landscape with different parameters of our standard model, for example, so of the coupling constants. So I would say this is in that spirit for sure, because obviously for many years I've been talking with Lee about"
},
{
"end_time": 1917.449,
"index": 72,
"start_time": 1889.07,
"text": " How do we get around the issues of how theories might determine the values of the standard model and what mechanisms exist? So one of the things I paid a lot of attention to when I worked in string phenomenology, which is how string theory can give us back the real world, was basically, yeah, this was a big question. And one way out, of course, is that if string theory gave you something like"
},
{
"end_time": 1941.442,
"index": 73,
"start_time": 1919.718,
"text": " like eternal inflation, then the idea there was that the different parts of the universe that are inflated would populate the stamp, you know, the different parameters and we happen to be living in one of them. So that's one, you hit the jackpot type of idea. The other one, so, but you know, I've always kept an open mind about"
},
{
"end_time": 1955.93,
"index": 74,
"start_time": 1941.664,
"text": " Other alternative ways of thinking about maybe there's something about the theory itself that's determined in this. And so the idea here is to really simply put a learn to think that maybe there's some kind of learning in the sense of artificial neural network."
},
{
"end_time": 1985.794,
"index": 75,
"start_time": 1956.596,
"text": " But instead of it being a neural network is the degrees of freedom. Instead of being a neural network, it's actually the matrices, which are now the fundamental degrees of freedom, that are playing the role of the perceptron. And then the weights are being adjusted. The hope is that it's going to be the parameters of the standard model. That's it. Interesting. One out I would say, to give myself an out here, is that a quote from Albert Einstein, you know,"
},
{
"end_time": 2015.179,
"index": 76,
"start_time": 1986.015,
"text": " If we knew what we were talking about, we wouldn't call it research. So there's a part of me that was still confused about a couple of things, which is why it's great talking to smart people like yourself. As I just read the title of the paper before I actually read the abstract of the paper before diving into it, I thought perhaps it was something like, okay, the weights change and the weights change in such a manner that if you follow them, they look like particles along a trajectory. That's interesting. Tell me more about that. That's interesting."
},
{
"end_time": 2039.821,
"index": 77,
"start_time": 2015.657,
"text": " With each pass, there's obviously a changing of the weights. Can this changing of the weights be seen as a trajectory? And then if so, can that trajectory map onto what we think the particle's trajectory should be? That's a great idea. No, no, no, that's a really good idea. That's a really good idea. And let me think about it. I'll get back to you. That's a really good idea, actually. Yeah."
},
{
"end_time": 2065.64,
"index": 78,
"start_time": 2043.916,
"text": " In a sense, you know, a way that you're right, you know, because if you think about this, let me say one thing about that. Sure. So let me get back to this. This share thing. So one one way to think about matrix theory. So, you know, to give some because there is abstract matrix. Now, let me imagine that I'm in three dimensions."
},
{
"end_time": 2091.169,
"index": 79,
"start_time": 2066.442,
"text": " So I have z, x, y. And now I'm going to put a particle in three dimensions. So I'm going to call this the location of this particle. I'm going to give it some vector x from the origin. And obviously, I can look at the components of this vector. So there's some component of the vector."
},
{
"end_time": 2120.896,
"index": 80,
"start_time": 2091.613,
"text": " I'm going to take that vector sign off and label a component xi, where i goes from 1 to 3. So x1 is x, x2 is y, x3 is z. So now I'm going to now think about this particle confined to live on a sphere. And now the sphere has some basic area, unit area."
},
{
"end_time": 2148.285,
"index": 81,
"start_time": 2121.544,
"text": " Now the picture in string theory is that actually these matrices correspond to the configuration of a particle in string theory called a D0 brain. So actually this will be a zero dimensional particle but it's fuzzy. So what happens is that in"
},
{
"end_time": 2178.456,
"index": 82,
"start_time": 2149.275,
"text": " smooth continuous space times, Xi is just some vector that will denote any position on my surface. But the fact that Xi and Xj, for example, don't commute, it corresponds to these d0 brains. So the idea is I have these d0 brains sitting around here, and their strings are basically attached to these d0 brains. So that when they cross each other, you know, brain one, the d0 particle"
},
{
"end_time": 2202.807,
"index": 83,
"start_time": 2179.002,
"text": " This is a D0 brain, right? D corresponds to a Dirichlet, meaning that a string ends on it with a Dirichlet boundary condition, and it ends at a point, right? So then you can now focus on the point particle, but a difference from an ordinary point particle in that it doesn't commute. The same way x and p don't commute in quantum mechanics. In this case, x1 and x2 is not going to commute."
},
{
"end_time": 2230.589,
"index": 84,
"start_time": 2203.183,
"text": " So what that corresponds to this thing called... Can I make a quick aside for the audience? Please, please. Whenever you have a DP brain, so PM is an integer, that means the spatial dimension. So if you ever hear D6 brains, it means it's a seven dimension because you have to plus one for time. So right now D0 essentially means point, but you could still have world lines, which is what I believe is captured in the BFSS model. Very nice. So like what you just said, this will be a D2 brain and that will be a membrane."
},
{
"end_time": 2262.517,
"index": 85,
"start_time": 2232.585,
"text": " For example, it helps clarify sometimes these small terms I know when I was learning, which by the way, just so you know, as a confession Stefan, I try my best to study for each interview assiduously. And this one, there was a personal family matter that I had to get to. And so I put a monkey wrench in my studying for this. And for the past 10 days or so, I knew nothing. I knew no turn simons. I knew no patriajan. I don't even know how to pronounce that."
},
{
"end_time": 2291.647,
"index": 86,
"start_time": 2262.756,
"text": " I basically had to learn all of this and I still know a modicum of it just to prep for this. So even before this, I didn't know what a D zero brain was. So I'm saying this because these are questions I had and I'm sure the audience as they're watching would have similar questions. Wonderful. Right. So that's a correctly pointed D and a D one, a D one brain would be a string. That's right. And therefore a D zero brain would be a point particle. And,"
},
{
"end_time": 2315.64,
"index": 87,
"start_time": 2291.886,
"text": " So the idea here is that the matrix that I just talked about, matrix theory, corresponds to the position of a D0 brain in a non-commutative or so-called fuzzy space-time. So that's a nice picture to have in your mind when we're thinking about matrix theories, what they could describe. They're describing the motions of these D0 brains"
},
{
"end_time": 2344.94,
"index": 88,
"start_time": 2315.896,
"text": " but in a space time that's not commutative. Now, we're not, it's not only describing that. That's just one limit of the theory where it's doing that, but it's a useful thing to think about. And another way you can think about it too is the membrane, for example, you can think of it basically as a collection of these zero brains that come together to form the membrane. So the basic building blocks in this matrix theory are these zero brains and the things they can do. And why is that interesting for the insight that you had there?"
},
{
"end_time": 2370.691,
"index": 89,
"start_time": 2345.401,
"text": " Because when I think about the interaction of these zero brains, for example, it corresponds to the commutator, XI, XJ. And if this is in some correspondence to WIJ, the weight matrices of a learner that you're talking about, then you remember a potential energy determines basically the trajectory"
},
{
"end_time": 2400.538,
"index": 90,
"start_time": 2371.101,
"text": " You know, sometimes I say that it's, it's often useful for people who watch this podcast to watch it once and be befuddled and not understand. And it's basically in the second passing that you get the true understanding. The way that I like to think about it is that one is thirsty, like, they're curious, they're inquisitive,"
},
{
"end_time": 2404.753,
"index": 91,
"start_time": 2401.032,
"text": " and so they want to drink but often it's it's best"
},
{
"end_time": 2431.613,
"index": 92,
"start_time": 2405.145,
"text": " Often it's not always the best to try and drink from the fire holes, not because you're going to fail drinking from the fire holes, but at least the point is to get wet. I think Wheeler said that people are trying to drink, but the point is to get wet. So how about I'm going to take a couple sentences from your paper with this abstruse, unfathomable language for most people. Then we're going to break them down term by term so that afterwards people can go through and decipher it and understand what was meant."
},
{
"end_time": 2460.486,
"index": 93,
"start_time": 2433.012,
"text": " Sure. Okay, so I believe this is just the abstract of the churn simons modified GR. So churn simons modified gravity is an effective extension of general relativity that captures leading order gravitational parity violation. So first of all, there's churn simons, we're going to explain that effective extension going to explain leading order going to explain and gravitational parity violation. So what is churn simons? Very good."
},
{
"end_time": 2489.701,
"index": 94,
"start_time": 2461.51,
"text": " His name after, of course, the authors, someone who I consider a friend and a mentor, Jim Simons, mathematician and billionaire, philanthropist, and polymath, and overall great guy. He's one of actually, he's one of the most humorous, funniest people, people I know."
},
{
"end_time": 2518.882,
"index": 95,
"start_time": 2490.503,
"text": " He just, he's, he makes me, anyway, so Jim is one of the architects of, yeah, it makes me laugh. And of course, his, his collaborator, Churn. So Churn Simonsley is based on this piece of math, which is a magical piece of math. And that basically has to do with something called"
},
{
"end_time": 2547.142,
"index": 96,
"start_time": 2519.48,
"text": " So if I give you a manifold, can I characterize properties of this manifold, in some cases topological properties of the manifold? For example, if you have a donut, you can characterize how many holes a manifold can have, no matter how much you deform the manifold locally,"
},
{
"end_time": 2576.544,
"index": 97,
"start_time": 2547.363,
"text": " There's an invariant, which is the number of holes that it has. An invariant because no matter how I change coordinates, whatever I do smoothly to this manifold, this thing's going to be. So is there a way to mathematically measure these types of topological things? And what Jim and Simon and Churns discovered was a new way, a new characteristic class called the Churn-Simon's, a new invariant called the Churn-Simon's invariant. And what's special about it for physicists"
},
{
"end_time": 2606.869,
"index": 98,
"start_time": 2576.886,
"text": " If you know the degrees of freedom already, like of our gauge theory, for example. So now let me get down to earth here. So if I give you a gauge theory, the gauge theory is described like electromagnetism or Yang or the standard model by a connection, right? So our gauge potential or the photon field, right? The photon field is this thing called a mu, right? And the turn Simon's theory says that if I give you, can you see this?"
},
{
"end_time": 2615.094,
"index": 99,
"start_time": 2607.21,
"text": " No. All right, so I'm not going to share screen. Hear that sound."
},
{
"end_time": 2642.125,
"index": 100,
"start_time": 2616.049,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 2668.285,
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"start_time": 2642.125,
"text": " There's also something called Shopify Magic, your AI-powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level. Join the ranks of businesses in 175 countries that have made Shopify the backbone."
},
{
"end_time": 2694.019,
"index": 102,
"start_time": 2668.285,
"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklyn. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at shopify.com slash theories, all lowercase."
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"text": " Razor blades are like diving boards. The longer the board, the more the wobble, the more the wobble, the more nicks, cuts, scrapes. A bad shave isn't a blade problem, it's an extension problem. Henson is a family-owned aerospace parts manufacturer that's made parts for the International Space Station and the Mars Rover."
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"text": " Now they're bringing that precision engineering to your shaving experience. By using aerospace-grade CNC machines, Henson makes razors that extend less than the thickness of a human hair. The razor also has built-in channels that evacuates hair and cream, which make clogging virtually impossible. Henson Shaving wants to produce the best razors, not the best razor business,"
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"text": " So that means no plastics, no subscriptions, no proprietary blades and no planned obsolescence. It's also extremely affordable. The Henson razor works with the standard dual edge blades that give you that old school shave with the benefits of this new school tech. It's time to say no to subscriptions and yes to a razor that'll last you a lifetime."
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"text": " Visit HensonShaving.com slash everything. If you use that code, you'll get two years worth of blades for free. Just make sure to add them to the cart. Plus 100 free blades when you head to H E N S O N S H A V I N G dot com slash everything and use the code everything. With TD Early Pay, you get your paycheck up to two business days early, which means you can go to tonight's game on a whim."
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},
{
"end_time": 2847.398,
"index": 108,
"start_time": 2818.319,
"text": " We're informed that if I give you an electromagnetism A mu, when mu runs from zero to four, this is the grant of X, right? It's a four-dimensional object, right? So the zero component of this is some scalar quantity, and then the X, Y, and Z will be the spatial part, I. So this is a zero, and this will be a I. So that'll be four dimensions. Now, this thing is actually"
},
{
"end_time": 2876.903,
"index": 109,
"start_time": 2847.995,
"text": " In electromagnetism, I can use this basically to determine basically the electric and the magnetic fields, right? But all the information of the electric and magnetic field is contained in AME, which is a connection. They call it the connection because if I take covariant derivatives of this connection, or if I move this around, this connection around some"
},
{
"end_time": 2901.971,
"index": 110,
"start_time": 2877.483,
"text": " In a gauge theory, in other words, and I could define curvature. That's weird. Okay. So I'm going to start again. You can define this so-called field strength tensor. I know this is review for a lot of people, but just to be for completion. And basically by taking derivatives of"
},
{
"end_time": 2929.735,
"index": 111,
"start_time": 2903.507,
"text": " where this is partial derivative with respect to zero, x, y, and z. I could define this object. So here's a beautiful thing about turn assignments. Turn assignments theory tells you that if I know F mu nu and I can get it from A mu, I could define this invariant in three dimensions, which is just A, let me say, tensor F."
},
{
"end_time": 2960.077,
"index": 112,
"start_time": 2930.384,
"text": " And when I mean by this tensor, it's really an anti-symmetric tensor product. So the churned Simons invariant, let me call it the wedge product. Okay, very good. It is a wedge. So I didn't want to mystify people, but it's what we call a wedge. That's right. So A wedge F is in fact proportional to this churned Simons invariant. And this thing, A wedge F,"
},
{
"end_time": 2982.654,
"index": 113,
"start_time": 2960.555,
"text": " They appear to be local quantities. They are, when I say local quantities, they're not topological, right? But when I take the wedge product, right, and I integrate this over, like say, if I have four dimensions and I take a three dimensional boundary, M3, that basically this thing is going to be, this thing is an invariant, right?"
},
{
"end_time": 3010.725,
"index": 114,
"start_time": 2983.285,
"text": " It's going to measure some kind of topological, it's going to measure a topological invariant. Okay. And when you say it's an invariant, do you mean it doesn't matter which M3 you take, you'll get the same value or what? Like what exactly is being invariant here? The value of this? Over what? So if this thing is some, yeah, if this thing is, you know, this thing is some, let me see."
},
{
"end_time": 3039.94,
"index": 115,
"start_time": 3011.493,
"text": " It's some integer modulo something, which I'm not remembering right now. But basically this integer modulo something, which I forget what it is, is the invariant. So that's now that's the math side of it. And I'm by no means a differential geometer. I'm just a physicist. I can just now tell you. So that's what that is mathematically."
},
{
"end_time": 3070.247,
"index": 116,
"start_time": 3040.776,
"text": " But there's a lot to it in the math literature, right? And it's all right. It was a great math. It was a tremendous mathematical discovery. But the thing that's amazing is that Turing-Simons theory has found itself at home in Nobel Prize winning discoveries in physics. Like when Jim and Turing were coming up, they had no idea it would actually be applied. They just made this mathematical discovery."
},
{
"end_time": 3099.667,
"index": 117,
"start_time": 3070.503,
"text": " And now, like, you know, anywhere from the fractional quantum Hall effect, it's, it's, you know, it's found there in the standard model. It's a key, it plays a key role in establishing anomalies and anomaly cancellation. In fact, the churn Simon's term, I can say something even cool about this in the standard model, the churn Simon's form was called a churn sign form, which is, as I said,"
},
{
"end_time": 3129.94,
"index": 118,
"start_time": 3100.247,
"text": " A wedge F, right? That's for a certain dimension, correct? It's like one dimension for this or... So in this case, this is in three dimensions, yeah. I see, I see. Let's be in three dimensions. It could be also in four dimensions, three or four dimensions, right? Ah, I didn't know. So A wedge F, right? So this A wedge F here, and it turns out that"
},
{
"end_time": 3158.951,
"index": 119,
"start_time": 3130.52,
"text": " is proportional to a current. So in the standard model, we have currents, right? You know, the electromagnetic current. And one of the most important things in the standard model is that these currents are conserved. So for example, I look at, you know, current going in is equal to current coming out, which is a statement that D mu of the current, J mu, right, is zero. Right."
},
{
"end_time": 3187.91,
"index": 120,
"start_time": 3159.565,
"text": " But, you know, this comes from Maxwell's equation that says that, you know, this is basically coming from the statement that d mu, f mu nu, right, is j nu. Right? So if I take another derivative of this thing, then by definition, you see it comes from Maxwell's equations. So what's important here? It turns out that this is no longer the case in the standard model when I turn on quantum corrections."
},
{
"end_time": 3218.473,
"index": 121,
"start_time": 3188.49,
"text": " This is a major, this is so-called the ABJ anomaly, but actually this can be, when I turn on quantum corrections, this is proportional to D of the turned Simons. I'm being schematic here, okay? Yeah, and when you say when you turn on quantum corrections, what do you mean by that? When you add a turned Simons term? Very good. To me, to say when I say turn on quantum corrections, is that if I look at basically"
},
{
"end_time": 3248.575,
"index": 122,
"start_time": 3219.241,
"text": " say the interaction of in quantum electrodynamics. If I say I look at a photon that basically, you know, I can take an electron and it could scatter off and, you know, of a photon, right? This is like an electron E prime. I can imagine like doing things like having another photon like here, right? That will be a quantum effect. And this is now sort of looking like something called, well,"
},
{
"end_time": 3278.763,
"index": 123,
"start_time": 3249.411,
"text": " But you can have other quantum effects, so-called loop diagrams. And there's one special one called a triangle diagram like this, where I have an electron loop, for example, going around and then photons coming in like this. So I can have basically this type of quantum effect. This quantum effect, if you go and calculate it using Feynman's, you know,"
},
{
"end_time": 3303.439,
"index": 124,
"start_time": 3279.155,
"text": " Um, rules will give you this thing here. I see. And this is the famous result of Adela, Bell, and Jaquiv. Um, the ABJ anomaly. So it turns out the standard model will do this and this is not good. Yeah. And this is not good. Why? It's not good because"
},
{
"end_time": 3333.217,
"index": 125,
"start_time": 3303.797,
"text": " The big deal there is that it actually violates the fundamental principle of quantum mechanics, which is it violates unitarity, the conservation of probability. So you can probably see where this is coming from, because if you can now think about this loosely as the probability current, then this is no longer zero. And in quantum mechanics, the probability"
},
{
"end_time": 3362.432,
"index": 126,
"start_time": 3333.473,
"text": " Current, probability current has to be conserved. So it turns out that Chern-Simon's theory is a part of the Standard Model. And it just so happens though that the Standard Model, all the contributions of all the currents correspond to all the different forces, completely cancel. So when I sum over all the currents,"
},
{
"end_time": 3388.643,
"index": 127,
"start_time": 3363.166,
"text": " Okay. Some of all the anomalies, it turns out that they, it vanishes in a standard model. So that's what makes our standard model quite unique, actually, mathematically, that it cancels anomalies. So that's another place Chern-Simons theory shows up. Okay. And then the other place that shows up is actually in string theory. In string theory, the Chern-Simons theory shows up to actually"
},
{
"end_time": 3416.954,
"index": 128,
"start_time": 3390.401,
"text": " In a magical way, it also plays a role in canceling the anomalies in string theory as well. It's called a Green-Schwartz mechanism. Right, right, right. Turn Simon's gravity now is another place that I played a role in pushing over my career as a way of thinking about gravity that has the turn Simon's term in it."
},
{
"end_time": 3432.585,
"index": 129,
"start_time": 3418.353,
"text": " Can we go back"
},
{
"end_time": 3461.954,
"index": 130,
"start_time": 3432.995,
"text": " What an anomaly is, is when there's a violation of the conserved current. But I'm unsure, is that all that anomalies are? Are there other types of anomalies other than quantum anomalies? In other words, whenever someone says there's an anomaly, are they always referring to that the right hand side is no longer zero? Very good. So let me, good question. So let me just say another in general, if I, this is a general statement I'm making about anomalies. Okay. For any current that is conserved,"
},
{
"end_time": 3491.783,
"index": 131,
"start_time": 3462.398,
"text": " That is conserved. I'm going to put on the right hand side the letter A. If it's not equal to zero and there's an A, that A is called the anomaly. That's literally what it is. So when A is zero, then the current is conserved. And the question you're asking is, can an anomaly arise in a non-quantum way? That's a good question."
},
{
"end_time": 3527.261,
"index": 132,
"start_time": 3497.722,
"text": " So one thing, the calculations that are done to determine the anomaly, to my knowledge, are all quantum considerations. But I see no reason why you can't, in some theory, which I can't recall right now, generate an anomaly classically. Okay, so another question that"
},
{
"end_time": 3553.78,
"index": 133,
"start_time": 3528.08,
"text": " Especially undergrads as I know I had is let's say you have the Klein-Gordon and they say, well, it's not unitary. It doesn't conserve probability across time. Well, what's the big deal about that? Because so what if you add some extra, let's say lumps on the probability distribution, why can't you just simply constantly reweight it down to normalize it? So why can't you normalize it at every given infinitesimal moment?"
},
{
"end_time": 3585.794,
"index": 134,
"start_time": 3557.739,
"text": " Is my question making sense? Do you understand or should I restate it? You could always that's right. You can always re normalize. That's what we call re normalize. And that's you know, you can always re normalize. But if you find yourself in a situation that even when you re normalize, it still gets violated, then you're in trouble. I see. I see. Yeah. Is there a way of determining a priori whether that a on the right hand side at the bottom equation is re normalizable? Or is that some large"
},
{
"end_time": 3616.647,
"index": 135,
"start_time": 3587.329,
"text": " Very good. That's right. So the A that's generated actually has a divergence as well. And that divergence, when I say divergence, I mean, there's an infinity when I actually, you know, take"
},
{
"end_time": 3644.36,
"index": 136,
"start_time": 3617.261,
"text": " When I integrate out, when I integrate to, you know, to high, high momentum, right? And this, because remember this A is coming from the internal legs. And that notice, I would say that that's getting into, you know, notice, this is a question, the question that I think this is pointed to is, what is it about the anomaly?"
},
{
"end_time": 3674.292,
"index": 137,
"start_time": 3644.633,
"text": " that's leading you to deduce that the theory is not unitary. And this has to do with something called award identities. And the minute you have these anomalies, you can show that these award identities, which are identities having to do the unitarity of the theory, is violated. I need to think more about that. I don't have an intuition for it."
},
{
"end_time": 3703.456,
"index": 138,
"start_time": 3674.889,
"text": " Sure, and then also looking at this middle equation, the one that has the sum with the D and the CS, why is it a difficult problem to get rid of an anomaly when it seems like, well, if my understanding is correct, you add a certain term to a Lagrangian, if it's as simple as that, in some cases it is. So you add a certain, in this case, a turnsimus term, perhaps then an interaction term with the turnsimus term, but you add a term nonetheless, then you go through this"
},
{
"end_time": 3733.575,
"index": 139,
"start_time": 3704.224,
"text": " No, we do have these anomaly canceling conditions in the standard model. And what that boils down to is"
},
{
"end_time": 3762.841,
"index": 140,
"start_time": 3733.882,
"text": " For the anomalies to cancel in the standard model, the charge assignments, the way you identify the charges of the quarks, the leptons and the quarks and the leptons, and the color of the quarks, and the gauge groups. That's what I mean by the color, the isospin as well as the charges. The charges, the assignments, the fact that the quarks have one fractional charge,"
},
{
"end_time": 3783.217,
"index": 141,
"start_time": 3763.49,
"text": " is precisely because when I add up the anomalies from all the other interactions, so those charge assignments are the things that actually are allowing this anomaly to cancel. I see. Interesting."
},
{
"end_time": 3810.572,
"index": 142,
"start_time": 3783.899,
"text": " I want to know, what do you consider to be a theory of everything? The reason I ask this is when I asked, well, some people say, well, it needs to incorporate consciousness or needs to explain the origins of the universe. Some people just say, unify gravity in the standard model. What does the theory of everything mean to you? It's a really good question. Well, I mean, I have my ambitions now are"
},
{
"end_time": 3839.428,
"index": 143,
"start_time": 3811.92,
"text": " I would say that, for example, if string theory was able to provide as a solution that meets the standard of what a solution is in string theory, that gives us back, say, something like, at the very least, an early universe scenario that is consistent with observation."
},
{
"end_time": 3856.34,
"index": 144,
"start_time": 3840.128,
"text": " Maybe it's inflation, maybe it's an alternative to inflation. I would literally say that string theory, therefore, modulo its difficulty and tell me why that solution is preferred over other solutions would be a fear of everything. All right."
},
{
"end_time": 3873.763,
"index": 145,
"start_time": 3856.681,
"text": " And then I would add about the more like the questions of like, okay, higher level organizational properties of matter, including life and including consciousness. I have some thoughts about that too, but I would say that, you know, at this level, I would call that a theory of everything."
},
{
"end_time": 3902.978,
"index": 146,
"start_time": 3874.138,
"text": " So it sounds like that's been a common thread throughout your entire career because around 2000, 2001 or so, but you've been working at it probably in 2000, you had the inflation of the D brain, D brain annihilation. And that seemed at least seem to produce something that looks akin to the big bang. And I believe you use some data to show, I'm not sure if you, if you made a prediction and you showed how it matches with prediction, I'm not sure about that, but either way, that sounds like a through line. Yeah. So, um,"
},
{
"end_time": 3933.148,
"index": 147,
"start_time": 3903.729,
"text": " I was trained as a string cosmologist, meaning that someone that knows both string theory and enough cosmology, enough of each, but certainly not a master of either. Because back then, this was the year 2000, 1999, 2000, the call was, can we... Some people felt string theory wasn't developed enough. Some of us felt it was developed enough to then ask questions of"
},
{
"end_time": 3959.872,
"index": 148,
"start_time": 3933.524,
"text": " Can we reproduce something like cosmic inflation? So I went to my first postdoc trying to do that. And that was my take on how to do that. So I guess the fact that it was published meant that it met some standards. But one of the things it did do was it opened the floodgates for other string theorists. And I certainly wasn't the first and the only one. But anyway, open the floodgates for others to then"
},
{
"end_time": 3989.206,
"index": 149,
"start_time": 3960.299,
"text": " improve or develop different ideas, but similar ideas, you know, with string theory, that somehow these D-brains are playing some role in describing the early universe and four dimensions out of 10 dimensions. Did you do that work at UBC? Very good. I spent a lot of my time thinking about the idea when I was at UBC as a grad student. But then I"
},
{
"end_time": 4016.271,
"index": 150,
"start_time": 3989.991,
"text": " really did it when I was a postdoc at Imperial College in London. I remember the first time we talked, I think the only time we talked about a year ago, that's how long this podcast has been in the making. You said, oh, Jai Mungo, Jai Mungo, wait, I went to school with your brother. Okay. Do you mind telling me a story about my brother? I think he's a genius. I remember when I, okay, so"
},
{
"end_time": 4045.879,
"index": 151,
"start_time": 4017.142,
"text": " First of all, one thing I think is interesting to note is that, you know, my parents immigrated from Trinidad when I was a kid to New York City and, you know, all throughout my growing up and I kind of was, I was alone. I was the only one, you know, there were lots of other really bright people around me, but I felt like, okay, I'm this immigrant guy from the Bronx and there weren't really many people I saw that looked like me or that was from a similar cultural background."
},
{
"end_time": 4073.882,
"index": 152,
"start_time": 4046.442,
"text": " And maybe you take that in as a young person and maybe, well, maybe I'm not meant to be as good as I want. And let me just speak it as a younger person when I was a teenager and, you know, into college. So when I went to UBC and I met this guy, Sebastian Jaimungal, who was at the Blackboard, like, like completely destroying it. I mean, he was like, you know, me and Damien, the other grad students,"
},
{
"end_time": 4097.329,
"index": 153,
"start_time": 4074.138,
"text": " We looked at this guy like, you know, this guy is like, you know, this guy is like a total badass. He just kind of knew everything. And he was also, you know, one of the things that I realized I was so, had left an impression on me, actually, he actually inspired this in me. So if there's something I say I owe Sebastian, it was"
},
{
"end_time": 4125.23,
"index": 154,
"start_time": 4097.619,
"text": " that he was not only somebody that was highly versed in quantum field theory and string theory, I mean, he got a postdoc to go to Princeton, right, the top place in the world at that time, one of the top places for theoretical physics. So he not only did that, I mean, was that good, right, that he got the top postdoc in the world, but he was versed also in condensed matter theory. He was, you know, so he was one of these people that he was"
},
{
"end_time": 4152.142,
"index": 155,
"start_time": 4125.742,
"text": " verse in all these branches of theoretical physics. And that really was the thing that allowed me to break the chains of the disciplinary boundaries that we create for ourselves. He was somebody that really inspired that. So, and so anyway, meeting him also gave me a confidence booster because I was like, oh, wait a minute, look at this, you know, this other like, you know, I guess he's from Trinidad, Canadian Trinidadian, right?"
},
{
"end_time": 4181.749,
"index": 156,
"start_time": 4152.637,
"text": " He was born in Trinidad. From my background, he was one of the top grad students in the world in theoretical physics. That gave me a real confidence booster. We also spoke a lot. We talked a lot of physics and I learned a lot from him. He actually was the one that taught me wedge products when I was a grad student. Give Sebastian a big hug for me. I will, man. Tell him to come visit me."
},
{
"end_time": 4210.708,
"index": 157,
"start_time": 4182.637,
"text": " Did you have doubts about your own mathematical ability or your own bet? If whether or not you could, not that you wanted to, maybe I'm sure you had doubts. Should I go into this? But could you, did you have the ability? So did you ever doubt your own ability? Big time, big time. Yeah. Big time. And I remember I, um, in fact, I remember when I was a graduate student, I knew I was deeply interested in the big questions and I, but I actually was going to settle for less. And,"
},
{
"end_time": 4233.541,
"index": 158,
"start_time": 4211.067,
"text": " Because internally I didn't feel I had what it took. And everybody else was just really mathematical and really knew things that I didn't know and I felt was going to be such a learning curve. And I remember one time that we had this visitor that had come visit Brown's physics department."
},
{
"end_time": 4263.882,
"index": 159,
"start_time": 4234.224,
"text": " He was one of the most brilliant string theorists. And he carried himself as if he was some kind of guru. I remember he used to walk. I was like, is this guy some kind of yogi or something? And his name was Sumit Das. And he used to come visit the string theorists at Brown. And he'd be there on weekends. And one day I was hanging out, and he started talking to me. And I was like, why is this string theorist talking to me?"
},
{
"end_time": 4291.015,
"index": 160,
"start_time": 4264.377,
"text": " And then I asked him, I said, I felt comfortable. I was like, is that something that like, you know, if you want to do strength theory, how good do you, do you need to do this? He goes, no, no, no. All you have to do is be passionate about it and just go for it. And somehow the way he said it to me made me feel like, well, maybe I can do this. Right. So I definitely, I owe, I definitely want to give, I owe it to submit Das, you know, for, for kind of playing that role, just saying, Hey, you can do this."
},
{
"end_time": 4319.462,
"index": 161,
"start_time": 4291.63,
"text": " But, you know, that still lives at me. That still lives at me. I still feel like I, yeah, I, you know, my strengths are not with, you know, knowing a whole bunch of math. Although I love math and I love learning from mathematicians and I, you know, you know, there's a place where we play, we have to play on our strengths and know what they are. In my case, I'm, you know, kind of intuitive. I have pictures. I play with thought experiments."
},
{
"end_time": 4345.486,
"index": 162,
"start_time": 4319.872,
"text": " It's important to talk to people, to have soundboards, and one of the things that's very important to me is actually having soundboards that are not always experts in my field. So I find things like this to be very useful also to my research, like conversations like this. You're doing a service to physics research. Thank you, thank you. So what age was that when you met with that guy Sumit, I believe his name is Sumit Das?"
},
{
"end_time": 4375.469,
"index": 163,
"start_time": 4346.152,
"text": " Yes, Sumit Das. I was a first year graduate student and I was actually trying to be an experimentalist at the time. Not because it wasn't experimental work is as hard or even harder than theory work. That's the asterisk for Brian Keating. Yes, exactly. But I guess what I'm saying was that it was a time where what my real interests were, I was suppressing it."
},
{
"end_time": 4405.725,
"index": 164,
"start_time": 4376.681,
"text": " Yeah, what advice do you have? Because there are quite a few people who are watching this who don't have a background in university. Maybe they have some training in mathematics, but that's it. Maybe some rudimentary physics that they've seen from an MIT OpenCourseWare video. But they want to understand string theory, M theory, well,"
},
{
"end_time": 4433.08,
"index": 165,
"start_time": 4406.203,
"text": " Yeah, I would say, you know, like if you can't basically"
},
{
"end_time": 4459.36,
"index": 166,
"start_time": 4433.677,
"text": " Yeah, that's a really good one. I mean, it depends on, you know, whether or not you can maybe go back to some kind of school. But there are lots of, you know, online presence now, information online, like I'm thinking about even things like Lenny Susskind's course. But even like one thing I find really interesting is that the Permit Institute has online, they have made"
},
{
"end_time": 4488.456,
"index": 167,
"start_time": 4459.855,
"text": " They've made their online seminar series. Jump in, listen to these seminars, go online. The other thing is there are some really good books now. So, for example, like Lenny Suskin has a book called Theoretical Minimum, which I endorse. I mean, they're really good. I read them, actually. It's a good place to kind of build some foundation and then actually go online and pull out some problem sets."
},
{
"end_time": 4515.213,
"index": 168,
"start_time": 4488.831,
"text": " and try playing and working with these problem sets and get up, you know, join a group of friends and work for these problem sets together. I mean, in practicing problems, the reason why you want to practice things like problems that have been solved already is that you're building arsenal of solved problems and they can be used as a launch pad to solve unsolved problems, right? So kind of getting a sense of what's been solved out there."
},
{
"end_time": 4533.541,
"index": 169,
"start_time": 4515.623,
"text": " And then I actually recommend one of the reasons why actually, and this is not an advertisement, I literally wrote my second book precisely because I wanted to fill a vacuum in terms of"
},
{
"end_time": 4563.251,
"index": 170,
"start_time": 4533.916,
"text": " how people can start thinking about research problem. What are the cutting edge things that we're thinking about now? And it was written very much in the spirit of Richard Feynman's character of physical law and a brief history of time to kind of carve some space out exactly for that person who wants to get a sense of what's out there. What are people thinking about? And what are the unsolved problems? And what are the directions that people are afraid of or is holding the field back?"
},
{
"end_time": 4591.886,
"index": 171,
"start_time": 4563.541,
"text": " from again from the opinion of a you know so in other words imagine i'm somebody's thesis advisor right um like a phd thesis or a master's thesis advisor and i and i had to disappear for a year i would leave this book with with that thesis thesis student right so those are three things three three concrete things i'll get your book get what's the book the name of the book and do you have it right in front of you i don't have the"
},
{
"end_time": 4613.695,
"index": 172,
"start_time": 4592.125,
"text": " I just gave my book away to a student of mine. The book is called Fear of a Black Universe, An Outsider's Guide to the Future of Physics. That's the subtitle. Now when I hear that, to me it sounds like a book about race and science. Is it a book about that or exclusively about that or minorly about that? Minorly about that. I'll say 10% of the book is about"
},
{
"end_time": 4633.49,
"index": 173,
"start_time": 4614.309,
"text": " is about identity in science. Of course, we can include race in that, but we can include personality, different modes of ways of thinking. But the title was also a play, it was a nod to one of my favorite rap bands when I was in college called Public Enemy."
},
{
"end_time": 4661.971,
"index": 174,
"start_time": 4634.019,
"text": " That's something you and I also have in common. Not only are we from Trinidad, but we used to rap, although I think you used to do the beatboxing. I was more of a beatbox and a beat maker. I wish I could rap, so one of these days we might have to do something together. That'd be great, wouldn't it? Yeah, yeah. Okay, getting... Okay, you know what, first of all, about Brian Keating. Brian Keating's your friend, correct? He's my best friend, yeah. Yeah, I'm gonna prove to you that he's not your friend. Okay, see this? Yeah. Okay, hold on."
},
{
"end_time": 4690.333,
"index": 175,
"start_time": 4662.875,
"text": " See that? See that thumbnail? Yeah. Yeah. No friend. No friend would leave your thumbnail like that. That's the worst thumbnail I've ever seen of anyone. I'm I'm going to tell Brian to change. Yeah, you gotta tell him. Okay, that's a good one. I'm just that's a joke. I'm just kidding around but still. No, I don't. I don't. I actually. Yeah. Caught him in the middle of a sneeze and then you chose that. Right, right, right. I'm going to I'm going to get on him. I will get on him about that."
},
{
"end_time": 4713.336,
"index": 176,
"start_time": 4691.544,
"text": " Okay, how has the process of learning for you changed now that you're older? What would if let's imagine you could advise your young self practices to keep practices to drop practices to adopt? You're advising your 20 maybe even 2530 year old self."
},
{
"end_time": 4742.398,
"index": 177,
"start_time": 4714.07,
"text": " About what though? About learning something like string theory or learning something like... Oh, yes, yes, yes, yes. I think it's important to combine practice with play. So rather than, you know, if I, you know, if I'm learning something like the equations of motion coming from varying the string world sheet action, for example,"
},
{
"end_time": 4760.435,
"index": 178,
"start_time": 4743.029,
"text": " It's important that I not only know how to correctly vary the Euler-Lagrange, how to obtain the Euler-Lagrange equations, and why the calculus of variation that applied for a point particle would also apply for a string world sheet action."
},
{
"end_time": 4790.384,
"index": 179,
"start_time": 4761.305,
"text": " But it's important that once I get this that I play with those equations. I literally play with them. I move them around. I play with the rules of the math. I break the you know, I actually break the rules and see what happens like the same way a kid plays with a toy. What would be an example of trying to break the rule? Just making a mistake or what or making a purposeful mistake and seeing where it leads? Yeah, make it literally make a purposeful mistake and see where it leads. Exactly. That's interesting. Yeah. So I'm one for"
},
{
"end_time": 4817.534,
"index": 180,
"start_time": 4791.135,
"text": " playing with breaking the equations. Well, you know, kids don't try it at home, but this is definitely something you can try at home. And you might learn something, but when you go out and you give a talk or you try to write a paper, you're obviously not going to put that mistake there. But you do those things just to see. Again, that's kind of like"
},
{
"end_time": 4843.439,
"index": 181,
"start_time": 4817.654,
"text": " Yeah, that to me is just like, you know, the idea of playing with things. What would be an example of a time that you played? You purposefully did something incorrect in order to see where it lead. What would be the time that that led to an insight? Can you give me? Well, I think the paper that I wrote with Michael Peskin and Shaheen Sheikh Jabari on leptogenesis or the origin of matter over antimatter, we"
},
{
"end_time": 4871.408,
"index": 182,
"start_time": 4843.643,
"text": " proposed that this can take place during the period of early universe called Cosmic Inflation. And that actually came from putting a place filler in. So how do you create matter over antimatter? Well, you need to exactly have an anomaly. And then what I was doing was I didn't know what the answer would be, but I put the answer I needed to be in there."
},
{
"end_time": 4897.381,
"index": 183,
"start_time": 4871.681,
"text": " clearly violated the Einstein equations, right? And then after like, you know, whatever, I mean, thinking about talking about it, having sound boards, it's important to have sound boards, you know, to have people that you can talk with who will not judge you, but actually take something dumb that you've said and throw back to you in some meaningful, more meaningful way. So Michael Peskin, my postdoc advisor was that guy, and Shaheen was that guy. So"
},
{
"end_time": 4926.391,
"index": 184,
"start_time": 4897.722,
"text": " And then next thing you know it takes form and next thing we discover, well actually the real story about that was that we were thinking that it maybe was torsion, this idea of torsion that would source the baryony symmetry, that turned out to not work but again the torsion thing had a tensorial structure meaning the way the indices are moving around and when I went to Caltech that year and I visited Mark Kamenig, the great cosmologist Mark Kamenigkowski"
},
{
"end_time": 4946.681,
"index": 185,
"start_time": 4926.988,
"text": " And then I was telling Mark the idea, and Mark goes, oh, you should take a look at this paper I wrote. It might be useful. And then when I look at the paper, it had actually, for other reasons, it had this Charm Simon's thing. When I came back to Stanford, we started playing with that and it turned out to work. So that's an example of like,"
},
{
"end_time": 4974.582,
"index": 186,
"start_time": 4948.541,
"text": " So I don't know if that was like deliberately making a mistake, but it was sort of like, yeah, I think that in this case you put a place filler in. You're fudging. You're literally fudging. It's what Einstein did. He put a fudge factor in to make it work. Right. For dark energy. In this case, there was no anomaly, but you needed there to be an anomaly because there is an asymmetry. We needed it to be a harmless anomaly. Okay. So for the people listening, when there's that J in the current"
},
{
"end_time": 5000.179,
"index": 187,
"start_time": 4975.401,
"text": " J isn't always current as in electric charge current. Yes. It can be other types of conserved quantities or quantities that need to be conserved. Yes. Okay. So what would, so in that example, it would look like D mu and then J mu at the top. What would that J represent for assuming? Okay."
},
{
"end_time": 5029.991,
"index": 188,
"start_time": 5000.64,
"text": " So this will be the current associated with leptons. So the electron is a lepton, the neutrinos are leptons, right? So these are the leptons and there's a quantity called a lepton, the lepton number, right? The same way you have like an electric charge is actually a leptonic charge. And that leptonic charge, it can be violated by an anomaly. And that one is fine because it's so-called global anomaly. It doesn't depend on space time."
},
{
"end_time": 5060.469,
"index": 189,
"start_time": 5030.828,
"text": " And those anomalies, sorry, I want to make sure what you, I don't want to lose. Okay. So you said that the lepton charge can be violated by an anomaly. You mean to what do you mean when you say it can be violated by anomaly? It's not just because the way that I see it is that you have your theory and then you find out, Oh, it's anomalous. It's not that, Oh, I can make this anomalous because I feel like I can make any theory anomalous. Very good. So the left and it's standard model, the lepton, it turns out that the lepton current is not anomalous."
},
{
"end_time": 5090.845,
"index": 190,
"start_time": 5061.408,
"text": " With exception, and this is where the exception is, if you turn gravity on, there's a gravitational anomaly. And the thing that's doing that is the gravitational churn Simon's term. And it turns out that if you have a gravitational configuration, meaning in a gravitational field, that gives you a non-vanishing churn Simon's gravitational term, it could source lepton number."
},
{
"end_time": 5120.094,
"index": 191,
"start_time": 5092.466,
"text": " I want to talk about something that sounds like it's not inspirational, but it is. There are certain no-go theorems in physics and in math, but let's talk about physics. What are some examples of no-go theorems that turned out to be a go theorem, like you could find your way around it?"
},
{
"end_time": 5153.387,
"index": 192,
"start_time": 5124.718,
"text": " Firstly, you should explain to the audience what a no-go theorem is. Very good. A no-go theorem is a statement, so I'll give you an example of a no-go theorem, and maybe I can... Actually, let me... So a no-go theorem is Weinberg's no-go theorem about any adjustment mechanism for the cosmological constant. So the statement says that"
},
{
"end_time": 5182.09,
"index": 193,
"start_time": 5153.814,
"text": " You can't use, say, in this case, a scalar field with a potential to relax, to relax the cosmological concept. And then he went and like actually did some calculations and showed that actually if you had such a theory that you cannot use that to cancel out the cosmological concept. All right. And that is true. But in that theorem. Hear that sound?"
},
{
"end_time": 5209.155,
"index": 194,
"start_time": 5183.08,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 5235.316,
"index": 195,
"start_time": 5209.155,
"text": " There's also something called Shopify Magic, your AI-powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level. Join the ranks of businesses in 175 countries that have made Shopify the backbone."
},
{
"end_time": 5261.049,
"index": 196,
"start_time": 5235.316,
"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklyn. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com slash theories, all lowercase."
},
{
"end_time": 5290.213,
"index": 197,
"start_time": 5261.049,
"text": " Go to Shopify.com slash theories now to grow your business no matter what stage you're in Shopify.com slash theories. That theorem there were some axioms or some assumptions about in this case that if that scalar field relaxes to a back a ground state remember the field is can roll and then when it gets to its ground state or to its minimum the minimum of its potential if that ground state"
},
{
"end_time": 5316.476,
"index": 198,
"start_time": 5290.555,
"text": " is Poincare invariant, then what Weinberg said is true. But if the vacuum state is not Poincare invariant, then that assumption, that no-go theorem doesn't apply because you've relaxed that assumption. So now you have a loophole. So then people realize that by now constructing so-called P of X theories."
},
{
"end_time": 5342.517,
"index": 199,
"start_time": 5316.783,
"text": " These are theories where the scalar field is actually has a non-trivial kinetic term. And those theories have ground states where the kinetic energy is still non-vanishing, right? And it's not a Poincare invariant vacuum. So recent manifestations of trying to solve the cosmological constant problem have, by really good people, have used those"
},
{
"end_time": 5370.657,
"index": 200,
"start_time": 5343.456,
"text": " those types of relaxation mechanisms that evade Weinberg's no-go theorem or evades one of the assumptions of that no-go theorem. The reason I said that... Yeah, yeah, it's actually inspirational. And the reason is that it seems clear. Oh, you have a no-go. Someone said there is no way. Look, this is math. This is physics. There is no way around it. But then you realize, well, there are hidden assumptions. You mentioned axioms. I call them anthem memes, which are just"
},
{
"end_time": 5399.48,
"index": 201,
"start_time": 5370.896,
"text": " unstated assumptions embedded in your question or embedded in your statement. And one of my favorite ones is, is Witten, I think it was just Witten, but though it could be Witten in Weinberg in 1980, where he said, okay, if you want a spin half larger than spin half particle, and it has a conserved a Lorentz covariant current, it can't exist if it's massless. And then same with it can't exist greater than one and be massless and have a conserved stress energy tensor."
},
{
"end_time": 5423.2,
"index": 202,
"start_time": 5399.821,
"text": " The assumption that was made was so implicit that they never made it explicit and they didn't realize, I don't know if they realized, until someone else, I don't know, maybe it's Juan Maldicino came along and said, well, okay, that's right."
},
{
"end_time": 5452.585,
"index": 203,
"start_time": 5423.524,
"text": " It cannot exist in this space time, but it can exist in another space time. And I believe that's part of the origin of the holographic principle. No, that's very good. That's very good. I think excellent point. Now, I don't remember, but I think, though, that the Weinberg-Witten theorem does make an assumption about the online space sign. And I can see how anti-dissidia space, which is the space sign ADS-CFT is based on, holography,"
},
{
"end_time": 5481.971,
"index": 204,
"start_time": 5452.875,
"text": " that version, I could see how that could avoid the Weinberg-Witten theorem exactly because in ADS-CFT, that's right, it's beautiful in the sense that the, let me just for the audience to say that it basically is a theory that says that in gravity in one higher dimension, so let's say I had a four-dimensional gravity theory, it's completely encoded in a non-gravitational theory living at the boundary of that four-dimensional"
},
{
"end_time": 5512.09,
"index": 205,
"start_time": 5482.5,
"text": " theory with no gravity and that theory that has no gravity is related to Yang-Mills theory where there's no gravity and the idea here is that where does gravity, how does gravity emerge and one I think simple minor idea is that in the Yang-Mills theory you can have condensates or degrees of freedom that emerge that come together collectively right to then form the graviton which would be a version of this Weinberg. If I need to get a graviton in the space time, I have to build it out of the"
},
{
"end_time": 5541.425,
"index": 206,
"start_time": 5512.637,
"text": " Can you explain why is it that the Graviton is said to have spin-2 when, for people who are just learning about this for the first time, it seems arbitrary. Well, why are you saying the Graviton has spin-2? Why are you saying that there's a particle associated at all with gravity? Because gravity, we've been told since we've been teenagers, it's not a force, it's the curvature of time and space, space-time and so on."
},
{
"end_time": 5563.404,
"index": 207,
"start_time": 5541.783,
"text": " So firstly, why does there have to be a particle associated with gravity in the same way there are particles associated with other interactions? And second, why does it have to be spin two? Yeah, so the spin will correspond in this case to the helicity of the particle. And just like engage, I mean, if you look at a gauge field, a mu, the index mu now becomes basically related to the"
},
{
"end_time": 5588.729,
"index": 208,
"start_time": 5564.019,
"text": " If I have an electromagnetic wave propagating, the polarization tensor, E mu, is carrying the information about the spin, about all the helicity in this case, meaning the momentum projected onto how the particle is spinning. That's the helicity. So you can trace that back to the fact that this gauge field has one tensorial vector index, space-time index."
},
{
"end_time": 5618.404,
"index": 209,
"start_time": 5589.07,
"text": " So if I now have a spin two particle out, I have two of these indices now. And that's exactly the tensorial form of the transverse traceless gravitational perturbation. However, to say it's a quantum particle would spin to is an extra, I would say, thing. General relativity doesn't tell you anything about, you know, that if I look at general relativity, it's a classical theory. But if I go through and make the same procedure,"
},
{
"end_time": 5648.49,
"index": 210,
"start_time": 5619.104,
"text": " and say, oh, look, the same way I do quantum field theory, I work in Minkowski space, there's a procedure, right? Perturb the field, the gravitational field, there's a tiny perturbation, and then define some kind of state that in some sort of modes, you know, oscillations with creation and annihilation operators. That's where you're going to start seeing the spin two quantum numbers come pop out. But from where I stand, that is in a that's not, you know, that's not part of"
},
{
"end_time": 5673.66,
"index": 211,
"start_time": 5648.712,
"text": " That's an extra assumption of doing quantum field theory in a weakly curved space. I'm sure you've heard Weinstein say that maybe we shouldn't be quantizing gravity, that we should be geometrizing the quantum. Have you taken a look at geometric unity? I have. I have taken a deep look at it, yes. Okay, what are your thoughts?"
},
{
"end_time": 5703.729,
"index": 212,
"start_time": 5674.241,
"text": " Well, I think, well, the mathematics is definitely very advanced. I think it's a beautiful idea, actually. I think it's a really nice idea. I don't know what the word is, but you start off with four dimensions, a Lorentz group, and then you do this, you think of all the components, all the ten components in this four-dimensional world,"
},
{
"end_time": 5730.265,
"index": 213,
"start_time": 5704.241,
"text": " You let that vary. So therefore you have a bundle structure like a fiber and all these components are now a fiber, a fiber over this four dimensional space. And that somehow then gives you something that starts looking like a grand unified group. Maybe it's SO10 or something like that. So the 10 components of this fiber is like M4 fiber over SO10 maybe."
},
{
"end_time": 5758.353,
"index": 214,
"start_time": 5730.879,
"text": " Again, I'm bastardizing Eric's idea, but I like this idea that somehow you just start with that data and then the mathematics just naturally gives you this extra gauge structure that seems to have embedded in the standalone. Now the devil's in the details and I know that there's some criticisms that need to be ironed out, but I think that's kind of what we do when we do good theory. You put it out, you give it your best shot,"
},
{
"end_time": 5786.647,
"index": 215,
"start_time": 5758.814,
"text": " And especially if you're doing it alone, I think that then others jump in and then they improve it or they find a mistake. That's actually what the refereeing process is anyway. Any paper that I write, well, the first thing is I write the paper or I work it out, I do something, I get far enough where I feel confident I have something, but there's always places where I have blind spots, I give a seminar,"
},
{
"end_time": 5813.353,
"index": 216,
"start_time": 5787.022,
"text": " And the seminar is usually where I get feedback before I put the paper out. Then I put the paper out, and then I put up a publication. And then usually the referees further help me understand what's going on, actually. And if they find a bad, that it's not publishable, fine, I learn something new, I move on. That's happened to me many times. So I think that, you know, that component is missing."
},
{
"end_time": 5842.858,
"index": 217,
"start_time": 5814.104,
"text": " I think that component is missing precisely because, you know, Eric is, you know, sort of going at a lot of this alone. And I encourage him, he put it out and I think that people should read it and take it very seriously and play with it and scrutinize it. And I think that there might be some gems in there. OK, even if it's not, it doesn't turn out to pan out to be correct in, you know,"
},
{
"end_time": 5870.913,
"index": 218,
"start_time": 5843.575,
"text": " in terms of what it's trying to solve, which is unifying the standard model with general relativity in this new way. At the very least, for me at least, I'm reading it or I've read it so that I can learn some things. I've definitely learned some interesting things. And it got me thinking about unification in different ways now. So it's valuable. We should have more of that. Have you read Wolfram's paper or Wolfram's physics project?"
},
{
"end_time": 5898.831,
"index": 219,
"start_time": 5871.817,
"text": " A little bit. The answer is I intend to. I intend to when I have some time. I do know that it is related to some ideas in graph theory. I also think that, again, it's some nice ideas out there. It may strike some resonance with other things like matrix theories and other approaches. But I'm all one for let's populate"
},
{
"end_time": 5926.613,
"index": 220,
"start_time": 5899.411,
"text": " the theory landscape with ideas and let's scrutinize it and learn from it. The reason I ask that is that there is a direct quote from you, I believe in your autodidactic universe paper about how there's how reality works. And then there's how we model it. And our models are somewhat like approximations, but then they get closer and closer to the real world. And then you start to wonder how much of the real world is these computational techniques underneath?"
},
{
"end_time": 5954.974,
"index": 221,
"start_time": 5927.227,
"text": " I don't have the exact line, but it reminds me of almost verbatim. That's what Wolfram thinks. He thinks because computers are so powerful. This is not exactly what he thinks or why he thinks and I'm just paraphrasing, but computers are so powerful and the computation under his models are so general and so powerful and so predictive in a certain sense that perhaps that is what the universe is. It's computation underneath. That's beautiful."
},
{
"end_time": 5972.705,
"index": 222,
"start_time": 5957.21,
"text": " Okay, I know I don't want to take up too much more of your time I can keep honestly I keep talking to you for"
},
{
"end_time": 5997.927,
"index": 223,
"start_time": 5973.166,
"text": " I would like to. I also wanted to bring to the forefront, because there are quite a few mathematicians and physicists who watch this podcast, and for the physicists in particular, I'm interested in unification. That's the name of the channel, Theories of Everything. It's been proposed for quite some time now, almost 20 years now."
},
{
"end_time": 6026.135,
"index": 224,
"start_time": 5998.285,
"text": " that geometric algebra should be seen as the standard force for unification or the standard language of unification. David Hastings, I believe. He's agreed to be on the show, I just have to book a date with him. Categorical, category theory as well. So categorical unification, whatever that means. That was proposed by quite a few people, James Weatherwall comes to mind and Elaine Landry had a book on quantum, sorry, on category theory for philosophers but had a few sections on category theory as applied"
},
{
"end_time": 6055.759,
"index": 225,
"start_time": 6026.135,
"text": " to physics for the purpose of unification so i'm extremely interested in that and bring a bit more attention to that there are there's coal furry have you heard of coal coal furry yeah yeah yeah yeah yeah so i want to have her on i've just yeah she's she's doing very cool stuff yeah yeah i i i love her little her mini youtube series on the quaternion and then ciara marledo i want to have on however i don't know she's like"
},
{
"end_time": 6073.404,
"index": 226,
"start_time": 6056.374,
"text": " ghosting me. It doesn't matter how many times I send her an email, she will not respond. And I don't know why. I don't know if she has. What's her name? Chiara Marledo. It's the student of David Joyce. Oh, yeah, I don't know her at all. Yeah, I don't know her at all."
},
{
"end_time": 6100.708,
"index": 227,
"start_time": 6074.07,
"text": " You got to get going. I got to maybe half the questions. No, no, but let's reschedule and continue. We can do that. Yeah, let's do that. I'm around, so I just literally just got set up today. So now that I got the system going, just let me know and I'm happy to continue talking. Great. And I'm also like a little bit tired and frazzled. I think the next time you get me, now that I know kind of your style, I'll be able to do some better stuff here."
},
{
"end_time": 6126.254,
"index": 228,
"start_time": 6100.776,
"text": " Sure. All right. Well, you did great. Oh, thanks, man. Whatever is better, it will be accepted. Yeah. And yeah, and seriously, tell, tell Sebastian, so what's up? I will, I will. The field, the field messenger, but I'm sure he's but I'll actually I'd like to get some advice from him about some because I'm also thinking I'm not between you and me. I'm actually looking at my options outside of physics, he says. Oh, yeah. Yeah. Yeah. So he's in math, finance. I don't know if you know."
},
{
"end_time": 6140.623,
"index": 229,
"start_time": 6127.5,
"text": " Exactly. So I'm actually thinking about that direction myself, because I'm friends with Jim Simons. So why not, you know, because I kind of want to talk with him and get some, you know, talk with him, you know. Yeah. So let me know if he's ever interested."
},
{
"end_time": 6162.005,
"index": 230,
"start_time": 6142.875,
"text": " The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash C-U-R-T-J-A-I-M-U-N-G-A-L. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you."
},
{
"end_time": 6193.899,
"index": 231,
"start_time": 6164.753,
"text": " Dogs are an important part of our lives, and keeping them protected is a top priority, especially against nasty parasites. That's why you've got to check out NexGuard Plus, a foxeloner, moxidectin, and pyrantal chewable tablets. NexGuard Plus chews provide one-and-done monthly protection that kills fleas and ticks, prevents heartworm disease, plus it treats and controls roundworms and hookworms. That's a whole lot of protection packed into a delicious, beef-flavored, soft chew designed to make monthly dosing easy and enjoyable."
},
{
"end_time": 6209.633,
"index": 232,
"start_time": 6193.899,
"text": " So the next time you're at the vet, ask about NexGuard Plus Choose. They're the one and done monthly parasite protection you want for your dog. Use with caution in dogs with a history of seizures or neurologic disorders. Dogs should be tested for existing heartworm infection prior to starting a preventive."
}
]
}No transcript available.