Joe Rogan - Eric Weinstein Explains Gauge Symmetry

So back to gauge theory, gauge symmetry. What the hell was that? All right. Well, here's the, here's the craziest thing. Okay. There is a very confusing visual image of the fundamental unit that you need to appreciate what gauge symmetry is all about. And, uh, I had Jamie load it up, um, under the tab called planet hop. And this is going to be HOPF. HOPF. What the fuck am I looking at? You are looking at the most important object in the universe. What? That looks like some, uh, trippy screensaver on your laptop. Take another puff, my friend, because it's worth it. Uh, this is what you're looking at is a principal fiber bundle. And it's, uh, and it is the earth. Those are the continents I'm looking at. That's the cool part about it, which is this is very confusing to figure out what you're looking at, but it's finite. In other words, if we stay for an hour or two on this and we actually answer all your questions, you will actually know what a principal bundle is and you will know the arena in which gauge theory exists for folks at home that are just listening and they, what the fuck are these guys talking about? What is the name of this video, Jamie? It's not a video. It's a small file on a page I typed in planet hop and it was the first thing that showed up on math.toronto.edu. Okay. So extended thing. Planet H O P F for anybody who wants to look at this, if you're just listening and you have no idea why I'm freaking out. So this, this was done by a friend of mine named drawer Barna ton. I actually coded the same thing up. Um, strangely enough, didn't do as brilliant a job of coloring it. And this looks amazing by the way. So, okay. What you're looking at is a two dimensional sphere. That is the surface of the earth where an extra circle is included at every point on the surface of that sphere, which you're now visualizing and that extra circle, which would be called the fiber. Um, when you take the totality of all of those circles together, one for each point on the surface of the sphere, they create something called a three sphere that is all the points that are one unit of distance away from the origin in four dimensional space. So that three dimensional sphere is the analog of a two dimensional sphere sitting in three dimensional space. So think about a caramel apple. If you've ever made caramel apples, you get a disc of caramel and you wrap it around the sphere that is the apple surface, right? So this is the three dimensional version of caramel wrapped around the three dimensional, uh, sphere sitting in four dimensional space. Now, do you understand any of this, Jamie? I'm trying. Well, dude, it's totally trippy, right? And so we're not going to get it completely during this session. However, I think I lack the tools. I don't think so. If we lack the time. So the first thing is you were finding out that one of your friends thinks this is the most important object in the universe and you've never even heard of it. Right. Much less know that there's one visual example. What's the fuck? How's this happening? I know exactly. It does look fucking crazy. Well, okay. This is what was discovered in the mid 1970s as the connection between mathematics and different, what we call differential geometry and the discipline of particle theory. So two guys, uh, Jim Simons, the world's now the world's most successful hedge fund manager and C N Yang, a person who might are arguably be the world's first or second greatest living theoretical physicist had a lunch seminar. And they said, why don't we figure out how do we talk to each other? And what they found out is they both had developed a version of this picture. And independently, independently. So it was the Rosetta stone that. Unleashed a revolution. So when Lawrence Krauss was talking to you about gauge theory, he was saying things about chess boards and you color it white and you color it black. It's super confusing to me. I would rather your people be confused about an actual example of the object on which we do gauge theory that you can visually see. Right. Now, if I started to tell you what gauge theory is, it's pretty simple. So here's an, here's a description. I never hear anyone say. When you're doing differential calculus, I don't know if you remember differential calculus, you're trying to figure out the slopes of lines instantaneous rise over the run. So that always makes sense to people. Okay. I figure out how fast it's going up versus how fast it's going across. But a question arises, which is where do you measure the rise from? So for example, if I say, what is the height of Mount Everest? Jamie will say. 30 was 35,000. Yeah. Something like that. Something crazy like that. Right. Just go a thousand and say base. Well, let's get an internet connection. Let's take a guess. What do you think it is? I don't know. I can't remember. I want to say it's 35,000. What do you think? I thought it was 29. 29 0 2 9. What's the highest? What's the highest one? Is it K2? All right. K2 is second, right? Is it? Is Everest the highest? Yeah. But okay. So Everest 29, would you say 29? 29 0 2 9. Oh, 29. Above what? Sea level. Okay. Where is Mount Everest located? The Himalayas. What's what sea? Uh, there's no ocean there. Right. So like we snuck in, it's above sea level and there's no ocean. So we start from the center of the earth. We have this structure called the geoid, which is the interpolation of sea level as if sea level, as if the earth was only ocean and there was no tide. Right. And as if there's some sort of a. So we snuck in the reference level. That's my point is that we teach these kids to repeat why it's 29,000 and change above sea level. And there's no sea. Right. So that reference level is the magic of gauge theory. Right. Which is that we measure the rise over the run based on a custom level. So a level that we all agree upon. So for example, let's imagine that you and I are in some country experiencing hyperinflation. Right. And I'm your boss and you say, dude, I need a raise. I say, well, look, I've told you, I would hire you for, you know, 10,000 DNRs a month. And you say, yeah, I said, well, your salary is constant. I took the derivative of it. I've paid you 10,000 last month, 10,000 this month. So you're getting the same amount derivative equals zero. It's constant salary. Now you have to come back at me in calculus and you say, no, I don't like your notion of the derivative because what you're doing is you're measuring the absolute number of DNRs that you're paying me. But what I want to do is I want to measure it in purchasing power because I'm losing money every month that you don't increase my salary. So I now come up with a version of the calculus in which my salary is not constant because it's being measured relative to purchasing power rather than absolute units. That's gauge theory is that you're bringing in a reference level that does the differentiation. So you're measuring rise over run by customizing the problem. So these were two different applications of the calculus. The cheating employer says, I want to go with constant DNRs. The gifted employee says, not so fast. I know gauge theory. I want to use a custom reference level, which is purchasing power. Right. So it's like sneaking the geoid into Tibet to measure Everest. I've got my custom level. Does this make sense to you? Yes. It makes sense. Right. But now explain it. Say what he said. Uh, well, I mean, we would need a new reference of what we're, what you want to measure, what would I make a new conversation to have a, like a flat level. Right. Right. I guess. Yeah. It would be really difficult for me to recall a day from now. Maybe. Like the weed. No, it's not that my health. So we might help. Yeah. It might be called that. Pop a mushroom cap. See what's up. It's, um, it's still in reference to quantum physics, like how you would use gauge symmetry, well, but let's look at some more cool stuff with the visual cortex, because everything that we can do visually should inform what we can do linguistically. So you should push everything into the visual realm that you can. Uh, what do you mean by that? Like, well, I just showed you the hop vibration, which is the only. In some sense, the only mature picture I can show you of a principal vibration in geometry or physics that is honest and has the full complexity. It's got a certain kind of knottedness to it. It's got something that we would call curvature and it is visualizable. And so it would be better that we spent, you know, a day or two on this most important object, which we think reality is based around and that you visually got comfortable with it. And then you said, okay, now tell me again, what gauge symmetry is. And then instead of Lawrence talking about this chess board and the colors and all this stuff by analogy, you'd actually be seeing gauge theory visually. Like I could program a computer and have done so to show you visually what a gauge theory is, and it takes some time to sort of understand what the trippy pictures are. But if let's bring up the Escher staircase. And Jamie has a nice wrinkle on this that instead of using MC Escher staircase, he's got this animated guy who just keeps going down. Hmm. All right. Now what's going on with those stairs? Now the stairs are sort of an optical illusion because obviously it can't just keep going down, but then you build these systems like rock, paper, scissors. What's the best thing to throw in rock, paper, scissors? Well, it depends on what you throw. Well, but we should be able to agree that rock is better than scissors. Rock is better than scissors. Rock is better than scissors. The paper is better than rock. Right. So you go around that thing. And now the point is that you get to like rock is much better than rock. Right. And that seems crazy. Now that concept would be what we would call hollonomi. The weird sentence rock is better than rock because of that going around the loop. Why rock is better than rock? I don't get it. Well, rock is better than scissors. Scissors is better than paper. Right. Paper is better than rock. So by transitivity, rock is therefore better than rock because you went around the loop and came back to rock. It's like MMA math. Yeah. Yeah. Or if like, if you're, if you're changing, uh, currencies and you don't spend any of it because you keep losing, using your credit card, by the time you come home, you had more money than when you left because the exchange rates did some thing so that when you changed into each currency, you somehow got richer. But by saying rock is better than rock, you're denying the fact they're exactly the same. Well, no, you're not, you're not addressing it. You just want to continue the same. That's the linguistic fallacy. Right. So the idea that this system here, so those stairs in engaged theory would be these reference levels for the derivative. And you can have situations where the reference levels don't knit flatly together. Right. And so by virtue of that, we would say that the system has curvature. Curvature is the Escherness of, of these better than transitive statements. What we're looking at folks, for people who are just listening, we're looking at, if you've never seen those Escher, uh, etches, those sketches, they're very strange because what there are is a bunch of staircases that appear to always be going downhill, even if one of them is above the other one, it's very strange. Very strange. And this one we're watching an animated guy roll down this staircase constantly, even though it really looks like somehow or another, it must go up somewhere, but you don't ever see it going up. But it's also a factor of the illusion of perspective and how it's drawn and, and, you know, playing games with lines. Exactly. But if you do this very weird experiment, which we didn't know about into the late fifties called the Aranoff-Bohm experiment. Um, if you run, um, a, uh, electric, uh, current through a wire that's insulated, um, it's, it appears not to have any electromagnetic field outside, uh, of the insulation, however, if you do some sort of quantum interference experiment, you can tell that there's current going through because it affects the phage phase shift, let's say of an electron orbiting that insulated electromagnetic system. So nobody thought that that was going to happen because they thought, well, an insulator would keep the, we thought the electromagnetic field is what determines the shift in the electron, but it's insulated. So there is no electromagnetic field to worry about. It turned out that it wasn't the electromagnetic field alone. It was some previous geometric concept, which was called the electromagnetic potential that determined something about the phase shift. So this Escher staircase in the case of electromagnetism, it's like the photons are the analog of those steps. They're partially would determine the derivative operators, these reference levels, and again, in our discussion of the, uh, am I paying you the right amount in a hyperinflationary economy? So all of these things, you're trying to figure out, well, that's an optical illusion, but that effect actually occurs in some systems, not as an optical illusion. Yes. Right. So this weirdness, um, requires a fair amount in terms of either study of math or learning visualizations, but there's no way to achieve it in my experience with linguistic communications, like all the stuff that gets said about, you know, the universe is expanding or let me tell you what a gauge theory is and why there's a reason it's confusing. It's because it doesn't make any effing sense. Right. I see what you're saying. Sort of, but so this is, this is like what Feynman said. If you think, you know, quantum physics, you don't know quantum physics. Well, there's, there's some of that, like there's, you know, one of the most important things in the world is this thing called a spinner, like the electrons and the protons correspond to things called spinners and the average person has no idea that spinners exist. What's more spinners have a property that when I tell it to you linguistically won't make any sense. All right. Let's do this with coffee. Okay. So yeah. Thank you, sir. Perfect. All right. Now here's the problem. Hold your cup. Nope. From the bottom. And here's the first challenge without spilling it. Okay. I want you, and without readjusting your grip on the bottom of your cup, I want you to turn your cup 360 degrees. No, no, no, sorry. Turn your, your fingers should not change on the cup. Okay. Turn the cup 360 degrees without spilling it and try to take a sip. Okay. That didn't work. No. Now, without coming back, how would you take a sip? If I got it all the way around that way? Yeah. Mr. Joojitsa, man. I would have to. I would have to help myself. Yeah. No, no, you're going to do it. All right. You ready? Yeah. Okay. Here we go. Are you going to go around the circle? 360. Okay. Right. Now I'm screwed if I don't bring it back underneath. Oh, I see. So that system required 720 degrees of rotation unexpectedly. Oh, you just keep going. Right. Okay. Now the idea that there are objects that don't come back to themselves under 360 degrees of rotation, but require 720 is probably something you've never thought about before in your life. Right. But without that, you wouldn't have the poly exclusion principle. You wouldn't have the stability of matter. And this thing is called the Philippine wine dance. Jamie, do you want to? Yeah. That's not very seductive, Joe. It seems like some very odd ethnic dance. Yeah. But like maybe you could do 11th planet jujitsu. Here we go. So this spinner is one of the coolest, most important objects anywhere. And it was discovered to be important in physics by a guy named Paul Dirac. Right. It's fun. Okay. So this 720 theory is entirely responsible for the world that we live in. This is so bizarre to watch this in animation. And nobody knows about it. Right. Like unless you're hanging out with physicists, they don't tell you that electromagnetism has to do with the fact that there's a secret circle at every point in space and time that's invisible to you. They don't tell you that there's stuff that requires 720 degrees of rotation. They just say mind blowing stuff about. Whoa. So what is happening in this 720 degrees of rotation in the quantum world? There's an object that is requiring this just the way the cup arm system requires 720 degrees of rotation. What object is this? It's called a spinner. And that spinner is how we model the electron, the neutrino, corks, all that is spinorial matter. Sir. That's a good long pause. I like it. Yeah. And what, where does this fit in, in our model of the universe? Like what is the function of this? Why is it there? What is it? How do we know it's there? Well, we know it's there, um, because, uh, when Dirac, so there was this problem with like the Schrodinger equation, Schrodinger equation takes one derivative in terms of the direction of time and takes two derivatives in the direction of all the spatial directions. But because Einstein told us that space and time are woven together for the theory to be relativistic, you need the same number of derivatives of time as of space, because space time is sort of one kind of semi unified object. All right. That means you either have to boost the number of derivatives of time up to two to match the two derivatives in the directions of space, or you have to knock the two direct derivatives in the spatial directions down to one derivative to get it to be equal. Now, one direction gets you to something called the Klein Gordon equation. What Dirac did is he took a square root of the Klein Gordon equation to get these spinners. So he had these numbers. He didn't understand at first that he was going to get kicked into this world of spinners. He came up with a square root equation in which A times B thought to be numbers was not equal to B times A was like equal to the negative of B times A. So it was like, what two numbers when, when you multiply them matter in which order, there wasn't numbers. It was matrices. So this was one of the great insights, you know, rival to Einstein in terms of the depth of what it told us about the universe. Most of us haven't really heard of Paul Dirac. We don't realize that he has one of the three most important equations in physics. Now, in, when you say three most important, important in how it's applicable to everyday life or important in how it's given us an understanding in quantum physics or important how it's understand it's, it's understanding is significant to quantum physics. We're talking about our, we're talking about bedrock reality. Like you and I are having a conversation and if you're a matrix fan and what we might call the construct, what is the construct made of? It's made, so the way I do it is I think of it as a newspaper story. There's where and when did it happen? There was who and what was involved and there's how and why. Okay. So where and when is space and time clearly? The who and the what to me, let's say the who is the spinorial stuff. It's like electrons, protons, neutrons, quarks, the stuff that we're made of. And then you and I are only able to see each other because we're passing photons back and forth, which are force particles. They're not spinorial. They come back to themselves after 360 degrees. They don't require 720. So this is sort of the, you know, if you were going to go to a play, you'd have the dramatic personnel of the play given to you at the beginning. So this is what this universe is. It's a story about space and time, where and when, about what is in that, you know, like who are the players and what equipment are they using? That's like bosons and fermions. And then there's the how and the why, which is the equations and the Lagrangians that go through.