Lawrence Krauss explains Gauge symmetry - The Joe Rogan Experience

Hello freak bitches. Yeah, we want to believe. We really want to believe just like the X-Files. But eventually, when nature tells us otherwise, we throw out those beliefs like yesterday's newspaper. That's why science is so neat. Now, people that are listening to this are probably going, what is gauge symmetry, dude? You just passed over that and you said it was crazy. Is there a way that you could possibly just give a small synopsis? Sure, I'll give, we'll try. We'll see how we do. So, it turns out that there's a fundamental principle in nature which really was discovered by this wonderful woman mathematician, Emmy Nerther, who wasn't even allowed to get a job because she was a woman at the turn of the century. But she discovered, so there's things we say, and we tell kids, unfortunately in schools, energy is conserved and momentum is conserved, and it sounds like the Ten Commandments, like we come up with them because we like them. And now we understand them differently. We understand that everything that is conserved, that doesn't change in the world, is due to a fundamental symmetry of nature. So, energy is conserved because we now understand the laws of physics don't change over time. So, as long as you contest that the laws of physics are the same tomorrow as they are today, then we know energy is conserved. It's not something we take on faith. It's a mathematical consequence of that. Momentum conservation is a consequence of the fact that the laws of physics don't change from place to place. That they're the same in this studio here as they would be if we were having this conversation in New York. That seems reasonable, and she showed mathematically it's the case. So, there's a famous, everyone's experiences who learned any physics, conservation of charge. You know, the electric charge in any system doesn't change magically over time. That's a fundamental property of electricity and magnetism. You got something on the charge of the beginning, it's got to be the same at the end. That's a consequence of the fact that it's arbitrary. There's a symmetry of nature that says, you know, Benjamin Franklin called electrons negative, negatively charged. But it doesn't mean anything because I could have called them positively charged. It's just an arbitrary definition. If I changed every negative charge in the world to positive charge, and every positive charge to negative charge, everything would work the same way. A symmetry of nature represents something that doesn't change about nature when you make a change in a definition. So, making every, calling electrons positively charged and protons negatively charged would not make the world difference. It's an arbitrary name. Martians could call electrons positively charged and protons negatively charged. There's nothing fundamentally important about the word positive charge. It doesn't mean any different than a negative charge. So I could change every, right now, I could make all, I could change the charge on every electron in the universe and flip it. It's signed. So every electron is negatively charged now. But now suddenly I'm God and I make every electron positively charged and I make every proton negatively charged. Nothing about the laws of physics will change. I don't understand that. Why wouldn't it change? I mean, is there a function of them being positive or negatively charged? No, no, it's just a name. That's why it's like, it's like calling, I could call up, down and down up and it wouldn't make it. As long as it's a noise you make with your mouth. Yeah, exactly. So the name I give it is irrelevant. Okay, so it's not like you would change the actual function of the electron. No, no, exactly. I call, it's electrically charged. That's important. And it repels other electrons because they have the same electric charge. That's important, right? Two electrically negative charged particles repel. But look, if I made them both two positive charged particles, they'd also repel. So the physical consequences would not change at all depending upon how I named them. I see what you're saying. Okay, now, so the example I used in the book to try and sort of describe that is a chess board. You got white squares and black squares and you play with the white chessmen. If I changed all the white squares into black squares and I rotated the board by 90 degrees, it would look identical. And if I changed the black players to white players and the white players to black players, the game of chess would be identical. Nothing would change about it. So what's white and what's black is kind of arbitrary, right? It doesn't matter, which is good because if it kind of wasn't, then chess wouldn't be a fun game because if you always had black, you might win. If you always had white, you might win. But it's the same, right? So I could change all white squares to black squares and black squares to white squares and the game of chess would not change. So that's a symmetry of the chess board. And that's like electric charge, white being negative or positive and black being, you know, so let's say white is negative and black is positive. If I switched all black to white or negative positive, nothing would change about the game of chess. If I switch negative to positive in the universe, nothing changes in the universe. The game of life, the game of physics would not change. The rules wouldn't change. The dynamics, everything would remain the same about the universe. So that you could sort of, even that is not so easy. I can tell from looking at your face, it's already not so easy. Okay. But you can sort of accept that. Yes. Okay. Okay. That's the easy part. Okay. So here's what gauge symmetry says. And this is really weird. I can actually do better than that. I can arbitrarily change each white square in a chess board to a black square. I can choose randomly which white squares to change to black squares. And I can still make the game of chess the same if I just have a rule book. And the rule book tells me, oh, if you're on that square, you can do what you could have done if it was a white square. So if I have the rule book, then it doesn't matter what colors the squares are. If I know I was in the square that used to be white, but I call black and I look at it and say, okay, my knight can do this in that square, but I couldn't do that. Right. So if I have a rule book, then I'm arbitrarily free to change the color of each square in a chess board as long as a rule book tells me what I've done. Right. That's that's electromagnetism because it turns out electromagnetism as a symmetry that says, you know what, I could change the definition of the charge on electron here, but in the next room differently. So I could call this electron positive and that one negative. And it wouldn't change anything as long as I had a rule book that told me that I'd made that change and how and how the electromagnetic interaction would be the same. As long as I I'm free to change the definition of what I call positive and negative charge locally, not globally. That means I can do it differently here and there. As long as I have a rule book that says, you know what, that electron used to be negative. So it'll still repel this electron here, even though I call it positive and I call that negative. I've changed locally the definition, but I also change the rules. I understand that. I understand the need for the rule book. Now it turns out that the rule book really tells you it's a rule at each point in space, right? It's a rule tells you what you can and can't do at each point in space. So we call that a function because a function is a number or a rule at each point in space. A function at space is exactly that. Well, it turns out the function that does that is the electromagnetic field. If you ask what would be the mathematical characteristics of a quantity that would make sure the rules remain the same. No matter what I called an electron place to place and you ask how I could write it down mathematically, it would have exactly the mathematical form of the electromagnetic field. The thing that we call the electric field or magnetic field. The mathematics of it is precisely fixed by being able to allow us to change the definition of charge from place to place in a way that doesn't change the ultimate dynamics. It doesn't change the way the world works. It's prescribed by the mathematics of the rule book is prescribed and the mathematics of that rule book turns out magically almost to be exactly the mathematics of Maxwell's equations which are the equations of electromagnetism. Here's where it gets squirrely from me. Why would you do that? Why would you change the definitions? Why would you need that rule book? Well, because, I mean, what it says is that nature somehow has a symmetry. It doesn't depend, you don't want to, but it says nature has designed itself such that the definition of electric charge from place to place is arbitrary. It really came, if you want to step back, Einstein told us that length and time are kind of relative, they depend upon the observer, and his theory of general relativity actually said, I can define locally what my coordinate system is, what my length is, what my time is. I can define that arbitrarily locally, and it may differ from place to place. My rulers could differ from place to place, but the universe doesn't care because there's this thing called the gravitational field that takes into account of that, and nature has that symmetry. So it doesn't matter if I change the rule book, if I change what I define as space and time locally, the universe behaves exactly the same. So when you say by symmetry, do you mean essentially there's a balance, that there's always going to be an equal number of negatives and positives, and that you change the- So that's a- The functions of each one, it balances itself out, is what you're saying? Well that's sort of a consequence. It says that the universe can't be charged, ultimately. But no, it really says that that's a quality of nature that nature doesn't care about. Namely, that's a label, but nature has a symmetry. In physics, symmetries are things when you make changes, then the object doesn't change. Take a sphere, okay? A sphere, you can rotate it. But it looks like a sphere, no matter what rotation you make. That's a symmetry of the sphere, that's why it's so beautiful mathematically. Nature's the same way. I can take another quantity, I'll call it electric charge at this point, and I can change it. If you want to say make a rotation in some internal space, you can imagine an internal space, positive and negative charges were part of some continuum. I make a rotation. And nature doesn't care about it. It's a symmetry of the equations that govern nature. But it turns out, the reason this is important, let me step back again, because your face tells it all. I wish that people could see it. They can. So, what we've discovered is that the playing field determines the rules. The characteristics of the playing field determine the rules. If baseball, if you played baseball and there were five bases instead of four, the rules would be different. If the distance between home plate and first base was a mile, the rules would be different. If you had 25 out of fielders in out field, it would be different, okay? So the playing field determines the rules, right? Baseball would be a very different game if it were played on a field that's different. What we've discovered in nature is we used to think the forces were kind of fundamental. You know, Newton told us F equals ma and all that. What we've discovered is the thing that really constrains what can happen in the world is the playing field and the characteristics of the playing field. And for physicists, what determines the characteristics of the playing field are the symmetries of that playing field. In fact, baseball, the fact that it looks like a diamond, is a symmetry, right? The playing field looks the same. I could call first base home plate and home plate first base if I rotated the whole field, right? It determines, in some sense, that's a characteristic of baseball that sort of determines the rules of the game, okay? And what we've learned is what's really fundamental in nature is the characteristics of that playing field and what determines the characteristics of that playing field are the symmetries of nature. The things that demonstrate to us that what we think is fundamental is really just an arbitrary label, like electric charge, as we've discovered, is an arbitrary label, locally as well as globally. And that determines the whole nature of the forces that can happen. Once you say that electric charge is an arbitrary thing and nature doesn't care what you call positive and negative from here or Mars, that determines the nature of the force of what we call the electromagnetic force. It's completely prescribed. And it turns out that's true for all the forces in nature. The nature of gravity is determined, as Einstein showed, by the fact that you can change what I define as one meter here, and on Mars call one meter something else and nature doesn't care what I label as a meter. It turns out gravity takes that into account and says what we define as length is irrelevant. The fundamental gravitational field is due to a curvature of space that is independent of what we define as length or time, locally. It's a weird thing, but it's a property of space and time that Einstein discovered for general relativity, we've discovered it for electromagnetism. It turns out all the forces in nature respect that same kind of mathematical symmetry, that there's some quantity that you can change in your equations. I can change its definition in the equations, but the physics remains the same. And the nature of the equations is prescribed, the mathematical form of the equations is prescribed precisely by the requirement that I can change, in the case of electric charge, that electric charge is arbitrary. I can call an electron positive or negative anywhere I want in space, and the equations don't care. That prescribes the form of the equations. They have to have a very particular form, a unique form, and that unique form happens to be the form that it has. Now, so you can say, look, it's an accident that really there's something fundamental, that the equations have this form and we've discovered this mathematical symmetry is an accident. Or you can say that the mathematical symmetry is fundamental, it's a property of nature, and it prescribes the form of the kind of forces that nature, that the world allows. When you say that it's fundamental, that the symmetry is fundamental, do you see the symmetry, do you study like ecosystems, do you study like- I know about them, but I'm- But do you ever contemplate them when you're thinking about theoretical physics? Do you ever look at like how these animals sort of stay in balance in these ecosystems? Well, the mathematics- Well, the mathematics, I mean, that's the great thing about physics, about science in general. It's kind of like Hollywood, if it works you copy it. And so we often find the same mathematical formalisms apply to vastly different systems. So there's a very famous set of equations of predator and prey for ecosystems, and you can look at those equations, and they're the same kind of equations that apply in many different systems in oatmeal boiling. And also, it's amazing how the same mathematics appears in very different systems, and we can therefore use what we've learned in one case to apply to another. That's why we copy it, because it works so broadly. It's amazing that very few equations turn out to so broadly describe so many vastly different systems. And predator-prey relationships, which is, I think, what you're talking about in ecosystems, how, you know, there's a very- And even with plants as well, I mean, like the full system. Yeah, once you- and it becomes more complicated when you include more variables. But physics, of course, is generally much easier than many ecosystems. That's why I do physics. It's so much easier. Because it's really the low-hanging fruit. Nature- Maybe for you. Well, I know, but- For most people listening to this, there's probably 100 people that have driven into trees by now. Like, what in the fuck is this guy talking about? I'm glad there's people like you out there that are contemplating this stuff. It can feel good that the laws of physics are independent of whether they've run into the trees. Yes. I'm sure that gives them great comfort. Yeah, exactly. It's just-