Daniel and Kelly’s Extraordinary Universe - What hidden symmetry is controlling the Universe?

Episode Date: September 30, 2021

Daniel and Jorge dive deep into quantum theory and explain gauge symmetry, the foundation of all modern physics. Learn more about your ad-choices at https://www.iheartpodcastnetwork.comSee omnystudio.com/listener for privacy information.

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We talk about your questions, we give some answers, we make a bunch of silly jokes. As usual, and we tackle all kinds of questions, including. including what happens if I fall into a black hole or is there another version of you out there? That's right. Like usual, we tackle the deepest, darkest, biggest, craziest questions about this incredible cosmos. If you want to support the podcast, please get the book and get a copy not just for yourself, but, you know, for your nieces and nephews, cousins, friends, parents, dogs, hamsters. And for the aliens. So get your copy of Frequently Asked Questions About the Universe. It's available for Pre-order Now, coming out November 2nd.

You can find more details at the book's website, UniverseFaQ.com. Thanks for your support. And if you have a hamster that can read, please let us know. We'd love to have them on the podcast. Hey, Daniel, I have a complaint to file about physics. Who do I talk to?

Oh, you can lay it on me. I'll pass it on to the right people. All right. You're the ombudsman for all of physics. It's good to know. All right, so I feel like physics is pretty good about answering how questions. Hmm, you mean like, how old is the universe or how big is it? Yeah, just like that.

All right, well, that sounds pretty good. What's your complaint? Well, I feel like the real questions that humanity wants to know are the why questions, you know? Like, why do we have this universe? Why is it like this and not like that? You know, I'm going to have to direct you, I think, to the philosophy department. Oh, man, you're going to pass the buck. Well, I don't know how else to answer it.

why question. Yeah, and I don't know why I asked you these questions in the first place. You ask a meta question, you get sent to the metaphysics department. Are you the meta-umbudsman? Hi, I'm Jorge. I'm a cartoonist and the creator of PhD comics. Hi, I'm Daniel. I'm a particle physicist. and a professor at UC Irvine, where I actually am also a member of the philosophy department. Oh, are you really? So you're a card-carrying philosopher? Technically I am, though I have no education in philosophy. I just started showing up at the

Philosophy of Science seminars and eventually they were like, who are you? And then they give me a joint appointment. Wow. I guess they let anyone in who shows up. Is that in? Like there's not that much of a demand for philosophy membership? Well, I think joint appointments are free. So yes, the bar is not that high. Nice. Do you have to teach classes in philosophy? I am not qualified to teach classes in philosophy. Well, I feel like physics, you know, asked a lot of very philosophical questions or questions that border on philosophy, right? Like, why is the universe like this? Or why do we have a universe, right?

Like, you're asking these questions as physicists, right? Yeah, a lot of the answers we get to questions in physics do have big philosophical implications. And I think it's important. That's why I started going to these seminars to understand, like, what if we discover this or what if we discover that or what is it really mean, man. Physics can tell you what's going on, but only philosophy can tell you what it means. Well, it's kind of a layer thing, right? Because you can ask, like, why does the apple fall from the tree? And you can say, well, it's gravity. But, you know, once you start digging deeper, like, why do we have gravity? Then it starts to get philosophical. Yeah. And then

you can ask, like, what kind of answer will satisfy your question? And then you have a philosophical answer about philosophical questions. Yeah, or like, why have philosophical answers? Philosophy of philosophy. Wow. You can get a PhD in philosophy, I guess. It's the start of the endless loop. But anyways, welcome to our podcast, Daniel and Jorge explained the universe, a production of iHeartRadio. In which we go meta and meta meta about the nature of the universe. We ask all the questions about how the universe is, and then we also ask the questions about why it is and what that means. Because we don't just want a description of the universe. We want an understanding of the universe. We want to know why the universe is this way and not any other

way or maybe if it could have been that other way. We seek not just to describe, but also to explain. And that's what we're doing here, exploring the universe and explaining it to you. Yeah, because it is a big universe and one of which you can ask a lot of questions, because it is not just kind of a big universe and a pretty mysterious universe, but it's also kind of a beautiful universe. It is, in fact, a beautiful universe, not just in the vistas that we partake in the wonderful night skies, but also. in the mechanisms for how it works. Sometimes you look at the mathematics

for the way things work at the quantum level and you're like, wow, that's pretty neat. I couldn't have designed the universe so beautiful or so clever. It does feel sometimes like we are uncovering a work of great beauty. Yeah, because the universe does seem to have rules, right? Like it's not a willy-nilly universe

where anything can happen. It seems to have rules and the structure to it. And as you say, it sort of feels clever in a way. Can you talk about that? Yeah, it's just maybe our approach. is just sort of subjective. But one of the most incredible things we've discovered is that the universe can be described

in terms of mathematical laws. Why do we even think that it was possible to write down equations that predict what will happen in our universe? And that only some equations will work, right? Like, it's sort of like you can't just write down any random equation and say that's physics. It's math, but it's not necessarily physics.

The same way you can't just write down a string of words and say, here's my novel, right? Not every string of words is a novel. So we use math. as a language to express physics, but then you can also look at that math and say, wow, that really clicks together nicely, or this makes a lot of sense,

or this tells you something about the nature of the universe because it uses this math and not that other kind of math. And then you get into the philosophy questions. Like, what does it mean that we have a universe that's like this and not like that? Right. That's pretty interesting, the idea that, you know, like all physics is math, but not all math is physics.

Like not all possible equations have a physical reality to them. Absolutely. You can describe lots of hypothetical universes out there using mathematics, but they don't necessarily describe the universe we live in. And, you know, there are lots of beautiful theories about physics that were mathematically really nice, but just didn't describe our universe. And so they ended up like tossed in the dustbin of physics history. Oh, man. You have a reject pile for beautiful theory. We do because the universe gets to say what the universe chooses. And sometimes it's a little surprising and a little bit messy, but often we can find something.

elegance, some nice description of it that reveals something about the universe. And then you go off and chew and you're like, that's really interesting that the universe has this structure. What does that mean about its like fundamental nature? One of my favorite examples is very simple. It just comes from conservation of momentum. Like this is something we observe in the universe. We notice that if you bang two rocks together, that at the end, you have the same amount of momentum as you did in the beginning. It's changed direction a little bit perhaps, but all the momentum is the same. It's something we observe. And you can ask like, well, why is that? Why is momentum conserved? And we have this deep theory of physics that tells us why, but it just

brings up more questions. It turns out that momentum is conserved because space is uniform, because you can do the same experiment here and somewhere else and on Jupiter, and you should get the same answer. One thing leads to the other. Because space is uniform, momentum is conserved. But then that just brings up the question like, well, why is space uniform? Why is it true? That you can do the same experiment here or in Alpha Centauri and you should get the same answers. Why are the laws of physics the same everywhere in space? But that seems to be the way our universe is. And that's the way it is, Ben.

And it's also sort of a good thing that it is, right? Like, it would be weird, or could you even have a functioning universe if things weren't all smooth and working the same way everywhere? Like, wouldn't it be just complete chaos? Well, that is the job of science fiction authors, right? To imagine different universes and say, like, what would it be like to live in that universe, to be a scientist in that universe and discover that you lived in that universe

instead of this one. What stories could you tell in that universe? So I think there are probably very different physical consequences of living in the universe like that where the loss of physics change with space or with time. But this is the one that we live in. I think you could imagine ways to live and ways life might even arise,

but it would be vastly different from the universe that we know. Well, now you're giving me kind of a fear of missing out. What if there's a better part of the universe that we're not living in? Like, what if the grass is really, like, greener on the other side of the galaxy. Yeah, well, you know, we haven't even discovered how green our grass is. There's so much

we don't know about the universe, so much to discover so many beautiful things that will be revealed in the future that will amaze you. So stick around in this universe, I recommend it. There's a lot of green grass left to cut. It's interesting, you said that word earlier, elegant. You know, I feel like I hear a lot of

physicists say that word sometimes that the universe feels really elegant in the way the rules and the laws work. And that's kind of what we'll be talking about today. is one of these elegances of the universe. And what we're looking for to describe the universe is a simple description. You know, you could describe the universe

as just like, here's a list of all the physics experiments anybody's ever done and the results. That's great. That describes the universe. But it doesn't give you any insight. It doesn't give you that like, aha, that's because they're all following the same rule. And that's the job of physics

is to boil down a bunch of experiments, a bunch of observations into a simple rule. And it's when you see that, rule and you say, wow, it's incredible, that's something that's so simple can have all these consequences. That's when you feel like you're looking at some elegance. You're like understanding a deep truth about the nature of the universe. You've revealed something at a lower level than anybody has seen before. You've like peeled back a layer of reality and seeing a simple description that leads to all the incredible complexity that we see in our universe. And I guess, you know,

one of the things that we feel is simple or a way to give things a certain sense of elegant, is this idea of symmetry, like if something is symmetric, somehow as humans, it instills in us a sense of like, oh, that looks perfect or that looks, you know, elegant or beautiful. Yeah, and it also sort of feels democratic. Like, to me, it's nice that the universe doesn't prefer any location in space. You can do your experiment here or somewhere else, and it doesn't make a difference. And, you know, there are real consequences to that symmetry. That symmetry means only certain laws of physics are allowed. Like, in that case, only laws of physics that conserve momentum are allowed. that comes directly from that symmetry. And we've discovered lots of these kinds of symmetries.

You know, another one that people are probably familiar with is the fact that there's no up or down in space. Like you do your experiment in space, it doesn't really matter which direction your experimental apparatus is pointing. You can spin it in another direction and it should get the same result. That's another symmetry. It says the universe doesn't prefer a direction, not just a location, but a direction. And that gives you another rule.

It says that all the laws of physics that you write have to also conserve angular momentum, which is separate from just momentum, right? This is like how much something is spinning. So every time you discover a symmetry, something where the universe doesn't care about something or gives you the same answer, no matter how you spin or move something, that tells you something about the laws of physics

that are consistent with that symmetry, the laws of physics that can describe our universe. Yeah, so today on the podcast, we'll be talking about what hidden symmetry controls the universe. It sounds like a dark conspiracy here, Daniel. There's something hidden controlling things. People smoking cigars, wearing gray suits, and deciding what laws of physics can we have?

Or were you going for some click-bate action here? I'm just trying to, you know, get a little bit of reflection from the X-Files glamour. That's all. Yeah, we should title it like the hidden dark secret that controls the universe. Click to find out more. But yeah, there seems to be a symmetry to the universe. And I feel like, you know, maybe physicists use this word differently than how most people understand it. Because I think, you know, to most people, symmetry means, like, if something is symmetric, it means, like, it's the same.

If you look at it, you know, the right half and the left half is the same, or it's like the mirror image of something else. Or there's some sort of reflection or some, like, equality between left and right or two directions. I think that's what people mostly think about symmetry. But physicists think of symmetry, it's kind of a different concept in physics, right? It's about how the mathematical equations stay the same no matter how you transform them. Yeah, but it's also closely related, I think, to be able's intuitive sense of symmetry. Like, think about the examples you mentioned, the sphere, for example. You know, there's a rotational symmetry there.

You have a perfect sphere, you rotate it, you get the same sphere, right? And so nothing has changed for the sphere. It's the same. Or even if you reflect it through a mirror down its middle, you get the same sphere. So there are symmetries in the sphere that would be. change how you interact with the sphere. And we talk about the same things in physics. We say, look, if you do this experiment and you just rotate your axes, you make X into Y and Y into Z or whatever, you should get the same answer. You know, it's like spin the experiment or spin the

universe. It doesn't matter. You should get the same answer. And so fundamentally, when we talk about symmetry, we mean, do you get the same laws of physics if you apply some transformation or some rotation or some change to your axes or how you've defined things. And so that's what we mean when we talk about symmetry. Right, right. Like a butterfly is symmetric, right? Like the left side and the right side is symmetric. But you can also think of it as like the left wing.

If I put it through a mirror, it'll look just like the right wing. Yeah. Maybe. Actually, I don't even know are all butterflies exactly symmetric? Probably they're not exactly. But in our cartoon, right, assume a symmetric butterfly. Then in that case, yeah, you put it up to a mirror and you see exactly the same other half. Right. And at least it look the same or similar. And so this symmetry idea is very important

physics because it almost like, I don't know, defines the loss of physics at the fundamental level or it's something that's important for them to work, right? Yeah. Well, what happens is that we notice the universe following certain rules. You know, for example, we notice that the universe doesn't create or destroy electric charge. Like you have a bunch of it. It doesn't go away. You can't destroy it and you can't make any more. Right. And so that's like a rule the universe. universe seems to be following. And then we ask questions like, well, what symmetry gives you that rule? Why can't you create or destroy electric charge? What rule is it fundamentally following? And what we discovered or what M. E. Nother discovered about 100 years ago is that every time you see the

universe following a rule is because there's a basic symmetry. There's something about the universe that's preserved that has this kind of symmetric property where it doesn't depend on how you spin it or reflect it or whatever. And that's where these conservation laws come from. So that's very, very Every time you see a conservation, it means you can discover a symmetry of the universe, which tells you something pretty basic about like the very structure of reality. All right. And even the reality in the mirror as well. I will get into that.

But I guess more specifically, it has something to do with something called gauge symmetry, right? G-A-U-G-E symmetry. Yeah. All of our laws of physics in the standard model are built on this principle of gauge symmetry. And we'll dig into exactly what that means on today's episode. but it turns out to be something really deep about the way particles operate and their relationships with each other. All right. We'll take a dive into that symmetry, but first we were wondering how many people out there know or have heard of this concept of gauge symmetry. So Daniel went out there into the internet to ask people, what is gauge symmetry?

And so if you are interested in answering really hard questions about secrets of the universe with no chance to prepare at all and then have thousands of people hear your answers, please write to us to Questions at Dan. and Jorge.com. It's a lot more fun than it sounds. Think about it for a second. Do you know what gage symmetry is? Here's what people had to say. Gage symmetry is how one would gauge the symmetry between a binary set of stars. And obviously that's incorrect, but there you go. I am not sure what gauge symmetry is, but perhaps it was a very smart scientist person that explained some kind of symmetry in the universe or in physics. Gate symmetry, it has something to do with electricity or charges. It doesn't matter what direction in a circuit or in what direction you look at particles or whatever.

Like the charges are symmetrical in, it doesn't matter if there's a pleasure or minus. From my point of view, gauge symmetry, well, it happened to me once I, when my instrument cluster from my truck broke down and all the gauges were at zero, so they were symmetric. So this is gauge symmetry from my point of view. Let's break it down. Gage symmetry is when you make a transformation on a field, which, turns one particle into a different one maintaining obviously because it's symmetric maintaining some properties of that particle I think if I recall correctly gauge is basically measurements so gauge symmetry might be that one

measurement in one unit basically described in a different unit possibly well I guess the gauge symmetry is when my front tire and my rear tire of my bicycle show the same amount of pressure. Then I would have two gauges and they are symmetric. Otherwise, I have no idea. All right. It seems to be kind of a mystery to our listeners. The secret cabal has done a good job of hiding itself in the backroom to the universe.

It's really hidden. Well, I guess it's a weird word because in general, we use the word gauge to like gauge something, right? To like measure something. like a pressure gauge is something that tells you how much pressure is in your bicycle tires or your fuel gauge tells you how much fuel you have in your car. And so what does it mean then to have gauge symmetry in your equations of physics? So it comes from the era of the railroads when people who are still laying down a bunch of new tracks and they have to decide like how far apart do you make the tracks.

You make them one meter apart or a meter and a half or whatever. And everybody had like different choices. And that makes them incompatible, right? You can't drive your train if the gauge is. wrong and so somebody just has to like make a choice and then it doesn't really matter you can still build railroads if they're a meter apart or half a meter apart or whatever it still works you just got to make a choice and so that arises sometimes in physics where there's like an arbitrary choice you have to make like where do you call height equals zero or where do you call electrical potential

equals zero and it shouldn't affect how your physics works it doesn't change anything for how your experiments should work but you do have to make a choice it's almost like a scale maybe or like a starting point? Is that what you mean? Like a scale, like is this railroad track, you know, this wide or is it narrow? It's sort of that way in physics where you have to say, all right, what scale are we talking about when we're talking about these electrical fields? Yeah, and you just like, you need a number and so you have to pick a starting point. That's a good way to think about it. But it doesn't affect anything, right? It's just like it seems like an arbitrary choice. You know, one simple example is like, think about a book falling off of a shelf and wondering like, well, how fast is it going when it hits the

floor. Well, the answer to that question depends on the height of the shelf because the taller of the shelf, the faster it is when it's hitting the floor and the shorter the shelf, the slower it is when it hits the floor. But it doesn't depend, you know, mostly on how high your shelf is above sea level. You know, so like where do you call height equals zero? Do you say height equals zero a thousand meters below my floor or at my floor or above my floor? You can do all the calculations. You get the same answer no matter where you put like height equals zero in your physics problem. That's just an arbitrary choice doesn't affect your answer. So that's an example of, you know, making a gauge choice.

And so this word gauge was chosen to sort of like, you know, harken back to the age of the railroads, but really what it means is an arbitrary parameter of your theory. I see. You were saying physicists picked a word that had nothing to do with the thing. But she wanted to confuse the rest of the population. Is that what you're saying? Yeah, your ancestors should have been called on 100 years ago

when they were naming this thing. I totally agree. it's a ridiculous word and it's become so important so we say it all the time now gauge theory is everything the whole standard model of physics is a gauge theory it's almost like the theory only tells you changes or how it changes from a starting point is that kind of what you're saying but the answer it kind of depends on where you start right and it has a you know a lot of history like electromagnetism which you know predates the standard model in particle physics by a long time you know Maxwell noticed this in his equations when he was putting together his equations of

electromagnetism, he noticed that you could change these. You could like add an arbitrary number. Not exactly just a number. It has to have like a disappearing curl to it. But you could add something to the theory and it wouldn't change any of the predictions. And so you can have basically like different sets of Maxwell's equations. And they call these different gauges like the Kulam gauge or the Lorentz gauge. People chose different sets of equations. They all make exactly the same predictions. You just like pick one. There's like a whole family of these equations. And they all make exactly the same predictions you can use any of them as long as you're consistent they're almost like floating theories i guess you might say right and so then there's the idea that within these

theories you can have a certain symmetry to them and so that's what gauge symmetry is and so let's get into why it's important for our equations of the universe and what does it all mean man but first let's take a quick break i don't write songs god write songs i take dictation i didn't even know you've been a for over 10 years. I think culture is any space that you live in that develops you. On a recent episode of Culture Raises Us podcast, I sat down with Warren Campbell, Grammy-winning producer, pastor, and music executive

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about the hidden conspiracy here that's controlling everything, Daniel. This is one of those podcasts. That's right. We are bringing you the hard truth today, folks. We are tearing off the veil. We are revealing who's really behind everything. That's right. That's why this podcast is encrypted, right? We're encrypting this. We're not putting our names on the title of the podcast either, right? That's right. But we are doxing the true masters of the universe today. Oh, there you go. That's another all title for physicists. You're doxing the universe.

you're exposing it. We are, exactly, we are. All right, so we talked about what a gauge theory is. It's like a theory that it sort of floats, that it tells you how things change, but it sort of depends on where you start them. And so that's kind of what a gauge theory is. And so then what's gauge symmetry?

So gauge symmetry is when you have a theory that has a gauge in it, right, so you can make this choice, but it makes the same prediction regardless of your choice. So as we talked about electromagnetism, It doesn't matter if you use the Kulam gauge or the Lorentz gauge. You write down different equations, but they predict exactly the same behavior of like electrons moving through fields or magnets being generated. It doesn't matter.

So there's a gauge symmetry there. You can pick your gauge, but it doesn't affect the physical predictions. I see. But then how did the name symmetry come from? Because it's not, you know, like maybe I would have said it's gauge invariant or gauge doesn't care less about gauge. But the word symmetric to me sort of means like a reflection or like a mirror. image. Yeah, well, you can transform from one gauge to another without changing your predictions, just like you can rotate a sphere through an arbitrary angle without changing the sphere. It's still a

sphere. And so a gauge theory is one that you can transform in a certain way from one gauge to another without changing your predictions. We'll talk about various gauge symmetries today. Some of them are a lot like rotations of a sphere. All right. Are we saying that the laws of physics with the universe are gauge symmetric or we noticed that they were gauge symmetric. Yeah, it's really fascinating. The laws of physics in the universe have really weird and surprising gauge symmetries much more than you would expect. And they have real consequences. Like we talked about every time there's a symmetry of the universe that leads to a conservation law. And so what we can do is we can say, oh, maybe this is why we have conservation of electric charge or conservation of other things. It's because there are these

symmetries in the universe. And then we can ask the deep questions like, well, why does the universe, have that weird gauge symmetry. What does that mean? This is not just like an arbitrary thing we write down in our rooms with pencil and paper. It's something deep about the universe that respects this symmetry. Meaning like if you work at the equations of the universe, you notice that they're gauge symmetric. And because of those symmetries, then things like conservation momentum happen. Yes, exactly. And so, you know, we notice that those things definitely happen in our universe and we discovered that that means that there must be these symmetries, which is really, interesting. All right. Well, maybe talk to us a little bit about why it's important and how it has

to do with quantum mechanics. Yeah. So the standard model of particle physics and quantum mechanics has a lot of gauge symmetries in it. And one that comes from quantum mechanics comes from the wave function. Like we talked in this program before about what happens to little particles in experiments. Like what determines whether an electron is going to go left or going to go right when it interacts with something else. That's determined by the wave function, which tells it like the various probability to go here or the probability to go there. But there's a little step there, which we've glossed over, but it's actually really, really important.

It's not the wave function itself that tells an electron, whether it has a probability to go left or to go right. It's the square of the wave function. The wave function squared, the way function multiplied by itself, that determines the probability to go left or to go right. And that's because the wave function itself is a complex number, you know, like one plus I or two minus I or whatever. And so it doesn't have real values.

So you have to square it. to get real values. And there's a symmetry there because it means that the wave function or minus the wave function give exactly the same predictions. So you're saying like

at the fundamental level of particle physics, like particles that make up our universe, they're symmetric, like starting from that because the wave function that describes it is symmetric in itself.

In terms of it, the probability though, right? Like the original wave function is not symmetric, but if you square it to get the probability, then it is symmetric.

Yeah, if you take every wave function and you multiply, by minus 1, it doesn't change anything in the laws of physics. That's what we're saying. So take the whole universe's wave function, or if you don't believe in that, take the wave function of all the particles, multiply all of them by the same number, nothing changes. The laws of physics predict exactly the same outcomes.

It doesn't matter because it's only sensitive to wave functions squared. So you have a freedom there, a choice. Do we start with a positive wave functions or do we start with the negative wave functions? It doesn't matter. So there's a symmetry. Really? It doesn't matter? Like it won't affect at all when it comes out?

It won't affect at all because you take it and you square it. All physical predictions depend only on the wave function squared. All right. So then that means that all particles in the universe are symmetric. What does that mean? It's actually a little bit more general than just multiplying it by minus one. You can actually multiply it by a rotation in the complex plane. And I don't think we should get too far into the math.

But just think about it like you can rotate these things by an arbitrary angle and you still get the same number. And so that makes a lot of sense if you just do it to everything. Like you multiply the whole universe by minus one. one, nothing changes because you've been consistent. You change the way function of my electrons and your electrons and somebody else's electrons. That's called a global symmetry, affect the whole universe. And that's not so surprising. But there's something else that the universe has, which is a very different and much, much deeper symmetry. It turns out that the universe is symmetric to local gauge invariance, which means you can make this kind of transformation differently at every point in space. You can say,

like here I'm going to multiply all my wave functions by plus one over in Jupiter. I'm going to multiply them by minus one. And in Alpha Centauri, I'm going to do something different. So that's a local gauge invariance that says that you can have like an infinite number of these different ideas about gauges. Wait, what do you mean? But you just told me that it's globally invariant. Like it doesn't matter what you do to it anywhere.

But now you're saying that it does matter what you do to it locally. Yeah. So global gauge invariance the universe definitely has. But if you want local gauge. invariance, right? That's harder. That says, well, now I want to be able to multiply my wave functions by plus one or minus one and do it differently everywhere. And you might immediately say like, okay, well, that obviously doesn't work, right? Because you have to be consistent. Otherwise, like the interference terms of the wave functions are not going to come out right. And you're

right. The universe by itself for an electron doesn't have local gauge invariance because if you change the gauge here and you change it somewhere else, then it will affect the predictions. So the universe, if all you have in it are electrons, doesn't have local gauge invariance. And then if this played a fun game, they said, well, what if we added something? What if we added something else to the universe so that we did have local gauge and variance? Something that, like, corrected for that. So take the universe that just has electrons in it and ask for local gauge and variance,

and you break that, right? Like, immediately you don't have local gauge and variance because you're changing electrons differently everywhere. Well, now if you, like, add something to the universe to try to fix it, to compensate for this change you've made, you have to add a new. piece. And that new piece, if you look at the mathematics of it, is exactly the electromagnetic field. I think you lost me a little while ago, to be honest. So I guess it's the difference between local and global. Is it like, kind of like if I let go of my book from a three-story building,

it's not, I won't get the same velocity at the bottom as if I drop it from a one-story building. Is that kind of what you mean? Yes. Or let's say you want to define your altitude differently based on where you are in the world. Like currently we have a single global definition of altitude. relative to sea level. But what if you wanted to choose your height definition to be different if you're here or if you're over there, if you're in Irvine or Pasadena or New York? All of a sudden, you know, as you move across the country, your height would be changing constantly like, oh, I'm higher, I'm lower, I'm higher, I'm lower. It wouldn't make any sense. You'd get crazy physical predictions. Like the book would still fall the same way, wouldn't it? The book would still fall the same way.

And so your theory wouldn't work. If you'd like throw a ball as a parabola and it's moving across the ground and you're constantly changing like the definition of height, then you're not going to get sensible predictions, right? The ball obviously does move smoothly and so your physical theory doesn't work anymore if your definition of height is changing as the ball is moving. Is it like, you know, my equation, my prediction won't work if I use meters in England or if I use feet here in the U.S.,

like that's what you mean. Like you want a theory to be indifferent about whether you use feet or meters. Yeah. And so global invariance is like, well, let's just use meters everywhere. that makes sense, or let's use feet everywhere, but let's be consistent. Local invariance is like, no, I want to get to pick my units differently everywhere. And so that's a much higher standard. Like to have laws of physics that allow you to have that much freedom to make any choice

at any point in the universe is a much higher standard. Oh, right? Because I guess it would have to be like irrelevant, right, almost. Exactly. It's like it doesn't matter if you weigh something in England or in the U.S., whether you use meters because meters doesn't figure into it. That's kind of what you want, right? Exactly.

All right. So you're saying that the universe doesn't seem to have that local gauge invariance, meaning it does matter if you use meters or feet, but you're saying there's a way to get that back. There is a way to get that back. You can say, what would the universe have to look like to have local gauge invariants? Like take your electron, it's flying through space, and what if you want to be able to multiply its wave function by an arbitrary number at a different point in space and have that number be different everywhere in space? Is there a way to do that?

Is there a universe you could construct? that would follow that, that would respect your local gauge invariance that would allow you to have that much freedom. And it turns out there is. If you add a photon, so if you have just electrons in the universe, no local gauge invariance. But if you add an electromagnetic field, which gives you photons, boom, you get local gauge invariants for free. What? Wait, okay, so somehow the fix for this solution, but for all equations or for just some particles? You're saying the solution to making things be a meter or feet independent,

is to add the electromagnetic field. Yes, the electromagnetic field is the thing that can perfectly compensate and give you local gauge invariance. Like you can derive it. You can say, here's the wave function for the electron. I'm going to add an arbitrary phase to it, which is like multiplying it by an arbitrary number.

And you can say, well, now my predictions are wrong. They're different. What would I need to add to my equations to compensate for that, to cancel out this baloney that I've added? And what you need to add has exactly the same mathematical structure as the electromagnetic field. It is the electromagnetic field. So the presence of the electromagnetic field

is what preserves local gauge invariants. So you're saying the electromagnetic field preserves symmetry for the electron or for like everything in the entire universe? For the electron's wave function, yes. So we're talking just about the electron and its wave function. It is feet and meter independent.

But if you add the electromagnetic field, then it is independent. Oh, I guess the electron has its own field too. The electron has its own field. Yeah, there's the electron field. And now we're saying that if we want this local gauge invariance where we can multiply arbitrary numbers to the electron field, that can't happen unless you have this exact, very specific requirement of another field that hangs out and basically compensates for that

and takes care of that for you. And it turns out that that field is the electromagnetic field. And photons basically exist in order to preserve local gauge invariants. Well, you're saying the only reason we have light is to make electrons happy? Well, here's the philosophy, right? Like, do we have light because the universe preserves local gauge and variance, and that's the only law of physics that allows that, one that has photons? Or do we have photons because we have local gauge invariants, right? Like, which direction does it go, you know, is a fun philosophy question. But what we do know is that we have photons, we have electrons,

and we have the electromagnetic field, both of those two things. And together, they seem to have this amazing, weird property of local gauge and variance where you can must. multiply it by an arbitrary number, and that number can be different at different points in the universe, and it doesn't change the predictions. These two fields work together in this really crazy and an interesting way. That's interesting, but it only applies to the electron. Like, what about quarks, right? Quarks have a field, I think, and we can ask the same questions. Is the quark also locally symmetric, you know, meat and feet independent here in the U.S.? And is there a separate field then that also fixes that symmetry?

Fascinating question. You're absolutely right. This applies to the electron. It also applies to any particle that has electric charge. So, for example, the muon has this same property. The muon, you can multiply it by an arbitrary number. And you also get local gauge invariance because the muon is charged and it also communicates with the photon field.

And yes, corks have electric charge, so they do the same thing. In fact, turns out that's what it means to have electric charge. Electric charge means you couple to the photon field because electric charge just means you feel electric fields. You're like influenced by electromagnetic fields, which is the field of the photon. And so the reason we have electricity and magnetism, the reason we have electric charge is because these particles have this property. A really fascinating thing is we didn't know necessarily like do muons feel the same photon as electrons? Like it could have been there's a different field to preserve the muons, local gauge, variance and the electrons.

But of course, we know there's a single photon, the same photon that an electron emits can be absorbed by a muon. But it didn't have to be that way. You could have lived in the universe with like an electron photon and a muon photon and a tau photon and lots of different kinds of photons in it. All right.

So then it seems like the electromagnetic field is the thing that preserves the symmetry for all particles that fuel the electric charge. And so that's what makes the equations for all these particles symmetric and that's beautiful and maybe even clever. All right, let's get into what it all means for the universe and our understanding of it. But first, let's take another quick break.

I don't write songs. God write songs. I take dictation. I didn't even know you've been a pastor for over 10 years. I think culture is any space that you live in that develops you. On a recent episode of Culture Raises Us podcast, I sat down with Warren Campbell, Grammy-winning producer, pastor, and music executive to talk about the beats, the business, and the legacy behind some of the biggest names in gospel, R&B, and hip-hop.

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Maroon 5. Sammy Hagar. McCray, the offspring, Tim McGraw. Tickets are on sale now at AXS.com. Get your tickets today. AXS.com. Your entire identity has been fabricated. Your beloved brother goes missing without a trace. You discover the depths of your mother's illness, the way it has echoed and reverberated throughout your life, impacting your very legacy. Hi, I'm Danny Shapiro. And these are just a few of the professional. found and powerful stories, I'll be mining on our 12th season of Family Secrets. With over 37 million downloads, we continue to be moved and inspired by our guests and their courageously told

stories. I can't wait to share 10 powerful new episodes with you, stories of tangled up identities, concealed truths, and the way in which family secrets almost always need to be told. I hope you'll join me and my extraordinary guests for this new season of Family Secrets. Listen to Family Secrets Season 12 on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. All right, we're going deep here today, Daniel, I feel like you really throwing us down a rabbit hole here. Like, what is the nature of the electric magnetic field? Is it exists only to give symmetry to these particles or do particles have the symmetry

because of the electromagnetic field? It's a big philosophical question. Yeah, well, you know, I'm responding to your challenge. You remember when we were talking about the weak force and does it push or pull? And I said, well, one day we're going to have to go deep and talk about gauge symmetry. You said, bring it on.

I got time. So here we are. I don't think you can prove that I said that, can you? We didn't record it, did we? I think we do have a recording. I was just listening to it yesterday. Well, I might officially regret it right now. No, but this is pretty interesting.

All right, so it seems like the universe likes this symmetry, this local symmetry. It likes, and to do that, it has this field, this electromagnetic field, and that's kind of how the universe works. And thank goodness, right, because that's how we get light. Yeah, that's why the universe is literally so brilliant. Nice. It's a nice, light, light joke there. But I guess what does it mean, Daniel? I'm not sure what it means, you know, we live in this universe that has photons in it,

and that means that we live in a universe that respects local gauge invariance. Like, why does our universe respect this super weird, very specific, difficult symmetry? You know, why can you multiply wave functions by any number, and have that be a different number at every place in the universe? And still, it doesn't matter. Like, it's fascinating. I don't know what that means about the universe, but it means that local gauge and variance is deeply, deeply built in to the very structure of reality.

So I think we need like another 100 years of philosophers smoking banana peels thinking about why that is to tell us like, you know, why reality is this way and not some other way. But it also has very physical consequences for the nature of reality. Well, I guess a question maybe before we get into too deep into that is, does this also apply to particles that don't feel the electromagnetic force? Like aren't there particles that don't feel the photons and things like that, right? And do they have their own field that also preserves that symmetry? They do not.

Neutrinos, for example, do not have this symmetry. And neutrinos do not have electric charge and do not interact with the electromagnetic field and do not talk to photons. And if neutrinos did have this symmetry, they would have electric charge. And that's sort of what it means to have electric charge is that you have this symmetry. And then there's a field out there that, like, compensates for it. And so no, neutrinos do not have this symmetry. You can't do this same thing to neutrinos.

They have another weird difference. symmetry, which is why they feel the weak force. And quarks have multiple symmetries, which is why they feel the strong force also. But we can talk about that in a minute. It's almost like you're saying that the forces in the universe are, you know, there to maintain this symmetry in the universe. Exactly. And that's why we call the photon a gauge boson.

And we call these things gauge fields and gauge forces because it seems like the forces, either they exist in order to do this or they exist because of this, or this is the only way to have a universe because of this symmetry, but every force exists in order to preserve some local gauge and variance for the particles. It's almost like they're forcing the universe. You know, I made that same joke in that other podcast episode, and you said, I kind of forced it. Well, now I'm trying to be symmetric.

You know, I'm copying the same joke, but I'm doing it on the other side. You're force-feeding me, my own puns back to me. I'm being clever, right? Yeah, and the nature of that field is really fascinating. Like, for example, because we have this local gauge invariance and you have these photons, that's why we have charge conservation. Remember how we talked about how every symmetry of the universe leads to a conservation of something.

That's nother's theorem. So the fact that you conserve this property of electrons is why you cannot create or destroy electric charge. How does preserving symmetry lead to these conservation laws, which seem important, right? Yeah, well, we're going to have a whole episode about Nuthers theorem to get into like the intuition behind it. But right now, all you need to know is that every time you identify a symmetry of the laws of physics, that directly tells you that there's something that's conserved. Just like the symmetry of moving your experiment somewhere else leads to conservation of momentum.

And the symmetry of rotating your experiment leads to conservation of angular momentum. Well, the symmetry of rotating your electron from plus wave function to minus wave function leads to conservation of charge. I mean, it's the same concept for the other forces, right? Strong and the weak force. It's the same concept for the other forces, but it's a different symmetry. And in those cases, it's a much more complicated symmetry. So, for example, the strong force has not just like plus and minus charge, right? It has three different kinds of charge, red, green, and blue.

And it actually follows a much more complicated local gauge invariance. It turns out for the strong force, you can not just multiply the wave function by minus one. you can rotate the color space like take red and map it to green and green and map it to blue and blue and map it back to red okay you can do this kind of rotation and you can have a different rotation at every place in space like green here is blue there is half red plus half green over here and you can do that and it's fine and it will not change the nature of your predictions for how the strong force works because you have a bunch of glue on fields that exist to compensate for that to sort of correct for that.

You're saying like these symmetries, it's almost like a three-way symmetry, right? Like it's not just like a mirror, but it's like a house of mirrors kind of. Yeah, exactly. And just like the sphere, right? The sphere is a much more complicated symmetry than just like reflection.

You can rotate the sphere and you can rotate it in different ways. You can rotate it about its equator or about its pole or about some other direction. There's actually three fundamental symmetries of the sphere. The same thing is true for color space

for the strong force. And that's why we have eight gluons because the strong force is a much more complicated local gauge invariance. It requires more fields. There are actually eight different gluon fields required just to preserve this force. And so, but it's described by the same fundamental mathematics. And this is why, if you've heard that group theory is important for particle physics, this is why, because group theory describes exactly how these rotations work

and sort of like the set of different rotations that you can have. And so the reason the strong force exists is because quarks have this weird, property that you can rotate their color in an arbitrary way different points in space and the gluon fields are there to compensate. That's why they exist. So then I guess do physicists see force as something totally different than most people think about it? You know, when I think of a force, it's like pushing and pulling, or as they usually describe it, it's like, you know, an electron throws a photon to another electron and that, you know, the throwing of the photon and the receiving of the photon is a way to kind of exchange, you know, a push or a pull or energy.

But now it seems like these fields are just there to preserve some kind of symmetry. Is that kind of why you see forces differently? Yeah, and that's that moment of elegance I was talking about. Like we start very simply in the world, seeing the world around us and categorizing and listing our observations. Oh, that apple fell from the tree or my friend fell down the canaan, you know, or I felt this weird magnetism. That's a pretty dark scenario there.

He used three a friend down the canyon. Hopefully not a podcast that goes. Thinking about the applications of gravity. And we just describe all of those things in terms of our experiences. But, you know, that's not necessarily the most natural way to do it. And that's why physics takes us and we transform our intuitive experiences into like a list of observations and look for mathematical patterns. And then we discover, oh, these things are actually connected to those things. And it turns out we've been looking at this all the wrong way.

And those are my favorite moments in physics when we discover, oh, we think about forces this way. Actually, they probably exist for this totally other reason. And we've come at it in this weird way just because of our experience. And so you get this like flash of deep insight when you're like, oh, the universe fits together in this beautiful mathematically elegant way. If you think about it in terms of forces, you know, recovering local gauge invariants instead of, you know, building anti-gravity machines to protect your clumsy friend. I guess how would you describe it then when an electron pushes on another electron and the exchange photons? How do physicists see it?

How do you see it in terms of preserving the symmetry? Yeah, well, physicists see it in terms of carrying those rotations. Like a photon sort of carries that rotation. You know, that's what a photon does. It rotates from one gauge to another gauge. And so when an electron communicates with another electron somewhere else in space, it's sort of like communicating about the differences in their gauge.

And so that's what a photon does, it carries that information. And that's what gluons do. Gluons rotate things through color space. They're like, okay, this quark over here is a green cork. That cork is a blue cork. You know, I've got to communicate from here to here, and I'm going to change the green to the blue as I move along.

The forces are sort of like there to connect these objects, and they do so by rotating the gauge from one place to another. And I think that's most clearly seen in terms of the weak force. The weak force has the same sort of structure, but then again, in a different internal symmetry space. It's almost like two electrons are gauging each other. It's like, you know, an electron interacts with the electromagnetic fields. If it moves, it creates some sort of disturbance that then has to be kind of squared away somewhere else by another electron.

And then that transfer of, you know, wiggle or disturbance is what you would call a photon. Yes, like patching up your checkbook at the end of the month, photons are there to like find those pennies and move them from one column to enough. to make everything add up in the end. Hopefully, they don't get too creative. Like I sometimes, like I may or may not do sometimes. Electromagnetic accounting. Exactly. Or maybe that's what quantum accounting really is.

There really is a quantum accounting firm. Yeah, where you have money and don't have money at the same time. You're both rich and broke at the same time. And, you know, I got an email this morning from a listener, Yvonne, who is asking me about why I say that the weak force makes sense to all be together. Like, why the Ws and Zs all make sense to be in a single. field and also with the electromagnetic field. But like, you can also ask like, why don't you consider the W plus and the W minus and the Z all just separate forces? Why isn't the weak force three different

forces? Why do you even try to put these things together? And the reason are these symmetries that we discover that like the W plus by itself doesn't preserve local gauge invariance. But when you put the W plus and the W minus and the Z together, then they do. So together, these three fields work really hard to preserve another kind of invariance, different from the one that's for the electron and different from the one that's for quarks. And this is why we have the weak force because it preserves rotations in this thing called weak iso spin space. And so these three fields together do that. And as you say, you can put electromagnetism and the weak force together to make an even super theory which preserves a different number altogether that individually neither the two forces preserve.

Right. It's almost like the more complicated. these symmetries are, the more forces you need to patch them up. Yeah. And of course, the really super fascinating wrinkle is that that symmetry, electro-week symmetry, the symmetry that's preserved by the photon together with the two Ws and the Z, that one doesn't actually work. That one's broken. That one isn't actually preserved by the universe.

And the reason for that is the Higgs boson. The Higgs boson breaks that symmetry. And that's why it exists. That's how we were able to detect that it does exist because we saw, oh, this symmetry doesn't actually work. We need something else out there to break this symmetry. And that's what the Higgs does.

And that's why the Ws and the Zs are massive while the photon and the gluons are massless. That's wild. Like maybe the only reason we have mass is to patch up these breaks. Yeah, well, the only reason we have mass is because this one symmetry is broken. This electro-weak symmetry

isn't actually something the universe respects because the Higgs breaks it. If we didn't have the Higgs, then the W and the Z would be massless and so would all the other particles, and we wouldn't have any mass without the Higgs. Don't we have other, like, violations of symmetry also all over the theory of physics, right? Aren't there all kinds of different charge and parity violations?

There are, yes. And so we have a lot of these approximate symmetries or broken symmetries. And an approximate symmetry is like, well, maybe we're just missing a piece. Like, we're not talking about the right thing. Like, we think we've identified the thing that's being preserved, the thing with the universe respects, but we must be looking at it from the, like the wrong angle. We don't quite have it right. You know, for example, like if you had a cube and, you know, you can rotate the cube and you still get a cube, right? But what if you're not looking at it

from the right point of view? You're only looking at like a 2D slice of the cube. And so the symmetry of it is not exactly preserved. So in some of these cases, we're probably just like, don't have the full picture yet. We haven't really discovered what it is the universe is preserving. Like maybe it's not broken. Maybe we're just missing something. Yeah, maybe we're just missing. We haven't seen the full picture. But so far, we haven't, which means that to us, it does look like a broken universe. Yeah, but some of these symmetries are perfect. Like, charge conservation is not one we've ever seen broken.

Like, no particle has ever broken conservation of charge. Like, a photon has never turned into two electrons or electrons don't just disappear into neutral particles. As far as we know, that is a perfect symmetry of the universe, charge conservation. All right. Well, I guess that tells us a little bit more about the universe. You know, there's these hidden symmetries, these hidden almost rules. right that sort of govern everything and that may even like give rise to things that we take for granted like light maybe that's just the universe's way of trying to stay beautiful yeah the way

I think about it is that you can't have a universe that respects this symmetry without the photon like the photon is absolutely necessary in order to have a universe that respects this symmetry so therefore we do have a universe that respects this symmetry now the question we can ask is like well why What a weird thing for a universe to insist on. What does that mean? And I think that's the kind of thing that in 100 years, people will look back and be like, oh, my gosh, that was so obvious. The universe was screaming the answer to you. But here we are in the forefront of ignorance.

We don't really know what this clue means yet. So I think it does mean something deep about the universe. We just still need to digest it. So come on, philosophers. Tell us what it all means. Well, it sounds like the answer might come from physics, right? You're saying, like, maybe we don't know why now, but maybe in the future to a physicist that will seem. obvious, right? Like maybe there is a physical answer to these why questions. And just because

we don't know what they are now, you're bumping them over to the philosophy department. Yeah. And it could also come from mathematics. We didn't appreciate the structure of these symmetries until we learned group theory from mathematics. It turns out that perfectly describes everything that's going on here. Mathematicians invented it for like totally other reasons because they just like thinking about how things rotate in their minds. But it could be that what we've discovered now needs like some new branch of mathematics to describe it and give us like an understanding of what the meaning is intuitively. So it might just be that we need to invent new mathematical words and concepts to fit these things together into a deeper understanding. I see. You're passing

the bug now to the mathematics department. You're like blame everyone but us. You know, it's like when poets invent new words. You know, I think English professors are like, hmm, can you really just do that, you know? And so I don't know if mathematicians want us inventing the new math. You know, I think they, you know, really would prefer to do that themselves. I see. Now you're blaming the English department as well. That's right. I'm good at this.

Bring on the department, I can blame them for it. Discern symmetry about you, Daniel. I feel like you're trying to preserve your job. Look, we made these crazy discoveries. Everybody else needs to tell us what's going on. No, it's really fun to think about. And this is one of the reasons why I agreed to join the philosophy department here because I do like to think about what it means about the universe.

Because in the end, that's why we're doing these experiments, It's not because we like to write down tidy mathematical equations, but because we hope that by doing so, they will speak to us, and they will tell us, look, the universe follows this rule. The universe has to be this way, and we'll get some understanding of why. It is a pretty perplexing universe. And you know what, whether or not it's beautiful or broken, we still love it. You know, no pressure.

You don't have to tell us everything. You know, we're just here for you. Or because of you? I don't know. Maybe that's another philosophical department. We do love the universe, though. true. All right. Well, we hope you enjoyed that. Thanks for joining us. See you next time. Why are TSA rules so confusing?

You got a hoot of you, I'll take it all! I'm Manny. I'm Noah. This is Devin. And we're best friends and journalists with a new podcast called No Such Thing, where we get to the bottom of questions like that. Why are you screaming at me? I can't expect what to do.

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