What hidden symmetry is controlling the Universe?

Published Sep 30, 2021, 5:00 AM

Daniel and Jorge dive deep into quantum theory and explain gauge symmetry, the foundation of all modern physics.

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Hi.

I'm David Ego from the podcast Inner Cosmos, which recently hit the number one science podcast in America. I mean neuroscientists at Stanford, and I've spent my career exploring the three pound universe in our heads.

Join me weekly to explore the relationship.

Between your brain and your life, because the more we know about what's running under the hood, bet or we can steer our lives. Listen to Inner Cosmos with David Eagleman on the iHeartRadio app, Apple Podcasts or wherever you get your podcasts.

Guess what, Well, what's that mango?

I've been trying to write a promo for our podcast, Part Time Genius, but even though we've done over two hundred.

And fifty episodes, we don't really talk about murders or cults. I mean, we did just cover the Illuminati of cheese, so I feel like that makes us pretty edgy. We also solve mysteries like how Chinese is your Chinese food?

And how do.

Dollar stores make money? And then of course can you game a dog show?

So what you're saying is everyone should be listening.

Listen to Part Time Genius on the iHeartRadio app or wherever you get your podcasts.

Hey, it's Horehand Daniel here, and we want to tell you about our new book.

It's called Frequently ask Questions about the Universe.

Because you have questions about the universe, and so we decided to write a book all about them.

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 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.

So if you want to support the podcast, please get the book and get a copy of 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 is available for pre order now, coming out November two. You can find more details at the book's website universe faq dot 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 umbutsman for all the physics. It's good to know, all right. So I feel like physics it's 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 gonna have to direct you, I think, to the philosophy department.

Oh, man, you're going to pass the book.

Well, I don't know how else to answer a why question?

Yeah, And I don't know why I ask you these questions in the first place.

You ask a meta question, you get sent to the metaphysics department.

Are you the meta umbutzman or Hey, I'm a cartoonist and the creator of PhD comments.

Hi, I'm Daniel. I'm a particle physicist and a professor at U c 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, 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 and 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 a 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? What does 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 diggetting 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 pH philosophy. I guess it's the start of the endless sleep. But anyways, welcome to our podcast, Daniel and Jorge Explain 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 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 Neeley 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 appreciation 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. Like 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 like 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 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 dust bin 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 some 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 It's like fundamental nature. One of my favorite examples is very simple. It just comes from conservation of momentum. 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 than 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 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 function in universe if things weren't all smooth and work 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 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 laws 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 waves 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 like 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 and 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. It's 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 simple 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 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 elegance, is this idea of symmetry. Like if something is symmetric somehow, as humans, it's instills in us a sense of like, oh, that looks perfect. Where 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 discovered lots of these kinds of symmetries.

You know.

Another one that people 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 resces. 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 to THEE on the podcast, we'll be talking about what hidden symmetry controls the universe. Not dumb dumb 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 where you going for some clickbait 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, like 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's 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. That's kind of I think that's what people mostly think about symmetry. But physicists think of symmetry. It's a 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 wouldn't 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 axis, you make X into Y and win and to z or whatever, you should get the same answer. You know, it's like a 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 baxies 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 sign on 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, you know, maybe actually I don't even know our 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 it 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 laws 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 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 Amy Nother discovered about one hundred 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 what. And that's where these conservation laws come from. So that's very, very powerful. 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. All right, we'll get into that, but I guess more specifically, it has something to do with something called gauge symmetry, right, gauge 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 here you're answers, please write to us two questions at Danielanjorge dot 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 have to say.

Gauge 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.

Gage 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 charters are symmetrical in It doesn't matter if there's a pleasure or minus.

From my point of view, gage symmetry. Well it happened to me, was I when my instrumental cluster from my truck broke down, and all the goages were at zero, so they were symmetric. So this is goage symmetry from my point of view.

Let's break it down.

Gauge 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 there 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 back into universe.

It's really hidden. Well, I guess it's a weird word because we 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 are still laying down a bunch of new tracks and they had to decide like how far apart you make the tracks, to 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 equal zero or where do you call electrical potential equal 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 you know, 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 the shelf, the faster it is when it's hitting the floor, and the shorter of 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 equal zero? Do you say height equal zero one? 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 equal 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 the word that had nothing to do with the thing. But where were the rest of other population?

Is that what you're saying, Yeah, your ancestors should have been called on one hundred 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 it only tells you change or how it changes from a starting point. Is that kind of what you're saying, But the answer kind of depends on where you start.

Right mm hmm, and it has 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 Kulum 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 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, so 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.

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All right, we're talking 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 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 gauge theory is. It's like a theory that 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 erd. 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 instead 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. And we'll talk about various gage 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 we 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 to 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 know it's that they're gauge symmetric. And because of those symmetries, then things like conservation, willmenttum 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.

Yes, 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 on electron whether it has a probablity to go left or to go right. It's the square of the wave function, the wave function square the wave 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 particles physics, like particles that make up our universe, there's 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 it by minus one, 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, right, 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 the 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 what comes out.

It won't affect at all. Because you take it and you square it, all physical predictions depend only on the wave functions 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, and 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, nothing changes because you've been consistent. You change the wave 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 invariants, 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 the by minus one, and in Alpha Centauria I'm gonna 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 game.

Wait, what 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 in variance the universe definitely has. But if you want local gauge invariants, 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 the 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 in variants, 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 in variance. And then physics 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 in variance, something that like corrected for that. So take the universe that just has electrons in it and ask for local gauge in variants, and you break that right like immediately, you don't have local gauge in variants 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 the difference between local and global is it like kind of like if I let go of my book on a 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 low, Or it wouldn't make any sense. You'd get crazy physical predictions.

Like the book would still fall the same way.

Would 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 US. 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 a 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, 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 US 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 we the universe doesn't seem to have that local gauge in variance, meaning it doesn't 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 in variants? Like, take your electron is flying through space, and what if you want to be able to like multiply its wavefunction 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 in variance 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 in variants. But if you add an electromagnetic field, which gives you photons, boom, you get local gauge in variants 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 invariants 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 blogny that I've added and once 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.

For you're saying the electromagnetic field for serve symmetry for the electron, or for like everything in the entire universe.

For the electron wave function.

Yes, so we're talking just about the electron and its wave function. It is feed and meter indpendent. But if you had the electromatic 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 in variance, 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 in variants.

Well, you're saying that 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 in variants 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 in variants? 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 in variants where you can 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 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 like is the quark also locally symmetric meat and feet independent here in the US 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 in variants because the muon is charged, also communicates with the photon field. And yes, quarks 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 gage in variants and the electrons. But of course we know there's a single photon, the same photon that electron em myths can be absorbed by a muon. But it didn't have to be that way. You could have lived in a universe with like 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 this thing that serves the symmetry for all particles that feel 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.

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Hi, I'm David Eagleman from the podcast Inner Cosmos, which recently hit the number one science podcast in America. I'm a neuroscientists at Stanford and I've spent my career exploring the three pound universe in our heads.

We're looking at a whole new.

Series of episodes this season to understand why and how our lives look the way they do. Why does your memory drift so much? Why is it so hard to keep a secret, When should you not trust your intuition? Why do brains so easily fall for magic tricks? And why do they love conspiracy theories. I'm hitting these questions and hundreds more because the more we know about what's running under the hood, bet or we can steer our lives. Join me weekly to explore the relationship between your brain and your life by digging into unexpected questions. Listen to Inner Cosmos with David Eagleman on the iHeartRadio app, Apple Podcasts, or wherever you get your podcasts.

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We think of Franklin as the doddling dude flying a kite in the rain, but those experiments are the most important scientific discoveries of the time.

I'm Evan Ratliff.

Last season, we tackled the ingenuity of Elon Musk with biographer Walter Isaacson. This time we're diving into the story of Benjamin Franklin, another genius who's desperate to be dusted off from history.

His media empire makes him the most successful self made business person in America.

I mean, he was.

Never early to bed, an early to rise type person. He's enormously famous. Women start wearing their hair in what was called the coiffor a La Franklin.

And who's more relevant now than ever.

The only other person who could have possibly been the first would have been Benjamin Franklin, but he's too old and once Washington been doing.

Listen to on Benjamin Franklin with Walter Isaacson on the iHeartRadio app, Apple podcasts or wherever you get your podcasts.

All right, we're going deep here today, Daniel. I feel I feel like you really throw us down a rabbit hole here, Like what is the nature of the electric magnetic field? Like does it exist 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 week fource and does it push or pull? And I said, well, one day we're gonna have to go deep and talk about gauge symmetry, and you said, bring it on. I got time, So here you are.

I don't think you can prove that, I said that, can you? We've didn't record it.

I think we do have a recording. I was just listening to it yesterday.

Well, I might officially regret it, right, No, 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 electronic magnetic field. And that's kind of how the universe works. And thank goodness, right, because that's how we get liked.

Yeah, that's why the universe is literally so brilliant.

Nice, it's a nice light like joke. 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 the universe that respects local gauge invariants. 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 it 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 in variance is deeply, deeply built into the very structure of reality. So I think we need like another one hundred years of philosophers smoking banana peels thinking about why that is to tell us, like, you know, why reality is this way in not some other way, but it also has very physical consequences for the nature of reality.

Well, I guess the 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 field the photons and things like that, right? 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 the same thing to neutrinos. They have another weird different 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 invariants 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, 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. Y, 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 Noether's theorem. So the fact that you can serve 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 Nother's theorem to get in 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 this 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 wavefunction 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 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 and variance. It turns out, for the strong force, you cannot 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 that 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 in variance, it requires more fields. They're 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 physicist c 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 canyon, you know, or I felt this weird magnetism.

That's a pretty dark scenario there, these three of a friend down the canyon. Hopefully not a podcast that post.

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 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 in variants 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 their differences in their gauge. And so that's what a photon does, is 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 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 field. If it moved, 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, way 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 another to make everything add up in the end.

Hopefully they don't get too creative like I sometimes I may or may not.

Do something electromagnetic accounting exactly. Well, 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 w's and the z's all makes sense to be in a single field and also with the electromagnetic field. But like you could 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 are you even trying to put these things together? And the reason are these symmetry that we discover that like the W plus by itself doesn't preserve local gate invariance. But when you put the W plus and the W minus and the Z together, than 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 isospin 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 all together 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 electroweak 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 violations of symmetry also all over the theory of physics, right, aren't there all kinds of different charge and parody violations?

There are, yes, And so we have these 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 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 two D 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 yes, that tell us 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 one hundred 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 white 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 destruction 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 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. A certain symmetry about you, Daniel. I feel like you're trying to preserve your jobs. 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, 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, that's true.

All right, Well, we hope you enjoyed that. Thanks for joining us, See you next time.

Thanks for listening, and remember that Daniel and Jorge explain the Universe is a production of iHeartRadio. Or more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact. But the people in the dairy industry are. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. How is us dairy tackling greenhouse gases? Many farms use anaerobic digestors to turn the methane from manure into renewable energy that can power farms, towns, and electric cars. Visit you asdairy dot COM's last sustainability to learn more.

Hi, I'm David Eagleman from the podcast Inner Cosmos, which recently hit the number one science podcast in America.

I mean neuroscientists at.

Stanford and I've spent my career exploring the three pound universe in our heads.

Join me weekly to explore the relationship between your brain and your life.

Because the more we know about what's running under the hood, better we can steer our lives. Listen to Inner Cosmos with David Eagleman on the iHeartRadio app, Apple Podcasts, or wherever you get your podcasts.

Parents looking for a screen free, fun and engaging way to teach your kids the Bible. As a mom, I was looking for the same thing, so I created Kids Bible Stories podcast. Thousands of families are raving about it, and kids actually request to listen. With captivating sound effects, voices, and an apply section at the end of spark meaningful conversations, it's a hit with both kids and parents. Listen to Kids Bible storye podcast on the iHeartRadio app, Apple Podcasts, or wherever you get your podcasts.

Daniel and Jorge Explain the Universe

A fun-filled discussion of the big, mind-blowing, unanswered questions about the Universe. In each e 
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