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Speaker 1: Hey, it's Jorhan Daniel here and we want to tell

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Speaker 1: you about our new book. It's called Frequently Asked Questions

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Speaker 1: about the Universe because you have questions about the universe,

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Speaker 1: and so we decided to write a book all about them.

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Speaker 1: We talk about your questions, we give some answers, we

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Speaker 1: make a bunch of silly jokes as usual, and we

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Speaker 1: tackle all kinds of questions, including what happens if I

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Speaker 1: fall into a black hole? Or is there another version

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Speaker 1: of you out there that's right? Like usual, we tackle

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Speaker 1: the deepest, darkest, biggest, craziest questions about this incredible cosmos.

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Speaker 1: If you want to support the podcast, please get the

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Speaker 1: book and get a copy not just for yourself, but

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Speaker 1: you know, for your nieces and nephews, cousins, friends, parents, dogs, hamsters,

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Speaker 1: and for the aliens. So get your copy of Frequently

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Speaker 1: Asked Questions about the Universe is available for pre order now,

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Speaker 1: coming out November two. You can find more details at

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Speaker 1: the book's website, Universe f a Q dot com. Thanks

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Speaker 1: for your support, and if you have a hamster that

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Speaker 1: can read, please let us know. We'd love to have

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Speaker 1: them on the podcast. Hey, Daniel, I have a complaint

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Speaker 1: to file about physics. Who do I talk to? Oh,

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Speaker 1: you can lay it on me. I'll pass it on

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Speaker 1: to the right people. All right, you're the unbutsman for

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Speaker 1: all the physics. It's good to know, alright. So I

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Speaker 1: feel like physics it's pretty good about answering how questions?

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Speaker 1: You mean, like how old is the universe? Or how

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Speaker 1: big is it? Yeah? Just like that? All right, Well

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Speaker 1: that sounds pretty good. What's your complaint? Well, I feel

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Speaker 1: like the real questions that humanity wants to know are

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Speaker 1: the why questions, you know, like why do we have

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Speaker 1: this universe? Why is it like this? And not like that.

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Speaker 1: You know, I'm gonna have to direct you, I think,

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Speaker 1: to the philosophy department. Oh, man, you're gonna pass the buck. Well,

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Speaker 1: I don't know how else to answer a why question. Yeah,

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Speaker 1: and I don't know why I ask you these questions

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Speaker 1: in the first place. You ask a meta question, you

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Speaker 1: get sent to the metaphysics department, the meta unbutsman. Hi

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Speaker 1: am or Hey, I'm a cartoonists and the creator of

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Speaker 1: PhD comments. Hi. I'm Daniel. I'm a particle physicist and

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Speaker 1: a professor at U C Irvine, where I actually am

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Speaker 1: also a member of the philosophy department. Oh are you

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Speaker 1: really so you're a card caring philosopher? Technically I am so.

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Speaker 1: I have no education in philosophy. I just started showing

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Speaker 1: up at the philosophy of science seminars and eventually they

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Speaker 1: were like, who are you? And then they give me

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Speaker 1: a joint appointment. I guess they let anyone in that hand, like,

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Speaker 1: there's not that much of a demand for philosophy membership. Well,

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Speaker 1: I think joint appointments are free, so yes, the bar

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Speaker 1: is not that high. Nice. Do you have to teach

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Speaker 1: classes in philosophy? I am not qualified to teach classes

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Speaker 1: in philosophy. Well, I feel like physics, you know, asked

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Speaker 1: a lot of very philosophical questions or questions that border

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Speaker 1: on philosophy, right, like why is the universe like this?

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Speaker 1: Or why do we have a universe? Right? Like you're

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Speaker 1: asking these questions as physicists, right, Yeah, A lot of

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Speaker 1: the answers we get to questions in physics do have

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Speaker 1: big philosophical implications, and I think it's important. That's why

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Speaker 1: I started going to these seminars to understand like what

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Speaker 1: if we discover this or what if we discover that

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Speaker 1: what does it really mean? Man, Physics can tell you

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Speaker 1: what's going on, but only philosophy can tell you what

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Speaker 1: it means. Well, it's kind of a layer thing, right

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Speaker 1: because you can ask like why does the apple fall

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Speaker 1: from the tree and you can say, well, it's gravity.

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Speaker 1: But you know, once you start dig getting deeper, like

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Speaker 1: why do we have gravity, then it starts to get philosophical. Yeah,

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Speaker 1: and then you can ask like what kind of answer

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Speaker 1: will satisfy your question? And then you have a philosophical

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Speaker 1: answer about philosophical questions, yeah, or like why have philosophical

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Speaker 1: answers philosophy of philosophy? Wow, you can get a h

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Speaker 1: and philosophy. I guess it's the start of the Endless sleep.

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Speaker 1: But anyways, welcome to our podcast Daniel and Jorge Explain

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Speaker 1: the Universe, a production of I Heart Radio in which

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Speaker 1: we go meta and meta meta about the nature of

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Speaker 1: the universe. We ask all the questions about how the

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Speaker 1: universe is, and then we also ask the questions about

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Speaker 1: why it is and what that means. Because we don't

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Speaker 1: just want a description of the universe, we want an

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Speaker 1: understanding of the universe. We want to know why the

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Speaker 1: universe is this way and not any other way, or

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Speaker 1: maybe if it could have been that other way. We

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Speaker 1: seek not just to describe but also to explain, and

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Speaker 1: that's what we're doing here, exploring the universe and explaining

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Speaker 1: it to you. Yeah, because it is a big universe

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Speaker 1: and one of which you can ask a lot of questions.

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Speaker 1: Because it is not just kind of a big universe

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Speaker 1: and a pretty mysterious universe, but it's also kind of

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Speaker 1: a beautiful universe. It is, in fact a beautiful universe,

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Speaker 1: not just in the vistas that we partake in in

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Speaker 1: the wonderful night skies, but also in the mechanisms for

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Speaker 1: how it works. Sometimes you look at the mathematics for

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Speaker 1: the way things work at the quantum level and you're like, wow,

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Speaker 1: that's pretty neat. I couldn't have designed the universe so

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Speaker 1: beautiful or so clever. It does feel sometimes like we

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Speaker 1: are uncovering a w of great beauty. Yeah, because the

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Speaker 1: universe does seem to have rules, right, Like it's it's

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Speaker 1: not a willy nearly universe where anything can happen. It

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Speaker 1: seems to have rules and the structure to it. And

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Speaker 1: as you say, it sort of feels clever in a

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Speaker 1: way can you talk about that? Yeah, it's just maybe

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Speaker 1: our appreciation is just sort of subjective. But one of

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Speaker 1: the most incredible things we've discovered is that the universe

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Speaker 1: can be described in terms of mathematical laws. Like why

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Speaker 1: do we even think that it was possible to write

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Speaker 1: down equations that predict what will happen in our universe

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Speaker 1: and that only some equations will work, right, Like, it's

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Speaker 1: sort of like you can't just write down any random

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Speaker 1: equation and say that's physics. It's math, but it's not

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Speaker 1: necessarily physics, the same way you can't just like write

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Speaker 1: down a string of words and say here's my novel. Right,

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Speaker 1: Not every string of words is a novel. So we

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Speaker 1: use math as a language to express physics. But then

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Speaker 1: you can also look at that math and say, wow,

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Speaker 1: that really clicks together nicely, or this makes a lot

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Speaker 1: of sense, or this tells you something about the nature

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Speaker 1: the universe because it uses this math and not that

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Speaker 1: other kind of math. And then you get into the

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Speaker 1: lossopy questions like what does it mean that we have

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Speaker 1: a universe that's like this and not like that? Right,

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Speaker 1: that's pretty interesting. The idea that you know, like all

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Speaker 1: physics is math, but not all math is physics, like

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Speaker 1: not all possible equations have a physical reality to them. Absolutely,

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Speaker 1: you can describe lots of hypothetical universes out there using mathematics,

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Speaker 1: but they don't necessarily describe the universe we live in.

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Speaker 1: And you know, there are lots of beautiful theories about

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Speaker 1: physics that were mathematically really nice but just didn't describe

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Speaker 1: our universe, and so they ended up like tossed in

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Speaker 1: the dustbin of physics history. Man, you have a reject

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Speaker 1: pile for beautiful theory. We do because the universe gets

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Speaker 1: to say what the universe chooses, and sometimes it's a

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Speaker 1: little surprising and a little bit messy, but often we

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Speaker 1: can find some elegance, some nice description of it that

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Speaker 1: reveals something about the universe. And then you go off

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Speaker 1: and chew and you're like, that's really interesting that the

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Speaker 1: universe has this structure. What does that mean about It's

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Speaker 1: like fundamental nature. One of my favorite examples is very simple.

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Speaker 1: It just comes from conservation shi of momentum, Like this

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Speaker 1: is something we observe in the universe. We notice that

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Speaker 1: if you bang two rocks together that at the end

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Speaker 1: you have the same amount of momentum as you did

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Speaker 1: in the beginning. It's changed direction a little bit, perhaps,

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Speaker 1: but all the momentum is the same. It's something we

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Speaker 1: observe and you can ask, like, well, why is that?

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Speaker 1: Why is momentum conserved? And we have this deep theory

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Speaker 1: of physics that tells us why, But it just brings

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Speaker 1: up more questions. It turns out that momentum is conserved

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Speaker 1: because space is uniform, because you can do the same

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Speaker 1: experiment here and somewhere else and on Jupiter and you

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Speaker 1: should get the same answer. One thing leads to the other,

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Speaker 1: because space is uniform, momentum is conserved. But then that

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Speaker 1: just brings up the question like, well, why is space uniform?

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Speaker 1: Why is it true that you can do the same

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Speaker 1: experiment here or an Alpha Centauri and you should get

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Speaker 1: the same answers? Why the laws of physics the same

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Speaker 1: everywhere in space? But that seems to be the way

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Speaker 1: our universe is, and that's the way it is, and

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Speaker 1: it's also sort of a good thing that it is, right,

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Speaker 1: Like it would be weird or could you even have

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Speaker 1: a functioning universe if things were at all smooth and

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Speaker 1: working the same way everywhere, Like wouldn't it be just

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Speaker 1: complete chaos. Well, that is the job of science fiction authors,

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Speaker 1: right to imagine different universes and like, what would it

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Speaker 1: be like to live in that universe? To be a

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Speaker 1: scientist in that universe and discover that you lived in

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Speaker 1: that universe instead of this one? What stories could you

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Speaker 1: tell in that universe? So I think there are probably

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Speaker 1: very different physical consequences of living in the universe like

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Speaker 1: that where the laws of physics change with space or

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Speaker 1: with time. But this is the one that we live in.

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Speaker 1: I think you could imagine ways to live and waves

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Speaker 1: life might even arise, but it would be vastly different

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Speaker 1: from the universe that we know. Well, now you're giving

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Speaker 1: me kind of fear of missing out. What if there's

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Speaker 1: like a better part of the universe that we're not

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Speaker 1: living in, Like what if the grass is really like

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Speaker 1: greener on the other side of the galaxy? Yeah, well,

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Speaker 1: you know, we haven't even discovered how green our grass is.

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Speaker 1: There's so much we don't know about the universe, so

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Speaker 1: much to discover, so many beautiful things that will be

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Speaker 1: revealed in the future that will amaze you. So stick

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Speaker 1: around in this universe. I recommend it. There's a lot

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Speaker 1: of green grass left to cut. It's interesting you said

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Speaker 1: that word earlier. Elegant. You know, I feel like I

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Speaker 1: hear a lot of physicists say that words sometimes, that

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Speaker 1: the universe feels really elegant in the way the rules

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Speaker 1: and the laws work. And that's kind of we'll be

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Speaker 1: talking about today. Is is one of these elegances of

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Speaker 1: the universe. And what we're looking for to describe the

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Speaker 1: universe is a simple description. You know, you could describe

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Speaker 1: the universe. It's just like, here's a list of all

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Speaker 1: the physics experiments anybody's ever done and the results. That's great,

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Speaker 1: that describes the universe, but it doesn't give you any insight.

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Speaker 1: It doesn't give you that like ah ha. That's because

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Speaker 1: they're all following the same rule. And that's the job

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Speaker 1: of physics is to boil down a bunch of experiments,

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Speaker 1: a bunch of observations into a simple rule. And it's

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Speaker 1: when you see that simple rule and you say, wow,

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Speaker 1: it's incredible. That's something that's so simple can have all

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Speaker 1: these consequences. That's when you feel like you're looking at

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Speaker 1: some elegance. You're like understanding a deep truth about the

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Speaker 1: nature of the universe. You've revealed something at a lower

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Speaker 1: level than anybody has seen before. You've peeled back a

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Speaker 1: layer of reality and seeing a simple description that leads

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Speaker 1: to all the incredible complexity that we see in our universe.

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Speaker 1: And I guess you know, one of the things that

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Speaker 1: we feel is simple or a way to give things

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Speaker 1: a certain sense of elegance, is this idea of symmetry.

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Speaker 1: Like if something is symmetric somehow, as humans, it's instills

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Speaker 1: in as a sense of like, oh, that looks perfect

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Speaker 1: or that looks you know, elegant or beautiful. Yeah, and

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Speaker 1: it also sort of feels democratic, Like to me, it's

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Speaker 1: nice that the universe doesn't prefer any location in space

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Speaker 1: and you can do your experiment here or somewhere else

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Speaker 1: and it doesn't make a difference. And you know, there

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Speaker 1: are real consequences to that symmetry. That symmetry means only

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Speaker 1: certain laws of physics are allowed, like in that case,

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Speaker 1: only laws of physics that conserve momentum are allowed. That

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Speaker 1: comes directly from that symmetry, And we discovered lots of

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Speaker 1: these kinds of symmetries. You know. Another one and that

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Speaker 1: people are probably familiar with, is the fact that there's

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Speaker 1: no up or down in space. Like you do your

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Speaker 1: experiment in space, it doesn't really matter which direction your

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Speaker 1: experimental apparatus is pointing. You can spin it in another

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Speaker 1: direction and it should get the same result. That's another symmetry.

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Speaker 1: It says the universe doesn't prefer a direction, not just

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Speaker 1: a location, but a direction. And that gives you another rule.

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Speaker 1: It says that all the laws of physics you right,

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Speaker 1: have to also conserve angular momentum, which is separate from

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Speaker 1: just momentum. Right, This is like how much something is spinning.

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Speaker 1: So every time you discover a symmetry, something that where

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Speaker 1: the universe doesn't care about something or gives you the

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Speaker 1: same answer no matter how you spin or move something

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Speaker 1: that tells you something about the laws of physics that

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Speaker 1: are consistent with that symmetry, the laws of physics that

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Speaker 1: can describe our universe. Yeah, so to be on the podcast,

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Speaker 1: we'll be talking about what hidden symmetry controls the universe.

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Speaker 1: Sounds like a dark conspiracy here, Daniel. There's something hidden

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Speaker 1: controlling things. People smoking cigars, wearing gray suits and deciding

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Speaker 1: what laws of physics can we have or where are

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Speaker 1: you going for some click bait action here. I'm just

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Speaker 1: trying to, you know, get a little bit of reflection

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Speaker 1: from the X file glamour, that's all. Yeah, we should

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Speaker 1: title it like the hidden dark Secret that controls the universe,

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Speaker 1: like to find out more. But yeah, there seems to

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Speaker 1: be a symmetry to the universe. And I feel like,

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Speaker 1: you know, maybe physicists use this word differently than how

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Speaker 1: most people understand it, because I think, you know, to

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Speaker 1: most people's symmetry means like if something is symmetric, it

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Speaker 1: means like it's the same if you look at it,

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Speaker 1: you know, the right half and the left half is

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Speaker 1: the same, or it's like the mirror image of something else,

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Speaker 1: or there's some sort of reflection or some like equality

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Speaker 1: between left and right or two directions. That's kind of

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Speaker 1: I think that's what people mostly think about symmetry. But

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Speaker 1: physicists think of symmetry. It's a kind of a different

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Speaker 1: concept in physics, right, It's about how the mathematical equations

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Speaker 1: stay the same no matter how you transform them. Yeah,

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Speaker 1: but it's also closely related, I think, to people's intuitive

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Speaker 1: sense of symmetry. Like think about the examples you mentioned

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Speaker 1: the sphere for example, you know there's a rotational symmetry.

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Speaker 1: There you have a perfect sphere, you rotate it, you

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Speaker 1: get the same sphere, right, and so nothing has changed

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Speaker 1: for the sphere. It's the same. Or even if you

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Speaker 1: reflect it through a mirror down its middle, you get

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Speaker 1: the same sphere. So there are symmetries in the sphere

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Speaker 1: that wouldn't change how you interact with the sphere. And

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Speaker 1: we talk about the same things in physics. We say, look,

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Speaker 1: if you do this experiment and you just rotate your axes,

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Speaker 1: you make X into Y and Y and z or whatever,

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Speaker 1: you should get the same answer. You know, it's like

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Speaker 1: a spin the experiment or spin the universe. It doesn't matter.

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Speaker 1: You should get the same answer. And so fundamentally, when

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Speaker 1: we talk about symmetry, we mean do you get the

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Speaker 1: same laws of physics if you apply some transformation or

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Speaker 1: some rotation or some change to your axes or how

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Speaker 1: you've defined things. And so that's what we mean when

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Speaker 1: we talk about symmetry right right like like like a

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Speaker 1: butterfly is symmetric, right like the left side and the

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Speaker 1: right side is symmetric. But you can also think of

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Speaker 1: it as like the left wing if I put it

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Speaker 1: through a mirror, it will look just like the right wing. Yeah,

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Speaker 1: you know maybe actually I don't even know. Are all

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Speaker 1: butterflies exactly symmetric? Probably they're not exactly, but in our cartoon, right,

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Speaker 1: assume a symmetric butterfly. Then in that case, yeah, you

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Speaker 1: put it up to a mirror and you see the

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Speaker 1: exactly the same other half, right, and at least it

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Speaker 1: look the same or similar. And so this symmetry idea

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Speaker 1: is very important physics because it almost, like I don't know,

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Speaker 1: defines the laws of physics at the fundamental level, or

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Speaker 1: it's something that's important for them to work, right. Yeah, Well,

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Speaker 1: what happens is that we notice the universe following certain rules.

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Speaker 1: You know, for example, we notice that the universe doesn't

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Speaker 1: create or destroy electric charge, like you have a bunch

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Speaker 1: of it, It doesn't go away, you can't destroy it,

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Speaker 1: and you can't make anymore. Right, And so that's like

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Speaker 1: a rule the universe seems to be following. And then

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Speaker 1: we ask questions like, well, what symmetry gives you that rule?

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Speaker 1: Why can't you create or destroy electric charge? What rule

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Speaker 1: is it fundamentally following? And what we discovered or what

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Speaker 1: eman author discovered about a hundred years ago. Is that

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Speaker 1: every time you see the universe following a rule is

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Speaker 1: because there's a basic symmetry. There's something about the universe

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Speaker 1: that's preserved that has this kind of symmetric property where

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Speaker 1: it doesn't depend on how you been it or reflected

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Speaker 1: or whatever. And that's where these conservation laws come from.

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Speaker 1: So that's very, very powerful. Every time you see a

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Speaker 1: conservation it means you can discover a symmetry of the universe,

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Speaker 1: which tells you something pretty basic about like the very

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Speaker 1: structure of reality, all right, and even the reality in

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Speaker 1: the mirror as well. We'll get into that, but I

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Speaker 1: guess more specifically, it has something to do with something

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Speaker 1: called gauge symmetry, right, g A U G E symmetry. Yeah,

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Speaker 1: all of our laws of physics in the Standard Model

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Speaker 1: are built on this principle of gauge symmetry, and we'll

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Speaker 1: dig into exactly what that means on today's episode. But

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Speaker 1: it turns out to be something really deep about the

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Speaker 1: way particles operate and their relationships with each other. All right,

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Speaker 1: we'll take a dive into that symmetry. But first we

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Speaker 1: were wondering how many people out there no or have

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Speaker 1: heard of this concept of gauge symmetry. So Daniel went

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Speaker 1: out there into the internet to ask people what is

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Speaker 1: gauge symmetry? And so, if you are interested in answering

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Speaker 1: really hard questions about secrets of the universe with no

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Speaker 1: chance to prepare at all, and then have the thousands

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Speaker 1: of people here your answers, please write to us two

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Speaker 1: questions at Daniel and Jorge dot com. It's a lot

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Speaker 1: more fun than it sounds. Think about it for a second.

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Speaker 1: Do you know what gage symmetry is? Here's what people

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Speaker 1: have to say. Gage symmetry is how one would gauge

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Speaker 1: the symmetry between a binary set of stars. And obviously

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Speaker 1: that's incorrect, but there you go. I am not sure

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Speaker 1: what gauge symmetry is, but perhaps it was a very

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Speaker 1: smart scientist person that explain some kind of symmetry in

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Speaker 1: the universe or in physics. Gage symmetry it has something

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Speaker 1: to do with electricity or charges. It doesn't matter what

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Speaker 1: direction in a circuit, or in what direction you look

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Speaker 1: at particles or whatever, like the charters are symmetrical in

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Speaker 1: It doesn't matter if there's a pleasure of minus. From

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Speaker 1: my point of view, gage symmetry. Well, it happened to me,

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Speaker 1: was I when my instrument cluster from my truck broke

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Speaker 1: down and all the gorges were at zero, so they

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Speaker 1: were symmetric. So this is gage symmetry from my point

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Speaker 1: of view. Let's break it down. Gauge symmetry is when

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Speaker 1: you make a transformation on a field which turns one

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Speaker 1: particle into a different one, maintaining, obviously, because it's symmetric,

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Speaker 1: maintaining some properties of that particle. I think, if I

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Speaker 1: recall correctly, gauge is basically measurements, So gauge symmetry might

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Speaker 1: be that one measurement in one unit basically described in

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Speaker 1: a different unit. Possibly. Well, I guess the gauge symmetry

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Speaker 1: is when my front tire and my rear tire of

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Speaker 1: my bicycle show the same amount of pressure. Then I

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Speaker 1: would have two gauges and they are symmetric. Otherwise I

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Speaker 1: have no idea. All right, it's it seems to be

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Speaker 1: um kind of a mystery to our listeners. The secret

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Speaker 1: Cabal has done a good job of hiding itself. It's

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Speaker 1: really hidden. Well, I guess it's a weird word because

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Speaker 1: we in general we use the word gauge to like

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Speaker 1: gauge something right, to like measure something like a pressure

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Speaker 1: gauge is something that tells you how much pressure is

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Speaker 1: in your bicycle tires, or your fuel gauge tells you

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Speaker 1: how much fuel you have in your car. And so

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Speaker 1: what does it mean then to have gauge symmetry in

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Speaker 1: your equations of physics? So it comes from the era

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Speaker 1: of the railroads, when people were still laying down a

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Speaker 1: bunch of new tracks and they have to decide, like

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Speaker 1: how far apart you make the tracks? Do you make

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Speaker 1: them one meter apart or a meter and a half

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Speaker 1: or whatever, And everybody had like different choices, and that

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Speaker 1: makes them incompatible. Right, you can't drive your train if

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Speaker 1: the gauge is wrong, and so somebody just has to

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Speaker 1: make a choice, and that doesn't really matter. You can

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Speaker 1: still build railroads if there are a meter apart or

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Speaker 1: half a meter apart or or whatever. It still works.

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Speaker 1: You just gotta make a choice, And so that arises

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Speaker 1: sometimes in physics where there's like an arbitrary choice you

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Speaker 1: have to make, like where do you call height equal

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Speaker 1: zero or where do you call electrical potential equal zero?

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Speaker 1: And it shouldn't affect how your physics works. It doesn't

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Speaker 1: change anything for how your experiments should work, but you

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Speaker 1: do have to make a choice. It's almost like a

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Speaker 1: scale maybe, or like a starting point. Is that what

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Speaker 1: you mean? Like, you know, like a scale, like is

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Speaker 1: this railroad track, you know, this wide or is it narrower.

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Speaker 1: It's sort of that way in physics where you have

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Speaker 1: to say, all right, what scale are we talking about

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Speaker 1: when we're talking about these electrical fields? Yeah, and you

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Speaker 1: just like you need a number, and so you have

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Speaker 1: to pick a starting point. That's a good way to

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Speaker 1: think about it. But it doesn't affect anything, right, It's

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Speaker 1: just like it seems like an arbitrary choice, you know.

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Speaker 1: One simple example is like think about a book falling

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Speaker 1: off of a shelf and wondering like, well, how fast

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Speaker 1: is it going when it hits the floor? Well, the

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Speaker 1: answer to that question depends on the height of the shelf,

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Speaker 1: because the taller the shelf, the faster it is when

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Speaker 1: it's hitting the floor, and the shorter the shelf, the

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Speaker 1: slower it is when it hits the floor. But it

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Speaker 1: doesn't depend, you know, mostly on how high your shelf

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Speaker 1: is above sea level. You know, so like where do

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Speaker 1: you call high equal zero. Do you say high equal

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Speaker 1: zero a thousand meters below my floor or at my

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Speaker 1: floor or above my floor. You can do all the calculations,

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Speaker 1: you get the same answer no matter where you put

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Speaker 1: like height equal zero in your physics problem. That's just

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Speaker 1: an arbitrary choice, doesn't affect your answer. So that's an

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Speaker 1: example of you know, making a gauge choice. And so

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Speaker 1: this word gauge was chosen to sort of like, you know,

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Speaker 1: harken back to the age of the railroads. But really

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Speaker 1: what it means is an arbitrary parameter of your theory.

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Speaker 1: I see you're saying, physicists pick the word that had

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Speaker 1: nothing to do with the thing. But where the rest

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Speaker 1: of the population is that what you're saying your ancestors

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Speaker 1: should have been called on a hundred years ago when

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Speaker 1: they were naming this thing. I totally agree. It's a

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Speaker 1: ridiculous word, and it's become so important, so we say

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Speaker 1: it all the time now. Gauge theory is everything. The

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Speaker 1: whole standard model of physics is a gauge theory. It's

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Speaker 1: almost like the theory only tells you changes or how

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Speaker 1: it changes from a starting point. Is that kind of

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Speaker 1: what you're saying, But the answer it kind of depends

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Speaker 1: on where you start, right, and it has a you

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Speaker 1: know a lot of history, like electromagnetism, which you know

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Speaker 1: predates the standard model in particle physics by a long time.

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Speaker 1: You know. Maxwell noticed this in his equations. When he

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Speaker 1: was putting together his equations of electromagnetism, he noticed that

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Speaker 1: you could change these. You could like add an arbitrary number,

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Speaker 1: not exactly just a number has to have like a

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Speaker 1: disappearing curl to it. But you could add something to

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Speaker 1: the theory and it wouldn't change any of the predictions.

430
00:21:32,200 --> 00:21:34,679
Speaker 1: And so you can have basically like different sets of

431
00:21:34,720 --> 00:21:37,679
Speaker 1: Maxwell's equations, and they call these different gauges, like the

432
00:21:37,760 --> 00:21:41,280
Speaker 1: Coolum gauge or the Lorenz gauge. People chose different sets

433
00:21:41,280 --> 00:21:44,280
Speaker 1: of equations. They all make exactly the same predictions. You

434
00:21:44,400 --> 00:21:46,639
Speaker 1: just like pick one. There's like a whole family of

435
00:21:46,680 --> 00:21:49,840
Speaker 1: these equations and they all make exactly the same predictions.

436
00:21:49,920 --> 00:21:51,840
Speaker 1: You can use any of them as long as you're consistent.

437
00:21:51,960 --> 00:21:55,200
Speaker 1: They're almost like floating theories. I guess you might say, right,

438
00:21:55,280 --> 00:21:57,560
Speaker 1: And so then there's the idea that within these theories

439
00:21:57,760 --> 00:21:59,879
Speaker 1: you can have a certain symmetry to them. And so

440
00:22:00,000 --> 00:22:02,800
Speaker 1: that's what gauge symmetry is. And so let's get into

441
00:22:02,800 --> 00:22:05,680
Speaker 1: why it's important for our equations of the universe and

442
00:22:05,720 --> 00:22:08,680
Speaker 1: what does it all mean. Man, But first let's take

443
00:22:08,680 --> 00:22:23,879
Speaker 1: a quick break. All right, we're talking about the hidden

444
00:22:24,320 --> 00:22:28,520
Speaker 1: conspiracy here that's controlling everything, Daniel. This is one of

445
00:22:28,560 --> 00:22:31,480
Speaker 1: those podcasts. That's right. We are bringing you the hard

446
00:22:31,520 --> 00:22:34,600
Speaker 1: truth today, folks. We are tearing off the veil. We

447
00:22:34,640 --> 00:22:38,160
Speaker 1: are revealing who's really behind everything. That's right. That's why

448
00:22:38,200 --> 00:22:41,240
Speaker 1: this podcast is encrypted. Right, we're encrypting this. We're not

449
00:22:41,280 --> 00:22:43,760
Speaker 1: putting our names on the title of the podcast either, right,

450
00:22:44,240 --> 00:22:46,960
Speaker 1: that's right. But we are doxing the true masters of

451
00:22:47,000 --> 00:22:51,720
Speaker 1: the universe today. There you go. That's another title for physicists.

452
00:22:51,720 --> 00:22:56,080
Speaker 1: You're boxing the universe, you're exposing it. We are exactly

453
00:22:56,200 --> 00:22:59,159
Speaker 1: we are, all right. So we talked about what gauge

454
00:22:59,400 --> 00:23:03,040
Speaker 1: theory is. It's like a theory that sort of floats

455
00:23:03,080 --> 00:23:05,040
Speaker 1: that it tells you how things change, but it sort

456
00:23:05,040 --> 00:23:08,640
Speaker 1: of depends on where you start them. And so that's

457
00:23:08,680 --> 00:23:10,360
Speaker 1: kind of what a gage theory is. And so then

458
00:23:10,359 --> 00:23:13,639
Speaker 1: what's gauge symmetry. So gage symmetry is when you have

459
00:23:13,720 --> 00:23:15,720
Speaker 1: a theory that has a gauge in it, right, So

460
00:23:15,800 --> 00:23:17,760
Speaker 1: you can make this choice, but it makes the same

461
00:23:17,800 --> 00:23:21,880
Speaker 1: prediction regardless of your choice. So, as we talked about electromagnetism,

462
00:23:21,880 --> 00:23:24,159
Speaker 1: it doesn't matter if you use the Coolum gauge or

463
00:23:24,160 --> 00:23:27,000
Speaker 1: the Lorenz gauge. You write down different equations, but they

464
00:23:27,040 --> 00:23:30,280
Speaker 1: predict exactly the same behavior of like electrons moving through

465
00:23:30,359 --> 00:23:33,720
Speaker 1: fields or magnets being generated. It doesn't matter. So there's

466
00:23:33,760 --> 00:23:36,600
Speaker 1: a gauge symmetry there. You can pick your gauge, but

467
00:23:36,680 --> 00:23:40,040
Speaker 1: it doesn't affect the physical predictions. I see. But then

468
00:23:40,160 --> 00:23:42,280
Speaker 1: how did the name symmetry come from? Because it's not

469
00:23:42,600 --> 00:23:44,200
Speaker 1: you know, like maybe I would have said it's gauge

470
00:23:44,200 --> 00:23:48,399
Speaker 1: invariant or gauge doesn't care less about gauge. But the

471
00:23:48,440 --> 00:23:50,520
Speaker 1: words and metrics to me sort of means like a

472
00:23:50,560 --> 00:23:53,240
Speaker 1: reflection or like a mirror image. Yeah. Well, you can

473
00:23:53,240 --> 00:23:58,440
Speaker 1: transform from one gauge to another without changing your predictions,

474
00:23:58,480 --> 00:24:01,760
Speaker 1: just like you can rotate a sphere through an arbitrary

475
00:24:01,760 --> 00:24:05,240
Speaker 1: angle without changing the sphere. It's still a sphere. And

476
00:24:05,280 --> 00:24:08,080
Speaker 1: so a gauge theory is one that you can transform

477
00:24:08,160 --> 00:24:10,760
Speaker 1: in a certain way from one gauge to another without

478
00:24:10,840 --> 00:24:14,160
Speaker 1: changing your predictions. And we'll talk about various gauge symmetries today.

479
00:24:14,200 --> 00:24:16,800
Speaker 1: Some of them are a lot like rotations of a sphere.

480
00:24:16,960 --> 00:24:19,120
Speaker 1: All right, are we saying that the laws of physics

481
00:24:19,119 --> 00:24:22,600
Speaker 1: with the universe are gauge symmetric or we noticed that

482
00:24:22,640 --> 00:24:25,680
Speaker 1: they were gauge symmetric. Yeah, it's really fascinating. The laws

483
00:24:25,680 --> 00:24:28,800
Speaker 1: of physics of the universe have really weird and surprising

484
00:24:28,880 --> 00:24:32,000
Speaker 1: gauge symmetries, much more than you would expect, and they

485
00:24:32,040 --> 00:24:34,920
Speaker 1: have real consequences, Like we talked about, every time there's

486
00:24:34,920 --> 00:24:37,800
Speaker 1: a symmetry the universe that leads to a conservation law.

487
00:24:37,880 --> 00:24:39,880
Speaker 1: And so what we can do is we can say, oh,

488
00:24:39,920 --> 00:24:42,880
Speaker 1: maybe this is why we have conservation of electric charge

489
00:24:42,960 --> 00:24:45,640
Speaker 1: or conservation to other things. It's because there are these

490
00:24:45,640 --> 00:24:47,800
Speaker 1: symmetries in the universe. And then we can ask the

491
00:24:47,800 --> 00:24:50,879
Speaker 1: deep questions like, well, why does the universe have that

492
00:24:51,000 --> 00:24:53,520
Speaker 1: weird gauge symmetry? What does that mean? This is not

493
00:24:53,600 --> 00:24:55,960
Speaker 1: just like an arbitrary thing we write down in our

494
00:24:56,040 --> 00:24:58,600
Speaker 1: rooms with pencil and paper. It's something deep about the

495
00:24:58,720 --> 00:25:02,000
Speaker 1: universe that respects this symmetry, meaning like if you work

496
00:25:02,040 --> 00:25:04,440
Speaker 1: at the equations of the universe. You noticed that they're

497
00:25:04,440 --> 00:25:08,520
Speaker 1: gauge symmetric, and because of those symmetries, then things like

498
00:25:08,560 --> 00:25:13,159
Speaker 1: conservation a momentum happen, yes, exactly, and so you know,

499
00:25:13,200 --> 00:25:16,000
Speaker 1: we notice that those things definitely happen in our universe,

500
00:25:16,080 --> 00:25:18,320
Speaker 1: and we discovered that that means that there must be

501
00:25:18,480 --> 00:25:21,760
Speaker 1: these symmetries, which is really interesting. All right, well, maybe

502
00:25:21,800 --> 00:25:24,000
Speaker 1: talk to us a little bit about why it's important

503
00:25:24,040 --> 00:25:26,360
Speaker 1: and how it has to do with quantum mechanics. Yes,

504
00:25:26,440 --> 00:25:29,320
Speaker 1: so the standard model of particle physics and quantum mechanics

505
00:25:29,520 --> 00:25:32,480
Speaker 1: has a lot of gauge symmetries in it, and one

506
00:25:32,520 --> 00:25:35,360
Speaker 1: that comes from quantum mechanics comes from the wave function.

507
00:25:35,440 --> 00:25:37,399
Speaker 1: Like we talked to this program before about what happens

508
00:25:37,400 --> 00:25:40,600
Speaker 1: to little particles and experiments, like what determines whether an

509
00:25:40,600 --> 00:25:42,320
Speaker 1: electron is going to go left or we're going to

510
00:25:42,440 --> 00:25:45,080
Speaker 1: go right when it interacts with something else. That's determined

511
00:25:45,080 --> 00:25:47,359
Speaker 1: by the wave function, which tells it like the various

512
00:25:47,359 --> 00:25:50,000
Speaker 1: probability to go here or the probability to go there.

513
00:25:50,119 --> 00:25:52,560
Speaker 1: But there's a little step there which we've glossed over,

514
00:25:52,640 --> 00:25:55,600
Speaker 1: but it's actually really really important. It's not the wave

515
00:25:55,640 --> 00:25:58,359
Speaker 1: function itself that tells an electron whether it has a

516
00:25:58,359 --> 00:26:00,439
Speaker 1: probability to go left or to go right. It's the

517
00:26:00,560 --> 00:26:03,399
Speaker 1: square of the wave function, the wave function square the

518
00:26:03,440 --> 00:26:07,919
Speaker 1: way function multiplied by itself, that determines the probability to

519
00:26:07,960 --> 00:26:09,920
Speaker 1: go left or to go right. And that's because the

520
00:26:09,960 --> 00:26:12,959
Speaker 1: wave function itself is a complex number, you know, like

521
00:26:13,200 --> 00:26:16,919
Speaker 1: one plus i or two minus i or whatever, and

522
00:26:17,000 --> 00:26:19,440
Speaker 1: so it doesn't have real values, so you have to

523
00:26:19,520 --> 00:26:22,400
Speaker 1: square it to get real values. And there's a symmetry

524
00:26:22,400 --> 00:26:25,920
Speaker 1: there because it means that the wave function or minus

525
00:26:26,000 --> 00:26:29,359
Speaker 1: the wave function give exactly the same predictions. So you're saying,

526
00:26:29,440 --> 00:26:33,200
Speaker 1: like at the fundamental level of particle physics, like particles

527
00:26:33,200 --> 00:26:37,120
Speaker 1: that make up our universe, they're symmetric, like starting from that,

528
00:26:37,400 --> 00:26:40,439
Speaker 1: because the wave function that describes it is symmetric in

529
00:26:40,480 --> 00:26:43,000
Speaker 1: itself in terms of it the probability though right, like

530
00:26:43,240 --> 00:26:45,480
Speaker 1: the original wave function is not symmetric, but if you

531
00:26:45,520 --> 00:26:47,960
Speaker 1: square it to get the probability, then it is symmetrica

532
00:26:48,040 --> 00:26:50,399
Speaker 1: if you take every wave function and you multiply it

533
00:26:50,400 --> 00:26:53,359
Speaker 1: by minus one, it doesn't change anything in the laws

534
00:26:53,359 --> 00:26:55,800
Speaker 1: of physics. That's what we're saying. So take the whole

535
00:26:55,920 --> 00:26:57,879
Speaker 1: universe's wave function, or if you don't believe in that,

536
00:26:57,920 --> 00:27:00,160
Speaker 1: take the wave function of all the particles, multiple by

537
00:27:00,160 --> 00:27:03,000
Speaker 1: all of them by the same number. Nothing changes, right,

538
00:27:03,040 --> 00:27:05,399
Speaker 1: The laws of physics predict exactly the same outcomes. It

539
00:27:05,400 --> 00:27:08,960
Speaker 1: doesn't matter because it's only sensitive to wave functions squared.

540
00:27:09,200 --> 00:27:11,159
Speaker 1: So you have a freedom there a choice. Do we

541
00:27:11,200 --> 00:27:13,160
Speaker 1: start with the positive way functions or do we start

542
00:27:13,160 --> 00:27:15,520
Speaker 1: with the negative wave functions. It doesn't matter. So there's

543
00:27:15,520 --> 00:27:18,879
Speaker 1: a symmetry. Really it doesn't matter, like, won't effect at

544
00:27:18,880 --> 00:27:20,680
Speaker 1: all what it comes out. It won't affect at all

545
00:27:20,720 --> 00:27:23,120
Speaker 1: because you take it and you square it. All physical

546
00:27:23,119 --> 00:27:26,280
Speaker 1: predictions depend only on the wave functions squared. All right,

547
00:27:26,320 --> 00:27:29,080
Speaker 1: So then that means that all particles in the universe

548
00:27:29,080 --> 00:27:31,080
Speaker 1: are a symmetric What does that mean. It's actually a

549
00:27:31,080 --> 00:27:33,720
Speaker 1: little bit more general than just multiplying it by minus one.

550
00:27:34,000 --> 00:27:37,000
Speaker 1: You can actually multiply it by a rotation in the

551
00:27:37,000 --> 00:27:39,080
Speaker 1: complex plane. And I don't think we should get too

552
00:27:39,119 --> 00:27:40,679
Speaker 1: far into the math, but just think about it, like,

553
00:27:40,800 --> 00:27:43,800
Speaker 1: you can rotate these things by an arbitrary angle and

554
00:27:43,840 --> 00:27:45,720
Speaker 1: you still get the same number. And so that makes

555
00:27:45,720 --> 00:27:47,440
Speaker 1: a lot of sense if you just do it. To everything.

556
00:27:47,480 --> 00:27:50,480
Speaker 1: Like you multiply the whole universe by minus one, nothing

557
00:27:50,560 --> 00:27:52,840
Speaker 1: changes because you've been consistent. You change the way function

558
00:27:52,880 --> 00:27:56,000
Speaker 1: of my electrons and your electrons and somebody else's electrons.

559
00:27:56,280 --> 00:27:59,520
Speaker 1: That's called a global symmetry affect the whole universe, And

560
00:27:59,760 --> 00:28:02,119
Speaker 1: that's not so surprising. But there's something else so the

561
00:28:02,200 --> 00:28:05,200
Speaker 1: universe has, which is a very different and much much

562
00:28:05,280 --> 00:28:08,960
Speaker 1: deeper symmetry. It turns out that the universe is symmetric

563
00:28:09,000 --> 00:28:12,760
Speaker 1: to local gauge invariance, which means you can make this

564
00:28:12,840 --> 00:28:16,560
Speaker 1: kind of transformation differently at every point in space. You

565
00:28:16,560 --> 00:28:18,760
Speaker 1: can say like here, I'm gonna multiply all my way

566
00:28:18,800 --> 00:28:21,639
Speaker 1: functions by plus one. Over in Jupiter, I'm gonna multiply

567
00:28:21,760 --> 00:28:24,159
Speaker 1: my minus one and an alpha centauri, I'm gonna do

568
00:28:24,200 --> 00:28:27,360
Speaker 1: something different. So that's a local gauge invariance that says

569
00:28:27,400 --> 00:28:30,120
Speaker 1: that you can have like an infinite number of these

570
00:28:30,240 --> 00:28:34,159
Speaker 1: different ideas about gauges. Wait, what what do you mean?

571
00:28:34,240 --> 00:28:36,720
Speaker 1: But you just told me that it's globally invariant, like

572
00:28:36,720 --> 00:28:39,120
Speaker 1: it doesn't matter what you do to it anywhere, But

573
00:28:39,200 --> 00:28:41,240
Speaker 1: now you're saying that it does matter what you do

574
00:28:41,320 --> 00:28:44,160
Speaker 1: to it locally. Yeah, so global gauge invariance the universe

575
00:28:44,200 --> 00:28:47,880
Speaker 1: definitely has. But if you want local gauge invariance, right,

576
00:28:48,040 --> 00:28:50,280
Speaker 1: that's harder. That says, well, now I want to be

577
00:28:50,360 --> 00:28:53,280
Speaker 1: able to multiply my wave functions by plus one or

578
00:28:53,280 --> 00:28:55,640
Speaker 1: minus one and do it differently everywhere. And you might

579
00:28:55,680 --> 00:28:58,480
Speaker 1: immediately say like, okay, well that obviously doesn't work right

580
00:28:58,560 --> 00:29:01,160
Speaker 1: because you have to be consistent otherwise they like the

581
00:29:01,200 --> 00:29:03,280
Speaker 1: interference terms of the way functions are not going to

582
00:29:03,400 --> 00:29:06,240
Speaker 1: come out right. And you're right. The universe by itself,

583
00:29:06,400 --> 00:29:09,880
Speaker 1: for an electron, doesn't have local gauge invariance because if

584
00:29:09,880 --> 00:29:12,400
Speaker 1: you change the gauge here and you change it somewhere else,

585
00:29:12,600 --> 00:29:15,320
Speaker 1: then it will affect the predictions. So the universe, if

586
00:29:15,320 --> 00:29:18,200
Speaker 1: all you have in it, our electrons, doesn't have local

587
00:29:18,240 --> 00:29:21,000
Speaker 1: gauge invariants. And then if played a fun game, they said, well,

588
00:29:21,200 --> 00:29:23,320
Speaker 1: what if we added something What if we added something

589
00:29:23,360 --> 00:29:25,680
Speaker 1: else to the universe so that we did have local

590
00:29:25,680 --> 00:29:29,440
Speaker 1: gauge invariance, something that like corrected for that. So take

591
00:29:29,480 --> 00:29:32,320
Speaker 1: the universe that just has electrons in it and ask

592
00:29:32,400 --> 00:29:35,760
Speaker 1: for local gauge invariants, and you break that right, like immediately,

593
00:29:35,760 --> 00:29:38,800
Speaker 1: you don't have local gauge invariants because you're changing electrons

594
00:29:38,800 --> 00:29:41,640
Speaker 1: differently everywhere. Well, now, if you like add something to

595
00:29:41,760 --> 00:29:44,600
Speaker 1: the universe to try to fix it, to compensate for

596
00:29:44,680 --> 00:29:47,200
Speaker 1: this change you've made, you have to add a new piece.

597
00:29:47,520 --> 00:29:50,000
Speaker 1: And that new piece, if you look at the mathematics

598
00:29:50,000 --> 00:29:53,600
Speaker 1: of it, is exactly the electromagnetic field. I think you

599
00:29:53,680 --> 00:29:56,560
Speaker 1: lost me a little while, to be honest, So I

600
00:29:56,600 --> 00:29:59,280
Speaker 1: guess it's difference between local and global. Is it like

601
00:29:59,360 --> 00:30:01,640
Speaker 1: kind of like if I let go of my book

602
00:30:01,960 --> 00:30:04,600
Speaker 1: on a from a three story building, it's not I

603
00:30:04,640 --> 00:30:06,760
Speaker 1: won't get the same velocity at the bottom as if

604
00:30:06,760 --> 00:30:08,720
Speaker 1: I drop it from a one story building. Is that

605
00:30:08,800 --> 00:30:10,280
Speaker 1: kind of what do you mean? Yes? Or let's say

606
00:30:10,280 --> 00:30:12,760
Speaker 1: you want to define your altitude differently based on where

607
00:30:12,800 --> 00:30:15,000
Speaker 1: you are in the world, Like currently we have a

608
00:30:15,040 --> 00:30:18,160
Speaker 1: single global definition of altitude relative to sea level. But

609
00:30:18,200 --> 00:30:20,400
Speaker 1: what if you wanted to choose your height definition to

610
00:30:20,440 --> 00:30:22,880
Speaker 1: be different if you're here or if you're over there,

611
00:30:22,920 --> 00:30:25,280
Speaker 1: if you're an Irvine or Pasadena or New York. All

612
00:30:25,320 --> 00:30:28,240
Speaker 1: of a sudden, you know, as you move across the country,

613
00:30:28,440 --> 00:30:30,800
Speaker 1: your height would be changing constantly, like oh, I'm higher,

614
00:30:30,800 --> 00:30:33,200
Speaker 1: I'm lower I'm higher, I'm lower. It wouldn't make any sense.

615
00:30:33,200 --> 00:30:36,080
Speaker 1: You'd get crazy physical predictions, like the book would still

616
00:30:36,120 --> 00:30:38,000
Speaker 1: fall the same way, wouldn't it. The book would still

617
00:30:38,040 --> 00:30:39,920
Speaker 1: fall the same way, and so your theory wouldn't work.

618
00:30:40,200 --> 00:30:42,480
Speaker 1: If you'd like to throw a ball as a parable,

619
00:30:42,640 --> 00:30:46,520
Speaker 1: and it's moving across the ground and you're constantly changing

620
00:30:46,560 --> 00:30:48,480
Speaker 1: like the definition of height, then you're not going to

621
00:30:48,560 --> 00:30:51,640
Speaker 1: get sensible predictions. Right. The ball obviously does move smoothly,

622
00:30:51,880 --> 00:30:54,160
Speaker 1: and so your physical theory doesn't work anymore if your

623
00:30:54,160 --> 00:30:56,960
Speaker 1: definition of height is changing as the ball is moving.

624
00:30:57,120 --> 00:30:59,920
Speaker 1: Is it, like, you know, my equation, my prediction one word,

625
00:31:00,240 --> 00:31:03,160
Speaker 1: if I use meters in England or if I use

626
00:31:03,280 --> 00:31:05,280
Speaker 1: feet here in the US, Like that's what you mean?

627
00:31:05,320 --> 00:31:08,800
Speaker 1: Like you want a theory to be different about whether

628
00:31:08,960 --> 00:31:12,680
Speaker 1: you use feed or meters. Yeah, and so global invariance

629
00:31:12,720 --> 00:31:14,960
Speaker 1: is like, well, let's just use meters everywhere that makes sense,

630
00:31:15,200 --> 00:31:18,000
Speaker 1: or let's use feed everywhere, but let's be consistent. Local

631
00:31:18,040 --> 00:31:19,800
Speaker 1: invariance is like, no, I want to get to pick

632
00:31:19,840 --> 00:31:23,400
Speaker 1: my units differently everywhere, and so that's a much higher standard,

633
00:31:23,440 --> 00:31:25,840
Speaker 1: like to have the laws of physics that allow you

634
00:31:25,840 --> 00:31:28,320
Speaker 1: to have that much freedom to make any choice at

635
00:31:28,360 --> 00:31:31,640
Speaker 1: any point in the universe is a much higher standard, oh, right,

636
00:31:31,680 --> 00:31:33,840
Speaker 1: because I guess it would have to be like irrelevant,

637
00:31:33,960 --> 00:31:37,200
Speaker 1: right almost exactly. It's like it doesn't matter if you

638
00:31:37,240 --> 00:31:40,320
Speaker 1: weigh something in England or in the US, whether you

639
00:31:40,440 --> 00:31:42,800
Speaker 1: use meters, because meters doesn't figure into it. That's kind

640
00:31:42,800 --> 00:31:45,560
Speaker 1: of what you want, right exactly, all right, So you're

641
00:31:45,600 --> 00:31:48,080
Speaker 1: saying that we the universe doesn't seem to have that

642
00:31:48,280 --> 00:31:51,600
Speaker 1: local gauge invariance, meaning it doesn't matter if you use

643
00:31:51,640 --> 00:31:53,600
Speaker 1: meters or feed but you're saying, there's a way to

644
00:31:53,760 --> 00:31:56,000
Speaker 1: get that back. There is a way to get that back.

645
00:31:56,160 --> 00:31:58,440
Speaker 1: You can say, what would the universe have to look

646
00:31:58,480 --> 00:32:01,480
Speaker 1: like to have local gage invariants? Like take your electron

647
00:32:01,840 --> 00:32:04,200
Speaker 1: is flying through space, and what if you want to

648
00:32:04,240 --> 00:32:06,080
Speaker 1: be able to like multiply it's a wave functioned by

649
00:32:06,080 --> 00:32:08,560
Speaker 1: an arbitrary number at a different point in space, and

650
00:32:08,600 --> 00:32:11,520
Speaker 1: how that number be different everywhere in space? Is there

651
00:32:11,560 --> 00:32:13,680
Speaker 1: a way to do that? Is there a universe you

652
00:32:13,680 --> 00:32:16,760
Speaker 1: could construct that would follow that, that would respect your

653
00:32:16,800 --> 00:32:18,680
Speaker 1: local gauge invariance that would allow you to have that

654
00:32:18,760 --> 00:32:21,280
Speaker 1: much freedom. And it turns out there is if you

655
00:32:21,320 --> 00:32:23,720
Speaker 1: add a photon. So if you have just electrons in

656
00:32:23,760 --> 00:32:26,880
Speaker 1: the universe, no local gauge invariance. But if you add

657
00:32:26,880 --> 00:32:30,280
Speaker 1: an electromagnetic field, which gives you photons, boom, you get

658
00:32:30,360 --> 00:32:33,960
Speaker 1: local gauge invariants for free. Well what wait, okay, so

659
00:32:34,120 --> 00:32:38,000
Speaker 1: somehow the fix for this solution, but for all equations,

660
00:32:38,040 --> 00:32:41,080
Speaker 1: for just some particles, you're saying, the solution to making

661
00:32:41,120 --> 00:32:44,880
Speaker 1: things be meter or feet independent is to add the

662
00:32:44,920 --> 00:32:49,040
Speaker 1: magnetic electromagnetic field. Yes, the electromagnetic field is the thing

663
00:32:49,080 --> 00:32:53,240
Speaker 1: that can perfectly compensate and give you local gauge invariants

664
00:32:53,240 --> 00:32:55,440
Speaker 1: like you can derive it. You can say, here's the

665
00:32:55,480 --> 00:32:58,160
Speaker 1: wave function for the electron. I'm going to add an

666
00:32:58,280 --> 00:33:00,880
Speaker 1: arbitrary phase to it, which is multiplying it by an

667
00:33:00,960 --> 00:33:03,360
Speaker 1: arbitrary number. And you can say, well, now my predictions

668
00:33:03,360 --> 00:33:05,680
Speaker 1: are wrong, they're different. What would I need to add

669
00:33:05,680 --> 00:33:08,560
Speaker 1: to my equations to compensate for that to cancel out?

670
00:33:08,840 --> 00:33:11,160
Speaker 1: This bologna that I've added and once you need to

671
00:33:11,200 --> 00:33:15,760
Speaker 1: add has exactly the same mathematical structure as the electromagnetic field.

672
00:33:15,760 --> 00:33:18,880
Speaker 1: It is the electromagnetic field. So the presence of the

673
00:33:18,920 --> 00:33:23,440
Speaker 1: electromagnetic field is what preserves local gauge invariance. For it's

674
00:33:23,560 --> 00:33:28,640
Speaker 1: you're saying, the electromagnetic field preserved symmetry for the electron

675
00:33:28,760 --> 00:33:31,560
Speaker 1: or for like everything in the entire universe for the

676
00:33:31,600 --> 00:33:34,440
Speaker 1: electrons wave function. Yes, so we're talking just about the

677
00:33:34,440 --> 00:33:37,880
Speaker 1: electron and its way function. It is feet and meter independent.

678
00:33:37,920 --> 00:33:41,040
Speaker 1: But if you had the electromatic field, then it is independent. Oh,

679
00:33:41,120 --> 00:33:43,000
Speaker 1: I guess the electron has its own field to the

680
00:33:43,040 --> 00:33:46,000
Speaker 1: electron has its own field. Yeah, there's the electron field.

681
00:33:46,040 --> 00:33:48,520
Speaker 1: And now we're saying that if we want this local

682
00:33:48,560 --> 00:33:51,160
Speaker 1: gauge invariance where we can multiply arbitrary numbers to the

683
00:33:51,160 --> 00:33:55,080
Speaker 1: electron field, that can't happen unless you have this exact,

684
00:33:55,200 --> 00:33:58,520
Speaker 1: very specific requirement of another field that hangs out and

685
00:33:58,560 --> 00:34:01,840
Speaker 1: basically compensates for that and takes care of that for you.

686
00:34:02,160 --> 00:34:05,240
Speaker 1: And it turns out that that field is the electromagnetic field,

687
00:34:05,240 --> 00:34:10,040
Speaker 1: and photons basically exist in order to preserve local gauge invariants.

688
00:34:10,280 --> 00:34:12,520
Speaker 1: What you're saying that the only reason we have light

689
00:34:12,800 --> 00:34:16,560
Speaker 1: is to make electrons happy. Well, here's the philosophy, right, Like,

690
00:34:16,880 --> 00:34:20,280
Speaker 1: do we have light because the universe preserves local gauge invariants?

691
00:34:20,280 --> 00:34:22,880
Speaker 1: And that's the only law of physics that allows that

692
00:34:22,920 --> 00:34:26,480
Speaker 1: one that has photons. Or do we have photons because

693
00:34:26,520 --> 00:34:29,440
Speaker 1: we have local gauge invariants? Right? Like which direction does

694
00:34:29,440 --> 00:34:32,240
Speaker 1: it go? Uh? You know is a fun philosophy question.

695
00:34:32,560 --> 00:34:35,200
Speaker 1: But what we do know is that we have photons,

696
00:34:35,239 --> 00:34:37,960
Speaker 1: we have electrons, and we have the electromagnetic field. Both

697
00:34:38,000 --> 00:34:40,440
Speaker 1: of those two things, and together they seem to have

698
00:34:40,520 --> 00:34:43,800
Speaker 1: this amazing, weird property of local gauge invariance where you

699
00:34:43,800 --> 00:34:46,399
Speaker 1: can multiply up an arbitrary number and that number can

700
00:34:46,440 --> 00:34:48,839
Speaker 1: be different at different points in the universe and it

701
00:34:48,880 --> 00:34:51,680
Speaker 1: doesn't change the predictions. These two fields work to gather

702
00:34:52,000 --> 00:34:55,520
Speaker 1: in this really crazy and interesting way. That's interesting, but

703
00:34:55,640 --> 00:34:58,759
Speaker 1: it only applies to the electron. Like what about quarts, right,

704
00:34:58,840 --> 00:35:02,640
Speaker 1: quarks have a field, I think, and we can ask

705
00:35:02,640 --> 00:35:06,480
Speaker 1: the same questions like is the cork also locally symmetric?

706
00:35:06,800 --> 00:35:10,279
Speaker 1: You know, meat and feed independent here in the US

707
00:35:10,360 --> 00:35:13,920
Speaker 1: And is there's a separate field then that also fixes

708
00:35:13,960 --> 00:35:17,520
Speaker 1: that symmetry. Fascinating question. You're absolutely right. This applies to

709
00:35:17,560 --> 00:35:21,040
Speaker 1: the electron. It also applies to any particle that has

710
00:35:21,120 --> 00:35:25,440
Speaker 1: electric charge. So for example, the muan has this same property.

711
00:35:25,760 --> 00:35:28,560
Speaker 1: The muan, you can multiply by an arbitrary number, and

712
00:35:28,600 --> 00:35:31,800
Speaker 1: you also get local gauge invariants because the muan is charged,

713
00:35:31,840 --> 00:35:34,879
Speaker 1: and it also communicates with the photon field. And yes,

714
00:35:34,960 --> 00:35:37,520
Speaker 1: corks have electric charge, so they do the same thing.

715
00:35:37,560 --> 00:35:40,400
Speaker 1: In fact, turns out that's what it means to have

716
00:35:40,560 --> 00:35:44,879
Speaker 1: electric charge. Electric charge means you couple to the photon field.

717
00:35:44,920 --> 00:35:48,799
Speaker 1: Because electric charge just means you feel electric fields. You're

718
00:35:48,800 --> 00:35:52,960
Speaker 1: like influenced by electromagnetic fields, which is the field of

719
00:35:53,000 --> 00:35:56,279
Speaker 1: the photon. And so the reason we have electricity and magnetism,

720
00:35:56,320 --> 00:35:59,320
Speaker 1: the reason we have electric charge is because these particles

721
00:35:59,400 --> 00:36:02,720
Speaker 1: have this property. A really fascinating thing is we didn't

722
00:36:02,719 --> 00:36:07,200
Speaker 1: know necessarily, like do muans feel the same photon as electrons,

723
00:36:07,280 --> 00:36:09,400
Speaker 1: Like it could have been there's a different feel to

724
00:36:09,520 --> 00:36:13,319
Speaker 1: preserve the muans local gauge invariants and the electrons. But

725
00:36:13,400 --> 00:36:15,719
Speaker 1: of course we know there's a single photon, the same

726
00:36:15,719 --> 00:36:18,840
Speaker 1: photon that an electronomists can be absorbed by a muan.

727
00:36:19,000 --> 00:36:20,560
Speaker 1: But it didn't have to be that way. You could

728
00:36:20,600 --> 00:36:23,400
Speaker 1: have lived in the universe with like electron photon and

729
00:36:23,480 --> 00:36:26,360
Speaker 1: a muan photon and a towel photon and lots of

730
00:36:26,400 --> 00:36:28,279
Speaker 1: different kinds of photons in it. All right, So then

731
00:36:28,360 --> 00:36:31,759
Speaker 1: it seems like the electromagnetic field is this thing that

732
00:36:32,000 --> 00:36:36,840
Speaker 1: preserves the symmetry for all particles that feel the electric charge,

733
00:36:37,719 --> 00:36:40,200
Speaker 1: and so that's what makes the equations for all these

734
00:36:40,239 --> 00:36:44,799
Speaker 1: particles symmetric. And that's beautiful and maybe even clever. All right,

735
00:36:44,840 --> 00:36:47,840
Speaker 1: let's get into what it all means for the universe

736
00:36:47,920 --> 00:36:50,680
Speaker 1: and our understanding of it. But first let's take another

737
00:36:50,840 --> 00:37:06,000
Speaker 1: quick break. All right, we're going deep here today, Daniel.

738
00:37:06,040 --> 00:37:08,520
Speaker 1: I feel I feel like you really thrown us down

739
00:37:08,560 --> 00:37:10,560
Speaker 1: a rabbit hole here, Like what is the nature of

740
00:37:10,600 --> 00:37:13,640
Speaker 1: the electric magnetic field? Like does it exists only to

741
00:37:13,719 --> 00:37:17,160
Speaker 1: give symmetry to these particles? Or do particles have the

742
00:37:17,239 --> 00:37:21,400
Speaker 1: symmetry because of the electromagnetic field. It's a big philosophical question. Yeah. Well,

743
00:37:21,440 --> 00:37:23,319
Speaker 1: you know, I'm responding to your challenge. You remember when

744
00:37:23,360 --> 00:37:25,719
Speaker 1: we were talking about the weak force and does it

745
00:37:25,840 --> 00:37:27,920
Speaker 1: push or pull? And I said, well, one day we're

746
00:37:27,920 --> 00:37:29,920
Speaker 1: gonna have to go deep and talk about gauge symmetry,

747
00:37:29,920 --> 00:37:32,640
Speaker 1: and you said, bring it on. I got time. So here.

748
00:37:33,400 --> 00:37:34,840
Speaker 1: I don't think you can prove that, I said that,

749
00:37:34,960 --> 00:37:37,320
Speaker 1: can you? We didn't record it. I think we do

750
00:37:37,440 --> 00:37:41,360
Speaker 1: have a recording I was just listening to yesterday. I

751
00:37:41,480 --> 00:37:43,719
Speaker 1: might officially regret it right now. No, but this is

752
00:37:43,800 --> 00:37:47,200
Speaker 1: pretty interesting, all right. So it seems like the universe

753
00:37:47,760 --> 00:37:51,800
Speaker 1: likes this symmetry, this local symmetry likes uh, and to

754
00:37:51,920 --> 00:37:55,800
Speaker 1: do that, it has this field electro magnetic field, and

755
00:37:56,000 --> 00:37:58,279
Speaker 1: that's kind of how the universe works. And thank goodness, right,

756
00:37:58,280 --> 00:38:00,200
Speaker 1: because that's how we get liked. Yeah, that to why

757
00:38:00,200 --> 00:38:05,239
Speaker 1: the universe is literally so brilliant. Don't don't nice. It's

758
00:38:05,239 --> 00:38:07,719
Speaker 1: a nice light light joke. But I guess what does

759
00:38:07,760 --> 00:38:09,800
Speaker 1: it mean, Daniel, I'm not sure what it means. You know,

760
00:38:10,000 --> 00:38:13,040
Speaker 1: we live in this universe that has photons in it,

761
00:38:13,280 --> 00:38:15,880
Speaker 1: and that means that we live in a universe that

762
00:38:16,000 --> 00:38:20,200
Speaker 1: respects local gauge invariance. Like why does our universe respect

763
00:38:20,280 --> 00:38:24,719
Speaker 1: this super weird, very specific, difficult symmetry. You know, why

764
00:38:24,760 --> 00:38:27,680
Speaker 1: can you multiply wave functions by any number and it

765
00:38:27,800 --> 00:38:29,800
Speaker 1: have that be a different number at every place in

766
00:38:29,880 --> 00:38:33,640
Speaker 1: the universe and still it doesn't matter. Like it's fascinating.

767
00:38:33,840 --> 00:38:35,640
Speaker 1: I don't know what that means about the universe, but

768
00:38:35,719 --> 00:38:39,040
Speaker 1: it means that local gauge in variance is deeply deeply

769
00:38:39,120 --> 00:38:42,520
Speaker 1: built into the very structure of reality. So I think

770
00:38:42,560 --> 00:38:45,400
Speaker 1: we need like another hundred years of philosophers smoking banana

771
00:38:45,440 --> 00:38:48,200
Speaker 1: peels thinking about why that is to tell us, like,

772
00:38:48,480 --> 00:38:50,440
Speaker 1: you know, why reality is this way and not some

773
00:38:50,600 --> 00:38:54,279
Speaker 1: other way, but it also has very physical consequences for

774
00:38:54,360 --> 00:38:57,080
Speaker 1: the nature of reality. Well, I guess the question, maybe

775
00:38:57,160 --> 00:38:59,480
Speaker 1: before we get into too deep into that, is does

776
00:38:59,560 --> 00:39:03,520
Speaker 1: this also apply to particles that don't feel the electromagnetic force? Like,

777
00:39:03,560 --> 00:39:06,719
Speaker 1: aren't there particles that don't feel the photons and things

778
00:39:06,760 --> 00:39:09,040
Speaker 1: like that, right? Do they have their own field that

779
00:39:09,160 --> 00:39:12,280
Speaker 1: also preserves that symmetry. They do not. Neutrinos, for example,

780
00:39:12,400 --> 00:39:14,880
Speaker 1: do not have this symmetry. And neutrinos do not have

781
00:39:15,040 --> 00:39:18,160
Speaker 1: electric charge and do not interact with the electromagnetic field

782
00:39:18,440 --> 00:39:21,520
Speaker 1: and do not talk to photons. And if neutrinos did

783
00:39:21,640 --> 00:39:24,279
Speaker 1: have this symmetry, they would have electric charge. And that's

784
00:39:24,280 --> 00:39:26,800
Speaker 1: sort of what it means to have electric charges, that

785
00:39:26,920 --> 00:39:29,399
Speaker 1: you have this symmetry, and then there's a field out

786
00:39:29,440 --> 00:39:32,160
Speaker 1: there that like compensates for it. And so no, neutrinos

787
00:39:32,280 --> 00:39:34,319
Speaker 1: do not have this symmetry. You can't do the same

788
00:39:34,360 --> 00:39:38,160
Speaker 1: thing to neutrinos. They have another weird different symmetry, which

789
00:39:38,280 --> 00:39:41,040
Speaker 1: is why they feel the weak force, and quarks have

790
00:39:41,239 --> 00:39:44,000
Speaker 1: multiple symmetries, which is why they feel the strong force also,

791
00:39:44,120 --> 00:39:45,560
Speaker 1: but we can talk about that in a minute. It's

792
00:39:45,560 --> 00:39:48,399
Speaker 1: almost like you're saying that the forces in the universe are,

793
00:39:49,440 --> 00:39:53,080
Speaker 1: you know, there to maintain this symmetry in the universe exactly.

794
00:39:53,320 --> 00:39:56,160
Speaker 1: And that's why we call the photon a gauge boson,

795
00:39:56,320 --> 00:39:59,680
Speaker 1: and we call these things gauge fields and gauge forces.

796
00:39:59,760 --> 00:40:02,600
Speaker 1: Bec as it seems like the forces either they exist

797
00:40:02,719 --> 00:40:05,040
Speaker 1: in order to do this, or they exist because of this,

798
00:40:05,400 --> 00:40:07,480
Speaker 1: or this is the only way to have a universe

799
00:40:07,560 --> 00:40:11,160
Speaker 1: because of this symmetry. But every force exists in order

800
00:40:11,239 --> 00:40:15,719
Speaker 1: to preserve some local gauge invariance for the particles. It's

801
00:40:15,719 --> 00:40:20,560
Speaker 1: almost like they're forcing the universe. You know, I made

802
00:40:20,600 --> 00:40:22,880
Speaker 1: that same joke in that other podcast episode, and you

803
00:40:22,960 --> 00:40:26,840
Speaker 1: said I kind of forced it. Well, I'm trying to

804
00:40:26,920 --> 00:40:29,480
Speaker 1: be symmetric. You know, I'm copying the same joke, but

805
00:40:29,600 --> 00:40:31,800
Speaker 1: I'm doing it on the other side. You're forced feeding

806
00:40:31,800 --> 00:40:36,120
Speaker 1: me my own puns back to me being clever, right, Yeah,

807
00:40:36,160 --> 00:40:38,640
Speaker 1: And the nature of that field is really fascinating, Like,

808
00:40:38,719 --> 00:40:42,920
Speaker 1: for example, because we have this local gauge invariance and

809
00:40:43,000 --> 00:40:46,359
Speaker 1: you have these photons. That's why we have charge conservation.

810
00:40:46,719 --> 00:40:49,400
Speaker 1: Remember how we talked about how every symmetry the universe

811
00:40:49,719 --> 00:40:53,239
Speaker 1: leads to a conservation of something that's Nothers theorem. So

812
00:40:53,360 --> 00:40:56,640
Speaker 1: the fact that you can serve this property of electrons

813
00:40:56,840 --> 00:41:00,799
Speaker 1: is why you cannot create or destroy electric charge. How

814
00:41:00,840 --> 00:41:06,000
Speaker 1: does preserving symmetry lead to these conservation laws which seemed important? Right, Yeah, Well,

815
00:41:06,000 --> 00:41:08,320
Speaker 1: we're gonna have a whole episode about Nurther's theorem to

816
00:41:08,440 --> 00:41:10,480
Speaker 1: get into like the intuition behind it all. Right, now,

817
00:41:10,560 --> 00:41:12,040
Speaker 1: all you need to know is that every time you

818
00:41:12,200 --> 00:41:16,480
Speaker 1: identify a symmetry of the laws of physics, that directly

819
00:41:16,560 --> 00:41:19,120
Speaker 1: tells you that there's something that's conserved. Just like the

820
00:41:19,200 --> 00:41:23,000
Speaker 1: symmetry of moving your experiments somewhere else leads to conservation

821
00:41:23,080 --> 00:41:26,399
Speaker 1: of momentum, and the symmetry of rotating your experiment leads

822
00:41:26,440 --> 00:41:30,120
Speaker 1: to conservation of angular momentum. Well, the symmetry of rotating

823
00:41:30,200 --> 00:41:33,640
Speaker 1: your electron from plus wave function to minus wave function

824
00:41:34,040 --> 00:41:36,879
Speaker 1: leads to conservation of charge. I mean it's the same

825
00:41:36,920 --> 00:41:39,640
Speaker 1: concept for the other forces, right, strong and the weak force.

826
00:41:39,800 --> 00:41:41,960
Speaker 1: It's the same concept for the other forces, but it's

827
00:41:41,960 --> 00:41:44,279
Speaker 1: a different symmetry, and in those cases it's a much

828
00:41:44,360 --> 00:41:48,560
Speaker 1: more complicated symmetry. So, for example, the strong force has

829
00:41:48,680 --> 00:41:51,319
Speaker 1: not just like plus and minus charge, right it has

830
00:41:51,520 --> 00:41:55,800
Speaker 1: three different kinds of charge, red, green, and blue, and

831
00:41:55,880 --> 00:41:59,920
Speaker 1: it actually follows a much more complicated local gauge invariant.

832
00:42:00,160 --> 00:42:02,400
Speaker 1: It turns out, for the strong force, you cannot just

833
00:42:02,640 --> 00:42:06,400
Speaker 1: multiply the way function by minus one. You can rotate

834
00:42:06,719 --> 00:42:09,600
Speaker 1: the color space, like take red and map into green,

835
00:42:09,719 --> 00:42:11,839
Speaker 1: and green and map itto blue and blue and map

836
00:42:11,880 --> 00:42:13,879
Speaker 1: it back to red. Okay, you can do this kind

837
00:42:13,880 --> 00:42:16,319
Speaker 1: of rotation, and you can have a different rotation at

838
00:42:16,400 --> 00:42:19,120
Speaker 1: every place in space, like green here is blue. There

839
00:42:19,840 --> 00:42:22,840
Speaker 1: is half red plus half green over here, And you

840
00:42:22,920 --> 00:42:24,600
Speaker 1: can do that and it's fine, and it will not

841
00:42:24,920 --> 00:42:28,080
Speaker 1: change the nature of your predictions for how the strong

842
00:42:28,160 --> 00:42:31,360
Speaker 1: force works, because you have a bunch of gluon fields

843
00:42:31,640 --> 00:42:34,280
Speaker 1: that exist to compensate for that, to sort of correct

844
00:42:34,360 --> 00:42:37,400
Speaker 1: for that. You're saying, like, like these symmetries, it's almost

845
00:42:37,440 --> 00:42:39,600
Speaker 1: like a three way symmetry, right, Like it's not just

846
00:42:39,760 --> 00:42:41,800
Speaker 1: like a mirror, but it's like a house of mirrors

847
00:42:41,960 --> 00:42:44,200
Speaker 1: kind of, yeah, exactly, and just like the sphere. Right,

848
00:42:44,239 --> 00:42:46,200
Speaker 1: the sphere is a much more complicated symmetry than just

849
00:42:46,320 --> 00:42:48,759
Speaker 1: like reflection. You can rotate the sphere, and you can

850
00:42:48,880 --> 00:42:51,120
Speaker 1: rotate it in different ways. You can rotate it about

851
00:42:51,160 --> 00:42:54,000
Speaker 1: its equator, or about its poll or about some other directions.

852
00:42:54,000 --> 00:42:57,319
Speaker 1: There's actually three fundamental symmetries of the sphere. The same

853
00:42:57,400 --> 00:43:00,239
Speaker 1: thing is true for color space for the strong force.

854
00:43:00,400 --> 00:43:03,320
Speaker 1: And that's why we have eight gluons. Because the strong

855
00:43:03,400 --> 00:43:06,759
Speaker 1: force is a much more complicated local gauge invariance. It

856
00:43:06,840 --> 00:43:11,440
Speaker 1: requires more fields. Are actually eight different gluon fields required

857
00:43:11,840 --> 00:43:15,280
Speaker 1: just to preserve this force and so, but it's described

858
00:43:15,280 --> 00:43:17,880
Speaker 1: by the same fundamental mathematics. And this is why. If

859
00:43:17,920 --> 00:43:20,440
Speaker 1: you've heard that group theory is important for particle physics,

860
00:43:20,680 --> 00:43:23,680
Speaker 1: this is why, because group theory describes exactly how these

861
00:43:23,840 --> 00:43:26,240
Speaker 1: rotations work and sort of like the set of different

862
00:43:26,320 --> 00:43:28,840
Speaker 1: rotations that you can have. And so the reason the

863
00:43:28,880 --> 00:43:33,000
Speaker 1: strong force exists is because quarks have this weird property

864
00:43:33,200 --> 00:43:36,000
Speaker 1: that you can rotate their color in an arbitrary way

865
00:43:36,000 --> 00:43:38,520
Speaker 1: a different points in space, and the gluon fields are

866
00:43:38,600 --> 00:43:41,520
Speaker 1: there to compensate. That's why they exist. So then I

867
00:43:41,600 --> 00:43:45,719
Speaker 1: guess do physicists c force as something totally different than

868
00:43:45,800 --> 00:43:47,640
Speaker 1: most people think about it. You know, when I think

869
00:43:47,680 --> 00:43:50,759
Speaker 1: of a force, it's like pushing and pulling, or as

870
00:43:50,840 --> 00:43:53,560
Speaker 1: they usually describe it, it's like, you know, an electron

871
00:43:53,840 --> 00:43:57,239
Speaker 1: throws a photon to another electron, and that you know,

872
00:43:57,560 --> 00:43:59,680
Speaker 1: the throwing of the photon and the receiving of the

873
00:43:59,680 --> 00:44:02,800
Speaker 1: photo on is a way to kind of exchange you know,

874
00:44:02,880 --> 00:44:04,840
Speaker 1: a push or a pool or energy. But now it

875
00:44:04,920 --> 00:44:07,520
Speaker 1: seems like these fields are just there to preserve some

876
00:44:07,640 --> 00:44:09,839
Speaker 1: kind of symmetry. Is that kind of why you see

877
00:44:09,880 --> 00:44:12,360
Speaker 1: forces differently? Yeah, and that's that moment of elegance I

878
00:44:12,480 --> 00:44:15,520
Speaker 1: was talking about, Like we start very simply in the world,

879
00:44:15,640 --> 00:44:20,799
Speaker 1: seeing the world around us and categorizing and listing our observations. Oh,

880
00:44:20,880 --> 00:44:23,000
Speaker 1: that apple fell from the tree, or my friend fell

881
00:44:23,080 --> 00:44:26,400
Speaker 1: down the canyon, you know, or I felt this weird magnetism.

882
00:44:26,520 --> 00:44:30,160
Speaker 1: That's a pretty dark scenario there, these three a friend

883
00:44:30,239 --> 00:44:33,840
Speaker 1: down the canyon. Hopefully not a podcast like cost thinking

884
00:44:33,920 --> 00:44:37,239
Speaker 1: about the applications of gravity, and we just describe all

885
00:44:37,239 --> 00:44:40,800
Speaker 1: of those things in terms of our experiences. But you know,

886
00:44:40,880 --> 00:44:43,440
Speaker 1: that's not necessarily the most natural way to do it.

887
00:44:43,560 --> 00:44:46,799
Speaker 1: And that's why physics takes us and we transform our

888
00:44:46,880 --> 00:44:50,600
Speaker 1: intuitive experiences into like a list of observations and look

889
00:44:50,640 --> 00:44:53,239
Speaker 1: for mathematical patterns, and then we discover all these things

890
00:44:53,280 --> 00:44:55,799
Speaker 1: are actually connected to those things, and it turns out

891
00:44:55,840 --> 00:44:58,160
Speaker 1: we've been looking at this all the wrong way. And

892
00:44:58,200 --> 00:45:00,719
Speaker 1: those are my favorite moments in physics when we discover, oh,

893
00:45:00,800 --> 00:45:03,880
Speaker 1: we think about forces this way, actually they probably exist

894
00:45:03,960 --> 00:45:06,560
Speaker 1: for this totally other reason, and we've come at it

895
00:45:06,640 --> 00:45:09,040
Speaker 1: in this weird way just because of our experience. And

896
00:45:09,120 --> 00:45:11,719
Speaker 1: so you get this like flash of deep insight when

897
00:45:11,760 --> 00:45:14,160
Speaker 1: you're like, oh, the universe fits together in this beautiful,

898
00:45:14,280 --> 00:45:17,640
Speaker 1: mathematically elegant way. If you think about it in terms

899
00:45:17,680 --> 00:45:21,480
Speaker 1: of forces, you know, recovering local gauge invariants instead of

900
00:45:21,800 --> 00:45:24,839
Speaker 1: you know, building anti gravity machines to protect your clumsy friend.

901
00:45:24,960 --> 00:45:26,839
Speaker 1: I guess how would you describe it? Then? When an

902
00:45:26,920 --> 00:45:30,920
Speaker 1: electron pushes on another electron and they exchange photons, how

903
00:45:30,960 --> 00:45:32,640
Speaker 1: did physicist see it? How do you see it in

904
00:45:32,840 --> 00:45:35,440
Speaker 1: terms of preserving the symmetry? Yeah, well, physicists see it

905
00:45:35,520 --> 00:45:39,040
Speaker 1: in terms of carrying those rotations, Like a photon sort

906
00:45:39,080 --> 00:45:41,839
Speaker 1: of carries that rotation, you know, that's what a photon does.

907
00:45:42,120 --> 00:45:45,560
Speaker 1: It rotates from one gauge to another gauge, and so

908
00:45:45,680 --> 00:45:49,080
Speaker 1: when an electron communicates with another electron somewhere else in space,

909
00:45:49,120 --> 00:45:52,920
Speaker 1: it's sort of like communicating about their differences in their gauge.

910
00:45:53,320 --> 00:45:56,000
Speaker 1: And so that's what a photon does. It carries that information,

911
00:45:56,520 --> 00:46:00,280
Speaker 1: and that's what gluons do. Gluons rotate things through colors space.

912
00:46:00,360 --> 00:46:03,280
Speaker 1: They're like, Okay, this cork over here is a green cork.

913
00:46:03,480 --> 00:46:05,200
Speaker 1: That cork is a blue cork. You know, I got

914
00:46:05,280 --> 00:46:07,640
Speaker 1: a communicate from here to here, and I'm gonna change

915
00:46:08,040 --> 00:46:10,560
Speaker 1: the green to the blue as I move along. The

916
00:46:10,640 --> 00:46:13,680
Speaker 1: forces are sort of like there to connect these objects,

917
00:46:13,719 --> 00:46:16,160
Speaker 1: and they do so by rotating the gauge from one

918
00:46:16,200 --> 00:46:18,959
Speaker 1: place to another. And I think that's most clearly seen

919
00:46:19,080 --> 00:46:21,839
Speaker 1: in terms of the weak force. The weak force has

920
00:46:21,920 --> 00:46:24,279
Speaker 1: the same sort of structure, but then again in a

921
00:46:24,440 --> 00:46:27,759
Speaker 1: different internal symmetry space. It's almost like two electrons are

922
00:46:28,040 --> 00:46:31,920
Speaker 1: gauging each other. It's like, you know, an electron interacts

923
00:46:31,960 --> 00:46:34,680
Speaker 1: with the electromagnetic fields. If it moves, it creates some

924
00:46:34,760 --> 00:46:36,920
Speaker 1: sort of disturbance that then has to be kind of

925
00:46:37,000 --> 00:46:40,759
Speaker 1: squared away somewhere else by another electron. And then that

926
00:46:41,000 --> 00:46:44,759
Speaker 1: transfer of you know, wiggle or disturbance is what you

927
00:46:44,800 --> 00:46:47,319
Speaker 1: would call a photon. Yes, like patching up your check

928
00:46:47,360 --> 00:46:49,440
Speaker 1: book at the end of the month. Photons are there

929
00:46:49,560 --> 00:46:52,319
Speaker 1: to like find those pennies and move them from one

930
00:46:52,360 --> 00:46:54,520
Speaker 1: to column to another to make everything out up in

931
00:46:54,560 --> 00:46:57,160
Speaker 1: the end. Hopefully they don't get too creative like I

932
00:46:57,360 --> 00:47:02,279
Speaker 1: sometimes I may or may not do electron magnetic accounting exactly. Well,

933
00:47:02,360 --> 00:47:04,640
Speaker 1: maybe that's what quantum accounting really is. There really is

934
00:47:04,680 --> 00:47:07,279
Speaker 1: a quantum accounting firm. Yeah, where you have money and

935
00:47:07,360 --> 00:47:09,879
Speaker 1: don't have money at the same time. You're both rich

936
00:47:09,960 --> 00:47:11,400
Speaker 1: and broke at the same time. And you know, I

937
00:47:11,440 --> 00:47:14,279
Speaker 1: got an email this morning from a listener Ivan, who

938
00:47:14,400 --> 00:47:17,480
Speaker 1: is asking me about why I say that the weak

939
00:47:17,560 --> 00:47:20,279
Speaker 1: force makes sense to all be together, Like why the

940
00:47:20,520 --> 00:47:22,759
Speaker 1: ws and zs all makes sense to be in a

941
00:47:22,920 --> 00:47:25,840
Speaker 1: single field and also with the electromagnetic field. But like

942
00:47:26,080 --> 00:47:28,040
Speaker 1: you can also ask, like why don't you consider the

943
00:47:28,239 --> 00:47:30,600
Speaker 1: W plus and the W minus and the Z all

944
00:47:30,680 --> 00:47:33,920
Speaker 1: just separate forces. Why isn't the weak force three different forces?

945
00:47:34,120 --> 00:47:36,160
Speaker 1: Why do you even try to put these things together?

946
00:47:36,360 --> 00:47:39,400
Speaker 1: And the reason are these symmetry? So we discover that

947
00:47:39,560 --> 00:47:43,480
Speaker 1: like the W plus by itself doesn't preserve local gauge invariants.

948
00:47:43,600 --> 00:47:45,320
Speaker 1: But when you put the W plus and the W

949
00:47:45,520 --> 00:47:49,520
Speaker 1: minus and the Z together, then they do. So together,

950
00:47:49,760 --> 00:47:53,879
Speaker 1: these three fields work really hard to preserve another kind

951
00:47:53,920 --> 00:47:56,680
Speaker 1: of invariance, different from the one that's for the electron,

952
00:47:56,800 --> 00:47:58,880
Speaker 1: and different from the one that's for corks. And this

953
00:47:59,040 --> 00:48:02,040
Speaker 1: is why we have the weak force, because it preserves rotations.

954
00:48:02,120 --> 00:48:05,480
Speaker 1: And this thing called weak isospin space. And so these

955
00:48:05,600 --> 00:48:08,360
Speaker 1: three fields together do that. And as you say, you

956
00:48:08,440 --> 00:48:11,920
Speaker 1: can put electromagnetism and the weak force together to make

957
00:48:11,960 --> 00:48:15,759
Speaker 1: an even super theory which preserves a different number altogether

958
00:48:16,160 --> 00:48:20,280
Speaker 1: that individually neither the two forces preserve. Right. It's almost

959
00:48:20,320 --> 00:48:24,080
Speaker 1: like the more complicated the symmetries are, the more forces

960
00:48:24,200 --> 00:48:27,000
Speaker 1: you need to patch them up. Yeah. And of course

961
00:48:27,080 --> 00:48:30,920
Speaker 1: the really super fascinating wrinkle is that that symmetry electroweak symmetry,

962
00:48:30,960 --> 00:48:33,680
Speaker 1: the symmetry that's preserved by the photon together with the

963
00:48:33,800 --> 00:48:36,480
Speaker 1: two ws and the Z, that one doesn't actually work,

964
00:48:36,760 --> 00:48:40,280
Speaker 1: That one's broken, that one isn't actually preserved by the universe.

965
00:48:40,360 --> 00:48:43,040
Speaker 1: And the reason for that is the Higgs boson. The

966
00:48:43,120 --> 00:48:47,040
Speaker 1: Higgs boson breaks that symmetry, and that's why it exists.

967
00:48:47,040 --> 00:48:49,480
Speaker 1: That's how we were able to detect that it does exist,

968
00:48:49,600 --> 00:48:53,040
Speaker 1: because we saw, oh, this symmetry doesn't actually work. We

969
00:48:53,120 --> 00:48:55,840
Speaker 1: need something else out there to break this symmetry, and

970
00:48:55,920 --> 00:48:58,320
Speaker 1: that's what the Higgs does. And that's why the ws

971
00:48:58,320 --> 00:49:01,279
Speaker 1: and disease are massive while the photon and the gluons

972
00:49:01,520 --> 00:49:04,279
Speaker 1: are massless. That's wild, Like, maybe the only reason we

973
00:49:04,360 --> 00:49:07,920
Speaker 1: have mass is to patch up these brakes. Yeah, well,

974
00:49:07,960 --> 00:49:09,960
Speaker 1: the only reason we have mass is because this one

975
00:49:10,080 --> 00:49:14,400
Speaker 1: symmetry is broken. This electroweak symmetry isn't actually something the

976
00:49:14,520 --> 00:49:17,239
Speaker 1: universe respects because the Higgs breaks it. If we didn't

977
00:49:17,280 --> 00:49:19,279
Speaker 1: have the Higgs, then the W and the Z would

978
00:49:19,280 --> 00:49:21,759
Speaker 1: be massless, and so would all the other particles, and

979
00:49:21,880 --> 00:49:24,080
Speaker 1: we wouldn't have any mass without the Higgs. Don't we

980
00:49:24,120 --> 00:49:28,120
Speaker 1: have other like violations of symmetry also all over the

981
00:49:28,760 --> 00:49:30,759
Speaker 1: theory of physics, right, are in there all kinds of

982
00:49:30,800 --> 00:49:34,120
Speaker 1: different charge and parody violations? There are, yes, And so

983
00:49:34,280 --> 00:49:36,920
Speaker 1: we have these a lot of these approximate symmetries or

984
00:49:37,000 --> 00:49:40,560
Speaker 1: broken symmetries, And an approximate symmetry is like, well, maybe

985
00:49:40,600 --> 00:49:43,000
Speaker 1: we're just missing a piece, Like we're not talking about

986
00:49:43,080 --> 00:49:46,000
Speaker 1: the right thing, Like we think we've identified the thing

987
00:49:46,120 --> 00:49:48,520
Speaker 1: that's being preserved, the thing with the universe respects, but

988
00:49:48,680 --> 00:49:50,800
Speaker 1: we must be looking at it from like the wrong angle.

989
00:49:51,080 --> 00:49:53,680
Speaker 1: We don't quite have it right, you know. For example,

990
00:49:53,800 --> 00:49:56,200
Speaker 1: like if you had a cube, and you know, you

991
00:49:56,280 --> 00:49:59,160
Speaker 1: can rotate the cube and you still get a cube, right,

992
00:49:59,320 --> 00:50:00,520
Speaker 1: But what if you're not looking at it from the

993
00:50:00,600 --> 00:50:01,840
Speaker 1: right point of view. You're only looking at like a

994
00:50:01,960 --> 00:50:04,520
Speaker 1: two D slice of the cube, and so the symmetry

995
00:50:04,560 --> 00:50:06,800
Speaker 1: of it is not exactly preserved. So in some of

996
00:50:06,880 --> 00:50:09,359
Speaker 1: these cases we're probably just like, don't have the full

997
00:50:09,400 --> 00:50:12,040
Speaker 1: picture yet. We haven't really discovered what it is the

998
00:50:12,200 --> 00:50:15,839
Speaker 1: universe is preserving. Like maybe it's not broken. Maybe we're

999
00:50:15,920 --> 00:50:18,439
Speaker 1: just missing something. Yeah, maybe we're just missing we haven't

1000
00:50:18,480 --> 00:50:21,000
Speaker 1: seen the full picture, but so far we haven't, which

1001
00:50:21,040 --> 00:50:23,960
Speaker 1: means that to us, it does look like a broken universe. Yeah,

1002
00:50:24,040 --> 00:50:26,719
Speaker 1: but some of these symmetries are perfect, Like charge conservation

1003
00:50:27,000 --> 00:50:29,600
Speaker 1: is not when we've ever seen broken, Like, no particle

1004
00:50:29,680 --> 00:50:32,799
Speaker 1: has ever broken conservation of charge, like a photon has

1005
00:50:32,840 --> 00:50:36,600
Speaker 1: never turned into two electrons or electrons don't just disappear

1006
00:50:36,719 --> 00:50:39,080
Speaker 1: into neutral particles. As far as we know, that is

1007
00:50:39,160 --> 00:50:42,560
Speaker 1: a perfect symmetry of the universe charge conservation. Alright, Well,

1008
00:50:42,719 --> 00:50:45,160
Speaker 1: I guess that tells us a little bit more about

1009
00:50:45,160 --> 00:50:48,280
Speaker 1: the universe. You know, there's these hidden symmetries, these hidden

1010
00:50:48,320 --> 00:50:51,759
Speaker 1: almost rules, right, that sort of govern everything, and that

1011
00:50:51,960 --> 00:50:54,759
Speaker 1: may even like give rise to things that we take

1012
00:50:54,800 --> 00:50:58,080
Speaker 1: for granted, like light. Maybe that's just the universe's way

1013
00:50:58,360 --> 00:51:01,319
Speaker 1: of trying to stay beautiful. Yeah, the way I think

1014
00:51:01,360 --> 00:51:03,840
Speaker 1: about it is that you can't have a universe that

1015
00:51:03,920 --> 00:51:07,080
Speaker 1: respects this symmetry without the photon. Like, the photon is

1016
00:51:07,120 --> 00:51:10,000
Speaker 1: absolutely necessary in order to have a universe that respects

1017
00:51:10,040 --> 00:51:12,960
Speaker 1: this symmetry. So therefore we do have a universe that

1018
00:51:13,040 --> 00:51:15,640
Speaker 1: respects this symmetry. Now, the question we can ask is like, well,

1019
00:51:15,760 --> 00:51:19,040
Speaker 1: why what a weird thing for universe to insist on?

1020
00:51:19,480 --> 00:51:21,719
Speaker 1: What does that mean? And I think that's the kind

1021
00:51:21,719 --> 00:51:23,400
Speaker 1: of thing that in a hundred years people look back

1022
00:51:23,400 --> 00:51:25,560
Speaker 1: and be like, oh my gosh, that was so obvious.

1023
00:51:25,640 --> 00:51:28,200
Speaker 1: The universe was screaming the answer to you. But here

1024
00:51:28,239 --> 00:51:30,200
Speaker 1: we are in the forefront of ignorance. We don't really

1025
00:51:30,280 --> 00:51:32,640
Speaker 1: know what this clue means yet. So I think it

1026
00:51:32,719 --> 00:51:34,879
Speaker 1: does mean something deep about the universe. We just still

1027
00:51:34,920 --> 00:51:37,360
Speaker 1: need to digest it. So come on, philosophers, tell us

1028
00:51:37,400 --> 00:51:39,280
Speaker 1: what it all means. Well, it sounds like the answer

1029
00:51:39,440 --> 00:51:41,840
Speaker 1: might come from physics, right, you're saying, like, maybe we

1030
00:51:41,960 --> 00:51:44,520
Speaker 1: don't know why now, but maybe in the future to

1031
00:51:44,640 --> 00:51:47,799
Speaker 1: a physicist that will seem obvious, right, Like, maybe there

1032
00:51:47,880 --> 00:51:50,400
Speaker 1: is a physical answer to these white questions, and just

1033
00:51:50,480 --> 00:51:52,640
Speaker 1: because we don't know what they are now, you're bumping

1034
00:51:52,680 --> 00:51:54,920
Speaker 1: them over to the philosophy department. Yeah, and it could

1035
00:51:54,960 --> 00:51:57,759
Speaker 1: also come from mathematics. We didn't appreciate the structure of

1036
00:51:57,760 --> 00:52:00,719
Speaker 1: these symmetries until we learned group theory from mathematics. It

1037
00:52:00,800 --> 00:52:04,399
Speaker 1: turns out that perfectly describes everything that's going on here.

1038
00:52:04,600 --> 00:52:07,359
Speaker 1: Mathematicians invented it for like totally other reasons, because they

1039
00:52:07,440 --> 00:52:09,960
Speaker 1: just like thinking about how things rotate in their minds.

1040
00:52:10,080 --> 00:52:12,080
Speaker 1: But it could be that what we've discovered now needs

1041
00:52:12,160 --> 00:52:15,160
Speaker 1: like some new branch of mathematics to describe it and

1042
00:52:15,280 --> 00:52:18,359
Speaker 1: give us like an understanding of what the meaning is. Intuitively,

1043
00:52:18,560 --> 00:52:20,360
Speaker 1: so it might just be that we need to invent

1044
00:52:20,719 --> 00:52:24,240
Speaker 1: new mathematical words and concepts to fit these things together

1045
00:52:24,320 --> 00:52:27,160
Speaker 1: into a deeper understanding. I see you're passing the bug

1046
00:52:27,239 --> 00:52:31,120
Speaker 1: now to the mathematics department. You're like, blame everyone but us.

1047
00:52:31,400 --> 00:52:34,040
Speaker 1: You know. It's like when poets invent new words, you know.

1048
00:52:34,160 --> 00:52:36,440
Speaker 1: I think English professors are like, can you really just

1049
00:52:36,600 --> 00:52:38,440
Speaker 1: do that? You know? And so I don't know if

1050
00:52:38,520 --> 00:52:41,080
Speaker 1: mathematicians want us inventing the new math, you know. I

1051
00:52:41,160 --> 00:52:43,640
Speaker 1: think they, you know, really would prefer to do that themselves.

1052
00:52:44,320 --> 00:52:46,719
Speaker 1: I see, now you're blaming the English department as well.

1053
00:52:47,080 --> 00:52:49,680
Speaker 1: That's right. I'm good at this. Bring out from the problem.

1054
00:52:49,719 --> 00:52:53,040
Speaker 1: I can blame them for it. The certain symmetry about you, Daniel,

1055
00:52:53,680 --> 00:52:57,879
Speaker 1: I feel like you're trying to preserve. Look, we made

1056
00:52:57,920 --> 00:53:01,040
Speaker 1: these crazy discoveries. Everybody else needs to tell what's going on.

1057
00:53:01,280 --> 00:53:02,880
Speaker 1: You know. It's really fun to think about. And this

1058
00:53:03,000 --> 00:53:04,680
Speaker 1: is one of the reasons why I agreed to join

1059
00:53:04,719 --> 00:53:06,759
Speaker 1: the philosophy department here, because I do like to think

1060
00:53:06,800 --> 00:53:09,160
Speaker 1: about what it means about the universe. Because in the end,

1061
00:53:09,239 --> 00:53:11,880
Speaker 1: that's why we're doing these experiments, not because we like

1062
00:53:12,000 --> 00:53:14,839
Speaker 1: to write down tidy mathematical equations, but because we hope

1063
00:53:15,040 --> 00:53:17,520
Speaker 1: that by doing so, they will speak to us, and

1064
00:53:17,560 --> 00:53:20,399
Speaker 1: they will tell us, Look, the universe follows this rule.

1065
00:53:20,440 --> 00:53:22,719
Speaker 1: The universe has to be this way, and we'll get

1066
00:53:22,800 --> 00:53:25,880
Speaker 1: some understanding of why it is a pretty perplexing universe.

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Speaker 1: And you know what, whether or not it's beautiful or broken,

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00:53:29,320 --> 00:53:31,920
Speaker 1: we we still love it. You know, no pressure, You

1069
00:53:31,920 --> 00:53:34,200
Speaker 1: don't have to tell us everything. You know, we're just

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00:53:34,320 --> 00:53:36,839
Speaker 1: here for you or because of you. I don't know, man,

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Speaker 1: that's another philosophical department. We do love the universe though,

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00:53:40,640 --> 00:53:43,120
Speaker 1: that's true. All right. Well, we hope you enjoyed dad,

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00:53:43,719 --> 00:53:54,040
Speaker 1: Thanks for joining us, see you next time. Thanks for listening,

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00:53:54,120 --> 00:53:56,840
Speaker 1: and remember that Daniel and Jorge explained. The universe is

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00:53:56,880 --> 00:54:00,239
Speaker 1: a production of I Heart Riding. For more podcast asked

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00:54:00,280 --> 00:54:02,839
Speaker 1: from my Heart Radio, visit the I Heart Radio app,

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Speaker 1: Apple Podcasts, or wherever you listen to your favorite shows.