Speaker 1: Hey, it's Jorhan Daniel here and we want to tell
Speaker 1: you about our new book. It's called Frequently Asked Questions
Speaker 1: about the Universe because you have questions about the universe,
Speaker 1: and so we decided to write a book all about them.
Speaker 1: We talk about your questions, we give some answers, we
Speaker 1: make a bunch of silly jokes as usual, and we
Speaker 1: tackle all kinds of questions, including what happens if I
Speaker 1: fall into a black hole? Or is there another version
Speaker 1: of you out there that's right? Like usual, we tackle
Speaker 1: the deepest, darkest, biggest, craziest questions about this incredible cosmos.
Speaker 1: If you want to support the podcast, please get the
Speaker 1: book and get a copy not just for yourself, but
Speaker 1: you know, for your nieces and nephews, cousins, friends, parents, dogs, hamsters,
Speaker 1: and for the aliens. So get your copy of Frequently
Speaker 1: Asked Questions about the Universe is available for pre order now,
Speaker 1: coming out November two. You can find more details at
Speaker 1: the book's website, Universe f a Q dot com. Thanks
Speaker 1: for your support, and if you have a hamster that
Speaker 1: can read, please let us know. We'd love to have
Speaker 1: them on the podcast. Hey, Daniel, I have a complaint
Speaker 1: to file about physics. Who do I talk to? Oh,
Speaker 1: you can lay it on me. I'll pass it on
Speaker 1: to the right people. All right, you're the unbutsman for
Speaker 1: all the physics. It's good to know, alright. So I
Speaker 1: feel like physics it's pretty good about answering how questions?
Speaker 1: You mean, like how old is the universe? Or how
Speaker 1: big is it? Yeah? Just like that? All right, Well
Speaker 1: that sounds pretty good. What's your complaint? Well, I feel
Speaker 1: like the real questions that humanity wants to know are
Speaker 1: the why questions, you know, like why do we have
Speaker 1: this universe? Why is it like this? And not like that.
Speaker 1: You know, I'm gonna have to direct you, I think,
Speaker 1: to the philosophy department. Oh, man, you're gonna pass the buck. Well,
Speaker 1: I don't know how else to answer a why question. Yeah,
Speaker 1: and I don't know why I ask you these questions
Speaker 1: in the first place. You ask a meta question, you
Speaker 1: get sent to the metaphysics department, the meta unbutsman. Hi
Speaker 1: am or Hey, I'm a cartoonists and the creator of
Speaker 1: PhD comments. Hi. I'm Daniel. I'm a particle physicist and
Speaker 1: a professor at U C Irvine, where I actually am
Speaker 1: also a member of the philosophy department. Oh are you
Speaker 1: really so you're a card caring philosopher? Technically I am so.
Speaker 1: I have no education in philosophy. I just started showing
Speaker 1: up at the philosophy of science seminars and eventually they
Speaker 1: were like, who are you? And then they give me
Speaker 1: a joint appointment. I guess they let anyone in that hand, like,
Speaker 1: there's not that much of a demand for philosophy membership. Well,
Speaker 1: I think joint appointments are free, so yes, the bar
Speaker 1: is not that high. Nice. Do you have to teach
Speaker 1: classes in philosophy? I am not qualified to teach classes
Speaker 1: in philosophy. Well, I feel like physics, you know, asked
Speaker 1: a lot of very philosophical questions or questions that border
Speaker 1: on philosophy, right, like why is the universe like this?
Speaker 1: Or why do we have a universe? Right? Like you're
Speaker 1: asking these questions as physicists, right, Yeah, A lot of
Speaker 1: the answers we get to questions in physics do have
Speaker 1: big philosophical implications, and I think it's important. That's why
Speaker 1: I started going to these seminars to understand like what
Speaker 1: if we discover this or what if we discover that
Speaker 1: what does it really mean? Man, Physics can tell you
Speaker 1: what's going on, but only philosophy can tell you what
Speaker 1: it means. Well, it's kind of a layer thing, right
Speaker 1: because you can ask like why does the apple fall
Speaker 1: from the tree and you can say, well, it's gravity.
Speaker 1: But you know, once you start dig getting deeper, like
Speaker 1: why do we have gravity, then it starts to get philosophical. Yeah,
Speaker 1: and then you can ask like what kind of answer
Speaker 1: will satisfy your question? And then you have a philosophical
Speaker 1: answer about philosophical questions, yeah, or like why have philosophical
Speaker 1: answers philosophy of philosophy? Wow, you can get a h
Speaker 1: and philosophy. I guess it's the start of the Endless sleep.
Speaker 1: But anyways, welcome to our podcast Daniel and Jorge Explain
Speaker 1: the Universe, a production of I Heart Radio in which
Speaker 1: we go meta and meta meta about the nature of
Speaker 1: the universe. We ask all the questions about how the
Speaker 1: universe is, and then we also ask the questions about
Speaker 1: why it is and what that means. Because we don't
Speaker 1: just want a description of the universe, we want an
Speaker 1: understanding of the universe. We want to know why the
Speaker 1: universe is this way and not any other way, or
Speaker 1: maybe if it could have been that other way. We
Speaker 1: seek not just to describe but also to explain, and
Speaker 1: that's what we're doing here, exploring the universe and explaining
Speaker 1: it to you. Yeah, because it is a big universe
Speaker 1: and one of which you can ask a lot of questions.
Speaker 1: Because it is not just kind of a big universe
Speaker 1: and a pretty mysterious universe, but it's also kind of
Speaker 1: a beautiful universe. It is, in fact a beautiful universe,
Speaker 1: not just in the vistas that we partake in in
Speaker 1: the wonderful night skies, but also in the mechanisms for
Speaker 1: how it works. Sometimes you look at the mathematics for
Speaker 1: the way things work at the quantum level and you're like, wow,
Speaker 1: that's pretty neat. I couldn't have designed the universe so
Speaker 1: beautiful or so clever. It does feel sometimes like we
Speaker 1: are uncovering a w of great beauty. Yeah, because the
Speaker 1: universe does seem to have rules, right, Like it's it's
Speaker 1: not a willy nearly universe where anything can happen. It
Speaker 1: seems to have rules and the structure to it. And
Speaker 1: as you say, it sort of feels clever in a
Speaker 1: way can you talk about that? Yeah, it's just maybe
Speaker 1: our appreciation is just sort of subjective. But one of
Speaker 1: the most incredible things we've discovered is that the universe
Speaker 1: can be described in terms of mathematical laws. Like why
Speaker 1: do we even think that it was possible to write
Speaker 1: down equations that predict what will happen in our universe
Speaker 1: and that only some equations will work, right, Like, it's
Speaker 1: sort of like you can't just write down any random
Speaker 1: equation and say that's physics. It's math, but it's not
Speaker 1: necessarily physics, the same way you can't just like write
Speaker 1: down a string of words and say here's my novel. Right,
Speaker 1: Not every string of words is a novel. So we
Speaker 1: use math as a language to express physics. But then
Speaker 1: you can also look at that math and say, wow,
Speaker 1: that really clicks together nicely, or this makes a lot
Speaker 1: of sense, or this tells you something about the nature
Speaker 1: the universe because it uses this math and not that
Speaker 1: other kind of math. And then you get into the
Speaker 1: lossopy questions like what does it mean that we have
Speaker 1: a universe that's like this and not like that? Right,
Speaker 1: that's pretty interesting. The idea that you know, like all
Speaker 1: physics is math, but not all math is physics, like
Speaker 1: not all possible equations have a physical reality to them. Absolutely,
Speaker 1: you can describe lots of hypothetical universes out there using mathematics,
Speaker 1: but they don't necessarily describe the universe we live in.
Speaker 1: And you know, there are lots of beautiful theories about
Speaker 1: physics that were mathematically really nice but just didn't describe
Speaker 1: our universe, and so they ended up like tossed in
Speaker 1: the dustbin of physics history. Man, you have a reject
Speaker 1: pile for beautiful theory. We do because the universe gets
Speaker 1: to say what the universe chooses, and sometimes it's a
Speaker 1: little surprising and a little bit messy, but often we
Speaker 1: can find some elegance, some nice description of it that
Speaker 1: reveals something about the universe. And then you go off
Speaker 1: and chew and you're like, that's really interesting that the
Speaker 1: universe has this structure. What does that mean about It's
Speaker 1: like fundamental nature. One of my favorite examples is very simple.
Speaker 1: It just comes from conservation shi of momentum, Like this
Speaker 1: is something we observe in the universe. We notice that
Speaker 1: if you bang two rocks together that at the end
Speaker 1: you have the same amount of momentum as you did
Speaker 1: in the beginning. It's changed direction a little bit, perhaps,
Speaker 1: but all the momentum is the same. It's something we
Speaker 1: observe and you can ask, like, well, why is that?
Speaker 1: Why is momentum conserved? And we have this deep theory
Speaker 1: of physics that tells us why, But it just brings
Speaker 1: up more questions. It turns out that momentum is conserved
Speaker 1: because space is uniform, because you can do the same
Speaker 1: experiment here and somewhere else and on Jupiter and you
Speaker 1: should get the same answer. One thing leads to the other,
Speaker 1: because space is uniform, momentum is conserved. But then that
Speaker 1: just brings up the question like, well, why is space uniform?
Speaker 1: Why is it true that you can do the same
Speaker 1: experiment here or an Alpha Centauri and you should get
Speaker 1: the same answers? Why the laws of physics the same
Speaker 1: everywhere in space? But that seems to be the way
Speaker 1: our universe is, and that's the way it is, and
Speaker 1: it's also sort of a good thing that it is, right,
Speaker 1: Like it would be weird or could you even have
Speaker 1: a functioning universe if things were at all smooth and
Speaker 1: working the same way everywhere, Like wouldn't it be just
Speaker 1: complete chaos. Well, that is the job of science fiction authors,
Speaker 1: right to imagine different universes and like, what would it
Speaker 1: be like to live in that universe? To be a
Speaker 1: scientist in that universe and discover that you lived in
Speaker 1: that universe instead of this one? What stories could you
Speaker 1: tell in that universe? So I think there are probably
Speaker 1: very different physical consequences of living in the universe like
Speaker 1: that where the laws of physics change with space or
Speaker 1: with time. But this is the one that we live in.
Speaker 1: I think you could imagine ways to live and waves
Speaker 1: life might even arise, but it would be vastly different
Speaker 1: from the universe that we know. Well, now you're giving
Speaker 1: me kind of fear of missing out. What if there's
Speaker 1: like a better part of the universe that we're not
Speaker 1: living in, Like what if the grass is really like
Speaker 1: greener on the other side of the galaxy? Yeah, well,
Speaker 1: you know, we haven't even discovered how green our grass is.
Speaker 1: There's so much we don't know about the universe, so
Speaker 1: much to discover, so many beautiful things that will be
Speaker 1: revealed in the future that will amaze you. So stick
Speaker 1: around in this universe. I recommend it. There's a lot
Speaker 1: of green grass left to cut. It's interesting you said
Speaker 1: that word earlier. Elegant. You know, I feel like I
Speaker 1: hear a lot of physicists say that words sometimes, that
Speaker 1: the universe feels really elegant in the way the rules
Speaker 1: and the laws work. And that's kind of we'll be
Speaker 1: talking about today. Is is one of these elegances of
Speaker 1: the universe. And what we're looking for to describe the
Speaker 1: universe is a simple description. You know, you could describe
Speaker 1: the universe. It's just like, here's a list of all
Speaker 1: the physics experiments anybody's ever done and the results. That's great,
Speaker 1: that describes the universe, but it doesn't give you any insight.
Speaker 1: It doesn't give you that like ah ha. That's because
Speaker 1: they're all following the same rule. And that's the job
Speaker 1: of physics is to boil down a bunch of experiments,
Speaker 1: a bunch of observations into a simple rule. And it's
Speaker 1: when you see that simple rule and you say, wow,
Speaker 1: it's incredible. That's something that's so simple can have all
Speaker 1: these consequences. That's when you feel like you're looking at
Speaker 1: some elegance. You're like understanding a deep truth about the
Speaker 1: nature of the universe. You've revealed something at a lower
Speaker 1: level than anybody has seen before. You've peeled back a
Speaker 1: layer of reality and seeing a simple description that leads
Speaker 1: to all the incredible complexity that we see in our universe.
Speaker 1: And I guess you know, one of the things that
Speaker 1: we feel is simple or a way to give things
Speaker 1: a certain sense of elegance, is this idea of symmetry.
Speaker 1: Like if something is symmetric somehow, as humans, it's instills
Speaker 1: in as a sense of like, oh, that looks perfect
Speaker 1: or that looks you know, elegant or beautiful. Yeah, and
Speaker 1: it also sort of feels democratic, Like to me, it's
Speaker 1: nice that the universe doesn't prefer any location in space
Speaker 1: and you can do your experiment here or somewhere else
Speaker 1: and it doesn't make a difference. And you know, there
Speaker 1: are real consequences to that symmetry. That symmetry means only
Speaker 1: certain laws of physics are allowed, like in that case,
Speaker 1: only laws of physics that conserve momentum are allowed. That
Speaker 1: comes directly from that symmetry, And we discovered lots of
Speaker 1: these kinds of symmetries. You know. Another one and that
Speaker 1: people are probably familiar with, is the fact that there's
Speaker 1: no up or down in space. Like you do your
Speaker 1: experiment in space, it doesn't really matter which direction your
Speaker 1: experimental apparatus is pointing. You can spin it in another
Speaker 1: direction and it should get the same result. That's another symmetry.
Speaker 1: It says the universe doesn't prefer a direction, not just
Speaker 1: a location, but a direction. And that gives you another rule.
Speaker 1: It says that all the laws of physics you right,
Speaker 1: have to also conserve angular momentum, which is separate from
Speaker 1: just momentum. Right, This is like how much something is spinning.
Speaker 1: So every time you discover a symmetry, something that where
Speaker 1: the universe doesn't care about something or gives you the
Speaker 1: same answer no matter how you spin or move something
Speaker 1: that tells you something about the laws of physics that
Speaker 1: are consistent with that symmetry, the laws of physics that
Speaker 1: can describe our universe. Yeah, so to be on the podcast,
Speaker 1: we'll be talking about what hidden symmetry controls the universe.
Speaker 1: Sounds like a dark conspiracy here, Daniel. There's something hidden
Speaker 1: controlling things. People smoking cigars, wearing gray suits and deciding
Speaker 1: what laws of physics can we have or where are
Speaker 1: you going for some click bait action here. I'm just
Speaker 1: trying to, you know, get a little bit of reflection
Speaker 1: from the X file glamour, that's all. Yeah, we should
Speaker 1: title it like the hidden dark Secret that controls the universe,
Speaker 1: like to find out more. But yeah, there seems to
Speaker 1: be a symmetry to the universe. And I feel like,
Speaker 1: you know, maybe physicists use this word differently than how
Speaker 1: most people understand it, because I think, you know, to
Speaker 1: most people's symmetry means like if something is symmetric, it
Speaker 1: means like it's the same if you look at it,
Speaker 1: you know, the right half and the left half is
Speaker 1: the same, or it's like the mirror image of something else,
Speaker 1: or there's some sort of reflection or some like equality
Speaker 1: between left and right or two directions. That's kind of
Speaker 1: I think that's what people mostly think about symmetry. But
Speaker 1: physicists think of symmetry. It's a kind of a different
Speaker 1: concept in physics, right, It's about how the mathematical equations
Speaker 1: stay the same no matter how you transform them. Yeah,
Speaker 1: but it's also closely related, I think, to people's intuitive
Speaker 1: sense of symmetry. Like think about the examples you mentioned
Speaker 1: the sphere for example, you know there's a rotational symmetry.
Speaker 1: There you have a perfect sphere, you rotate it, you
Speaker 1: get the same sphere, right, and so nothing has changed
Speaker 1: for the sphere. It's the same. Or even if you
Speaker 1: reflect it through a mirror down its middle, you get
Speaker 1: the same sphere. So there are symmetries in the sphere
Speaker 1: that wouldn't change how you interact with the sphere. And
Speaker 1: we talk about the same things in physics. We say, look,
Speaker 1: if you do this experiment and you just rotate your axes,
Speaker 1: you make X into Y and Y and z or whatever,
Speaker 1: you should get the same answer. You know, it's like
Speaker 1: a spin the experiment or spin the universe. It doesn't matter.
Speaker 1: You should get the same answer. And so fundamentally, when
Speaker 1: we talk about symmetry, we mean do you get the
Speaker 1: same laws of physics if you apply some transformation or
Speaker 1: some rotation or some change to your axes or how
Speaker 1: you've defined things. And so that's what we mean when
Speaker 1: we talk about symmetry right right like like like a
Speaker 1: butterfly is symmetric, right like the left side and the
Speaker 1: right side is symmetric. But you can also think of
Speaker 1: it as like the left wing if I put it
Speaker 1: through a mirror, it will look just like the right wing. Yeah,
Speaker 1: you know maybe actually I don't even know. Are all
Speaker 1: butterflies exactly symmetric? Probably they're not exactly, but in our cartoon, right,
Speaker 1: assume a symmetric butterfly. Then in that case, yeah, you
Speaker 1: put it up to a mirror and you see the
Speaker 1: exactly the same other half, right, and at least it
Speaker 1: look the same or similar. And so this symmetry idea
Speaker 1: is very important physics because it almost, like I don't know,
Speaker 1: defines the laws of physics at the fundamental level, or
Speaker 1: it's something that's important for them to work, right. Yeah, Well,
Speaker 1: what happens is that we notice the universe following certain rules.
Speaker 1: You know, for example, we notice that the universe doesn't
Speaker 1: create or destroy electric charge, like you have a bunch
Speaker 1: of it, It doesn't go away, you can't destroy it,
Speaker 1: and you can't make anymore. Right, And so that's like
Speaker 1: a rule the universe seems to be following. And then
Speaker 1: we ask questions like, well, what symmetry gives you that rule?
Speaker 1: Why can't you create or destroy electric charge? What rule
Speaker 1: is it fundamentally following? And what we discovered or what
Speaker 1: eman author discovered about a hundred years ago. Is that
Speaker 1: every time you see the universe following a rule is
Speaker 1: because there's a basic symmetry. There's something about the universe
Speaker 1: that's preserved that has this kind of symmetric property where
Speaker 1: it doesn't depend on how you been it or reflected
Speaker 1: or whatever. And that's where these conservation laws come from.
Speaker 1: So that's very, very powerful. Every time you see a
Speaker 1: conservation it means you can discover a symmetry of the universe,
Speaker 1: which tells you something pretty basic about like the very
Speaker 1: structure of reality, all right, and even the reality in
Speaker 1: the mirror as well. We'll get into that, but I
Speaker 1: guess more specifically, it has something to do with something
Speaker 1: called gauge symmetry, right, g A U G E symmetry. Yeah,
Speaker 1: all of our laws of physics in the Standard Model
Speaker 1: are built on this principle of gauge symmetry, and we'll
Speaker 1: dig into exactly what that means on today's episode. But
Speaker 1: it turns out to be something really deep about the
Speaker 1: way particles operate and their relationships with each other. All right,
Speaker 1: we'll take a dive into that symmetry. But first we
Speaker 1: were wondering how many people out there no or have
Speaker 1: heard of this concept of gauge symmetry. So Daniel went
Speaker 1: out there into the internet to ask people what is
Speaker 1: gauge symmetry? And so, if you are interested in answering
Speaker 1: really hard questions about secrets of the universe with no
Speaker 1: chance to prepare at all, and then have the thousands
Speaker 1: of people here your answers, please write to us two
Speaker 1: questions at Daniel and Jorge dot com. It's a lot
Speaker 1: more fun than it sounds. Think about it for a second.
Speaker 1: Do you know what gage symmetry is? Here's what people
Speaker 1: have to say. Gage symmetry is how one would gauge
Speaker 1: the symmetry between a binary set of stars. And obviously
Speaker 1: that's incorrect, but there you go. I am not sure
Speaker 1: what gauge symmetry is, but perhaps it was a very
Speaker 1: smart scientist person that explain some kind of symmetry in
Speaker 1: the universe or in physics. Gage symmetry it has something
Speaker 1: to do with electricity or charges. It doesn't matter what
Speaker 1: direction in a circuit, or in what direction you look
Speaker 1: at particles or whatever, like the charters are symmetrical in
Speaker 1: It doesn't matter if there's a pleasure of minus. From
Speaker 1: my point of view, gage symmetry. Well, it happened to me,
Speaker 1: was I when my instrument cluster from my truck broke
Speaker 1: down and all the gorges were at zero, so they
Speaker 1: were symmetric. So this is gage symmetry from my point
Speaker 1: of view. Let's break it down. Gauge symmetry is when
Speaker 1: you make a transformation on a field which turns one
Speaker 1: particle into a different one, maintaining, obviously, because it's symmetric,
Speaker 1: maintaining some properties of that particle. I think, if I
Speaker 1: recall correctly, gauge is basically measurements, So gauge symmetry might
Speaker 1: be that one measurement in one unit basically described in
Speaker 1: a different unit. Possibly. Well, I guess the gauge symmetry
Speaker 1: is when my front tire and my rear tire of
Speaker 1: my bicycle show the same amount of pressure. Then I
Speaker 1: would have two gauges and they are symmetric. Otherwise I
Speaker 1: have no idea. All right, it's it seems to be
Speaker 1: um kind of a mystery to our listeners. The secret
Speaker 1: Cabal has done a good job of hiding itself. It's
Speaker 1: really hidden. Well, I guess it's a weird word because
Speaker 1: we in general we use the word gauge to like
Speaker 1: gauge something right, to like measure something like a pressure
Speaker 1: gauge is something that tells you how much pressure is
Speaker 1: in your bicycle tires, or your fuel gauge tells you
Speaker 1: how much fuel you have in your car. And so
Speaker 1: what does it mean then to have gauge symmetry in
Speaker 1: your equations of physics? So it comes from the era
Speaker 1: of the railroads, when people were still laying down a
Speaker 1: bunch of new tracks and they have to decide, like
Speaker 1: how far apart you make the tracks? Do you make
Speaker 1: them one meter apart or a meter and a half
Speaker 1: or whatever, And everybody had like different choices, and that
Speaker 1: makes them incompatible. Right, you can't drive your train if
Speaker 1: the gauge is wrong, and so somebody just has to
Speaker 1: make a choice, and that doesn't really matter. You can
Speaker 1: still build railroads if there are a meter apart or
Speaker 1: half a meter apart or or whatever. It still works.
Speaker 1: You just gotta make a choice, And so that arises
Speaker 1: sometimes in physics where there's like an arbitrary choice you
Speaker 1: have to make, like where do you call height equal
Speaker 1: zero or where do you call electrical potential equal zero?
Speaker 1: And it shouldn't affect how your physics works. It doesn't
Speaker 1: change anything for how your experiments should work, but you
Speaker 1: do have to make a choice. It's almost like a
Speaker 1: scale maybe, or like a starting point. Is that what
Speaker 1: you mean? Like, you know, like a scale, like is
Speaker 1: this railroad track, you know, this wide or is it narrower.
Speaker 1: It's sort of that way in physics where you have
Speaker 1: to say, all right, what scale are we talking about
Speaker 1: when we're talking about these electrical fields? Yeah, and you
Speaker 1: just like you need a number, and so you have
Speaker 1: to pick a starting point. That's a good way to
Speaker 1: think about it. But it doesn't affect anything, right, It's
Speaker 1: just like it seems like an arbitrary choice, you know.
Speaker 1: One simple example is like think about a book falling
Speaker 1: off of a shelf and wondering like, well, how fast
Speaker 1: is it going when it hits the floor? Well, the
Speaker 1: answer to that question depends on the height of the shelf,
Speaker 1: because the taller the shelf, the faster it is when
Speaker 1: it's hitting the floor, and the shorter the shelf, the
Speaker 1: slower it is when it hits the floor. But it
Speaker 1: doesn't depend, you know, mostly on how high your shelf
Speaker 1: is above sea level. You know, so like where do
Speaker 1: you call high equal zero. Do you say high equal
Speaker 1: zero a thousand meters below my floor or at my
Speaker 1: floor or above my floor. You can do all the calculations,
Speaker 1: you get the same answer no matter where you put
Speaker 1: like height equal zero in your physics problem. That's just
Speaker 1: an arbitrary choice, doesn't affect your answer. So that's an
Speaker 1: example of you know, making a gauge choice. And so
Speaker 1: this word gauge was chosen to sort of like, you know,
Speaker 1: harken back to the age of the railroads. But really
Speaker 1: what it means is an arbitrary parameter of your theory.
Speaker 1: I see you're saying, physicists pick the word that had
Speaker 1: nothing to do with the thing. But where the rest
Speaker 1: of the population is that what you're saying your ancestors
Speaker 1: should have been called on a hundred years ago when
Speaker 1: they were naming this thing. I totally agree. It's a
Speaker 1: ridiculous word, and it's become so important, so we say
Speaker 1: it all the time now. Gauge theory is everything. The
Speaker 1: whole standard model of physics is a gauge theory. It's
Speaker 1: almost like the theory only tells you changes or how
Speaker 1: it changes from a starting point. Is that kind of
Speaker 1: what you're saying, But the answer it kind of depends
Speaker 1: on where you start, right, and it has a you
Speaker 1: know a lot of history, like electromagnetism, which you know
Speaker 1: predates the standard model in particle physics by a long time.
Speaker 1: You know. Maxwell noticed this in his equations. When he
Speaker 1: was putting together his equations of electromagnetism, he noticed that
Speaker 1: you could change these. You could like add an arbitrary number,
Speaker 1: not exactly just a number has to have like a
Speaker 1: disappearing curl to it. But you could add something to
Speaker 1: the theory and it wouldn't change any of the predictions.
Speaker 1: And so you can have basically like different sets of
Speaker 1: Maxwell's equations, and they call these different gauges, like the
Speaker 1: Coolum gauge or the Lorenz gauge. People chose different sets
Speaker 1: of equations. They all make exactly the same predictions. You
Speaker 1: just like pick one. There's like a whole family of
Speaker 1: these equations and they all make exactly the same predictions.
Speaker 1: You can use any of them as long as you're consistent.
Speaker 1: They're almost like floating theories. I guess you might say, right,
Speaker 1: And so then there's the idea that within these theories
Speaker 1: you can have a certain symmetry to them. And so
Speaker 1: that's what gauge symmetry is. And so let's get into
Speaker 1: why it's important for our equations of the universe and
Speaker 1: what does it all mean. Man, But first let's take
Speaker 1: a quick break. All right, we're talking about the hidden
Speaker 1: conspiracy here that's controlling everything, Daniel. This is one of
Speaker 1: those podcasts. That's right. We are bringing you the hard
Speaker 1: truth today, folks. We are tearing off the veil. We
Speaker 1: are revealing who's really behind everything. That's right. That's why
Speaker 1: this podcast is encrypted. Right, we're encrypting this. We're not
Speaker 1: putting our names on the title of the podcast either, right,
Speaker 1: that's right. But we are doxing the true masters of
Speaker 1: the universe today. There you go. That's another title for physicists.
Speaker 1: You're boxing the universe, you're exposing it. We are exactly
Speaker 1: we are, all right. So we talked about what gauge
Speaker 1: theory is. It's like a theory that sort of floats
Speaker 1: that it tells you how things change, but it sort
Speaker 1: of depends on where you start them. And so that's
Speaker 1: kind of what a gage theory is. And so then
Speaker 1: what's gauge symmetry. So gage symmetry is when you have
Speaker 1: a theory that has a gauge in it, right, So
Speaker 1: you can make this choice, but it makes the same
Speaker 1: prediction regardless of your choice. So, as we talked about electromagnetism,
Speaker 1: it doesn't matter if you use the Coolum gauge or
Speaker 1: the Lorenz gauge. You write down different equations, but they
Speaker 1: predict exactly the same behavior of like electrons moving through
Speaker 1: fields or magnets being generated. It doesn't matter. So there's
Speaker 1: a gauge symmetry there. You can pick your gauge, but
Speaker 1: it doesn't affect the physical predictions. I see. But then
Speaker 1: how did the name symmetry come from? Because it's not
Speaker 1: you know, like maybe I would have said it's gauge
Speaker 1: invariant or gauge doesn't care less about gauge. But the
Speaker 1: words and metrics to me sort of means like a
Speaker 1: reflection or like a mirror image. Yeah. Well, you can
Speaker 1: transform from one gauge to another without changing your predictions,
Speaker 1: just like you can rotate a sphere through an arbitrary
Speaker 1: angle without changing the sphere. It's still a sphere. And
Speaker 1: so a gauge theory is one that you can transform
Speaker 1: in a certain way from one gauge to another without
Speaker 1: changing your predictions. And we'll talk about various gauge symmetries today.
Speaker 1: Some of them are a lot like rotations of a sphere.
Speaker 1: All right, are we saying that the laws of physics
Speaker 1: with the universe are gauge symmetric or we noticed that
Speaker 1: they were gauge symmetric. Yeah, it's really fascinating. The laws
Speaker 1: of physics of the universe have really weird and surprising
Speaker 1: gauge symmetries, much more than you would expect, and they
Speaker 1: have real consequences, Like we talked about, every time there's
Speaker 1: a symmetry the universe that leads to a conservation law.
Speaker 1: And so what we can do is we can say, oh,
Speaker 1: maybe this is why we have conservation of electric charge
Speaker 1: or conservation to other things. It's because there are these
Speaker 1: symmetries in the universe. And then we can ask the
Speaker 1: deep questions like, well, why does the universe have that
Speaker 1: weird gauge symmetry? What does that mean? This is not
Speaker 1: just like an arbitrary thing we write down in our
Speaker 1: rooms with pencil and paper. It's something deep about the
Speaker 1: universe that respects this symmetry, meaning like if you work
Speaker 1: at the equations of the universe. You noticed that they're
Speaker 1: gauge symmetric, and because of those symmetries, then things like
Speaker 1: conservation a momentum happen, yes, exactly, and so you know,
Speaker 1: we notice that those things definitely happen in our universe,
Speaker 1: and we discovered that that means that there must be
Speaker 1: these symmetries, which is really interesting. All right, well, maybe
Speaker 1: talk to us a little bit about why it's important
Speaker 1: and how it has to do with quantum mechanics. Yes,
Speaker 1: so the standard model of particle physics and quantum mechanics
Speaker 1: has a lot of gauge symmetries in it, and one
Speaker 1: that comes from quantum mechanics comes from the wave function.
Speaker 1: Like we talked to this program before about what happens
Speaker 1: to little particles and experiments, like what determines whether an
Speaker 1: electron is going to go left or we're going to
Speaker 1: go right when it interacts with something else. That's determined
Speaker 1: by the wave function, which tells it like the various
Speaker 1: probability to go here or the probability to go there.
Speaker 1: But there's a little step there which we've glossed over,
Speaker 1: but it's actually really really important. It's not the wave
Speaker 1: function itself that tells an electron whether it has a
Speaker 1: probability to go left or to go right. It's the
Speaker 1: square of the wave function, the wave function square the
Speaker 1: way function multiplied by itself, that determines the probability to
Speaker 1: go left or to go right. And that's because the
Speaker 1: wave function itself is a complex number, you know, like
Speaker 1: one plus i or two minus i or whatever, and
Speaker 1: so it doesn't have real values, so you have to
Speaker 1: square it to get real values. And there's a symmetry
Speaker 1: there because it means that the wave function or minus
Speaker 1: the wave function give exactly the same predictions. So you're saying,
Speaker 1: like at the fundamental level of particle physics, like particles
Speaker 1: that make up our universe, they're symmetric, like starting from that,
Speaker 1: because the wave function that describes it is symmetric in
Speaker 1: itself in terms of it the probability though right, like
Speaker 1: the original wave function is not symmetric, but if you
Speaker 1: square it to get the probability, then it is symmetrica
Speaker 1: if you take every wave function and you multiply it
Speaker 1: by minus one, it doesn't change anything in the laws
Speaker 1: of physics. That's what we're saying. So take the whole
Speaker 1: universe's wave function, or if you don't believe in that,
Speaker 1: take the wave function of all the particles, multiple by
Speaker 1: all of them by the same number. Nothing changes, right,
Speaker 1: The laws of physics predict exactly the same outcomes. It
Speaker 1: doesn't matter because it's only sensitive to wave functions squared.
Speaker 1: So you have a freedom there a choice. Do we
Speaker 1: start with the positive way functions or do we start
Speaker 1: with the negative wave functions. It doesn't matter. So there's
Speaker 1: a symmetry. Really it doesn't matter, like, won't effect at
Speaker 1: all what it comes out. It won't affect at all
Speaker 1: because you take it and you square it. All physical
Speaker 1: predictions depend only on the wave functions squared. All right,
Speaker 1: So then that means that all particles in the universe
Speaker 1: are a symmetric What does that mean. It's actually a
Speaker 1: little bit more general than just multiplying it by minus one.
Speaker 1: You can actually multiply it by a rotation in the
Speaker 1: complex plane. And I don't think we should get too
Speaker 1: far into the math, but just think about it, like,
Speaker 1: you can rotate these things by an arbitrary angle and
Speaker 1: you still get the same number. And so that makes
Speaker 1: a lot of sense if you just do it. To everything.
Speaker 1: Like you multiply the whole universe by minus one, nothing
Speaker 1: changes because you've been consistent. You change the way function
Speaker 1: of my electrons and your electrons and somebody else's electrons.
Speaker 1: That's called a global symmetry affect the whole universe, And
Speaker 1: that's not so surprising. But there's something else so the
Speaker 1: universe has, which is a very different and much much
Speaker 1: deeper symmetry. It turns out that the universe is symmetric
Speaker 1: to local gauge invariance, which means you can make this
Speaker 1: kind of transformation differently at every point in space. You
Speaker 1: can say like here, I'm gonna multiply all my way
Speaker 1: functions by plus one. Over in Jupiter, I'm gonna multiply
Speaker 1: my minus one and an alpha centauri, I'm gonna do
Speaker 1: something different. So that's a local gauge invariance that says
Speaker 1: that you can have like an infinite number of these
Speaker 1: different ideas about gauges. Wait, what what do you mean?
Speaker 1: But you just told me that it's globally invariant, like
Speaker 1: it doesn't matter what you do to it anywhere, But
Speaker 1: now you're saying that it does matter what you do
Speaker 1: to it locally. Yeah, so global gauge invariance the universe
Speaker 1: definitely has. But if you want local gauge invariance, right,
Speaker 1: that's harder. That says, well, now I want to be
Speaker 1: able to multiply my wave functions by plus one or
Speaker 1: minus one and do it differently everywhere. And you might
Speaker 1: immediately say like, okay, well that obviously doesn't work right
Speaker 1: because you have to be consistent otherwise they like the
Speaker 1: interference terms of the way functions are not going to
Speaker 1: come out right. And you're right. The universe by itself,
Speaker 1: for an electron, doesn't have local gauge invariance because if
Speaker 1: you change the gauge here and you change it somewhere else,
Speaker 1: then it will affect the predictions. So the universe, if
Speaker 1: all you have in it, our electrons, doesn't have local
Speaker 1: gauge invariants. And then if played a fun game, they said, well,
Speaker 1: what if we added something What if we added something
Speaker 1: else to the universe so that we did have local
Speaker 1: gauge invariance, something that like corrected for that. So take
Speaker 1: the universe that just has electrons in it and ask
Speaker 1: for local gauge invariants, and you break that right, like immediately,
Speaker 1: you don't have local gauge invariants because you're changing electrons
Speaker 1: differently everywhere. Well, now, if you like add something to
Speaker 1: the universe to try to fix it, to compensate for
Speaker 1: this change you've made, you have to add a new piece.
Speaker 1: And that new piece, if you look at the mathematics
Speaker 1: of it, is exactly the electromagnetic field. I think you
Speaker 1: lost me a little while, to be honest, So I
Speaker 1: guess it's difference between local and global. Is it like
Speaker 1: kind of like if I let go of my book
Speaker 1: on a from a three story building, it's not I
Speaker 1: won't get the same velocity at the bottom as if
Speaker 1: I drop it from a one story building. Is that
Speaker 1: kind of what do you mean? Yes? Or let's say
Speaker 1: you want to define your altitude differently based on where
Speaker 1: you are in the world, Like currently we have a
Speaker 1: single global definition of altitude relative to sea level. But
Speaker 1: what if you wanted to choose your height definition to
Speaker 1: be different if you're here or if you're over there,
Speaker 1: if you're an Irvine or Pasadena or New York. All
Speaker 1: of a sudden, you know, as you move across the country,
Speaker 1: your height would be changing constantly, like oh, I'm higher,
Speaker 1: I'm lower I'm higher, I'm lower. It wouldn't make any sense.
Speaker 1: You'd get crazy physical predictions, like the book would still
Speaker 1: fall the same way, wouldn't it. The book would still
Speaker 1: fall the same way, and so your theory wouldn't work.
Speaker 1: If you'd like to throw a ball as a parable,
Speaker 1: and it's moving across the ground and you're constantly changing
Speaker 1: like the definition of height, then you're not going to
Speaker 1: get sensible predictions. Right. The ball obviously does move smoothly,
Speaker 1: and so your physical theory doesn't work anymore if your
Speaker 1: definition of height is changing as the ball is moving.
Speaker 1: Is it, like, you know, my equation, my prediction one word,
Speaker 1: if I use meters in England or if I use
Speaker 1: feet here in the US, Like that's what you mean?
Speaker 1: Like you want a theory to be different about whether
Speaker 1: you use feed or meters. Yeah, and so global invariance
Speaker 1: is like, well, let's just use meters everywhere that makes sense,
Speaker 1: or let's use feed everywhere, but let's be consistent. Local
Speaker 1: invariance is like, no, I want to get to pick
Speaker 1: my units differently everywhere, and so that's a much higher standard,
Speaker 1: like to have the laws of physics that allow you
Speaker 1: to have that much freedom to make any choice at
Speaker 1: any point in the universe is a much higher standard, oh, right,
Speaker 1: because I guess it would have to be like irrelevant,
Speaker 1: right almost exactly. It's like it doesn't matter if you
Speaker 1: weigh something in England or in the US, whether you
Speaker 1: use meters, because meters doesn't figure into it. That's kind
Speaker 1: of what you want, right exactly, all right, So you're
Speaker 1: saying that we the universe doesn't seem to have that
Speaker 1: local gauge invariance, meaning it doesn't matter if you use
Speaker 1: meters or feed but you're saying, there's a way to
Speaker 1: get that back. There is a way to get that back.
Speaker 1: You can say, what would the universe have to look
Speaker 1: like to have local gage invariants? Like take your electron
Speaker 1: is flying through space, and what if you want to
Speaker 1: be able to like multiply it's a wave functioned by
Speaker 1: an arbitrary number at a different point in space, and
Speaker 1: how that number be different everywhere in space? Is there
Speaker 1: a way to do that? Is there a universe you
Speaker 1: could construct that would follow that, that would respect your
Speaker 1: local gauge invariance that would allow you to have that
Speaker 1: much freedom. And it turns out there is if you
Speaker 1: add a photon. So if you have just electrons in
Speaker 1: the universe, no local gauge invariance. But if you add
Speaker 1: an electromagnetic field, which gives you photons, boom, you get
Speaker 1: local gauge invariants for free. Well what wait, okay, so
Speaker 1: somehow the fix for this solution, but for all equations,
Speaker 1: for just some particles, you're saying, the solution to making
Speaker 1: things be meter or feet independent is to add the
Speaker 1: magnetic electromagnetic field. Yes, the electromagnetic field is the thing
Speaker 1: that can perfectly compensate and give you local gauge invariants
Speaker 1: like you can derive it. You can say, here's the
Speaker 1: wave function for the electron. I'm going to add an
Speaker 1: arbitrary phase to it, which is multiplying it by an
Speaker 1: arbitrary number. And you can say, well, now my predictions
Speaker 1: are wrong, they're different. What would I need to add
Speaker 1: to my equations to compensate for that to cancel out?
Speaker 1: This bologna that I've added and once you need to
Speaker 1: add has exactly the same mathematical structure as the electromagnetic field.
Speaker 1: It is the electromagnetic field. So the presence of the
Speaker 1: electromagnetic field is what preserves local gauge invariance. For it's
Speaker 1: you're saying, the electromagnetic field preserved symmetry for the electron
Speaker 1: or for like everything in the entire universe for the
Speaker 1: electrons wave function. Yes, so we're talking just about the
Speaker 1: electron and its way function. It is feet and meter independent.
Speaker 1: But if you had the electromatic field, then it is independent. Oh,
Speaker 1: I guess the electron has its own field to the
Speaker 1: electron has its own field. Yeah, there's the electron field.
Speaker 1: And now we're saying that if we want this local
Speaker 1: gauge invariance where we can multiply arbitrary numbers to the
Speaker 1: electron field, that can't happen unless you have this exact,
Speaker 1: very specific requirement of another field that hangs out and
Speaker 1: basically compensates for that and takes care of that for you.
Speaker 1: And it turns out that that field is the electromagnetic field,
Speaker 1: and photons basically exist in order to preserve local gauge invariants.
Speaker 1: What you're saying that the only reason we have light
Speaker 1: is to make electrons happy. Well, here's the philosophy, right, Like,
Speaker 1: do we have light because the universe preserves local gauge invariants?
Speaker 1: And that's the only law of physics that allows that
Speaker 1: one that has photons. Or do we have photons because
Speaker 1: we have local gauge invariants? Right? Like which direction does
Speaker 1: it go? Uh? You know is a fun philosophy question.
Speaker 1: But what we do know is that we have photons,
Speaker 1: we have electrons, and we have the electromagnetic field. Both
Speaker 1: of those two things, and together they seem to have
Speaker 1: this amazing, weird property of local gauge invariance where you
Speaker 1: can multiply up an arbitrary number and that number can
Speaker 1: be different at different points in the universe and it
Speaker 1: doesn't change the predictions. These two fields work to gather
Speaker 1: in this really crazy and interesting way. That's interesting, but
Speaker 1: it only applies to the electron. Like what about quarts, right,
Speaker 1: quarks have a field, I think, and we can ask
Speaker 1: the same questions like is the cork also locally symmetric?
Speaker 1: You know, meat and feed independent here in the US
Speaker 1: And is there's a separate field then that also fixes
Speaker 1: that symmetry. Fascinating question. You're absolutely right. This applies to
Speaker 1: the electron. It also applies to any particle that has
Speaker 1: electric charge. So for example, the muan has this same property.
Speaker 1: The muan, you can multiply by an arbitrary number, and
Speaker 1: you also get local gauge invariants because the muan is charged,
Speaker 1: and it also communicates with the photon field. And yes,
Speaker 1: corks have electric charge, so they do the same thing.
Speaker 1: In fact, turns out that's what it means to have
Speaker 1: electric charge. Electric charge means you couple to the photon field.
Speaker 1: Because electric charge just means you feel electric fields. You're
Speaker 1: like influenced by electromagnetic fields, which is the field of
Speaker 1: the photon. And so the reason we have electricity and magnetism,
Speaker 1: the reason we have electric charge is because these particles
Speaker 1: have this property. A really fascinating thing is we didn't
Speaker 1: know necessarily, like do muans feel the same photon as electrons,
Speaker 1: Like it could have been there's a different feel to
Speaker 1: preserve the muans local gauge invariants and the electrons. But
Speaker 1: of course we know there's a single photon, the same
Speaker 1: photon that an electronomists can be absorbed by a muan.
Speaker 1: But it didn't have to be that way. You could
Speaker 1: have lived in the universe with like electron photon and
Speaker 1: a muan photon and a towel photon and lots of
Speaker 1: different kinds of photons in it. All right, So then
Speaker 1: it seems like the electromagnetic field is this thing that
Speaker 1: preserves the symmetry for all particles that feel the electric charge,
Speaker 1: and so that's what makes the equations for all these
Speaker 1: particles symmetric. And that's beautiful and maybe even clever. All right,
Speaker 1: let's get into what it all means for the universe
Speaker 1: and our understanding of it. But first let's take another
Speaker 1: quick break. All right, we're going deep here today, Daniel.
Speaker 1: I feel I feel like you really thrown us down
Speaker 1: a rabbit hole here, Like what is the nature of
Speaker 1: the electric magnetic field? Like does it exists only to
Speaker 1: give symmetry to these particles? Or do particles have the
Speaker 1: symmetry because of the electromagnetic field. It's a big philosophical question. Yeah. Well,
Speaker 1: you know, I'm responding to your challenge. You remember when
Speaker 1: we were talking about the weak force and does it
Speaker 1: push or pull? And I said, well, one day we're
Speaker 1: gonna have to go deep and talk about gauge symmetry,
Speaker 1: and you said, bring it on. I got time. So here.
Speaker 1: I don't think you can prove that, I said that,
Speaker 1: can you? We didn't record it. I think we do
Speaker 1: have a recording I was just listening to yesterday. I
Speaker 1: might officially regret it right now. No, but this is
Speaker 1: pretty interesting, all right. So it seems like the universe
Speaker 1: likes this symmetry, this local symmetry likes uh, and to
Speaker 1: do that, it has this field electro magnetic field, and
Speaker 1: that's kind of how the universe works. And thank goodness, right,
Speaker 1: because that's how we get liked. Yeah, that to why
Speaker 1: the universe is literally so brilliant. Don't don't nice. It's
Speaker 1: a nice light light joke. But I guess what does
Speaker 1: it mean, Daniel, I'm not sure what it means. You know,
Speaker 1: we live in this universe that has photons in it,
Speaker 1: and that means that we live in a universe that
Speaker 1: respects local gauge invariance. Like why does our universe respect
Speaker 1: this super weird, very specific, difficult symmetry. You know, why
Speaker 1: can you multiply wave functions by any number and it
Speaker 1: have that be a different number at every place in
Speaker 1: the universe and still it doesn't matter. Like it's fascinating.
Speaker 1: I don't know what that means about the universe, but
Speaker 1: it means that local gauge in variance is deeply deeply
Speaker 1: built into the very structure of reality. So I think
Speaker 1: we need like another hundred years of philosophers smoking banana
Speaker 1: peels thinking about why that is to tell us, like,
Speaker 1: you know, why reality is this way and not some
Speaker 1: other way, but it also has very physical consequences for
Speaker 1: the nature of reality. Well, I guess the question, maybe
Speaker 1: before we get into too deep into that, is does
Speaker 1: this also apply to particles that don't feel the electromagnetic force? Like,
Speaker 1: aren't there particles that don't feel the photons and things
Speaker 1: like that, right? Do they have their own field that
Speaker 1: also preserves that symmetry. They do not. Neutrinos, for example,
Speaker 1: do not have this symmetry. And neutrinos do not have
Speaker 1: electric charge and do not interact with the electromagnetic field
Speaker 1: and do not talk to photons. And if neutrinos did
Speaker 1: have this symmetry, they would have electric charge. And that's
Speaker 1: sort of what it means to have electric charges, that
Speaker 1: you have this symmetry, and then there's a field out
Speaker 1: there that like compensates for it. And so no, neutrinos
Speaker 1: do not have this symmetry. You can't do the same
Speaker 1: thing to neutrinos. They have another weird different symmetry, which
Speaker 1: is why they feel the weak force, and quarks have
Speaker 1: multiple symmetries, which is why they feel the strong force also,
Speaker 1: but we can talk about that in a minute. It's
Speaker 1: almost like you're saying that the forces in the universe are,
Speaker 1: you know, there to maintain this symmetry in the universe exactly.
Speaker 1: And that's why we call the photon a gauge boson,
Speaker 1: and we call these things gauge fields and gauge forces.
Speaker 1: Bec as it seems like the forces either they exist
Speaker 1: in order to do this, or they exist because of this,
Speaker 1: or this is the only way to have a universe
Speaker 1: because of this symmetry. But every force exists in order
Speaker 1: to preserve some local gauge invariance for the particles. It's
Speaker 1: almost like they're forcing the universe. You know, I made
Speaker 1: that same joke in that other podcast episode, and you
Speaker 1: said I kind of forced it. Well, I'm trying to
Speaker 1: be symmetric. You know, I'm copying the same joke, but
Speaker 1: I'm doing it on the other side. You're forced feeding
Speaker 1: me my own puns back to me being clever, right, Yeah,
Speaker 1: And the nature of that field is really fascinating, Like,
Speaker 1: for example, because we have this local gauge invariance and
Speaker 1: you have these photons. That's why we have charge conservation.
Speaker 1: Remember how we talked about how every symmetry the universe
Speaker 1: leads to a conservation of something that's Nothers theorem. So
Speaker 1: the fact that you can serve this property of electrons
Speaker 1: is why you cannot create or destroy electric charge. How
Speaker 1: does preserving symmetry lead to these conservation laws which seemed important? Right, Yeah, Well,
Speaker 1: we're gonna have a whole episode about Nurther's theorem to
Speaker 1: get into like the intuition behind it all. Right, now,
Speaker 1: all you need to know is that every time you
Speaker 1: identify a symmetry of the laws of physics, that directly
Speaker 1: tells you that there's something that's conserved. Just like the
Speaker 1: symmetry of moving your experiments somewhere else leads to conservation
Speaker 1: of momentum, and the symmetry of rotating your experiment leads
Speaker 1: to conservation of angular momentum. Well, the symmetry of rotating
Speaker 1: your electron from plus wave function to minus wave function
Speaker 1: leads to conservation of charge. I mean it's the same
Speaker 1: concept for the other forces, right, strong and the weak force.
Speaker 1: It's the same concept for the other forces, but it's
Speaker 1: a different symmetry, and in those cases it's a much
Speaker 1: more complicated symmetry. So, for example, the strong force has
Speaker 1: not just like plus and minus charge, right it has
Speaker 1: three different kinds of charge, red, green, and blue, and
Speaker 1: it actually follows a much more complicated local gauge invariant.
Speaker 1: It turns out, for the strong force, you cannot just
Speaker 1: multiply the way function by minus one. You can rotate
Speaker 1: the color space, like take red and map into green,
Speaker 1: and green and map itto blue and blue and map
Speaker 1: it back to red. Okay, you can do this kind
Speaker 1: of rotation, and you can have a different rotation at
Speaker 1: every place in space, like green here is blue. There
Speaker 1: is half red plus half green over here, And you
Speaker 1: can do that and it's fine, and it will not
Speaker 1: change the nature of your predictions for how the strong
Speaker 1: force works, because you have a bunch of gluon fields
Speaker 1: that exist to compensate for that, to sort of correct
Speaker 1: for that. You're saying, like, like these symmetries, it's almost
Speaker 1: like a three way symmetry, right, Like it's not just
Speaker 1: like a mirror, but it's like a house of mirrors
Speaker 1: kind of, yeah, exactly, and just like the sphere. Right,
Speaker 1: the sphere is a much more complicated symmetry than just
Speaker 1: like reflection. You can rotate the sphere, and you can
Speaker 1: rotate it in different ways. You can rotate it about
Speaker 1: its equator, or about its poll or about some other directions.
Speaker 1: There's actually three fundamental symmetries of the sphere. The same
Speaker 1: thing is true for color space for the strong force.
Speaker 1: And that's why we have eight gluons. Because the strong
Speaker 1: force is a much more complicated local gauge invariance. It
Speaker 1: requires more fields. Are actually eight different gluon fields required
Speaker 1: just to preserve this force and so, but it's described
Speaker 1: by the same fundamental mathematics. And this is why. If
Speaker 1: you've heard that group theory is important for particle physics,
Speaker 1: this is why, because group theory describes exactly how these
Speaker 1: rotations work and sort of like the set of different
Speaker 1: rotations that you can have. And so the reason the
Speaker 1: strong force exists is because quarks have this weird property
Speaker 1: that you can rotate their color in an arbitrary way
Speaker 1: a different points in space, and the gluon fields are
Speaker 1: there to compensate. That's why they exist. So then I
Speaker 1: guess do physicists c force as something totally different than
Speaker 1: most people think about it. You know, when I think
Speaker 1: of a force, it's like pushing and pulling, or as
Speaker 1: they usually describe it, it's like, you know, an electron
Speaker 1: throws a photon to another electron, and that you know,
Speaker 1: the throwing of the photon and the receiving of the
Speaker 1: photo on is a way to kind of exchange you know,
Speaker 1: a push or a pool or energy. But now it
Speaker 1: seems like these fields are just there to preserve some
Speaker 1: kind of symmetry. Is that kind of why you see
Speaker 1: forces differently? Yeah, and that's that moment of elegance I
Speaker 1: was talking about, Like we start very simply in the world,
Speaker 1: seeing the world around us and categorizing and listing our observations. Oh,
Speaker 1: that apple fell from the tree, or my friend fell
Speaker 1: down the canyon, you know, or I felt this weird magnetism.
Speaker 1: That's a pretty dark scenario there, these three a friend
Speaker 1: down the canyon. Hopefully not a podcast like cost thinking
Speaker 1: about the applications of gravity, and we just describe all
Speaker 1: of those things in terms of our experiences. But you know,
Speaker 1: that's not necessarily the most natural way to do it.
Speaker 1: And that's why physics takes us and we transform our
Speaker 1: intuitive experiences into like a list of observations and look
Speaker 1: for mathematical patterns, and then we discover all these things
Speaker 1: are actually connected to those things, and it turns out
Speaker 1: we've been looking at this all the wrong way. And
Speaker 1: those are my favorite moments in physics when we discover, oh,
Speaker 1: we think about forces this way, actually they probably exist
Speaker 1: for this totally other reason, and we've come at it
Speaker 1: in this weird way just because of our experience. And
Speaker 1: so you get this like flash of deep insight when
Speaker 1: you're like, oh, the universe fits together in this beautiful,
Speaker 1: mathematically elegant way. If you think about it in terms
Speaker 1: of forces, you know, recovering local gauge invariants instead of
Speaker 1: you know, building anti gravity machines to protect your clumsy friend.
Speaker 1: I guess how would you describe it? Then? When an
Speaker 1: electron pushes on another electron and they exchange photons, how
Speaker 1: did physicist see it? How do you see it in
Speaker 1: terms of preserving the symmetry? Yeah, well, physicists see it
Speaker 1: in terms of carrying those rotations, Like a photon sort
Speaker 1: of carries that rotation, you know, that's what a photon does.
Speaker 1: It rotates from one gauge to another gauge, and so
Speaker 1: when an electron communicates with another electron somewhere else in space,
Speaker 1: it's sort of like communicating about their differences in their gauge.
Speaker 1: And so that's what a photon does. It carries that information,
Speaker 1: and that's what gluons do. Gluons rotate things through colors space.
Speaker 1: They're like, Okay, this cork over here is a green cork.
Speaker 1: That cork is a blue cork. You know, I got
Speaker 1: a communicate from here to here, and I'm gonna change
Speaker 1: the green to the blue as I move along. The
Speaker 1: forces are sort of like there to connect these objects,
Speaker 1: and they do so by rotating the gauge from one
Speaker 1: place to another. And I think that's most clearly seen
Speaker 1: in terms of the weak force. The weak force has
Speaker 1: the same sort of structure, but then again in a
Speaker 1: different internal symmetry space. It's almost like two electrons are
Speaker 1: gauging each other. It's like, you know, an electron interacts
Speaker 1: with the electromagnetic fields. If it moves, it creates some
Speaker 1: sort of disturbance that then has to be kind of
Speaker 1: squared away somewhere else by another electron. And then that
Speaker 1: transfer of you know, wiggle or disturbance is what you
Speaker 1: would call a photon. Yes, like patching up your check
Speaker 1: book at the end of the month. Photons are there
Speaker 1: to like find those pennies and move them from one
Speaker 1: to column to another to make everything out up in
Speaker 1: the end. Hopefully they don't get too creative like I
Speaker 1: sometimes I may or may not do electron magnetic accounting exactly. Well,
Speaker 1: maybe that's what quantum accounting really is. There really is
Speaker 1: a quantum accounting firm. Yeah, where you have money and
Speaker 1: don't have money at the same time. You're both rich
Speaker 1: and broke at the same time. And you know, I
Speaker 1: got an email this morning from a listener Ivan, who
Speaker 1: is asking me about why I say that the weak
Speaker 1: force makes sense to all be together, Like why the
Speaker 1: ws and zs all makes sense to be in a
Speaker 1: single field and also with the electromagnetic field. But like
Speaker 1: you can also ask, like why don't you consider the
Speaker 1: W plus and the W minus and the Z all
Speaker 1: just separate forces. Why isn't the weak force three different forces?
Speaker 1: Why do you even try to put these things together?
Speaker 1: And the reason are these symmetry? So we discover that
Speaker 1: like the W plus by itself doesn't preserve local gauge invariants.
Speaker 1: But when you put the W plus and the W
Speaker 1: minus and the Z together, then they do. So together,
Speaker 1: these three fields work really hard to preserve another kind
Speaker 1: of invariance, different from the one that's for the electron,
Speaker 1: and different from the one that's for corks. And this
Speaker 1: is why we have the weak force, because it preserves rotations.
Speaker 1: And this thing called weak isospin space. And so these
Speaker 1: three fields together do that. And as you say, you
Speaker 1: can put electromagnetism and the weak force together to make
Speaker 1: an even super theory which preserves a different number altogether
Speaker 1: that individually neither the two forces preserve. Right. It's almost
Speaker 1: like the more complicated the symmetries are, the more forces
Speaker 1: you need to patch them up. Yeah. And of course
Speaker 1: the really super fascinating wrinkle is that that symmetry electroweak symmetry,
Speaker 1: the symmetry that's preserved by the photon together with the
Speaker 1: two ws and the Z, that one doesn't actually work,
Speaker 1: That one's broken, that one isn't actually preserved by the universe.
Speaker 1: And the reason for that is the Higgs boson. The
Speaker 1: Higgs boson breaks that symmetry, and that's why it exists.
Speaker 1: That's how we were able to detect that it does exist,
Speaker 1: because we saw, oh, this symmetry doesn't actually work. We
Speaker 1: need something else out there to break this symmetry, and
Speaker 1: that's what the Higgs does. And that's why the ws
Speaker 1: and disease are massive while the photon and the gluons
Speaker 1: are massless. That's wild, Like, maybe the only reason we
Speaker 1: have mass is to patch up these brakes. Yeah, well,
Speaker 1: the only reason we have mass is because this one
Speaker 1: symmetry is broken. This electroweak symmetry isn't actually something the
Speaker 1: universe respects because the Higgs breaks it. If we didn't
Speaker 1: have the Higgs, then the W and the Z would
Speaker 1: be massless, and so would all the other particles, and
Speaker 1: we wouldn't have any mass without the Higgs. Don't we
Speaker 1: have other like violations of symmetry also all over the
Speaker 1: theory of physics, right, are in there all kinds of
Speaker 1: different charge and parody violations? There are, yes, And so
Speaker 1: we have these a lot of these approximate symmetries or
Speaker 1: broken symmetries, And an approximate symmetry is like, well, maybe
Speaker 1: we're just missing a piece, Like we're not talking about
Speaker 1: the right thing, Like we think we've identified the thing
Speaker 1: that's being preserved, the thing with the universe respects, but
Speaker 1: we must be looking at it from like the wrong angle.
Speaker 1: We don't quite have it right, you know. For example,
Speaker 1: like if you had a cube, and you know, you
Speaker 1: can rotate the cube and you still get a cube, right,
Speaker 1: But what if you're not looking at it from the
Speaker 1: right point of view. You're only looking at like a
Speaker 1: two D slice of the cube, and so the symmetry
Speaker 1: of it is not exactly preserved. So in some of
Speaker 1: these cases we're probably just like, don't have the full
Speaker 1: picture yet. We haven't really discovered what it is the
Speaker 1: universe is preserving. Like maybe it's not broken. Maybe we're
Speaker 1: just missing something. Yeah, maybe we're just missing we haven't
Speaker 1: seen the full picture, but so far we haven't, which
Speaker 1: means that to us, it does look like a broken universe. Yeah,
Speaker 1: but some of these symmetries are perfect, Like charge conservation
Speaker 1: is not when we've ever seen broken, Like, no particle
Speaker 1: has ever broken conservation of charge, like a photon has
Speaker 1: never turned into two electrons or electrons don't just disappear
Speaker 1: into neutral particles. As far as we know, that is
Speaker 1: a perfect symmetry of the universe charge conservation. Alright, Well,
Speaker 1: I guess that tells us a little bit more about
Speaker 1: the universe. You know, there's these hidden symmetries, these hidden
Speaker 1: almost rules, right, that sort of govern everything, and that
Speaker 1: may even like give rise to things that we take
Speaker 1: for granted, like light. Maybe that's just the universe's way
Speaker 1: of trying to stay beautiful. Yeah, the way I think
Speaker 1: about it is that you can't have a universe that
Speaker 1: respects this symmetry without the photon. Like, the photon is
Speaker 1: absolutely necessary in order to have a universe that respects
Speaker 1: this symmetry. So therefore we do have a universe that
Speaker 1: respects this symmetry. Now, the question we can ask is like, well,
Speaker 1: why what a weird thing for universe to insist on?
Speaker 1: What does that mean? And I think that's the kind
Speaker 1: of thing that in a hundred years people look back
Speaker 1: and be like, oh my gosh, that was so obvious.
Speaker 1: The universe was screaming the answer to you. But here
Speaker 1: we are in the forefront of ignorance. We don't really
Speaker 1: know what this clue means yet. So I think it
Speaker 1: does mean something deep about the universe. We just still
Speaker 1: need to digest it. So come on, philosophers, tell us
Speaker 1: what it all means. Well, it sounds like the answer
Speaker 1: might come from physics, right, you're saying, like, maybe we
Speaker 1: don't know why now, but maybe in the future to
Speaker 1: a physicist that will seem obvious, right, Like, maybe there
Speaker 1: is a physical answer to these white questions, and just
Speaker 1: because we don't know what they are now, you're bumping
Speaker 1: them over to the philosophy department. Yeah, and it could
Speaker 1: also come from mathematics. We didn't appreciate the structure of
Speaker 1: these symmetries until we learned group theory from mathematics. It
Speaker 1: turns out that perfectly describes everything that's going on here.
Speaker 1: Mathematicians invented it for like totally other reasons, because they
Speaker 1: just like thinking about how things rotate in their minds.
Speaker 1: But it could be that what we've discovered now needs
Speaker 1: like some new branch of mathematics to describe it and
Speaker 1: give us like an understanding of what the meaning is. Intuitively,
Speaker 1: so it might just be that we need to invent
Speaker 1: new mathematical words and concepts to fit these things together
Speaker 1: into a deeper understanding. I see you're passing the bug
Speaker 1: now to the mathematics department. You're like, blame everyone but us.
Speaker 1: You know. It's like when poets invent new words, you know.
Speaker 1: I think English professors are like, can you really just
Speaker 1: do that? You know? And so I don't know if
Speaker 1: mathematicians want us inventing the new math, you know. I
Speaker 1: think they, you know, really would prefer to do that themselves.
Speaker 1: I see, now you're blaming the English department as well.
Speaker 1: That's right. I'm good at this. Bring out from the problem.
Speaker 1: I can blame them for it. The certain symmetry about you, Daniel,
Speaker 1: I feel like you're trying to preserve. Look, we made
Speaker 1: these crazy discoveries. Everybody else needs to tell what's going on.
Speaker 1: You know. It's really fun to think about. And this
Speaker 1: is one of the reasons why I agreed to join
Speaker 1: the philosophy department here, because I do like to think
Speaker 1: about what it means about the universe. Because in the end,
Speaker 1: that's why we're doing these experiments, not because we like
Speaker 1: to write down tidy mathematical equations, but because we hope
Speaker 1: that by doing so, they will speak to us, and
Speaker 1: they will tell us, Look, the universe follows this rule.
Speaker 1: The universe has to be this way, and we'll get
Speaker 1: some understanding of why it is a pretty perplexing universe.
Speaker 1: And you know what, whether or not it's beautiful or broken,
Speaker 1: we we still love it. You know, no pressure, You
Speaker 1: don't have to tell us everything. You know, we're just
Speaker 1: here for you or because of you. I don't know, man,
Speaker 1: that's another philosophical department. We do love the universe though,
Speaker 1: that's true. All right. Well, we hope you enjoyed dad,
Speaker 1: Thanks for joining us, see you next time. Thanks for listening,
Speaker 1: and remember that Daniel and Jorge explained. The universe is
Speaker 1: a production of I Heart Riding. For more podcast asked
Speaker 1: from my Heart Radio, visit the I Heart Radio app,
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