What hidden symmetry is controlling the Universe?

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

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Episode Transcript

Speaker 1 (00:01):
Hey, it's Jorhan Daniel here and we want to tell
you about our new book. It's called Frequently Asked Questions
about the Universe because you have questions about the universe,
and so we decided to write a book all about them.
We talk about your questions, we give some answers, we
make a bunch of silly jokes as usual, and we
tackle all kinds of questions, including what happens if I
fall into a black hole? Or is there another version

(00:22):
of you out there that's right? Like usual, we tackle
the deepest, darkest, biggest, craziest questions about this incredible cosmos.
If you want to support the podcast, please get the
book and get a copy not just for yourself, but
you know, for your nieces and nephews, cousins, friends, parents, dogs, hamsters,
and for the aliens. So get your copy of Frequently
Asked Questions about the Universe is available for pre order now,

(00:46):
coming out November two. You can find more details at
the book's website, Universe f a Q dot com. Thanks
for your support, and if you have a hamster that
can read, please let us know. We'd love to have
them on the podcast. Hey, Daniel, I have a complaint

(01:10):
to file about physics. Who do I talk to? Oh,
you can lay it on me. I'll pass it on
to the right people. All right, you're the unbutsman for
all the physics. It's good to know, alright. So I
feel like physics it's pretty good about answering how questions?
You mean, like how old is the universe? Or how
big is it? Yeah? Just like that? All right, Well
that sounds pretty good. What's your complaint? Well, I feel

(01:31):
like the real questions that humanity wants to know are
the why questions, you know, like why do we have
this universe? Why is it like this? And not like that.
You know, I'm gonna have to direct you, I think,
to the philosophy department. Oh, man, you're gonna pass the buck. Well,
I don't know how else to answer a why question. Yeah,
and I don't know why I ask you these questions
in the first place. You ask a meta question, you

(01:53):
get sent to the metaphysics department, the meta unbutsman. Hi
am or Hey, I'm a cartoonists and the creator of

(02:14):
PhD comments. Hi. I'm Daniel. I'm a particle physicist and
a professor at U C Irvine, where I actually am
also a member of the philosophy department. Oh are you
really so you're a card caring philosopher? Technically I am so.
I have no education in philosophy. I just started showing
up at the philosophy of science seminars and eventually they
were like, who are you? And then they give me

(02:35):
a joint appointment. I guess they let anyone in that hand, like,
there's not that much of a demand for philosophy membership. Well,
I think joint appointments are free, so yes, the bar
is not that high. Nice. Do you have to teach
classes in philosophy? I am not qualified to teach classes
in philosophy. Well, I feel like physics, you know, asked
a lot of very philosophical questions or questions that border

(02:56):
on philosophy, right, like why is the universe like this?
Or why do we have a universe? Right? Like you're
asking these questions as physicists, right, Yeah, A lot of
the answers we get to questions in physics do have
big philosophical implications, and I think it's important. That's why
I started going to these seminars to understand like what
if we discover this or what if we discover that

(03:17):
what does it really mean? Man, Physics can tell you
what's going on, but only philosophy can tell you what
it means. Well, it's kind of a layer thing, right
because you can ask like why does the apple fall
from the tree and you can say, well, it's gravity.
But you know, once you start dig getting deeper, like
why do we have gravity, then it starts to get philosophical. Yeah,
and then you can ask like what kind of answer
will satisfy your question? And then you have a philosophical

(03:39):
answer about philosophical questions, yeah, or like why have philosophical
answers philosophy of philosophy? Wow, you can get a h
and philosophy. I guess it's the start of the Endless sleep.
But anyways, welcome to our podcast Daniel and Jorge Explain
the Universe, a production of I Heart Radio in which
we go meta and meta meta about the nature of
the universe. We ask all the questions about how the

(04:02):
universe is, and then we also ask the questions about
why it is and what that means. Because we don't
just want a description of the universe, we want an
understanding of the universe. We want to know why the
universe is this way and not any other way, or
maybe if it could have been that other way. We
seek not just to describe but also to explain, and

(04:22):
that's what we're doing here, exploring the universe and explaining
it to you. Yeah, because it is a big universe
and one of which you can ask a lot of questions.
Because it is not just kind of a big universe
and a pretty mysterious universe, but it's also kind of
a beautiful universe. It is, in fact a beautiful universe,
not just in the vistas that we partake in in

(04:43):
the wonderful night skies, but also in the mechanisms for
how it works. Sometimes you look at the mathematics for
the way things work at the quantum level and you're like, wow,
that's pretty neat. I couldn't have designed the universe so
beautiful or so clever. It does feel sometimes like we
are uncovering a w of great beauty. Yeah, because the
universe does seem to have rules, right, Like it's it's

(05:05):
not a willy nearly universe where anything can happen. It
seems to have rules and the structure to it. And
as you say, it sort of feels clever in a
way can you talk about that? Yeah, it's just maybe
our appreciation is just sort of subjective. But one of
the most incredible things we've discovered is that the universe
can be described in terms of mathematical laws. Like why
do we even think that it was possible to write

(05:26):
down equations that predict what will happen in our universe
and that only some equations will work, right, Like, it's
sort of like you can't just write down any random
equation and say that's physics. It's math, but it's not
necessarily physics, the same way you can't just like write
down a string of words and say here's my novel. Right,
Not every string of words is a novel. So we
use math as a language to express physics. But then

(05:47):
you can also look at that math and say, wow,
that really clicks together nicely, or this makes a lot
of sense, or this tells you something about the nature
the universe because it uses this math and not that
other kind of math. And then you get into the
lossopy questions like what does it mean that we have
a universe that's like this and not like that? Right,
that's pretty interesting. The idea that you know, like all
physics is math, but not all math is physics, like

(06:10):
not all possible equations have a physical reality to them. Absolutely,
you can describe lots of hypothetical universes out there using mathematics,
but they don't necessarily describe the universe we live in.
And you know, there are lots of beautiful theories about
physics that were mathematically really nice but just didn't describe
our universe, and so they ended up like tossed in

(06:32):
the dustbin of physics history. Man, you have a reject
pile for beautiful theory. We do because the universe gets
to say what the universe chooses, and sometimes it's a
little surprising and a little bit messy, but often we
can find some elegance, some nice description of it that
reveals something about the universe. And then you go off
and chew and you're like, that's really interesting that the
universe has this structure. What does that mean about It's

(06:55):
like fundamental nature. One of my favorite examples is very simple.
It just comes from conservation shi of momentum, Like this
is something we observe in the universe. We notice that
if you bang two rocks together that at the end
you have the same amount of momentum as you did
in the beginning. It's changed direction a little bit, perhaps,
but all the momentum is the same. It's something we
observe and you can ask, like, well, why is that?

(07:16):
Why is momentum conserved? And we have this deep theory
of physics that tells us why, But it just brings
up more questions. It turns out that momentum is conserved
because space is uniform, because you can do the same
experiment here and somewhere else and on Jupiter and you
should get the same answer. One thing leads to the other,
because space is uniform, momentum is conserved. But then that

(07:37):
just brings up the question like, well, why is space uniform?
Why is it true that you can do the same
experiment here or an Alpha Centauri and you should get
the same answers? Why the laws of physics the same
everywhere in space? But that seems to be the way
our universe is, and that's the way it is, and
it's also sort of a good thing that it is, right,
Like it would be weird or could you even have

(07:57):
a functioning universe if things were at all smooth and
working the same way everywhere, Like wouldn't it be just
complete chaos. Well, that is the job of science fiction authors,
right to imagine different universes and like, what would it
be like to live in that universe? To be a
scientist in that universe and discover that you lived in
that universe instead of this one? What stories could you
tell in that universe? So I think there are probably

(08:19):
very different physical consequences of living in the universe like
that where the laws of physics change with space or
with time. But this is the one that we live in.
I think you could imagine ways to live and waves
life might even arise, but it would be vastly different
from the universe that we know. Well, now you're giving
me kind of fear of missing out. What if there's
like a better part of the universe that we're not

(08:40):
living in, Like what if the grass is really like
greener on the other side of the galaxy? Yeah, well,
you know, we haven't even discovered how green our grass is.
There's so much we don't know about the universe, so
much to discover, so many beautiful things that will be
revealed in the future that will amaze you. So stick
around in this universe. I recommend it. There's a lot
of green grass left to cut. It's interesting you said

(09:01):
that word earlier. Elegant. You know, I feel like I
hear a lot of physicists say that words sometimes, that
the universe feels really elegant in the way the rules
and the laws work. And that's kind of we'll be
talking about today. Is is one of these elegances of
the universe. And what we're looking for to describe the
universe is a simple description. You know, you could describe

(09:22):
the universe. It's just like, here's a list of all
the physics experiments anybody's ever done and the results. That's great,
that describes the universe, but it doesn't give you any insight.
It doesn't give you that like ah ha. That's because
they're all following the same rule. And that's the job
of physics is to boil down a bunch of experiments,
a bunch of observations into a simple rule. And it's

(09:42):
when you see that simple rule and you say, wow,
it's incredible. That's something that's so simple can have all
these consequences. That's when you feel like you're looking at
some elegance. You're like understanding a deep truth about the
nature of the universe. You've revealed something at a lower
level than anybody has seen before. You've peeled back a
layer of reality and seeing a simple description that leads

(10:03):
to all the incredible complexity that we see in our universe.
And I guess you know, one of the things that
we feel is simple or a way to give things
a certain sense of elegance, is this idea of symmetry.
Like if something is symmetric somehow, as humans, it's instills
in as a sense of like, oh, that looks perfect
or that looks you know, elegant or beautiful. Yeah, and
it also sort of feels democratic, Like to me, it's

(10:25):
nice that the universe doesn't prefer any location in space
and you can do your experiment here or somewhere else
and it doesn't make a difference. And you know, there
are real consequences to that symmetry. That symmetry means only
certain laws of physics are allowed, like in that case,
only laws of physics that conserve momentum are allowed. That
comes directly from that symmetry, And we discovered lots of

(10:46):
these kinds of symmetries. You know. Another one and that
people are probably familiar with, is the fact that there's
no up or down in space. Like you do your
experiment in space, it doesn't really matter which direction your
experimental apparatus is pointing. You can spin it in another
direction and it should get the same result. That's another symmetry.
It says the universe doesn't prefer a direction, not just
a location, but a direction. And that gives you another rule.

(11:07):
It says that all the laws of physics you right,
have to also conserve angular momentum, which is separate from
just momentum. Right, This is like how much something is spinning.
So every time you discover a symmetry, something that where
the universe doesn't care about something or gives you the
same answer no matter how you spin or move something
that tells you something about the laws of physics that
are consistent with that symmetry, the laws of physics that

(11:28):
can describe our universe. Yeah, so to be on the podcast,
we'll be talking about what hidden symmetry controls the universe.
Sounds like a dark conspiracy here, Daniel. There's something hidden
controlling things. People smoking cigars, wearing gray suits and deciding

(11:51):
what laws of physics can we have or where are
you going for some click bait action here. I'm just
trying to, you know, get a little bit of reflection
from the X file glamour, that's all. Yeah, we should
title it like the hidden dark Secret that controls the universe,
like to find out more. But yeah, there seems to
be a symmetry to the universe. And I feel like,

(12:11):
you know, maybe physicists use this word differently than how
most people understand it, because I think, you know, to
most people's symmetry means like if something is symmetric, it
means like it's the same if you look at it,
you know, the right half and the left half is
the same, or it's like the mirror image of something else,
or there's some sort of reflection or some like equality
between left and right or two directions. That's kind of

(12:33):
I think that's what people mostly think about symmetry. But
physicists think of symmetry. It's a kind of a different
concept in physics, right, It's about how the mathematical equations
stay the same no matter how you transform them. Yeah,
but it's also closely related, I think, to people's intuitive
sense of symmetry. Like think about the examples you mentioned
the sphere for example, you know there's a rotational symmetry.

(12:55):
There you have a perfect sphere, you rotate it, you
get the same sphere, right, and so nothing has changed
for the sphere. It's the same. Or even if you
reflect it through a mirror down its middle, you get
the same sphere. So there are symmetries in the sphere
that wouldn't change how you interact with the sphere. And
we talk about the same things in physics. We say, look,
if you do this experiment and you just rotate your axes,

(13:18):
you make X into Y and Y and z or whatever,
you should get the same answer. You know, it's like
a spin the experiment or spin the universe. It doesn't matter.
You should get the same answer. And so fundamentally, when
we talk about symmetry, we mean do you get the
same laws of physics if you apply some transformation or
some rotation or some change to your axes or how

(13:39):
you've defined things. And so that's what we mean when
we talk about symmetry right right like like like a
butterfly is symmetric, right like the left side and the
right side is symmetric. But you can also think of
it as like the left wing if I put it
through a mirror, it will look just like the right wing. Yeah,
you know maybe actually I don't even know. Are all
butterflies exactly symmetric? Probably they're not exactly, but in our cartoon, right,

(14:00):
assume a symmetric butterfly. Then in that case, yeah, you
put it up to a mirror and you see the
exactly the same other half, right, and at least it
look the same or similar. And so this symmetry idea
is very important physics because it almost, like I don't know,
defines the laws of physics at the fundamental level, or
it's something that's important for them to work, right. Yeah, Well,
what happens is that we notice the universe following certain rules.

(14:22):
You know, for example, we notice that the universe doesn't
create or destroy electric charge, like you have a bunch
of it, It doesn't go away, you can't destroy it,
and you can't make anymore. Right, And so that's like
a rule the universe seems to be following. And then
we ask questions like, well, what symmetry gives you that rule?
Why can't you create or destroy electric charge? What rule

(14:43):
is it fundamentally following? And what we discovered or what
eman author discovered about a hundred years ago. Is that
every time you see the universe following a rule is
because there's a basic symmetry. There's something about the universe
that's preserved that has this kind of symmetric property where
it doesn't depend on how you been it or reflected
or whatever. And that's where these conservation laws come from.

(15:04):
So that's very, very powerful. Every time you see a
conservation it means you can discover a symmetry of the universe,
which tells you something pretty basic about like the very
structure of reality, all right, and even the reality in
the mirror as well. We'll get into that, but I
guess more specifically, it has something to do with something
called gauge symmetry, right, g A U G E symmetry. Yeah,

(15:26):
all of our laws of physics in the Standard Model
are built on this principle of gauge symmetry, and we'll
dig into exactly what that means on today's episode. But
it turns out to be something really deep about the
way particles operate and their relationships with each other. All right,
we'll take a dive into that symmetry. But first we
were wondering how many people out there no or have
heard of this concept of gauge symmetry. So Daniel went

(15:48):
out there into the internet to ask people what is
gauge symmetry? And so, if you are interested in answering
really hard questions about secrets of the universe with no
chance to prepare at all, and then have the thousands
of people here your answers, please write to us two
questions at Daniel and Jorge dot com. It's a lot
more fun than it sounds. Think about it for a second.
Do you know what gage symmetry is? Here's what people

(16:11):
have to say. Gage symmetry is how one would gauge
the symmetry between a binary set of stars. And obviously
that's incorrect, but there you go. I am not sure
what gauge symmetry is, but perhaps it was a very

(16:32):
smart scientist person that explain some kind of symmetry in
the universe or in physics. Gage symmetry it has something
to do with electricity or charges. It doesn't matter what
direction in a circuit, or in what direction you look
at particles or whatever, like the charters are symmetrical in

(16:55):
It doesn't matter if there's a pleasure of minus. From
my point of view, gage symmetry. Well, it happened to me,
was I when my instrument cluster from my truck broke
down and all the gorges were at zero, so they

(17:16):
were symmetric. So this is gage symmetry from my point
of view. Let's break it down. Gauge symmetry is when
you make a transformation on a field which turns one
particle into a different one, maintaining, obviously, because it's symmetric,
maintaining some properties of that particle. I think, if I
recall correctly, gauge is basically measurements, So gauge symmetry might

(17:40):
be that one measurement in one unit basically described in
a different unit. Possibly. Well, I guess the gauge symmetry
is when my front tire and my rear tire of
my bicycle show the same amount of pressure. Then I
would have two gauges and they are symmetric. Otherwise I

(18:02):
have no idea. All right, it's it seems to be
um kind of a mystery to our listeners. The secret
Cabal has done a good job of hiding itself. It's
really hidden. Well, I guess it's a weird word because
we in general we use the word gauge to like
gauge something right, to like measure something like a pressure

(18:23):
gauge is something that tells you how much pressure is
in your bicycle tires, or your fuel gauge tells you
how much fuel you have in your car. And so
what does it mean then to have gauge symmetry in
your equations of physics? So it comes from the era
of the railroads, when people were still laying down a
bunch of new tracks and they have to decide, like
how far apart you make the tracks? Do you make

(18:45):
them one meter apart or a meter and a half
or whatever, And everybody had like different choices, and that
makes them incompatible. Right, you can't drive your train if
the gauge is wrong, and so somebody just has to
make a choice, and that doesn't really matter. You can
still build railroads if there are a meter apart or
half a meter apart or or whatever. It still works.
You just gotta make a choice, And so that arises
sometimes in physics where there's like an arbitrary choice you

(19:07):
have to make, like where do you call height equal
zero or where do you call electrical potential equal zero?
And it shouldn't affect how your physics works. It doesn't
change anything for how your experiments should work, but you
do have to make a choice. It's almost like a
scale maybe, or like a starting point. Is that what
you mean? Like, you know, like a scale, like is
this railroad track, you know, this wide or is it narrower.

(19:30):
It's sort of that way in physics where you have
to say, all right, what scale are we talking about
when we're talking about these electrical fields? Yeah, and you
just like you need a number, and so you have
to pick a starting point. That's a good way to
think about it. But it doesn't affect anything, right, It's
just like it seems like an arbitrary choice, you know.
One simple example is like think about a book falling
off of a shelf and wondering like, well, how fast
is it going when it hits the floor? Well, the

(19:52):
answer to that question depends on the height of the shelf,
because the taller the shelf, the faster it is when
it's hitting the floor, and the shorter the shelf, the
slower it is when it hits the floor. But it
doesn't depend, you know, mostly on how high your shelf
is above sea level. You know, so like where do
you call high equal zero. Do you say high equal
zero a thousand meters below my floor or at my
floor or above my floor. You can do all the calculations,

(20:14):
you get the same answer no matter where you put
like height equal zero in your physics problem. That's just
an arbitrary choice, doesn't affect your answer. So that's an
example of you know, making a gauge choice. And so
this word gauge was chosen to sort of like, you know,
harken back to the age of the railroads. But really
what it means is an arbitrary parameter of your theory.

(20:35):
I see you're saying, physicists pick the word that had
nothing to do with the thing. But where the rest
of the population is that what you're saying your ancestors
should have been called on a hundred years ago when
they were naming this thing. I totally agree. It's a
ridiculous word, and it's become so important, so we say
it all the time now. Gauge theory is everything. The

(20:55):
whole standard model of physics is a gauge theory. It's
almost like the theory only tells you changes or how
it changes from a starting point. Is that kind of
what you're saying, But the answer it kind of depends
on where you start, right, and it has a you
know a lot of history, like electromagnetism, which you know
predates the standard model in particle physics by a long time.
You know. Maxwell noticed this in his equations. When he

(21:16):
was putting together his equations of electromagnetism, he noticed that
you could change these. You could like add an arbitrary number,
not exactly just a number has to have like a
disappearing curl to it. But you could add something to
the theory and it wouldn't change any of the predictions.
And so you can have basically like different sets of
Maxwell's equations, and they call these different gauges, like the

(21:37):
Coolum gauge or the Lorenz gauge. People chose different sets
of equations. They all make exactly the same predictions. You
just like pick one. There's like a whole family of
these equations and they all make exactly the same predictions.
You can use any of them as long as you're consistent.
They're almost like floating theories. I guess you might say, right,
And so then there's the idea that within these theories
you can have a certain symmetry to them. And so

(22:00):
that's what gauge symmetry is. And so let's get into
why it's important for our equations of the universe and
what does it all mean. Man, But first let's take
a quick break. All right, we're talking about the hidden

(22:24):
conspiracy here that's controlling everything, Daniel. This is one of
those podcasts. That's right. We are bringing you the hard
truth today, folks. We are tearing off the veil. We
are revealing who's really behind everything. That's right. That's why
this podcast is encrypted. Right, we're encrypting this. We're not
putting our names on the title of the podcast either, right,
that's right. But we are doxing the true masters of

(22:47):
the universe today. There you go. That's another title for physicists.
You're boxing the universe, you're exposing it. We are exactly
we are, all right. So we talked about what gauge
theory is. It's like a theory that sort of floats
that it tells you how things change, but it sort
of depends on where you start them. And so that's

(23:08):
kind of what a gage theory is. And so then
what's gauge symmetry. So gage symmetry is when you have
a theory that has a gauge in it, right, So
you can make this choice, but it makes the same
prediction regardless of your choice. So, as we talked about electromagnetism,
it doesn't matter if you use the Coolum gauge or
the Lorenz gauge. You write down different equations, but they
predict exactly the same behavior of like electrons moving through

(23:30):
fields or magnets being generated. It doesn't matter. So there's
a gauge symmetry there. You can pick your gauge, but
it doesn't affect the physical predictions. I see. But then
how did the name symmetry come from? Because it's not
you know, like maybe I would have said it's gauge
invariant or gauge doesn't care less about gauge. But the
words and metrics to me sort of means like a

(23:50):
reflection or like a mirror image. Yeah. Well, you can
transform from one gauge to another without changing your predictions,
just like you can rotate a sphere through an arbitrary
angle without changing the sphere. It's still a sphere. And
so a gauge theory is one that you can transform
in a certain way from one gauge to another without

(24:10):
changing your predictions. And we'll talk about various gauge symmetries today.
Some of them are a lot like rotations of a sphere.
All right, are we saying that the laws of physics
with the universe are gauge symmetric or we noticed that
they were gauge symmetric. Yeah, it's really fascinating. The laws
of physics of the universe have really weird and surprising
gauge symmetries, much more than you would expect, and they

(24:32):
have real consequences, Like we talked about, every time there's
a symmetry the universe that leads to a conservation law.
And so what we can do is we can say, oh,
maybe this is why we have conservation of electric charge
or conservation to other things. It's because there are these
symmetries in the universe. And then we can ask the
deep questions like, well, why does the universe have that
weird gauge symmetry? What does that mean? This is not

(24:53):
just like an arbitrary thing we write down in our
rooms with pencil and paper. It's something deep about the
universe that respects this symmetry, meaning like if you work
at the equations of the universe. You noticed that they're
gauge symmetric, and because of those symmetries, then things like
conservation a momentum happen, yes, exactly, and so you know,
we notice that those things definitely happen in our universe,

(25:16):
and we discovered that that means that there must be
these symmetries, which is really interesting. All right, well, maybe
talk to us a little bit about why it's important
and how it has to do with quantum mechanics. Yes,
so the standard model of particle physics and quantum mechanics
has a lot of gauge symmetries in it, and one
that comes from quantum mechanics comes from the wave function.
Like we talked to this program before about what happens

(25:37):
to little particles and experiments, like what determines whether an
electron is going to go left or we're going to
go right when it interacts with something else. That's determined
by the wave function, which tells it like the various
probability to go here or the probability to go there.
But there's a little step there which we've glossed over,
but it's actually really really important. It's not the wave
function itself that tells an electron whether it has a

(25:58):
probability to go left or to go right. It's the
square of the wave function, the wave function square the
way function multiplied by itself, that determines the probability to
go left or to go right. And that's because the
wave function itself is a complex number, you know, like
one plus i or two minus i or whatever, and
so it doesn't have real values, so you have to

(26:19):
square it to get real values. And there's a symmetry
there because it means that the wave function or minus
the wave function give exactly the same predictions. So you're saying,
like at the fundamental level of particle physics, like particles
that make up our universe, they're symmetric, like starting from that,
because the wave function that describes it is symmetric in

(26:40):
itself in terms of it the probability though right, like
the original wave function is not symmetric, but if you
square it to get the probability, then it is symmetrica
if you take every wave function and you multiply it
by minus one, it doesn't change anything in the laws
of physics. That's what we're saying. So take the whole
universe's wave function, or if you don't believe in that,
take the wave function of all the particles, multiple by
all of them by the same number. Nothing changes, right,

(27:03):
The laws of physics predict exactly the same outcomes. It
doesn't matter because it's only sensitive to wave functions squared.
So you have a freedom there a choice. Do we
start with the positive way functions or do we start
with the negative wave functions. It doesn't matter. So there's
a symmetry. Really it doesn't matter, like, won't effect at
all what it comes out. It won't affect at all
because you take it and you square it. All physical

(27:23):
predictions depend only on the wave functions squared. All right,
So then that means that all particles in the universe
are a symmetric What does that mean. It's actually a
little bit more general than just multiplying it by minus one.
You can actually multiply it by a rotation in the
complex plane. And I don't think we should get too
far into the math, but just think about it, like,
you can rotate these things by an arbitrary angle and

(27:43):
you still get the same number. And so that makes
a lot of sense if you just do it. To everything.
Like you multiply the whole universe by minus one, nothing
changes because you've been consistent. You change the way function
of my electrons and your electrons and somebody else's electrons.
That's called a global symmetry affect the whole universe, And
that's not so surprising. But there's something else so the
universe has, which is a very different and much much

(28:05):
deeper symmetry. It turns out that the universe is symmetric
to local gauge invariance, which means you can make this
kind of transformation differently at every point in space. You
can say like here, I'm gonna multiply all my way
functions by plus one. Over in Jupiter, I'm gonna multiply
my minus one and an alpha centauri, I'm gonna do
something different. So that's a local gauge invariance that says

(28:27):
that you can have like an infinite number of these
different ideas about gauges. Wait, what what do you mean?
But you just told me that it's globally invariant, like
it doesn't matter what you do to it anywhere, But
now you're saying that it does matter what you do
to it locally. Yeah, so global gauge invariance the universe
definitely has. But if you want local gauge invariance, right,

(28:48):
that's harder. That says, well, now I want to be
able to multiply my wave functions by plus one or
minus one and do it differently everywhere. And you might
immediately say like, okay, well that obviously doesn't work right
because you have to be consistent otherwise they like the
interference terms of the way functions are not going to
come out right. And you're right. The universe by itself,
for an electron, doesn't have local gauge invariance because if

(29:09):
you change the gauge here and you change it somewhere else,
then it will affect the predictions. So the universe, if
all you have in it, our electrons, doesn't have local
gauge invariants. And then if played a fun game, they said, well,
what if we added something What if we added something
else to the universe so that we did have local
gauge invariance, something that like corrected for that. So take
the universe that just has electrons in it and ask

(29:32):
for local gauge invariants, and you break that right, like immediately,
you don't have local gauge invariants because you're changing electrons
differently everywhere. Well, now, if you like add something to
the universe to try to fix it, to compensate for
this change you've made, you have to add a new piece.
And that new piece, if you look at the mathematics
of it, is exactly the electromagnetic field. I think you

(29:53):
lost me a little while, to be honest, So I
guess it's difference between local and global. Is it like
kind of like if I let go of my book
on a from a three story building, it's not I
won't get the same velocity at the bottom as if
I drop it from a one story building. Is that
kind of what do you mean? Yes? Or let's say
you want to define your altitude differently based on where
you are in the world, Like currently we have a

(30:15):
single global definition of altitude relative to sea level. But
what if you wanted to choose your height definition to
be different if you're here or if you're over there,
if you're an Irvine or Pasadena or New York. All
of a sudden, you know, as you move across the country,
your height would be changing constantly, like oh, I'm higher,
I'm lower I'm higher, I'm lower. It wouldn't make any sense.
You'd get crazy physical predictions, like the book would still

(30:36):
fall the same way, wouldn't it. The book would still
fall the same way, and so your theory wouldn't work.
If you'd like to throw a ball as a parable,
and it's moving across the ground and you're constantly changing
like the definition of height, then you're not going to
get sensible predictions. Right. The ball obviously does move smoothly,
and so your physical theory doesn't work anymore if your
definition of height is changing as the ball is moving.

(30:57):
Is it, like, you know, my equation, my prediction one word,
if I use meters in England or if I use
feet here in the US, Like that's what you mean?
Like you want a theory to be different about whether
you use feed or meters. Yeah, and so global invariance
is like, well, let's just use meters everywhere that makes sense,
or let's use feed everywhere, but let's be consistent. Local

(31:18):
invariance is like, no, I want to get to pick
my units differently everywhere, and so that's a much higher standard,
like to have the laws of physics that allow you
to have that much freedom to make any choice at
any point in the universe is a much higher standard, oh, right,
because I guess it would have to be like irrelevant,
right almost exactly. It's like it doesn't matter if you
weigh something in England or in the US, whether you

(31:40):
use meters, because meters doesn't figure into it. That's kind
of what you want, right exactly, all right, So you're
saying that we the universe doesn't seem to have that
local gauge invariance, meaning it doesn't matter if you use
meters or feed but you're saying, there's a way to
get that back. There is a way to get that back.
You can say, what would the universe have to look
like to have local gage invariants? Like take your electron

(32:01):
is flying through space, and what if you want to
be able to like multiply it's a wave functioned by
an arbitrary number at a different point in space, and
how that number be different everywhere in space? Is there
a way to do that? Is there a universe you
could construct that would follow that, that would respect your
local gauge invariance that would allow you to have that
much freedom. And it turns out there is if you
add a photon. So if you have just electrons in

(32:23):
the universe, no local gauge invariance. But if you add
an electromagnetic field, which gives you photons, boom, you get
local gauge invariants for free. Well what wait, okay, so
somehow the fix for this solution, but for all equations,
for just some particles, you're saying, the solution to making
things be meter or feet independent is to add the

(32:44):
magnetic electromagnetic field. Yes, the electromagnetic field is the thing
that can perfectly compensate and give you local gauge invariants
like you can derive it. You can say, here's the
wave function for the electron. I'm going to add an
arbitrary phase to it, which is multiplying it by an
arbitrary number. And you can say, well, now my predictions
are wrong, they're different. What would I need to add

(33:05):
to my equations to compensate for that to cancel out?
This bologna that I've added and once you need to
add has exactly the same mathematical structure as the electromagnetic field.
It is the electromagnetic field. So the presence of the
electromagnetic field is what preserves local gauge invariance. For it's
you're saying, the electromagnetic field preserved symmetry for the electron

(33:28):
or for like everything in the entire universe for the
electrons wave function. Yes, so we're talking just about the
electron and its way function. It is feet and meter independent.
But if you had the electromatic field, then it is independent. Oh,
I guess the electron has its own field to the
electron has its own field. Yeah, there's the electron field.
And now we're saying that if we want this local
gauge invariance where we can multiply arbitrary numbers to the

(33:51):
electron field, that can't happen unless you have this exact,
very specific requirement of another field that hangs out and
basically compensates for that and takes care of that for you.
And it turns out that that field is the electromagnetic field,
and photons basically exist in order to preserve local gauge invariants.
What you're saying that the only reason we have light

(34:12):
is to make electrons happy. Well, here's the philosophy, right, Like,
do we have light because the universe preserves local gauge invariants?
And that's the only law of physics that allows that
one that has photons. Or do we have photons because
we have local gauge invariants? Right? Like which direction does
it go? Uh? You know is a fun philosophy question.
But what we do know is that we have photons,

(34:35):
we have electrons, and we have the electromagnetic field. Both
of those two things, and together they seem to have
this amazing, weird property of local gauge invariance where you
can multiply up an arbitrary number and that number can
be different at different points in the universe and it
doesn't change the predictions. These two fields work to gather
in this really crazy and interesting way. That's interesting, but

(34:55):
it only applies to the electron. Like what about quarts, right,
quarks have a field, I think, and we can ask
the same questions like is the cork also locally symmetric?
You know, meat and feed independent here in the US
And is there's a separate field then that also fixes
that symmetry. Fascinating question. You're absolutely right. This applies to

(35:17):
the electron. It also applies to any particle that has
electric charge. So for example, the muan has this same property.
The muan, you can multiply by an arbitrary number, and
you also get local gauge invariants because the muan is charged,
and it also communicates with the photon field. And yes,
corks have electric charge, so they do the same thing.
In fact, turns out that's what it means to have

(35:40):
electric charge. Electric charge means you couple to the photon field.
Because electric charge just means you feel electric fields. You're
like influenced by electromagnetic fields, which is the field of
the photon. And so the reason we have electricity and magnetism,
the reason we have electric charge is because these particles
have this property. A really fascinating thing is we didn't

(36:02):
know necessarily, like do muans feel the same photon as electrons,
Like it could have been there's a different feel to
preserve the muans local gauge invariants and the electrons. But
of course we know there's a single photon, the same
photon that an electronomists can be absorbed by a muan.
But it didn't have to be that way. You could
have lived in the universe with like electron photon and

(36:23):
a muan photon and a towel photon and lots of
different kinds of photons in it. All right, So then
it seems like the electromagnetic field is this thing that
preserves the symmetry for all particles that feel the electric charge,
and so that's what makes the equations for all these
particles symmetric. And that's beautiful and maybe even clever. All right,

(36:44):
let's get into what it all means for the universe
and our understanding of it. But first let's take another
quick break. All right, we're going deep here today, Daniel.

(37:06):
I feel I feel like you really thrown us down
a rabbit hole here, Like what is the nature of
the electric magnetic field? Like does it exists only to
give symmetry to these particles? Or do particles have the
symmetry because of the electromagnetic field. It's a big philosophical question. Yeah. Well,
you know, I'm responding to your challenge. You remember when
we were talking about the weak force and does it
push or pull? And I said, well, one day we're

(37:27):
gonna have to go deep and talk about gauge symmetry,
and you said, bring it on. I got time. So here.
I don't think you can prove that, I said that,
can you? We didn't record it. I think we do
have a recording I was just listening to yesterday. I
might officially regret it right now. No, but this is
pretty interesting, all right. So it seems like the universe
likes this symmetry, this local symmetry likes uh, and to

(37:51):
do that, it has this field electro magnetic field, and
that's kind of how the universe works. And thank goodness, right,
because that's how we get liked. Yeah, that to why
the universe is literally so brilliant. Don't don't nice. It's
a nice light light joke. But I guess what does
it mean, Daniel, I'm not sure what it means. You know,
we live in this universe that has photons in it,

(38:13):
and that means that we live in a universe that
respects local gauge invariance. Like why does our universe respect
this super weird, very specific, difficult symmetry. You know, why
can you multiply wave functions by any number and it
have that be a different number at every place in
the universe and still it doesn't matter. Like it's fascinating.

(38:33):
I don't know what that means about the universe, but
it means that local gauge in variance is deeply deeply
built into the very structure of reality. So I think
we need like another hundred years of philosophers smoking banana
peels thinking about why that is to tell us, like,
you know, why reality is this way and not some
other way, but it also has very physical consequences for

(38:54):
the nature of reality. Well, I guess the question, maybe
before we get into too deep into that, is does
this also apply to particles that don't feel the electromagnetic force? Like,
aren't there particles that don't feel the photons and things
like that, right? Do they have their own field that
also preserves that symmetry. They do not. Neutrinos, for example,
do not have this symmetry. And neutrinos do not have

(39:15):
electric charge and do not interact with the electromagnetic field
and do not talk to photons. And if neutrinos did
have this symmetry, they would have electric charge. And that's
sort of what it means to have electric charges, that
you have this symmetry, and then there's a field out
there that like compensates for it. And so no, neutrinos
do not have this symmetry. You can't do the same
thing to neutrinos. They have another weird different symmetry, which

(39:38):
is why they feel the weak force, and quarks have
multiple symmetries, which is why they feel the strong force also,
but we can talk about that in a minute. It's
almost like you're saying that the forces in the universe are,
you know, there to maintain this symmetry in the universe exactly.
And that's why we call the photon a gauge boson,
and we call these things gauge fields and gauge forces.

(39:59):
Bec as it seems like the forces either they exist
in order to do this, or they exist because of this,
or this is the only way to have a universe
because of this symmetry. But every force exists in order
to preserve some local gauge invariance for the particles. It's
almost like they're forcing the universe. You know, I made

(40:20):
that same joke in that other podcast episode, and you
said I kind of forced it. Well, I'm trying to
be symmetric. You know, I'm copying the same joke, but
I'm doing it on the other side. You're forced feeding
me my own puns back to me being clever, right, Yeah,
And the nature of that field is really fascinating, Like,
for example, because we have this local gauge invariance and

(40:43):
you have these photons. That's why we have charge conservation.
Remember how we talked about how every symmetry the universe
leads to a conservation of something that's Nothers theorem. So
the fact that you can serve this property of electrons
is why you cannot create or destroy electric charge. How
does preserving symmetry lead to these conservation laws which seemed important? Right, Yeah, Well,

(41:06):
we're gonna have a whole episode about Nurther's theorem to
get into like the intuition behind it all. Right, now,
all you need to know is that every time you
identify a symmetry of the laws of physics, that directly
tells you that there's something that's conserved. Just like the
symmetry of moving your experiments somewhere else leads to conservation
of momentum, and the symmetry of rotating your experiment leads

(41:26):
to conservation of angular momentum. Well, the symmetry of rotating
your electron from plus wave function to minus wave function
leads to conservation of charge. I mean it's the same
concept for the other forces, right, strong and the weak force.
It's the same concept for the other forces, but it's
a different symmetry, and in those cases it's a much
more complicated symmetry. So, for example, the strong force has

(41:48):
not just like plus and minus charge, right it has
three different kinds of charge, red, green, and blue, and
it actually follows a much more complicated local gauge invariant.
It turns out, for the strong force, you cannot just
multiply the way function by minus one. You can rotate
the color space, like take red and map into green,

(42:09):
and green and map itto blue and blue and map
it back to red. Okay, you can do this kind
of rotation, and you can have a different rotation at
every place in space, like green here is blue. There
is half red plus half green over here, And you
can do that and it's fine, and it will not
change the nature of your predictions for how the strong
force works, because you have a bunch of gluon fields

(42:31):
that exist to compensate for that, to sort of correct
for that. You're saying, like, like these symmetries, it's almost
like a three way symmetry, right, Like it's not just
like a mirror, but it's like a house of mirrors
kind of, yeah, exactly, and just like the sphere. Right,
the sphere is a much more complicated symmetry than just
like reflection. You can rotate the sphere, and you can
rotate it in different ways. You can rotate it about
its equator, or about its poll or about some other directions.

(42:54):
There's actually three fundamental symmetries of the sphere. The same
thing is true for color space for the strong force.
And that's why we have eight gluons. Because the strong
force is a much more complicated local gauge invariance. It
requires more fields. Are actually eight different gluon fields required
just to preserve this force and so, but it's described

(43:15):
by the same fundamental mathematics. And this is why. If
you've heard that group theory is important for particle physics,
this is why, because group theory describes exactly how these
rotations work and sort of like the set of different
rotations that you can have. And so the reason the
strong force exists is because quarks have this weird property
that you can rotate their color in an arbitrary way

(43:36):
a different points in space, and the gluon fields are
there to compensate. That's why they exist. So then I
guess do physicists c force as something totally different than
most people think about it. You know, when I think
of a force, it's like pushing and pulling, or as
they usually describe it, it's like, you know, an electron
throws a photon to another electron, and that you know,

(43:57):
the throwing of the photon and the receiving of the
photo on is a way to kind of exchange you know,
a push or a pool or energy. But now it
seems like these fields are just there to preserve some
kind of symmetry. Is that kind of why you see
forces differently? Yeah, and that's that moment of elegance I
was talking about, Like we start very simply in the world,
seeing the world around us and categorizing and listing our observations. Oh,

(44:20):
that apple fell from the tree, or my friend fell
down the canyon, you know, or I felt this weird magnetism.
That's a pretty dark scenario there, these three a friend
down the canyon. Hopefully not a podcast like cost thinking
about the applications of gravity, and we just describe all
of those things in terms of our experiences. But you know,
that's not necessarily the most natural way to do it.

(44:43):
And that's why physics takes us and we transform our
intuitive experiences into like a list of observations and look
for mathematical patterns, and then we discover all these things
are actually connected to those things, and it turns out
we've been looking at this all the wrong way. And
those are my favorite moments in physics when we discover, oh,
we think about forces this way, actually they probably exist

(45:03):
for this totally other reason, and we've come at it
in this weird way just because of our experience. And
so you get this like flash of deep insight when
you're like, oh, the universe fits together in this beautiful,
mathematically elegant way. If you think about it in terms
of forces, you know, recovering local gauge invariants instead of
you know, building anti gravity machines to protect your clumsy friend.

(45:24):
I guess how would you describe it? Then? When an
electron pushes on another electron and they exchange photons, how
did physicist see it? How do you see it in
terms of preserving the symmetry? Yeah, well, physicists see it
in terms of carrying those rotations, Like a photon sort
of carries that rotation, you know, that's what a photon does.
It rotates from one gauge to another gauge, and so

(45:45):
when an electron communicates with another electron somewhere else in space,
it's sort of like communicating about their differences in their gauge.
And so that's what a photon does. It carries that information,
and that's what gluons do. Gluons rotate things through colors space.
They're like, Okay, this cork over here is a green cork.
That cork is a blue cork. You know, I got
a communicate from here to here, and I'm gonna change

(46:08):
the green to the blue as I move along. The
forces are sort of like there to connect these objects,
and they do so by rotating the gauge from one
place to another. And I think that's most clearly seen
in terms of the weak force. The weak force has
the same sort of structure, but then again in a
different internal symmetry space. It's almost like two electrons are
gauging each other. It's like, you know, an electron interacts

(46:31):
with the electromagnetic fields. If it moves, it creates some
sort of disturbance that then has to be kind of
squared away somewhere else by another electron. And then that
transfer of you know, wiggle or disturbance is what you
would call a photon. Yes, like patching up your check
book at the end of the month. Photons are there
to like find those pennies and move them from one

(46:52):
to column to another to make everything out up in
the end. Hopefully they don't get too creative like I
sometimes I may or may not do electron magnetic accounting exactly. Well,
maybe that's what quantum accounting really is. There really is
a quantum accounting firm. Yeah, where you have money and
don't have money at the same time. You're both rich
and broke at the same time. And you know, I
got an email this morning from a listener Ivan, who

(47:14):
is asking me about why I say that the weak
force makes sense to all be together, Like why the
ws and zs all makes sense to be in a
single field and also with the electromagnetic field. But like
you can also ask, like why don't you consider the
W plus and the W minus and the Z all
just separate forces. Why isn't the weak force three different forces?
Why do you even try to put these things together?

(47:36):
And the reason are these symmetry? So we discover that
like the W plus by itself doesn't preserve local gauge invariants.
But when you put the W plus and the W
minus and the Z together, then they do. So together,
these three fields work really hard to preserve another kind
of invariance, different from the one that's for the electron,

(47:56):
and different from the one that's for corks. And this
is why we have the weak force, because it preserves rotations.
And this thing called weak isospin space. And so these
three fields together do that. And as you say, you
can put electromagnetism and the weak force together to make
an even super theory which preserves a different number altogether
that individually neither the two forces preserve. Right. It's almost

(48:20):
like the more complicated the symmetries are, the more forces
you need to patch them up. Yeah. And of course
the really super fascinating wrinkle is that that symmetry electroweak symmetry,
the symmetry that's preserved by the photon together with the
two ws and the Z, that one doesn't actually work,
That one's broken, that one isn't actually preserved by the universe.

(48:40):
And the reason for that is the Higgs boson. The
Higgs boson breaks that symmetry, and that's why it exists.
That's how we were able to detect that it does exist,
because we saw, oh, this symmetry doesn't actually work. We
need something else out there to break this symmetry, and
that's what the Higgs does. And that's why the ws
and disease are massive while the photon and the gluons

(49:01):
are massless. That's wild, Like, maybe the only reason we
have mass is to patch up these brakes. Yeah, well,
the only reason we have mass is because this one
symmetry is broken. This electroweak symmetry isn't actually something the
universe respects because the Higgs breaks it. If we didn't
have the Higgs, then the W and the Z would
be massless, and so would all the other particles, and

(49:21):
we wouldn't have any mass without the Higgs. Don't we
have other like violations of symmetry also all over the
theory of physics, right, are in there all kinds of
different charge and parody violations? There are, yes, And so
we have these a lot of these approximate symmetries or
broken symmetries, And an approximate symmetry is like, well, maybe
we're just missing a piece, Like we're not talking about

(49:43):
the right thing, Like we think we've identified the thing
that's being preserved, the thing with the universe respects, but
we must be looking at it from like the wrong angle.
We don't quite have it right, you know. For example,
like if you had a cube, and you know, you
can rotate the cube and you still get a cube, right,
But what if you're not looking at it from the
right point of view. You're only looking at like a
two D slice of the cube, and so the symmetry

(50:04):
of it is not exactly preserved. So in some of
these cases we're probably just like, don't have the full
picture yet. We haven't really discovered what it is the
universe is preserving. Like maybe it's not broken. Maybe we're
just missing something. Yeah, maybe we're just missing we haven't
seen the full picture, but so far we haven't, which
means that to us, it does look like a broken universe. Yeah,
but some of these symmetries are perfect, Like charge conservation

(50:27):
is not when we've ever seen broken, Like, no particle
has ever broken conservation of charge, like a photon has
never turned into two electrons or electrons don't just disappear
into neutral particles. As far as we know, that is
a perfect symmetry of the universe charge conservation. Alright, Well,
I guess that tells us a little bit more about
the universe. You know, there's these hidden symmetries, these hidden

(50:48):
almost rules, right, that sort of govern everything, and that
may even like give rise to things that we take
for granted, like light. Maybe that's just the universe's way
of trying to stay beautiful. Yeah, the way I think
about it is that you can't have a universe that
respects this symmetry without the photon. Like, the photon is
absolutely necessary in order to have a universe that respects

(51:10):
this symmetry. So therefore we do have a universe that
respects this symmetry. Now, the question we can ask is like, well,
why what a weird thing for universe to insist on?
What does that mean? And I think that's the kind
of thing that in a hundred years people look back
and be like, oh my gosh, that was so obvious.
The universe was screaming the answer to you. But here
we are in the forefront of ignorance. We don't really

(51:30):
know what this clue means yet. So I think it
does mean something deep about the universe. We just still
need to digest it. So come on, philosophers, tell us
what it all means. Well, it sounds like the answer
might come from physics, right, you're saying, like, maybe we
don't know why now, but maybe in the future to
a physicist that will seem obvious, right, Like, maybe there
is a physical answer to these white questions, and just

(51:50):
because we don't know what they are now, you're bumping
them over to the philosophy department. Yeah, and it could
also come from mathematics. We didn't appreciate the structure of
these symmetries until we learned group theory from mathematics. It
turns out that perfectly describes everything that's going on here.
Mathematicians invented it for like totally other reasons, because they
just like thinking about how things rotate in their minds.
But it could be that what we've discovered now needs

(52:12):
like some new branch of mathematics to describe it and
give us like an understanding of what the meaning is. Intuitively,
so it might just be that we need to invent
new mathematical words and concepts to fit these things together
into a deeper understanding. I see you're passing the bug
now to the mathematics department. You're like, blame everyone but us.
You know. It's like when poets invent new words, you know.

(52:34):
I think English professors are like, can you really just
do that? You know? And so I don't know if
mathematicians want us inventing the new math, you know. I
think they, you know, really would prefer to do that themselves.
I see, now you're blaming the English department as well.
That's right. I'm good at this. Bring out from the problem.
I can blame them for it. The certain symmetry about you, Daniel,
I feel like you're trying to preserve. Look, we made

(52:57):
these crazy discoveries. Everybody else needs to tell what's going on.
You know. It's really fun to think about. And this
is one of the reasons why I agreed to join
the philosophy department here, because I do like to think
about what it means about the universe. Because in the end,
that's why we're doing these experiments, not because we like
to write down tidy mathematical equations, but because we hope
that by doing so, they will speak to us, and
they will tell us, Look, the universe follows this rule.

(53:20):
The universe has to be this way, and we'll get
some understanding of why it is a pretty perplexing universe.
And you know what, whether or not it's beautiful or broken,
we we still love it. You know, no pressure, You
don't have to tell us everything. You know, we're just
here for you or because of you. I don't know, man,
that's another philosophical department. We do love the universe though,

(53:40):
that's true. All right. Well, we hope you enjoyed dad,
Thanks for joining us, see you next time. Thanks for listening,
and remember that Daniel and Jorge explained. The universe is
a production of I Heart Riding. For more podcast asked
from my Heart Radio, visit the I Heart Radio app,

(54:03):
Apple Podcasts, or wherever you listen to your favorite shows.