Speaker 1: The universe is like a big puzzle. It's a mystery
Speaker 1: for us to unravel. But it's not just a heaping
Speaker 1: pile of unorganized facts. There are patterns to the madness.
Speaker 1: There are clues that suggest a deep underlying organization. For example,
Speaker 1: if you multiply mass and velocity together something we call
Speaker 1: it momentum, you get a number which the universe seems
Speaker 1: to respect. You calculate the momentum of a bunch of rocks,
Speaker 1: You get some number. Then you bang them into each other,
Speaker 1: change their directions, break them into pieces. Whatever you calculate
Speaker 1: to momentum again, same number. The universe respects this number,
Speaker 1: conserves this weird combination of mass and velocity. Why does
Speaker 1: it care about mass times velocity? Does it not care
Speaker 1: about mass times acceleration or mass times ice cream or
Speaker 1: chocolate times velocity. For a long time, we had no idea.
Speaker 1: We just saw that it did respect this until a
Speaker 1: genius came along, a mathematician who, during a brief dabt
Speaker 1: in physics, made a connection that explained it all. Emmy
Speaker 1: Kneather pulled back a layer of reality to show us
Speaker 1: the deep underlying mechanism behind these conservation laws and not
Speaker 1: just about momentum, about anything the universe respects and conserves.
Speaker 1: Without her equation, we wouldn't have understood the beautiful mathematics,
Speaker 1: the foundations of the Standard model. We wouldn't have discovered
Speaker 1: the Higgs boson. So in honor of Emmy kne there's
Speaker 1: one hundred and forty third birthday, we're going to be
Speaker 1: diving into her life and her work. Welcome to Daniel
Speaker 1: and Kelly's extraordinarily momentous universe.
Speaker 2: Hello.
Speaker 3: I'm Kelly Wiener Smith. I study parasites and I get
Speaker 3: less metrical with it.
Speaker 1: I'm Daniel. I'm a particle physicist, and I'm getting rounder
Speaker 1: and rounder. I'm not sure what was happening over there.
Speaker 3: I might have both of those things happening concurrently, but
Speaker 3: it's okay.
Speaker 2: You know.
Speaker 3: The nice thing about getting older is that I care
Speaker 3: way less than I used to, so you know, freedom
Speaker 3: in that regard.
Speaker 1: I like to think that I'm approaching a spherical physicist,
Speaker 1: which is the approximation most physicists would make about themselves eventually. Anyway,
Speaker 1: it's a.
Speaker 3: Very efficient shape. I like that, and I like the
Speaker 3: idea that there's a goal in mind. Yeah, so today
Speaker 3: we are talking about a woman scientist who many people
Speaker 3: don't know, who they probably should. Do you remember when
Speaker 3: you first learned about Emmy whose last name I'm going
Speaker 3: to try to avoid saying.
Speaker 1: I do remember I learned about Emmy Nuther in graduate
Speaker 1: school when I was taking quantum field theory, because that's
Speaker 1: when you're thinking about the fields and how they oscillate
Speaker 1: and their symmetries very importantly. And I remember my professor
Speaker 1: Lawrence Hall writing this equation on the board, Nuther's theorem,
Speaker 1: and feeling like, oh, my gosh, that is so deep
Speaker 1: and powerful because it just told you so much about
Speaker 1: how the universe worked and connected these two ideas. And
Speaker 1: the equation itself is so simple, and when he derives
Speaker 1: it seems so obvious. But it's one of these things
Speaker 1: that it's so brilliant, it's so insightful that it's hard
Speaker 1: to take yourself back to before it was understood. It's
Speaker 1: like it changes the way you look at the universe
Speaker 1: so deeply that it's hard to remember how much of
Speaker 1: an insight it was.
Speaker 3: Oh that's beautiful, And I bet you have totally hooked
Speaker 3: our audience on learning all about this equation.
Speaker 1: I hope so, and it was in that same moment
Speaker 1: that he told us that this was an equation by
Speaker 1: a female physicist. And you know, that's unfortunately rare thing
Speaker 1: to hear, especially somebody contributing to physics in the early
Speaker 1: parts of this century. You know, physics is still not
Speaker 1: a place of gender balance, unfortunately, and in the early
Speaker 1: part of this century much much less so. And so
Speaker 1: hearing about the deep contribution nw they're made to physics
Speaker 1: is especially impressive given how long ago she did it.
Speaker 3: So I'm under the impression that she was a mathematician
Speaker 3: who jumped into physics to just dazzle everyone and then
Speaker 3: went back to math. Was math comparably bad about sex
Speaker 3: balance on faculty back then? I'm guessing the answer was
Speaker 3: yes and still is yes.
Speaker 1: The answer was yes and still is yes. Unfortunately, math
Speaker 1: is no better than physics. Like if you look at
Speaker 1: a breakdown of faculty in the United States, it's like
Speaker 1: twenty ish percent female in physics and in math departments. Yeah, absolutely,
Speaker 1: we still have a lot of the same problems that
Speaker 1: we did. Things are better it used to be one percent.
Speaker 1: Twenty percent is progress, but we have a long way
Speaker 1: to go. Not that we need exactly fifty percent female,
Speaker 1: exactly fifty percent male. But we know that this is
Speaker 1: emblematic of issues we have in our department that make
Speaker 1: it harder for women to succeed.
Speaker 3: Yep, all right, Well, lots of progress to make, and
Speaker 3: so we decided that we wanted to have a series
Speaker 3: of episodes about women's scientists who are amazing who you
Speaker 3: perhaps have never heard of, in response to actually a
Speaker 3: couple different listener questions that we got. And so this
Speaker 3: month we're going to have a few episodes of that type,
Speaker 3: and this is the one we're starting with today.
Speaker 1: Yeah, Emmy Nuther is maybe one of the greatest, most
Speaker 1: impactful geniuses you've never heard of. She made contribution to
Speaker 1: physics that impact you, impact our understanding of the universe.
Speaker 1: But she hasn't talked about nearly well enough. And so
Speaker 1: to get a sense for like, how much did people
Speaker 1: know about her? Have people heard about her? Do people
Speaker 1: understand the contribution she made? I went out there and
Speaker 1: asked people, Hey, do you know what Emmy Nuther revealed
Speaker 1: about the universe? So here are a bunch of answers
Speaker 1: from our volunteers, and if you'd like to participate for
Speaker 1: a future episode. Please don't be shy. We want to
Speaker 1: hear your voice on the pod. Write to us two
Speaker 1: questions at Danielandkelly dot org. So you've had a few
Speaker 1: clues already from our introduction, but do you know what
Speaker 1: Emmy Nuther revealed about the universe. Here's what our listeners
Speaker 1: had to say. That there's a simple relationship mathematically with
Speaker 1: symmetries in the universe. She revealed things that Noeita could.
Speaker 4: The one who came up at the idea of using
Speaker 4: type one A supernova as a way to measure the
Speaker 4: expansion rate of the universe. Amy Nota have revealed something
Speaker 4: about the translational symmetry in the universe, and that all
Speaker 4: positions in the universe are somewhat indistinguishable.
Speaker 1: There was a standard candle in the universe might have
Speaker 1: been a certain type of supernova.
Speaker 2: I have no idea, but I'm eager to find out mathematician,
Speaker 2: maybe back in Einstein's time, who came up with a
Speaker 2: really important concept but never got full credit for it.
Speaker 5: I'm sorry, I have no idea who that is.
Speaker 1: Emy unfortunately did not reveal anything about the universe to me, specifically,
Speaker 1: because I don't think i've ever heard the name.
Speaker 6: Where there is a conservation law, there will be some symmetries.
Speaker 6: And this changed the way that we approved which can
Speaker 6: bring together physical properties.
Speaker 7: Emmy North, another woman who deserved a Nobel price but
Speaker 7: did not get it, showed that symmetries in the universe
Speaker 7: were related to conservation laws.
Speaker 5: Why is anyother.
Speaker 6: Gonna be the name for the momentum?
Speaker 3: Oh, I guess she did something about momentum.
Speaker 5: I'm gonna have to go look this up.
Speaker 1: Ah, they might have proved that there's no either, just kidding.
Speaker 1: I think it had something to do with.
Speaker 3: Neutrinos or was it symmetry breaking something?
Speaker 5: Oh no, I have no idea who this person is
Speaker 5: at all, So it must be a woman and she
Speaker 5: did something really important and then took the credit, and
Speaker 5: that's why we have no idea who she is. Or
Speaker 5: maybe it's just me and everybody else does.
Speaker 3: So we had a handful of listeners who gave like
Speaker 3: spot on answer, which makes me wonder if we had
Speaker 3: asked a similar number of people who weren't listeners to
Speaker 3: our show, like a random draw from the population, what
Speaker 3: the answer would have been. Because I think we've got
Speaker 3: a population of listeners who are more likely than average
Speaker 3: to know the answer, but still there were plenty who didn't.
Speaker 3: And the last answer was just like spot.
Speaker 1: Oh man, yeah, I know. And there's some great guesses
Speaker 1: in here, like the no Ether love that joke.
Speaker 3: Nice yep yep epic. Let's jump right in. Tell us
Speaker 3: about all right, and I'm gonna try to say the name.
Speaker 3: Tell us about Emmy Noether.
Speaker 1: Neuter neuter.
Speaker 3: Yeah, that's not what you were saying earlier.
Speaker 1: My pronunciation of her name is probably going to vary
Speaker 1: a lot. There's not a lot of symmetry or conservation
Speaker 1: in my pronunciation of this name. It's a little uncomfortable
Speaker 1: for me, but I'm gonna do my best. I mean,
Speaker 1: Luther comes from a really interesting family. Her dad was
Speaker 1: a mathematician. She was born late eighteen hundreds, and so
Speaker 1: she comes from an academic background. You know. Her family
Speaker 1: valued thinking and education and sort of higher intellectual pursuits.
Speaker 1: Some of her brothers became scientists, another one became a mathematician.
Speaker 1: So her father is a well known mathematician, Max Nuther.
Speaker 1: Though eventually, of course, Emmy totally eclipsed him, so instead
Speaker 1: of Emmy being Max's daughter, now Max is like Emmy's father.
Speaker 1: Way to go, Emmy, you know, like the way and
Speaker 1: you go to pick up your kid at school. I'm
Speaker 1: just like Hazel's dad. I don't have a name. I'm
Speaker 1: just Hazel's dad.
Speaker 3: You know What's funny. I was the older sibling, but
Speaker 3: my brother George was way cooler than me. So even
Speaker 3: though I came first, everyone I met at our school
Speaker 3: was still like, oh, man, are you George's sister? And
Speaker 3: I was like, no, that's not supposed to work that way.
Speaker 3: But anyway, he was way cooler than me.
Speaker 1: So that's what happened exactly. Well, I'd be very proud
Speaker 1: to go down in history as Hazel's dad. I hope
Speaker 1: that happens anyway. Back then, though she comes from an
Speaker 1: academic family and her brothers were encouraged to pursue higher
Speaker 1: intellectual degrees, it's not an option that women had. So
Speaker 1: she was actually trained to be an English and French
Speaker 1: teacher at a finishing school, but she was like, man,
Speaker 1: I don't want to do that. I want to study math.
Speaker 1: She had like this deep appetite and this aptitude for
Speaker 1: math at a very early age. But the problem is
Speaker 1: in Germany, where she grew up, women were not allowed
Speaker 1: to enroll in universities, so she like tried to enroll
Speaker 1: in university to get a degree at Gottingen and they
Speaker 1: were just like no, So she just went anyway. She's
Speaker 1: like sat in on the lectures and she's like, I'm
Speaker 1: just gonna listen. Like they're talking about math. I'm here,
Speaker 1: I'm learning about it. And so she picked up a
Speaker 1: lot of math.
Speaker 3: That must have required some buy in from the faculty
Speaker 3: members right to not kick her out. Is there any
Speaker 3: sense for like, were the members of the maths department,
Speaker 3: you know, feeling differently than the members of the admissions group.
Speaker 3: Were they happy to have her there?
Speaker 1: Yeah, they certainly didn't kick her out right, and so
Speaker 1: she could sit in the back and she wasn't disturbing anybody.
Speaker 1: But you're right, people could have been like, this is
Speaker 1: deeply offensive. You must leave, and that didn't happen, and
Speaker 1: times were changing. It was only nineteen oh four, a
Speaker 1: couple of years later when erling In University decided to
Speaker 1: allow women to enroy. So she was sort of on
Speaker 1: the cusp of that, and then she immediately enrolled and
Speaker 1: she got a degree in math, and then she was
Speaker 1: fortunate in some way that she was hanging out in
Speaker 1: Gottingen right around the time when it was the center
Speaker 1: of the universe in terms of math and geometry. So like,
Speaker 1: obviously this is right around the time of Einstein and relativity, right,
Speaker 1: And he's a German professor, and like Germany was definitely
Speaker 1: the center of physics and math at the time. You
Speaker 1: got guys like David Hilbert Klein, Minkowski, Shortsiled. All these
Speaker 1: guys who made huge contributions and we're thinking deeply about
Speaker 1: the physics of space and time and relativity were all
Speaker 1: there like in Gottingen at the time, and so she
Speaker 1: worked with them. She did her PhD. And she got
Speaker 1: a PhD in nineteen oh seven, right, so like more
Speaker 1: than one hundred years ago. She was the second woman
Speaker 1: to ever get a PhD in math. So like really
Speaker 1: cutting edge. This is not an easy track, you know,
Speaker 1: somebody like me, I went into physics. I followed a path.
Speaker 1: It was laid out for me. You know, I knew
Speaker 1: exactly what to do and where to go. I'm not
Speaker 1: a trailblazer in any respect. You know, there's like a
Speaker 1: very clear track for me to follow.
Speaker 3: I think you're under selling yourself.
Speaker 1: But okay, I mean sure, I had to do a
Speaker 1: lot of hard problem sets, but you know, the track
Speaker 1: was there, it was clear what I needed to do.
Speaker 1: But she not only had to do the hard problems,
Speaker 1: she had to make her own path. You know, this
Speaker 1: is not something an established trajectory for folks. She was
Speaker 1: really resilient. When she got her PhD. She couldn't get
Speaker 1: a job. People just kept rejecting her because she was
Speaker 1: a woman. And so for the next eight years she
Speaker 1: did research in math and she taught, but she wasn't paid.
Speaker 1: She didn't have an official position. She just like hung around.
Speaker 1: She was just like a volunteer. But you know, she
Speaker 1: came from a wealthy family which could support her, so
Speaker 1: she didn't need to like go work as a seamstress,
Speaker 1: and she just followed her passion. In nineteen fifteen, for example,
Speaker 1: she applied for a position at Gottingen and she was
Speaker 1: rejected and the review committee said, quote, I have had
Speaker 1: up to now unsatisfactory experiences with female students. She's an exception,
Speaker 1: which is like, you know, thanks for grudgingly admitting that
Speaker 1: she has.
Speaker 3: Talents here with faint praise.
Speaker 1: Yeah, yeah, And then David Hilbert, who was like one
Speaker 1: of the greatest mathematicians in history and already recognized at
Speaker 1: the time, you know, clearly a leading mathematician of his age.
Speaker 1: He wrote and complained. He said, quote, I do not
Speaker 1: see that the sex of the candidate is an argument
Speaker 1: against her. After all, we are a university, not a bathhouse.
Speaker 3: That's great, I know, go Hilbert.
Speaker 1: But they weren't persuaded, and they did not invite her
Speaker 1: onto the faculty. So instead Hilbert signed up to teach
Speaker 1: a bunch of classes that he thought she would be
Speaker 1: good at teaching, and then he just had her teach
Speaker 1: in his place. So like, yeah, she got to teach,
Speaker 1: but she didn't get the job. So like, you know,
Speaker 1: there's pluses and minuses there, and maybe as sort of
Speaker 1: like a middle finger to the faculty, she ended up
Speaker 1: swimming a lot at the men's only pool.
Speaker 3: Ah, good for her. Do we happen to know if
Speaker 3: Hilbert paid her for her teaching labor or did he
Speaker 3: get the pay while she taught.
Speaker 1: He hired her as a teaching as, so she was
Speaker 1: paid sort of at the gradual student level even though
Speaker 1: she was doing faculty level work. And I don't know
Speaker 1: if he supplemented it privately.
Speaker 3: I mean, that's still more than she was going to
Speaker 3: get otherwise. And it's a chance to show everybody, screw you, guys,
Speaker 3: she can totally do this.
Speaker 1: Yeah, exactly. And you know, she just stuck around even
Speaker 1: though officially the institutions didn't want her there. Her colleagues
Speaker 1: valued her, like Hilbert knew that she was a genius.
Speaker 1: And all these guys were thinking about physics and thinking
Speaker 1: about Einstein's new theory of relativity, which is a very
Speaker 1: mathematical way to think about the universe and space and time.
Speaker 1: And you know, these are very new ideas mathematically, like
Speaker 1: Remont had just figured out how to think about higher
Speaker 1: dimensional spaces and surfaces in those spaces and to do
Speaker 1: this math, and Einstein had learned about it and used
Speaker 1: it to describe gravity, and so this was all very
Speaker 1: new and very exciting, and so there was a lot
Speaker 1: of talk between the mathematicians and the physicists. Emmy was
Speaker 1: mostly interested in math, like she was really excited about
Speaker 1: what we call algebra, which is much more than like
Speaker 1: you know, x equals seven plus y and manipulating equations
Speaker 1: like we learn in middle school algebra is a broader
Speaker 1: field that thinks about, you know, relationships between objects and symmetries.
Speaker 1: You have abstract algebra, linear algebra, you know, thinking about
Speaker 1: like vectors and matrices and rotations and symmetries, and it's
Speaker 1: a really fascinating and deep area of mathematics and very
Speaker 1: closely related to general relativity and what Einstein had done
Speaker 1: and thinking about the laws of physics. So this is
Speaker 1: the kind of thing she was very excited about, and
Speaker 1: so she was working mostly in abstract algebra, but she
Speaker 1: did spend an afternoon or two thinking about the problems
Speaker 1: in physics, which is when she came up with her
Speaker 1: famous Nuther's theorem.
Speaker 3: Oh man, I mean, algebra is great as long as
Speaker 3: it's not the word problem. I'm helping my daughter with
Speaker 3: those right now, and those are no fun. But algebra
Speaker 3: in general I could do for fun all day as
Speaker 3: long as it's not the word problems.
Speaker 1: You know, word problems are really challenging. Translating a paragraph
Speaker 1: into equations is really hard, and we have a whole
Speaker 1: class on just that here because a lot of students
Speaker 1: show up and they can do the math, but they
Speaker 1: don't know how to get to the math. You know,
Speaker 1: you have this problem and there's like a train, and
Speaker 1: there's times, and there's balls, and there's inclined planes or whatever.
Speaker 1: They don't know how to translate that into the math.
Speaker 1: And you know that's actually the core physics, knowing how
Speaker 1: to go from like here's a problem in the real world.
Speaker 1: How do I build a mathematical model that captures the
Speaker 1: essential bits of it that lets me calculate the answer?
Speaker 1: How do I convert this word problem into math? That's
Speaker 1: what physics is.
Speaker 2: Like.
Speaker 1: When you want to solve a problem in physics, you
Speaker 1: need to turn it into a mathematical model. But that's
Speaker 1: not easy, right, It's hard, and you got to teach
Speaker 1: it to people. And so a lot of people show
Speaker 1: up here and they struggle with that and they feel
Speaker 1: bad about it because they don't know how to do it.
Speaker 1: But like, the whole field of physics is basically that, like,
Speaker 1: turn this into a math problem. That's what we do,
Speaker 1: and so it's overlooked, I think and undertaught.
Speaker 3: This is though, what got me into science. Like I
Speaker 3: hated word problems in high school. But when I took
Speaker 3: an ecology class and our job was to think about
Speaker 3: a system like a predator prey system and we were
Speaker 3: asked to describe it with equation M. Like the first
Speaker 3: time I did that was the first time I thought,
Speaker 3: I'm going to spend the rest of my life as
Speaker 3: a scientist. This is so much fun, I think. I
Speaker 3: just don't like the like, you know, the train leaves
Speaker 3: it five and it's like, oh, this is boring, it's
Speaker 3: not real. But when you're trying to describe like the universe,
Speaker 3: that's much more.
Speaker 1: Inciting to me. Well, I remember this contrast my first
Speaker 1: year of college between my physics and philosophy classes, because
Speaker 1: in physics, you had a question and you're like, Okay,
Speaker 1: this electron is oscillating. What's going to happen over here
Speaker 1: on this attena over there? And you want an answer,
Speaker 1: But there is an answer, and you can get the
Speaker 1: answer by turning the problem into a math problem. And
Speaker 1: then math is either right or wrong, you know, and
Speaker 1: like there's rules about math and there's no arguing, Whereas
Speaker 1: in my philosophy class, which I also deeply enjoyed, you know,
Speaker 1: there's a question of like you have to pull a
Speaker 1: lever on this train to kill one person or let
Speaker 1: ten people die? What's right what's wrong, and man, we
Speaker 1: could argue forever we make any progress, and people could disagree,
Speaker 1: and you couldn't definitively say who was right and wrong.
Speaker 1: You couldn't turn it into a math problem. People have
Speaker 1: been arguing about that question for thousands of years and
Speaker 1: still nobody knows the answer. So to me, that was frustrating,
Speaker 1: anisode of a relief to get to, like turn something
Speaker 1: into a math problem. And yeah, I think that's probably
Speaker 1: why I became a scientist and not a philosopher.
Speaker 3: I like the comfort that math and statistics brings.
Speaker 1: Yeah, I agree, I agree.
Speaker 3: All right, So on that note, let's take a break,
Speaker 3: and then when we get back, let's figure out what
Speaker 3: Emmy revealed to the world. Okay, we're back. We're done
Speaker 3: geeking out about how much we love equations that describe
Speaker 3: animals in the rest of the universe. So now let's
Speaker 3: talk about what Emmy's amazing equations reveal about our universe.
Speaker 3: I guess that's still geeking fine.
Speaker 1: Geek, Yeah, it is good. That's what we're here for.
Speaker 1: This geek out deeply. Yeah. So, I mean, if there
Speaker 1: was an expert in algebra and thinking about equations and
Speaker 1: thinking about symmetries of those equations, you know, like very simply,
Speaker 1: if you have an equation like X equals ten, you
Speaker 1: could add two to both sides and it doesn't change
Speaker 1: the answer, right, X plus two equals twelve still reveals
Speaker 1: the same X. Right. There's no change there in the
Speaker 1: fundamental solution to the problem. And so this is the
Speaker 1: kind of thing she was thinking about, though, of course,
Speaker 1: lots of other kinds of changes and more dramatic things
Speaker 1: about the universe, because there's lots of fascinating symmetries in
Speaker 1: the universe. Like you know, take for example, a sphere, right,
Speaker 1: a perfect sphere, you rotate it, you still have a sphere. Right,
Speaker 1: There's no change in the sphereness of the sphere. And
Speaker 1: if you have a sphere in the universe and you
Speaker 1: spin it, it's going to interact with the universe the
Speaker 1: same way. It's going to bounce stuff off of it,
Speaker 1: it's going to gravitate, like, there's no fundamental change in
Speaker 1: how the universe treats it once you rotate the sphere.
Speaker 1: It's an example of a symmetry, and that's like the purest,
Speaker 1: cleanest kind of symmetry. You could also have other kinds
Speaker 1: of symmetries. Like let's say you have an object that's
Speaker 1: not a sphere, you know, like a cube, and you
Speaker 1: rotate the cube. Now the cube looks a little bit different, right,
Speaker 1: but in lots of situations it still acts the same.
Speaker 1: Put that cube in orbit around the Sun, and it
Speaker 1: doesn't matter how you've spun it, It's still going to
Speaker 1: have the same orbit. It doesn't change the orbit of
Speaker 1: the cube around the Sun. Dynamics of its orbit around
Speaker 1: the Sun don't change if it's a cube, or if
Speaker 1: it's a circle, or if even if you squeeze it
Speaker 1: and make it like a rod like, it only matters
Speaker 1: what its total mass is. Nothing else matters. So there
Speaker 1: are symmetries there to gravity. You can change this object,
Speaker 1: you can transform it, and not change the fundamental physics.
Speaker 1: So there's a symmetry to gravitation. You can transform the objects,
Speaker 1: but the equations don't change.
Speaker 3: So I assume that before Emmy came along, we probably
Speaker 3: understood that spheres in cubes were symmetrical. So what did
Speaker 3: she add to that? Did she add the understanding that
Speaker 3: that's going to be the case anywhere in the universe,
Speaker 3: or have we not gotten to her contribution.
Speaker 1: Yet we have not yet gotten to her contribution. But
Speaker 1: what she did is show us what these symmetries mean,
Speaker 1: the consequences of these symmetries. But first, let's get a
Speaker 1: little bit more comfortable with the kinds of symmetries that
Speaker 1: we're talking about here. Another really important and fundamental symmetry
Speaker 1: in the universe is location. We call this translation invariance,
Speaker 1: which is a fancy way of saying that if you
Speaker 1: do an experiment anywhere in the universe, you should get
Speaker 1: the same answer. Like, let's say you're measuring the speed
Speaker 1: of light. For example, you could do your experiment out
Speaker 1: in space near Jupiter. You could do your experiment in
Speaker 1: the space between the Milky Way and Andromeda. You could
Speaker 1: do it some other random place in the universe. This
Speaker 1: speed of light is just a number, and as long
Speaker 1: as you have perfect vacuum, doesn't matter where you are.
Speaker 1: You do your experiment anywhere you should get the same answer.
Speaker 3: So, say you were to measure something and it was
Speaker 3: different when you were near Jupiter, perhaps because Jupiter is massive,
Speaker 3: What does that tell you? Does that tell you that
Speaker 3: you're measuring something that's not symmetrical, and thus isn't related
Speaker 3: to what Emmy came up with.
Speaker 1: Yeah, that's a great question because you might think, oh,
Speaker 1: Daniel specifically was talking about measuring in a vacuum. But
Speaker 1: we know the speed of light isn't always the same
Speaker 1: if you're not in a vacuum, So what's going on there.
Speaker 1: The answer is a little technical, it may be unsatisfying,
Speaker 1: which is that you're measuring a different thing in that case,
Speaker 1: and you have to include Jupiter in your experiment. So,
Speaker 1: for example, if you're measuring the speed of light near
Speaker 1: a massive object, where you're measuring the speed of light
Speaker 1: through a glass crystal, then you're measuring something different than
Speaker 1: if you're measuring the speed of light in a vacuum.
Speaker 1: And so it doesn't matter where you are in the universe.
Speaker 1: If you measure the speed of light near Jupiter, like
Speaker 1: you want to know the speed of light through the
Speaker 1: atmosphere Jupiter, you got to bring Jupiter along with you
Speaker 1: and then do the experiment out in the middle of
Speaker 1: deep space or over here or over there. You should
Speaker 1: get the same answer. It doesn't depend on the actual space,
Speaker 1: right And what this tells us is that like space
Speaker 1: has no fundamental markings, there's no way you can identify
Speaker 1: where you are in space, which is something we kind
Speaker 1: of knew, all right, there's no like zero to the
Speaker 1: origin of space that means something deep. There's no way
Speaker 1: you can like figure out where you are in space.
Speaker 1: You can't like look up your fundamental coordinates in space
Speaker 1: because there aren't any. All we have in space are
Speaker 1: relative distances. I'm a meter from here, I'm ten meters
Speaker 1: from there, because all of space is the same.
Speaker 3: Okay, got it.
Speaker 1: So that's one example of a symmetry of the universe
Speaker 1: that's really important. And another is direction, Like it shouldn't
Speaker 1: matter what direction you're pointed in when you're measuring fundamental
Speaker 1: constants about the universe or doing an experiment, because the
Speaker 1: universe has no preferred direction. Right like here on the
Speaker 1: surface of the Earth, obviously there's an up and there's
Speaker 1: a down, and there's one definition of that that makes sense,
Speaker 1: right because we have gravity, and so we're near a
Speaker 1: gravitational field, and so it makes sense to call one
Speaker 1: direction up and one direction down. But if you're far
Speaker 1: from a planet, there is no direction that's like more
Speaker 1: up than down. If you mentally imagine the galaxy, you
Speaker 1: probably put it in your mind is a flat disc,
Speaker 1: and you imagine things above that disc and blow that disk,
Speaker 1: and you organize it in your mind. But you could
Speaker 1: also spin that galaxy at an angle and tilt it
Speaker 1: or look at it from another direction, and those are
Speaker 1: just as good. They're equivalent. Right. There's no like fundamental
Speaker 1: updirection out in the universe. There's no way to look
Speaker 1: at the milky Way that's right or wrong, and there's
Speaker 1: no way that the universe prefers any angle over another.
Speaker 3: Yeah, astronauts report finding this very confusing when they get
Speaker 3: up there, but they learn it quickly.
Speaker 1: There's yeah, And that's really countertit because it's not part
Speaker 1: of our experience because we live in a place where
Speaker 1: there is a defined up and down. And so in
Speaker 1: that same way, you might complain and say, well, your
Speaker 1: experiment can have a different outcome in the middle of
Speaker 1: deep space and near the surface of the Earth, And
Speaker 1: that's true, but you've got to include the Earth in
Speaker 1: your experiment, right. So if your experiment is like, how
Speaker 1: much do I weigh on a scale when there's no
Speaker 1: masses around me, the answer is going to be zero.
Speaker 1: No matter where you are in the universe, there's no
Speaker 1: part of space that depends on it. No angle matters
Speaker 1: in the universe. But if you're including a planet in
Speaker 1: your experiment, you know then you're going to measure the
Speaker 1: same value on the scale no matter where you and
Speaker 1: that planet are and the orientation of that planet. So
Speaker 1: you got to include the planet in the experiment in
Speaker 1: order to really get the symmetry.
Speaker 3: Got it, Okay? Are there symmetries we should talk about?
Speaker 1: There are so many fascinating symmetries. Like another important symmetry
Speaker 1: is time. We don't think that the laws of physics
Speaker 1: depend on time. We think, for example, the speed of
Speaker 1: light is the speed of light, and it's the same
Speaker 1: today as it's going to be tomorrow and a thousand
Speaker 1: years ago and a billion years ago. We think the
Speaker 1: speed of light is a constant. And this is sort
Speaker 1: of a fundamental assumption we make in science all the time.
Speaker 1: That's sometimes unspoken, that you can measure something and then
Speaker 1: come back twenty years later and measured again and you
Speaker 1: should get the same answer, right. I mean, you're measuring
Speaker 1: the same universe. It's the same thing. But it's not
Speaker 1: something that necessarily has to be right. It could be
Speaker 1: we live in the universe that is evolving and changing.
Speaker 1: We just sort of assume that the universe has physical law,
Speaker 1: and then we can do experiments to reveal those laws,
Speaker 1: and we can do it whenever we like. It doesn't
Speaker 1: matter if it's Christmas or if it's summer or whatever.
Speaker 1: And that's fascinating and very very useful. But that's like
Speaker 1: another symmetry of the universe.
Speaker 3: So I'm not really used to thinking of time as
Speaker 3: a thing that you can call symmetrical, like you know,
Speaker 3: for me, if something symmetrical are out, like the one
Speaker 3: side of my head has a lot more gray hair
Speaker 3: than the other. Thing is I'm thinking of like a
Speaker 3: shape that is not exactly the same.
Speaker 1: Yeah, So the way to think about it is this.
Speaker 1: It's like imagine applying a transformation and then seeing if
Speaker 1: there's a change. So, for example, you're thinking, the left
Speaker 1: half of my face is the same as the right
Speaker 1: half of my face. The transformation you're doing there is
Speaker 1: you're reflecting it, right, So it's called a reflection symmetry.
Speaker 1: If your face is symmetrical, then take your left side
Speaker 1: and reflect it onto your right side and they should
Speaker 1: look the same. Most people faces actually not that symmetrical.
Speaker 1: And so if you do that, you look kind of weird.
Speaker 1: But that's reflection symmetry, right, And so the concepts always
Speaker 1: have a transformation, and then a question you ask, like
Speaker 1: has this changed? So in your case, we're saying reflect
Speaker 1: your face through a mirror, and we're asking do you
Speaker 1: look different. In the case of time, for example, we're
Speaker 1: asking shift time forward by ten seconds or by a
Speaker 1: billion years? Do the laws of physics make any difference?
Speaker 1: Do your experiments get the same results or not? And
Speaker 1: so that's the sort of connection. You always have a
Speaker 1: transformation you're applying, and then you're asking is something changed
Speaker 1: or not?
Speaker 3: Okay, so what kind of transformations could you apply that
Speaker 3: are not symmetrical? Oh, I think that'll help me understand
Speaker 3: why time is symmetrical.
Speaker 1: Yeah, that's a great question. Something the universe is not
Speaker 1: symmetrical to is acceleration. Like take your experiment, and now
Speaker 1: take your experiment and put it on a rocket ship
Speaker 1: so that there's a thrust. It's like accelerating through space.
Speaker 1: You can get different answers, and you can think about
Speaker 1: this very simply, like say you're just in a box
Speaker 1: and your experiment is I have a ball on the floor,
Speaker 1: and I'm just watching it. If you're not accelerating, you're
Speaker 1: going to get one answer. If you are accelerating, then
Speaker 1: the ball is going to roll to the back of
Speaker 1: the box, right because it's not being accelerated and the
Speaker 1: box is being accelerated. It's like a bowling ball in
Speaker 1: the back of a truck. And so you're going to
Speaker 1: get a different answer. And so the universe is not
Speaker 1: symmetric to accelerations. Like, you accelerate your experiment, you're going
Speaker 1: to get different answers. You move your experiment, you shouldn't
Speaker 1: get a different answer. You spin your experiment to a
Speaker 1: different direction, you shouldn't get a different answer. You delay
Speaker 1: your experiment by a week, you shouldn't get a different answer.
Speaker 1: But if you accelerate it, you're definitely getting a different answer.
Speaker 1: So the universe not symmetric to acceleration.
Speaker 3: And does Emmy's equation predict what should be symmetrical and
Speaker 3: what shouldn't or that just requires some intuition.
Speaker 1: Oh yeah, that's another great question. No, it doesn't tell
Speaker 1: us what the symmetries are, but it does tell us
Speaker 1: that if you find a symmetry, it has a big
Speaker 1: consequences for how the universe behaves, and some of these
Speaker 1: symmetries are easy to think about, like or location or direction.
Speaker 1: They sort of make intuitive sense. By some of the
Speaker 1: most important symmetries turn out to be weird quantum mechanical
Speaker 1: quantities that we never really think about. We talked recently
Speaker 1: about like electrons. Electrons are quant mechanical objects, and we
Speaker 1: think of them as having like physical properties mass and
Speaker 1: direction and spin and this kind of stuff, that they
Speaker 1: also have weird quantum mechanical properties, like their wave functions
Speaker 1: can have a complex piece to them. By complex, I
Speaker 1: don't mean complicated. I mean like you know five plus
Speaker 1: four I the way some numbers are real numbers and
Speaker 1: some numbers are complex numbers. They have an imaginary component.
Speaker 1: Electron wave functions can have an imaginary component, and this
Speaker 1: isn't something you can measure, because whenever you measure the
Speaker 1: wave function, you always take its amplitude square. The imaginary
Speaker 1: part goes away. But it is a feature of the electron,
Speaker 1: and so you can think of it as like an angle,
Speaker 1: like you can rotate this thing through complex space. So
Speaker 1: electrons have these weird complex internal quantum mechanical angle that
Speaker 1: you can can't measure, and it turns out that the
Speaker 1: universe respects that you can rotate electrons through this angle
Speaker 1: and it doesn't change anything in the equations. So that's
Speaker 1: like another weird symmetry that the universe has. And if
Speaker 1: people want to read more about this, this is called
Speaker 1: you one symmetry of the Lugrongen. So it's not just
Speaker 1: like obvious physical symmetries that the universe has. We also
Speaker 1: have these weird internal quantum mechanical symmetries that have very
Speaker 1: deep consequences thanks to Nuther's theorem.
Speaker 3: We were talking about these angles on the episode where
Speaker 3: we were talking about charge and force. Isn't that right?
Speaker 3: And what context did they come up in? I guess
Speaker 3: they just came up in the wave function context.
Speaker 1: Yeah, Well, we were talking about why we have photons,
Speaker 1: and it turns out that you can't respect this weird
Speaker 1: electron angle without having photons. Photons are the things that
Speaker 1: make this weird electron angles symmetric in the equations of physics,
Speaker 1: and that has the big consequence thanks to Nother's theorem.
Speaker 1: But you have to have photons. You can't just do
Speaker 1: this in the universe with just electrons, and so some
Speaker 1: people like to say that the reason we have photons
Speaker 1: is to respect this electron symmetry.
Speaker 3: Okay, thanks, I'm expecting an honorary degree in physics one
Speaker 3: of these days, so I have to make these connections
Speaker 3: between episodes.
Speaker 1: I'm gonna give you a pod in physics. Eventually.
Speaker 3: This is the O stand for I went over my head.
Speaker 3: Oh God, oh man for not catching that they're going
Speaker 3: to take away the PhD I already have. I don't
Speaker 3: know who they is, but someone's taken it away. The man.
Speaker 3: All right, let's all take a break and ponder which
Speaker 3: university should be giving me my honorary PhD. And when
Speaker 3: we get back, we'll dive into the details of Notether's theorem.
Speaker 3: All right, we're back, Daniel. You've been sort of giving
Speaker 3: us tantalizing. It's about symmetries and what Notre taught us.
Speaker 3: Let's talk more about what her theorem's all about.
Speaker 1: Yes, so Notthern's theorem is really important. It tells us
Speaker 1: what it means that there's a symmetry in the universe.
Speaker 1: It tells us what the consequences are like. You might say, okay,
Speaker 1: so I can do my experiment here, or I can
Speaker 1: do it in the middle of deep space. I get
Speaker 1: the same answer, who cares? What does that mean about
Speaker 1: the universe? Well? Notther's theorem tells us what it means. Specifically,
Speaker 1: it tells us that any symmetry implies a conservation law.
Speaker 1: It means that there's something out there that the universe
Speaker 1: respects that if you calculate it, that number never changes,
Speaker 1: you know. So to think about what a conservation law is, like,
Speaker 1: let's say you have a little economy and people are
Speaker 1: spending money in trading on eggs for dollars or whatever.
Speaker 1: You can spend those dollars, but this dollar is still
Speaker 1: go somewhere, and they still are somewhere, right, So, like
Speaker 1: the number of dollars in a closed economy is conserved
Speaker 1: because you have a certain number of dollars and they're
Speaker 1: just going to move around, but the number of them
Speaker 1: doesn't change, right, So the total amount of money is
Speaker 1: conserved there. And I know that in real economics the
Speaker 1: total amount of money isn't conserved and value can be
Speaker 1: created in whatever. But like say you have a simple
Speaker 1: economy with a few dollars and they're just moving around,
Speaker 1: the dollars can flow. There's a current of money, but overall,
Speaker 1: there's a conservation of those dollars.
Speaker 3: Right, Okay, assume a spherical economy exactly.
Speaker 1: So another theorem tells us that all the symmetries we
Speaker 1: talked about previously and will go through each one, imply
Speaker 1: a conservation law in the universe. There's something that the
Speaker 1: universe respects these Every symmetry has a conservation law, and
Speaker 1: any conserved quantity implies that there's a symmetry there.
Speaker 3: We start with that sphere example.
Speaker 1: Yeah, so let's take a sphere and say we move
Speaker 1: it somewhere else. It's still a sphere, right, that hasn't changed.
Speaker 1: So what does that translation symmetry imply? It implies conservation
Speaker 1: of momentum. Right. The reason that the universe conserves momentum
Speaker 1: is because there is no special place in the universe.
Speaker 1: There are no markings in space. It doesn't matter where
Speaker 1: you do your experiment or where you take your measurement
Speaker 1: that you should get the same answer. Noother's theorem says,
Speaker 1: if that's true in your universe, then momentum is conserved.
Speaker 1: And that's kind of like a big leap. You're like, what,
Speaker 1: like I get there's a connection there. We have positions.
Speaker 1: But now we're talking about momentums and velocities, and like
Speaker 1: it's kind of crazy, right, Like what is momentum conservation anyway?
Speaker 1: It just says that if you calculate the momentum of stuff,
Speaker 1: which is mass times velocity, and then you let physics happen.
Speaker 1: Like you have two balls and they bounce off each other,
Speaker 1: and you measure their mass and their velocity beforehand, you
Speaker 1: add it up, you get a number. You measure their
Speaker 1: mass and velocity afterwards, and you calculate momentum and add
Speaker 1: all up. You get the same number. It's like if
Speaker 1: I buy eggs from you, I trade you dollars, the
Speaker 1: total number of dollars in the universe hasn't changed. Well,
Speaker 1: if we bounce balls off of each other, the amount
Speaker 1: of momentum in the universe hasn't changed. And that's because
Speaker 1: of notother's theorem. Another's theorem says we have momentum conservation
Speaker 1: because space is the same everywhere. It doesn't matter where
Speaker 1: you do your.
Speaker 3: Experiment, okay, and so if you do your experiment at
Speaker 3: different times, you get the same results. Because what is conserved.
Speaker 1: Time symmetry means that there's a conservation of energy. The
Speaker 1: reason we have conservation of energy is because of time symmetry,
Speaker 1: and Nuther's theorem connects these things. It tells you exactly
Speaker 1: what is conserved if you have a certain symmetry. And
Speaker 1: so there's this pairing between energy and time. There's a
Speaker 1: pairing between position and momentum, and Noutherar's theorem tells us that,
Speaker 1: like translation symmetry, position symmetry gives us conservation momentum, time
Speaker 1: symmetry gives us conservation of energy, and in fact it
Speaker 1: goes even deeper than that. That's a really useful definition
Speaker 1: of energy. Energy is the thing that's conserved if you
Speaker 1: have time symmetry. That's the way a lot of physicists
Speaker 1: think about energy now in terms of Nuther's theorem and
Speaker 1: these conservation laws, and it's hard to sort of wrap
Speaker 1: your mind around, like why is this? Can we understand
Speaker 1: how Nutherar's theorem connects these things?
Speaker 3: Can you give me an example of, like, if I
Speaker 3: do the double slit experiment, maybe I'm making it at
Speaker 3: two different times, how does that tell me about conservation
Speaker 3: of energy?
Speaker 1: Let's get to conservation of energy, because it's tricky, because
Speaker 1: it turns out energy is not actually conserved in the universe,
Speaker 1: which tells us something else about the universe. But let's
Speaker 1: go back to simple momentum and thinking about balls and
Speaker 1: thinking about what it tells us about the universe and
Speaker 1: how space is the same. Right, it's interesting that you
Speaker 1: could do the same experiment anywhere in the universe and
Speaker 1: get the same answer. Why does that tell us something
Speaker 1: about momentum. Well, imagine that we had a universe that
Speaker 1: didn't have the same kind of space everywhere. Let's say
Speaker 1: we had a universe that had an edge to it,
Speaker 1: like a wall, you know, like a place where if
Speaker 1: you tried to go there, you just bounced back. Right. Now,
Speaker 1: we have a universe where you have most of the
Speaker 1: same kind of space, normal space, but then you also
Speaker 1: have an edge bit, and an edge bit has special
Speaker 1: properties that if you hit it, you bounce back. Right.
Speaker 1: So do we have a momentum conservation in that universe? No,
Speaker 1: we don't, because what happens if you throw a ball
Speaker 1: against the edge of the universe it bounces back, it
Speaker 1: changes its momentum, and there's nothing to compensate for that. Usually,
Speaker 1: if I want to change the momentum of something, I
Speaker 1: bounce it against a wall, that wall pushes back and
Speaker 1: it absorbs that momentum. The walls like pushed in the
Speaker 1: other direction. But if I have the edge of the universe,
Speaker 1: it's like special magical bit of space that can just
Speaker 1: turn things around and change their momentum. Boom, I have
Speaker 1: violated conservation of momentum. So there's an example of how
Speaker 1: having the space not be the same everywhere will violate
Speaker 1: conservation momentum. You can't have conservation and momentum in that universe.
Speaker 1: And to me that's really deep because it tells us, hey,
Speaker 1: if momentum is conserved, that means space is the same
Speaker 1: everywhere and there isn't an edge to the universe. Boom.
Speaker 1: It's like amazing these moments when you can do an
Speaker 1: experiment here on Earth and from that concludes something about
Speaker 1: deep space super far away. Like what I love it
Speaker 1: when like the math clicks together and has these literally
Speaker 1: far reaching consequences, is about what may be happening super
Speaker 1: far away. You got moment That doesn't mean the universe
Speaker 1: is infinite, right, It means there's no special space in
Speaker 1: the universe. You could still have a finite universe, just
Speaker 1: not one with an edge. If we have a finite
Speaker 1: universe has to like wrap around it stuff. You can
Speaker 1: have a finite universe where every bit of space is
Speaker 1: the same.
Speaker 3: I know just enough about physics now to get my
Speaker 3: own way. So that's where we are in my learning career.
Speaker 7: All right.
Speaker 3: So we have talked about space bending or is it
Speaker 3: space time bending? Okay, but that doesn't change momentum, and
Speaker 3: so we still have conservation.
Speaker 1: Yes, you can still have conservation of momentum even if
Speaker 1: space time bends. Yeah, exactly, okay. And this is also
Speaker 1: really fascinating because it connects us with quantum mechanics, Like
Speaker 1: this is a general theory about the universe, but it
Speaker 1: tells us there's a deep connection between position and momentum.
Speaker 1: And we kind of already knew that because quantum mechanics
Speaker 1: says you can't know position and momentum simultaneously, that these
Speaker 1: two quantities are linked in a deep way, you know,
Speaker 1: Like why is it that if you measure position, you
Speaker 1: can't know momentum instead of if you measure position you
Speaker 1: can't know like angle or energy or something. Because there's
Speaker 1: a pairing between these two quantities, position and momentum, they're
Speaker 1: deeply connected with each other. And if you know something
Speaker 1: about like Fourya transforms, it's very natural to understand how
Speaker 1: you transform something from physical space to momentum space. You
Speaker 1: understand they're connected by these fourya transforms. They really are
Speaker 1: not independent quantities. They're two different sides of the same coin,
Speaker 1: and so Notther's theorem reveals that as well. So these
Speaker 1: are deep connections. So now if you want, we can
Speaker 1: talk about energy conservation and time translation invariance.
Speaker 3: First I want to ask did she have like one
Speaker 3: equation from which all of this popped out or was
Speaker 3: it a different equation for each one of these connections.
Speaker 1: It's a single equation. It tells you that if your
Speaker 1: laws of physics are invariant under some transformation, then it
Speaker 1: tells you what quantity is conserved. So you put in
Speaker 1: your laws of physics, which we usually describe in terms
Speaker 1: of a lagrangein, which is basically like kinetic energy minus
Speaker 1: potential energy, and then you do your transformation. You say, well,
Speaker 1: what happens if I change it by shifting it to
Speaker 1: the left or shifting it to the right. And if
Speaker 1: the answer is that you get the same lagrange in
Speaker 1: out the same fundamental laws of physics, then it tells
Speaker 1: you what quantity is conserved and as a single equation,
Speaker 1: so you can change the symmetry you're exploring and it
Speaker 1: will tell you what the conservation law is.
Speaker 3: Okay, all right, awesome, Well let's move on to energy.
Speaker 1: Yeah, so energy is super fascinating. And we were saying
Speaker 1: earlier that if the universe has time translation symmetry, meaning
Speaker 1: it doesn't matter when you do your experiment, then energy
Speaker 1: is conserved in the universe. Cool, And everybody thinks energy
Speaker 1: is conserved in the universe. You're taught energy is conserved
Speaker 1: in the universe. Energy conservation is fundamental, and people think
Speaker 1: about energy the way sort of we talk about dollars earlier, Like, yeah,
Speaker 1: I have energy here and I can transform it, but
Speaker 1: you can't create it or destroy it. Right, Like if
Speaker 1: I'm going really really fast and I slam on the brakes,
Speaker 1: where's my kinetic energy go It goes through friction into
Speaker 1: the heat of the break pads, you know. Or if
Speaker 1: you have a book on a shelf that has potential
Speaker 1: energy you knock it off, that's transformed into kinetic energy.
Speaker 1: Energy and mass can be transformed back and forth into
Speaker 1: each other. All this kind of stuff. It's really intuitive
Speaker 1: for people to think that energy is conserved in the universe.
Speaker 1: But that's only true if the laws of physics actually
Speaker 1: are invariant to time. And it turns out they're not quite.
Speaker 3: Oh no, how are they not quite? Everything you know
Speaker 3: is a line.
Speaker 1: Well, what we include in the laws of physics are
Speaker 1: the behavior of space time, and the expansion of space
Speaker 1: breaks that. So the universe is not the same as
Speaker 1: it was a billion years ago or five billion years ago.
Speaker 1: The universe is expanding. Space is expanding. So it turns
Speaker 1: out that space has to be static to satisfy this
Speaker 1: time invariance. Because like the amount of dark energy in
Speaker 1: the universe, the fraction of dark energy in the universe
Speaker 1: is changing, the fraction of matter in the universe is changing.
Speaker 1: So because we don't have time translation in VERYOCE, it's
Speaker 1: because the universe isn't actually the same fundamentally as it
Speaker 1: was five billion years ago. Energy is not conserved in
Speaker 1: our universe. Wow, And we can understand that very easily.
Speaker 1: But just by looking at the dark energy, like the
Speaker 1: universe is expanding, that makes more space. Dark energy is
Speaker 1: constant density, which means that as the universe expands, it
Speaker 1: doesn't get diluted. It's not like matter, where you make
Speaker 1: more space and you still have the same number of protons.
Speaker 1: The density has gone down, the amount of matter has
Speaker 1: stayed fixed. Dark energy is weird. As you make more space,
Speaker 1: because the density is constant, you get more dark energy.
Speaker 1: So dark energy is just increasing. Where is it coming from?
Speaker 1: It doesn't have to come from anywhere because energy not
Speaker 1: conserved in our universe. That's what Nother's theorem tells us.
Speaker 1: It tells us energy doesn't just flow. It can be increased,
Speaker 1: it can be created, and it can be destroyed. So
Speaker 1: Nother's theorem is all about flow in currents. It says
Speaker 1: that when you have a symmetry there's a current that's conserved,
Speaker 1: things can't be created or destroyed. They can only flow.
Speaker 1: But because time is not symmetric quantity in our universe,
Speaker 1: energy is not conserved. It doesn't have to flow. It
Speaker 1: can be created and destroyed. And that's a really deep
Speaker 1: thing to understand about the universe, because boy, do we
Speaker 1: have energy problems. And if we could just create energy, Wow,
Speaker 1: that would change our experience, right, that would be a
Speaker 1: big deal.
Speaker 3: And was this a revelation when the theorem came out
Speaker 3: or was this something we kind of had to handle on,
Speaker 3: but now it was proven.
Speaker 1: It was really troublesome actually, because Einstein didn't like to
Speaker 1: imagine that there was something in the universe that violated
Speaker 1: time translation in variance, and so he famously like rejected
Speaker 1: adding this to the equations partially for that reason. And
Speaker 1: it's only later when we discovered that the expansion of
Speaker 1: the universe was accelerating that we realized we needed this,
Speaker 1: and so yeah, that sort of blew up our whole
Speaker 1: thinking about how the universe works. I know we've said
Speaker 1: this on the podcast before, but it's hard for people
Speaker 1: to think in because they still write in and say,
Speaker 1: are you sure as an energy conserved? Like, it's not
Speaker 1: conserved in our universe, folks, unfortunately, And Another's theorem tells
Speaker 1: us what that means. It goes back and forth. Right,
Speaker 1: if you have a symmetry, it tells you what's conserved,
Speaker 1: and if you have a conservation, it tells you what
Speaker 1: the symmetry is. And like that's deeply important because the
Speaker 1: game of physics is to like figure out what is
Speaker 1: the puzzle of the universe, and recognizing the symmetries or
Speaker 1: the conservation laws is equivalent. It's like saying this is
Speaker 1: something that's important to the universe. It's fundamental, it's deep.
Speaker 1: Momentum is an important quantity in the universe for some reason,
Speaker 1: and the reason is connected to the reason that space
Speaker 1: is the same everywhere, the way that like the number
Speaker 1: of podcasts in the universe not an important quantity. The
Speaker 1: universe does not care. You can study podcasts and you
Speaker 1: will not learn anything fundamental about the universe, except if
Speaker 1: you listen to this podcast, you will learn a lot
Speaker 1: about the universe.
Speaker 3: The universe cares about this podcast, probably.
Speaker 1: But it's not like every time a podcast is created,
Speaker 1: another one is destroyed. If you discovered that that there
Speaker 1: was like a conservation law podcast that would tell you
Speaker 1: this some symmetry in the universe that's related to podcasting,
Speaker 1: I don't know what that would be. And you're really
Speaker 1: inside into how the universe works.
Speaker 3: So was Emmy appreciated for this contribution in her time
Speaker 3: or no? Because big people like Einstein were not willing
Speaker 3: to accept the results.
Speaker 1: People in the field definitely appreciated Nuther. Einstein said, quote
Speaker 1: Nuther was the most significant creative mathematical genius thus far
Speaker 1: produced since the higher education of women began, so there's
Speaker 1: a qualifying there. He's like, she's the smartest lady I
Speaker 1: ever met, and a lot of people since were like,
Speaker 1: she's just the smartest mathematician period. You don't have to
Speaker 1: put lady ye.
Speaker 3: Well, and also qualifying since women were allowed in academia,
Speaker 3: which was like seven years earlier or something like that. Right,
Speaker 3: that's a pretty big quality.
Speaker 1: It's a pretty big qualif But you know, Hilbert and
Speaker 1: all these folks, they knew what they were dealing with.
Speaker 1: They understood they were in the presence of genius. And
Speaker 1: she made a lot of important contributions in abstract algebra,
Speaker 1: like all huge contributions there. Like this is a small
Speaker 1: part of her legacy, but it literally underlies all of physics.
Speaker 1: Everything in physics is Nuther. There's a physicist, Ransom Stevens
Speaker 1: who said, quote, you can make a strong case that
Speaker 1: her theorem is the backbone on which all of modern
Speaker 1: physics is built. Like boom. You know, Maxwell, he did
Speaker 1: a little piece of it. Higgs, he found a little
Speaker 1: piece of it. But all at rest on the foundation
Speaker 1: of Nuther's theorem. All of our lagrongens. Every time we
Speaker 1: talk about particle physics and how it works. It always
Speaker 1: has to have symmetries and like symmetries and the group theory,
Speaker 1: which is another kind of abstract algebra. It's like so
Speaker 1: interwoven into the foundation of modern physics. It's like we're
Speaker 1: all playing in Nuther's backyard.
Speaker 3: So do you feel like she's being taught about in
Speaker 3: classes more often?
Speaker 2: Now?
Speaker 3: Like are we making up for the fact that we
Speaker 3: talked about you know, Einstein a lot, but those they
Speaker 3: are not really at all? Or is she still I mean,
Speaker 3: based on the audience responses, there's still plenty of folks
Speaker 3: who don't know about her.
Speaker 1: There's still plenty of folks that don't know about her,
Speaker 1: So she's not talked about enough. And I think that,
Speaker 1: you know, these things take time for somebody to get
Speaker 1: to Einstein's level of like cultural impact. They have to
Speaker 1: be celebrated in their time or there has to be
Speaker 1: like a campaign after they die to resuscitate their legacy
Speaker 1: and write books about them. And there just hasn't been
Speaker 1: as much attention paid. And you know, it takes effort,
Speaker 1: Like somebody's got to go out there and do the
Speaker 1: research and write the books and make this argument in
Speaker 1: order to have it rise above the level of noise
Speaker 1: in this chaotic media landscape. So it's not easy to
Speaker 1: sort of change the trajectory. But I think in this
Speaker 1: case it's very well deserved.
Speaker 3: Yep, sounds like there's a book project in there or
Speaker 3: a movie.
Speaker 1: Yeah, definitely, we need the Nether biopic for sure. Who's
Speaker 1: going to plant her? Maybe Rachel Weiss or something.
Speaker 3: Maybe I can't say I know what she looks like.
Speaker 3: I should look it up.
Speaker 1: And so, you know. Another's theorem tells us about the
Speaker 1: symmetries in the universe, and it makes a lot of
Speaker 1: sense when we think about translation symmetry. It gives us
Speaker 1: momentum conservation. Rotation symmetry that gives us angular momentum conservation,
Speaker 1: like the reason an angler momentum is conserving the universe,
Speaker 1: the reason galaxies are discs, the reason the Earth still
Speaker 1: spins is because the universe doesn't have a preferred direction.
Speaker 1: Time translation symmetry gives us energy conservation that weird internal
Speaker 1: electron angle symmetry we talked about earlier. Nuthu's theorem tells
Speaker 1: us what that means, and what it means is conservation
Speaker 1: of electric charge and that's pretty important in the universe.
Speaker 1: Like you can transfer electric charge, but you can't create
Speaker 1: it or destroy it. We have looked like we have
Speaker 1: tried to create a destroy electric charge. Nobody's ever seen
Speaker 1: a violation of that. That means that the universe really,
Speaker 1: really really wants this weird internal electron angle to be preserved.
Speaker 1: You know, it's fascinating, and this is like really deeply
Speaker 1: interwoven into the way we structure all the quantum field
Speaker 1: theories in physics.
Speaker 3: All right, so we should all get Emmy on a
Speaker 3: T shirt for starters, and we all need to have
Speaker 3: a poster with things that Emmy maybe didn't actually say. Yeah,
Speaker 3: because I heard a bunch of if Einstein posters do
Speaker 3: have like quotes that you probably never actually is that true?
Speaker 1: Yeah, And unfortunately, these days, if you google Einstein and
Speaker 1: look for images, there's a bunch of AI generated nonsense.
Speaker 1: It's not actually pictures of Einstein. So yeah, the information
Speaker 1: landscape is deeply polluted. But I think somebody out there
Speaker 1: who's like a Netflix executive should commission at like seven
Speaker 1: part Emmy Nuther biopic miniseries. And I promise you if
Speaker 1: you do that, you're going to win an Emmy for
Speaker 1: your Emmy series.
Speaker 3: Oh nice, nice, and we're available to hire to help out.
Speaker 1: Absolutely, Yes, I want to be on the set consulting.
Speaker 3: Yes, that sounds good. I'll play Emmy. I don't know
Speaker 3: what she looks like, but probably probably so did Emmy
Speaker 3: get to live a nice long life.
Speaker 1: So there were ups and downs, you know. She finally
Speaker 1: got a position after World War One, though she wasn't paid,
Speaker 1: and so she was working in Germany for a while.
Speaker 1: In nineteen thirty three, when the Nazis came to power, she,
Speaker 1: like many Jewish scientists, left. She went to Brent mahar
Speaker 1: and worked there and at the Institute for Advanced Studies,
Speaker 1: so in New Jersey. But later she died of complications
Speaker 1: of surgery on an ovarian syst So she got a
Speaker 1: very warm reception and she was very pleased to be
Speaker 1: in New Jersey. But she didn't last much longer. And
Speaker 1: so it's always a tragedy when somebody so smart dies
Speaker 1: so young, because I always imagine, like, what could they
Speaker 1: have contributed? What do we not know about the universe
Speaker 1: because this person died. You know, it's like thinking if
Speaker 1: Mozart had lived to seventy five, what music of his
Speaker 1: could we be enjoying today? We just don't know. It's
Speaker 1: just been deleted from the human experience.
Speaker 3: We're going to experience a similar feeling on our next
Speaker 3: episode when we talk about Nettie.
Speaker 1: Stevens, another female scientist.
Speaker 3: Another overlooked female scientist who tragically died young.
Speaker 1: All right, well, thanks to all the women out there
Speaker 1: making contributions to science. We hear you, We support you.
Speaker 1: We look forward to your biopic on Netflix, and.
Speaker 3: I'm available for hire.
Speaker 1: For those two.
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