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Speaker 1: The universe is like a big puzzle. It's a mystery

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Speaker 1: for us to unravel. But it's not just a heaping

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Speaker 1: pile of unorganized facts. There are patterns to the madness.

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Speaker 1: There are clues that suggest a deep underlying organization. For example,

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Speaker 1: if you multiply mass and velocity together something we call

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Speaker 1: it momentum, you get a number which the universe seems

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Speaker 1: to respect. You calculate the momentum of a bunch of rocks,

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Speaker 1: You get some number. Then you bang them into each other,

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Speaker 1: change their directions, break them into pieces. Whatever you calculate

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Speaker 1: to momentum again, same number. The universe respects this number,

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Speaker 1: conserves this weird combination of mass and velocity. Why does

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Speaker 1: it care about mass times velocity? Does it not care

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Speaker 1: about mass times acceleration or mass times ice cream or

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Speaker 1: chocolate times velocity. For a long time, we had no idea.

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Speaker 1: We just saw that it did respect this until a

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Speaker 1: genius came along, a mathematician who, during a brief dabt

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Speaker 1: in physics, made a connection that explained it all. Emmy

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Speaker 1: Kneather pulled back a layer of reality to show us

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Speaker 1: the deep underlying mechanism behind these conservation laws and not

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Speaker 1: just about momentum, about anything the universe respects and conserves.

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Speaker 1: Without her equation, we wouldn't have understood the beautiful mathematics,

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Speaker 1: the foundations of the Standard model. We wouldn't have discovered

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Speaker 1: the Higgs boson. So in honor of Emmy kne there's

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Speaker 1: one hundred and forty third birthday, we're going to be

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Speaker 1: diving into her life and her work. Welcome to Daniel

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Speaker 1: and Kelly's extraordinarily momentous universe.

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Speaker 2: Hello.

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Speaker 3: I'm Kelly Wiener Smith. I study parasites and I get

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Speaker 3: less metrical with it.

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Speaker 1: I'm Daniel. I'm a particle physicist, and I'm getting rounder

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Speaker 1: and rounder. I'm not sure what was happening over there.

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Speaker 3: I might have both of those things happening concurrently, but

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Speaker 3: it's okay.

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Speaker 2: You know.

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Speaker 3: The nice thing about getting older is that I care

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Speaker 3: way less than I used to, so you know, freedom

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Speaker 3: in that regard.

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Speaker 1: I like to think that I'm approaching a spherical physicist,

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Speaker 1: which is the approximation most physicists would make about themselves eventually. Anyway,

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Speaker 1: it's a.

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Speaker 3: Very efficient shape. I like that, and I like the

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Speaker 3: idea that there's a goal in mind. Yeah, so today

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Speaker 3: we are talking about a woman scientist who many people

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Speaker 3: don't know, who they probably should. Do you remember when

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Speaker 3: you first learned about Emmy whose last name I'm going

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Speaker 3: to try to avoid saying.

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Speaker 1: I do remember I learned about Emmy Nuther in graduate

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Speaker 1: school when I was taking quantum field theory, because that's

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Speaker 1: when you're thinking about the fields and how they oscillate

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Speaker 1: and their symmetries very importantly. And I remember my professor

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Speaker 1: Lawrence Hall writing this equation on the board, Nuther's theorem,

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Speaker 1: and feeling like, oh, my gosh, that is so deep

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Speaker 1: and powerful because it just told you so much about

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Speaker 1: how the universe worked and connected these two ideas. And

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Speaker 1: the equation itself is so simple, and when he derives

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Speaker 1: it seems so obvious. But it's one of these things

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Speaker 1: that it's so brilliant, it's so insightful that it's hard

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Speaker 1: to take yourself back to before it was understood. It's

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Speaker 1: like it changes the way you look at the universe

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Speaker 1: so deeply that it's hard to remember how much of

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Speaker 1: an insight it was.

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Speaker 3: Oh that's beautiful, And I bet you have totally hooked

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Speaker 3: our audience on learning all about this equation.

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Speaker 1: I hope so, and it was in that same moment

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Speaker 1: that he told us that this was an equation by

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Speaker 1: a female physicist. And you know, that's unfortunately rare thing

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Speaker 1: to hear, especially somebody contributing to physics in the early

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Speaker 1: parts of this century. You know, physics is still not

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Speaker 1: a place of gender balance, unfortunately, and in the early

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Speaker 1: part of this century much much less so. And so

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Speaker 1: hearing about the deep contribution nw they're made to physics

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Speaker 1: is especially impressive given how long ago she did it.

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Speaker 3: So I'm under the impression that she was a mathematician

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Speaker 3: who jumped into physics to just dazzle everyone and then

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Speaker 3: went back to math. Was math comparably bad about sex

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Speaker 3: balance on faculty back then? I'm guessing the answer was

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Speaker 3: yes and still is yes.

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Speaker 1: The answer was yes and still is yes. Unfortunately, math

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Speaker 1: is no better than physics. Like if you look at

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Speaker 1: a breakdown of faculty in the United States, it's like

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Speaker 1: twenty ish percent female in physics and in math departments. Yeah, absolutely,

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Speaker 1: we still have a lot of the same problems that

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Speaker 1: we did. Things are better it used to be one percent.

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Speaker 1: Twenty percent is progress, but we have a long way

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Speaker 1: to go. Not that we need exactly fifty percent female,

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Speaker 1: exactly fifty percent male. But we know that this is

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Speaker 1: emblematic of issues we have in our department that make

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Speaker 1: it harder for women to succeed.

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Speaker 3: Yep, all right, Well, lots of progress to make, and

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Speaker 3: so we decided that we wanted to have a series

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Speaker 3: of episodes about women's scientists who are amazing who you

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Speaker 3: perhaps have never heard of, in response to actually a

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Speaker 3: couple different listener questions that we got. And so this

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Speaker 3: month we're going to have a few episodes of that type,

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Speaker 3: and this is the one we're starting with today.

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Speaker 1: Yeah, Emmy Nuther is maybe one of the greatest, most

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Speaker 1: impactful geniuses you've never heard of. She made contribution to

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Speaker 1: physics that impact you, impact our understanding of the universe.

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Speaker 1: But she hasn't talked about nearly well enough. And so

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Speaker 1: to get a sense for like, how much did people

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Speaker 1: know about her? Have people heard about her? Do people

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Speaker 1: understand the contribution she made? I went out there and

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Speaker 1: asked people, Hey, do you know what Emmy Nuther revealed

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Speaker 1: about the universe? So here are a bunch of answers

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Speaker 1: from our volunteers, and if you'd like to participate for

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Speaker 1: a future episode. Please don't be shy. We want to

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Speaker 1: hear your voice on the pod. Write to us two

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Speaker 1: questions at Danielandkelly dot org. So you've had a few

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Speaker 1: clues already from our introduction, but do you know what

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Speaker 1: Emmy Nuther revealed about the universe. Here's what our listeners

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Speaker 1: had to say. That there's a simple relationship mathematically with

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Speaker 1: symmetries in the universe. She revealed things that Noeita could.

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Speaker 4: The one who came up at the idea of using

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Speaker 4: type one A supernova as a way to measure the

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Speaker 4: expansion rate of the universe. Amy Nota have revealed something

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Speaker 4: about the translational symmetry in the universe, and that all

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Speaker 4: positions in the universe are somewhat indistinguishable.

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Speaker 1: There was a standard candle in the universe might have

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Speaker 1: been a certain type of supernova.

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Speaker 2: I have no idea, but I'm eager to find out mathematician,

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Speaker 2: maybe back in Einstein's time, who came up with a

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Speaker 2: really important concept but never got full credit for it.

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Speaker 5: I'm sorry, I have no idea who that is.

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Speaker 1: Emy unfortunately did not reveal anything about the universe to me, specifically,

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Speaker 1: because I don't think i've ever heard the name.

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Speaker 6: Where there is a conservation law, there will be some symmetries.

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Speaker 6: And this changed the way that we approved which can

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Speaker 6: bring together physical properties.

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Speaker 7: Emmy North, another woman who deserved a Nobel price but

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Speaker 7: did not get it, showed that symmetries in the universe

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Speaker 7: were related to conservation laws.

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Speaker 5: Why is anyother.

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Speaker 6: Gonna be the name for the momentum?

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Speaker 3: Oh, I guess she did something about momentum.

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Speaker 5: I'm gonna have to go look this up.

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Speaker 1: Ah, they might have proved that there's no either, just kidding.

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Speaker 1: I think it had something to do with.

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Speaker 3: Neutrinos or was it symmetry breaking something?

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Speaker 5: Oh no, I have no idea who this person is

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Speaker 5: at all, So it must be a woman and she

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Speaker 5: did something really important and then took the credit, and

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Speaker 5: that's why we have no idea who she is. Or

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Speaker 5: maybe it's just me and everybody else does.

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Speaker 3: So we had a handful of listeners who gave like

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Speaker 3: spot on answer, which makes me wonder if we had

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Speaker 3: asked a similar number of people who weren't listeners to

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Speaker 3: our show, like a random draw from the population, what

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Speaker 3: the answer would have been. Because I think we've got

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Speaker 3: a population of listeners who are more likely than average

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Speaker 3: to know the answer, but still there were plenty who didn't.

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Speaker 3: And the last answer was just like spot.

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Speaker 1: Oh man, yeah, I know. And there's some great guesses

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Speaker 1: in here, like the no Ether love that joke.

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Speaker 3: Nice yep yep epic. Let's jump right in. Tell us

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Speaker 3: about all right, and I'm gonna try to say the name.

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Speaker 3: Tell us about Emmy Noether.

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Speaker 1: Neuter neuter.

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Speaker 3: Yeah, that's not what you were saying earlier.

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Speaker 1: My pronunciation of her name is probably going to vary

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Speaker 1: a lot. There's not a lot of symmetry or conservation

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Speaker 1: in my pronunciation of this name. It's a little uncomfortable

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Speaker 1: for me, but I'm gonna do my best. I mean,

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Speaker 1: Luther comes from a really interesting family. Her dad was

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Speaker 1: a mathematician. She was born late eighteen hundreds, and so

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Speaker 1: she comes from an academic background. You know. Her family

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Speaker 1: valued thinking and education and sort of higher intellectual pursuits.

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Speaker 1: Some of her brothers became scientists, another one became a mathematician.

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Speaker 1: So her father is a well known mathematician, Max Nuther.

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Speaker 1: Though eventually, of course, Emmy totally eclipsed him, so instead

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Speaker 1: of Emmy being Max's daughter, now Max is like Emmy's father.

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Speaker 1: Way to go, Emmy, you know, like the way and

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Speaker 1: you go to pick up your kid at school. I'm

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Speaker 1: just like Hazel's dad. I don't have a name. I'm

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Speaker 1: just Hazel's dad.

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Speaker 3: You know What's funny. I was the older sibling, but

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Speaker 3: my brother George was way cooler than me. So even

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Speaker 3: though I came first, everyone I met at our school

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Speaker 3: was still like, oh, man, are you George's sister? And

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Speaker 3: I was like, no, that's not supposed to work that way.

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Speaker 3: But anyway, he was way cooler than me.

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Speaker 1: So that's what happened exactly. Well, I'd be very proud

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Speaker 1: to go down in history as Hazel's dad. I hope

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Speaker 1: that happens anyway. Back then, though she comes from an

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Speaker 1: academic family and her brothers were encouraged to pursue higher

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Speaker 1: intellectual degrees, it's not an option that women had. So

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Speaker 1: she was actually trained to be an English and French

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Speaker 1: teacher at a finishing school, but she was like, man,

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Speaker 1: I don't want to do that. I want to study math.

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Speaker 1: She had like this deep appetite and this aptitude for

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Speaker 1: math at a very early age. But the problem is

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Speaker 1: in Germany, where she grew up, women were not allowed

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Speaker 1: to enroll in universities, so she like tried to enroll

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Speaker 1: in university to get a degree at Gottingen and they

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Speaker 1: were just like no, So she just went anyway. She's

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Speaker 1: like sat in on the lectures and she's like, I'm

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Speaker 1: just gonna listen. Like they're talking about math. I'm here,

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Speaker 1: I'm learning about it. And so she picked up a

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Speaker 1: lot of math.

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Speaker 3: That must have required some buy in from the faculty

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Speaker 3: members right to not kick her out. Is there any

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Speaker 3: sense for like, were the members of the maths department,

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Speaker 3: you know, feeling differently than the members of the admissions group.

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Speaker 3: Were they happy to have her there?

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Speaker 1: Yeah, they certainly didn't kick her out right, and so

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Speaker 1: she could sit in the back and she wasn't disturbing anybody.

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Speaker 1: But you're right, people could have been like, this is

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Speaker 1: deeply offensive. You must leave, and that didn't happen, and

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Speaker 1: times were changing. It was only nineteen oh four, a

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Speaker 1: couple of years later when erling In University decided to

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Speaker 1: allow women to enroy. So she was sort of on

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Speaker 1: the cusp of that, and then she immediately enrolled and

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Speaker 1: she got a degree in math, and then she was

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Speaker 1: fortunate in some way that she was hanging out in

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Speaker 1: Gottingen right around the time when it was the center

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Speaker 1: of the universe in terms of math and geometry. So like,

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Speaker 1: obviously this is right around the time of Einstein and relativity, right,

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Speaker 1: And he's a German professor, and like Germany was definitely

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Speaker 1: the center of physics and math at the time. You

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Speaker 1: got guys like David Hilbert Klein, Minkowski, Shortsiled. All these

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Speaker 1: guys who made huge contributions and we're thinking deeply about

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Speaker 1: the physics of space and time and relativity were all

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Speaker 1: there like in Gottingen at the time, and so she

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Speaker 1: worked with them. She did her PhD. And she got

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Speaker 1: a PhD in nineteen oh seven, right, so like more

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Speaker 1: than one hundred years ago. She was the second woman

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Speaker 1: to ever get a PhD in math. So like really

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Speaker 1: cutting edge. This is not an easy track, you know,

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Speaker 1: somebody like me, I went into physics. I followed a path.

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Speaker 1: It was laid out for me. You know, I knew

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Speaker 1: exactly what to do and where to go. I'm not

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Speaker 1: a trailblazer in any respect. You know, there's like a

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Speaker 1: very clear track for me to follow.

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Speaker 3: I think you're under selling yourself.

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Speaker 1: But okay, I mean sure, I had to do a

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Speaker 1: lot of hard problem sets, but you know, the track

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Speaker 1: was there, it was clear what I needed to do.

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Speaker 1: But she not only had to do the hard problems,

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Speaker 1: she had to make her own path. You know, this

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Speaker 1: is not something an established trajectory for folks. She was

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Speaker 1: really resilient. When she got her PhD. She couldn't get

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Speaker 1: a job. People just kept rejecting her because she was

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Speaker 1: a woman. And so for the next eight years she

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Speaker 1: did research in math and she taught, but she wasn't paid.

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Speaker 1: She didn't have an official position. She just like hung around.

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Speaker 1: She was just like a volunteer. But you know, she

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Speaker 1: came from a wealthy family which could support her, so

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Speaker 1: she didn't need to like go work as a seamstress,

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Speaker 1: and she just followed her passion. In nineteen fifteen, for example,

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Speaker 1: she applied for a position at Gottingen and she was

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Speaker 1: rejected and the review committee said, quote, I have had

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Speaker 1: up to now unsatisfactory experiences with female students. She's an exception,

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Speaker 1: which is like, you know, thanks for grudgingly admitting that

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Speaker 1: she has.

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Speaker 3: Talents here with faint praise.

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Speaker 1: Yeah, yeah, And then David Hilbert, who was like one

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Speaker 1: of the greatest mathematicians in history and already recognized at

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Speaker 1: the time, you know, clearly a leading mathematician of his age.

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Speaker 1: He wrote and complained. He said, quote, I do not

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Speaker 1: see that the sex of the candidate is an argument

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Speaker 1: against her. After all, we are a university, not a bathhouse.

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Speaker 3: That's great, I know, go Hilbert.

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Speaker 1: But they weren't persuaded, and they did not invite her

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Speaker 1: onto the faculty. So instead Hilbert signed up to teach

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Speaker 1: a bunch of classes that he thought she would be

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Speaker 1: good at teaching, and then he just had her teach

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Speaker 1: in his place. So like, yeah, she got to teach,

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Speaker 1: but she didn't get the job. So like, you know,

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Speaker 1: there's pluses and minuses there, and maybe as sort of

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Speaker 1: like a middle finger to the faculty, she ended up

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Speaker 1: swimming a lot at the men's only pool.

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Speaker 3: Ah, good for her. Do we happen to know if

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Speaker 3: Hilbert paid her for her teaching labor or did he

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Speaker 3: get the pay while she taught.

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Speaker 1: He hired her as a teaching as, so she was

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Speaker 1: paid sort of at the gradual student level even though

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Speaker 1: she was doing faculty level work. And I don't know

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Speaker 1: if he supplemented it privately.

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Speaker 3: I mean, that's still more than she was going to

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Speaker 3: get otherwise. And it's a chance to show everybody, screw you, guys,

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Speaker 3: she can totally do this.

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Speaker 1: Yeah, exactly. And you know, she just stuck around even

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Speaker 1: though officially the institutions didn't want her there. Her colleagues

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Speaker 1: valued her, like Hilbert knew that she was a genius.

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Speaker 1: And all these guys were thinking about physics and thinking

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Speaker 1: about Einstein's new theory of relativity, which is a very

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Speaker 1: mathematical way to think about the universe and space and time.

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Speaker 1: And you know, these are very new ideas mathematically, like

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Speaker 1: Remont had just figured out how to think about higher

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Speaker 1: dimensional spaces and surfaces in those spaces and to do

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Speaker 1: this math, and Einstein had learned about it and used

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Speaker 1: it to describe gravity, and so this was all very

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Speaker 1: new and very exciting, and so there was a lot

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Speaker 1: of talk between the mathematicians and the physicists. Emmy was

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Speaker 1: mostly interested in math, like she was really excited about

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Speaker 1: what we call algebra, which is much more than like

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Speaker 1: you know, x equals seven plus y and manipulating equations

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Speaker 1: like we learn in middle school algebra is a broader

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Speaker 1: field that thinks about, you know, relationships between objects and symmetries.

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Speaker 1: You have abstract algebra, linear algebra, you know, thinking about

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Speaker 1: like vectors and matrices and rotations and symmetries, and it's

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Speaker 1: a really fascinating and deep area of mathematics and very

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Speaker 1: closely related to general relativity and what Einstein had done

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Speaker 1: and thinking about the laws of physics. So this is

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Speaker 1: the kind of thing she was very excited about, and

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Speaker 1: so she was working mostly in abstract algebra, but she

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Speaker 1: did spend an afternoon or two thinking about the problems

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Speaker 1: in physics, which is when she came up with her

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Speaker 1: famous Nuther's theorem.

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Speaker 3: Oh man, I mean, algebra is great as long as

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Speaker 3: it's not the word problem. I'm helping my daughter with

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Speaker 3: those right now, and those are no fun. But algebra

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Speaker 3: in general I could do for fun all day as

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Speaker 3: long as it's not the word problems.

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Speaker 1: You know, word problems are really challenging. Translating a paragraph

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Speaker 1: into equations is really hard, and we have a whole

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Speaker 1: class on just that here because a lot of students

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Speaker 1: show up and they can do the math, but they

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Speaker 1: don't know how to get to the math. You know,

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Speaker 1: you have this problem and there's like a train, and

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Speaker 1: there's times, and there's balls, and there's inclined planes or whatever.

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Speaker 1: They don't know how to translate that into the math.

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Speaker 1: And you know that's actually the core physics, knowing how

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Speaker 1: to go from like here's a problem in the real world.

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Speaker 1: How do I build a mathematical model that captures the

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Speaker 1: essential bits of it that lets me calculate the answer?

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Speaker 1: How do I convert this word problem into math? That's

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Speaker 1: what physics is.

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Speaker 2: Like.

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Speaker 1: When you want to solve a problem in physics, you

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Speaker 1: need to turn it into a mathematical model. But that's

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Speaker 1: not easy, right, It's hard, and you got to teach

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Speaker 1: it to people. And so a lot of people show

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Speaker 1: up here and they struggle with that and they feel

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Speaker 1: bad about it because they don't know how to do it.

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Speaker 1: But like, the whole field of physics is basically that, like,

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Speaker 1: turn this into a math problem. That's what we do,

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Speaker 1: and so it's overlooked, I think and undertaught.

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Speaker 3: This is though, what got me into science. Like I

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Speaker 3: hated word problems in high school. But when I took

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Speaker 3: an ecology class and our job was to think about

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Speaker 3: a system like a predator prey system and we were

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Speaker 3: asked to describe it with equation M. Like the first

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Speaker 3: time I did that was the first time I thought,

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Speaker 3: I'm going to spend the rest of my life as

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Speaker 3: a scientist. This is so much fun, I think. I

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Speaker 3: just don't like the like, you know, the train leaves

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Speaker 3: it five and it's like, oh, this is boring, it's

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Speaker 3: not real. But when you're trying to describe like the universe,

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Speaker 3: that's much more.

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Speaker 1: Inciting to me. Well, I remember this contrast my first

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Speaker 1: year of college between my physics and philosophy classes, because

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Speaker 1: in physics, you had a question and you're like, Okay,

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Speaker 1: this electron is oscillating. What's going to happen over here

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Speaker 1: on this attena over there? And you want an answer,

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Speaker 1: But there is an answer, and you can get the

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Speaker 1: answer by turning the problem into a math problem. And

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Speaker 1: then math is either right or wrong, you know, and

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Speaker 1: like there's rules about math and there's no arguing, Whereas

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Speaker 1: in my philosophy class, which I also deeply enjoyed, you know,

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Speaker 1: there's a question of like you have to pull a

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Speaker 1: lever on this train to kill one person or let

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Speaker 1: ten people die? What's right what's wrong, and man, we

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Speaker 1: could argue forever we make any progress, and people could disagree,

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Speaker 1: and you couldn't definitively say who was right and wrong.

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Speaker 1: You couldn't turn it into a math problem. People have

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Speaker 1: been arguing about that question for thousands of years and

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Speaker 1: still nobody knows the answer. So to me, that was frustrating,

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Speaker 1: anisode of a relief to get to, like turn something

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Speaker 1: into a math problem. And yeah, I think that's probably

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Speaker 1: why I became a scientist and not a philosopher.

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Speaker 3: I like the comfort that math and statistics brings.

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Speaker 1: Yeah, I agree, I agree.

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Speaker 3: All right, So on that note, let's take a break,

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Speaker 3: and then when we get back, let's figure out what

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Speaker 3: Emmy revealed to the world. Okay, we're back. We're done

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Speaker 3: geeking out about how much we love equations that describe

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Speaker 3: animals in the rest of the universe. So now let's

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Speaker 3: talk about what Emmy's amazing equations reveal about our universe.

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Speaker 3: I guess that's still geeking fine.

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Speaker 1: Geek, Yeah, it is good. That's what we're here for.

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Speaker 1: This geek out deeply. Yeah. So, I mean, if there

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Speaker 1: was an expert in algebra and thinking about equations and

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Speaker 1: thinking about symmetries of those equations, you know, like very simply,

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Speaker 1: if you have an equation like X equals ten, you

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Speaker 1: could add two to both sides and it doesn't change

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Speaker 1: the answer, right, X plus two equals twelve still reveals

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Speaker 1: the same X. Right. There's no change there in the

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Speaker 1: fundamental solution to the problem. And so this is the

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Speaker 1: kind of thing she was thinking about, though, of course,

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Speaker 1: lots of other kinds of changes and more dramatic things

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Speaker 1: about the universe, because there's lots of fascinating symmetries in

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Speaker 1: the universe. Like you know, take for example, a sphere, right,

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Speaker 1: a perfect sphere, you rotate it, you still have a sphere. Right,

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Speaker 1: There's no change in the sphereness of the sphere. And

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Speaker 1: if you have a sphere in the universe and you

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Speaker 1: spin it, it's going to interact with the universe the

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Speaker 1: same way. It's going to bounce stuff off of it,

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Speaker 1: it's going to gravitate, like, there's no fundamental change in

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Speaker 1: how the universe treats it once you rotate the sphere.

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Speaker 1: It's an example of a symmetry, and that's like the purest,

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Speaker 1: cleanest kind of symmetry. You could also have other kinds

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Speaker 1: of symmetries. Like let's say you have an object that's

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Speaker 1: not a sphere, you know, like a cube, and you

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Speaker 1: rotate the cube. Now the cube looks a little bit different, right,

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Speaker 1: but in lots of situations it still acts the same.

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Speaker 1: Put that cube in orbit around the Sun, and it

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Speaker 1: doesn't matter how you've spun it, It's still going to

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Speaker 1: have the same orbit. It doesn't change the orbit of

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Speaker 1: the cube around the Sun. Dynamics of its orbit around

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Speaker 1: the Sun don't change if it's a cube, or if

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Speaker 1: it's a circle, or if even if you squeeze it

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Speaker 1: and make it like a rod like, it only matters

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Speaker 1: what its total mass is. Nothing else matters. So there

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Speaker 1: are symmetries there to gravity. You can change this object,

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Speaker 1: you can transform it, and not change the fundamental physics.

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Speaker 1: So there's a symmetry to gravitation. You can transform the objects,

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Speaker 1: but the equations don't change.

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Speaker 3: So I assume that before Emmy came along, we probably

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Speaker 3: understood that spheres in cubes were symmetrical. So what did

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Speaker 3: she add to that? Did she add the understanding that

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Speaker 3: that's going to be the case anywhere in the universe,

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Speaker 3: or have we not gotten to her contribution.

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Speaker 1: Yet we have not yet gotten to her contribution. But

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Speaker 1: what she did is show us what these symmetries mean,

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Speaker 1: the consequences of these symmetries. But first, let's get a

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Speaker 1: little bit more comfortable with the kinds of symmetries that

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Speaker 1: we're talking about here. Another really important and fundamental symmetry

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Speaker 1: in the universe is location. We call this translation invariance,

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Speaker 1: which is a fancy way of saying that if you

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Speaker 1: do an experiment anywhere in the universe, you should get

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Speaker 1: the same answer. Like, let's say you're measuring the speed

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Speaker 1: of light. For example, you could do your experiment out

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Speaker 1: in space near Jupiter. You could do your experiment in

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Speaker 1: the space between the Milky Way and Andromeda. You could

435
00:21:42,359 --> 00:21:44,840
Speaker 1: do it some other random place in the universe. This

436
00:21:44,960 --> 00:21:46,960
Speaker 1: speed of light is just a number, and as long

437
00:21:46,960 --> 00:21:49,720
Speaker 1: as you have perfect vacuum, doesn't matter where you are.

438
00:21:50,160 --> 00:21:53,320
Speaker 1: You do your experiment anywhere you should get the same answer.

439
00:21:53,600 --> 00:21:55,240
Speaker 3: So, say you were to measure something and it was

440
00:21:55,280 --> 00:21:58,320
Speaker 3: different when you were near Jupiter, perhaps because Jupiter is massive,

441
00:21:58,840 --> 00:22:00,720
Speaker 3: What does that tell you? Does that tell you that

442
00:22:00,720 --> 00:22:04,840
Speaker 3: you're measuring something that's not symmetrical, and thus isn't related

443
00:22:04,840 --> 00:22:05,919
Speaker 3: to what Emmy came up with.

444
00:22:06,119 --> 00:22:08,080
Speaker 1: Yeah, that's a great question because you might think, oh,

445
00:22:08,240 --> 00:22:10,679
Speaker 1: Daniel specifically was talking about measuring in a vacuum. But

446
00:22:10,680 --> 00:22:12,560
Speaker 1: we know the speed of light isn't always the same

447
00:22:13,000 --> 00:22:15,240
Speaker 1: if you're not in a vacuum, So what's going on there.

448
00:22:15,640 --> 00:22:17,840
Speaker 1: The answer is a little technical, it may be unsatisfying,

449
00:22:18,040 --> 00:22:20,760
Speaker 1: which is that you're measuring a different thing in that case,

450
00:22:20,800 --> 00:22:23,639
Speaker 1: and you have to include Jupiter in your experiment. So,

451
00:22:23,800 --> 00:22:26,080
Speaker 1: for example, if you're measuring the speed of light near

452
00:22:26,119 --> 00:22:28,320
Speaker 1: a massive object, where you're measuring the speed of light

453
00:22:28,400 --> 00:22:31,320
Speaker 1: through a glass crystal, then you're measuring something different than

454
00:22:31,359 --> 00:22:33,240
Speaker 1: if you're measuring the speed of light in a vacuum.

455
00:22:33,600 --> 00:22:36,280
Speaker 1: And so it doesn't matter where you are in the universe.

456
00:22:36,320 --> 00:22:38,840
Speaker 1: If you measure the speed of light near Jupiter, like

457
00:22:39,000 --> 00:22:40,280
Speaker 1: you want to know the speed of light through the

458
00:22:40,320 --> 00:22:42,520
Speaker 1: atmosphere Jupiter, you got to bring Jupiter along with you

459
00:22:42,800 --> 00:22:44,680
Speaker 1: and then do the experiment out in the middle of

460
00:22:44,720 --> 00:22:47,200
Speaker 1: deep space or over here or over there. You should

461
00:22:47,280 --> 00:22:50,440
Speaker 1: get the same answer. It doesn't depend on the actual space,

462
00:22:50,880 --> 00:22:53,600
Speaker 1: right And what this tells us is that like space

463
00:22:53,680 --> 00:22:57,520
Speaker 1: has no fundamental markings, there's no way you can identify

464
00:22:57,560 --> 00:22:59,359
Speaker 1: where you are in space, which is something we kind

465
00:22:59,359 --> 00:23:02,479
Speaker 1: of knew, all right, there's no like zero to the

466
00:23:02,520 --> 00:23:06,280
Speaker 1: origin of space that means something deep. There's no way

467
00:23:06,320 --> 00:23:08,800
Speaker 1: you can like figure out where you are in space.

468
00:23:08,880 --> 00:23:12,320
Speaker 1: You can't like look up your fundamental coordinates in space

469
00:23:12,359 --> 00:23:14,520
Speaker 1: because there aren't any. All we have in space are

470
00:23:14,560 --> 00:23:18,000
Speaker 1: relative distances. I'm a meter from here, I'm ten meters

471
00:23:18,000 --> 00:23:20,200
Speaker 1: from there, because all of space is the same.

472
00:23:20,520 --> 00:23:21,440
Speaker 3: Okay, got it.

473
00:23:21,520 --> 00:23:24,000
Speaker 1: So that's one example of a symmetry of the universe

474
00:23:24,040 --> 00:23:28,160
Speaker 1: that's really important. And another is direction, Like it shouldn't

475
00:23:28,200 --> 00:23:31,400
Speaker 1: matter what direction you're pointed in when you're measuring fundamental

476
00:23:31,400 --> 00:23:34,399
Speaker 1: constants about the universe or doing an experiment, because the

477
00:23:34,480 --> 00:23:37,639
Speaker 1: universe has no preferred direction. Right like here on the

478
00:23:37,680 --> 00:23:40,760
Speaker 1: surface of the Earth, obviously there's an up and there's

479
00:23:40,760 --> 00:23:43,399
Speaker 1: a down, and there's one definition of that that makes sense,

480
00:23:43,600 --> 00:23:46,720
Speaker 1: right because we have gravity, and so we're near a

481
00:23:46,720 --> 00:23:48,960
Speaker 1: gravitational field, and so it makes sense to call one

482
00:23:48,960 --> 00:23:51,520
Speaker 1: direction up and one direction down. But if you're far

483
00:23:51,560 --> 00:23:54,560
Speaker 1: from a planet, there is no direction that's like more

484
00:23:54,680 --> 00:23:58,919
Speaker 1: up than down. If you mentally imagine the galaxy, you

485
00:23:58,960 --> 00:24:01,240
Speaker 1: probably put it in your mind is a flat disc,

486
00:24:01,320 --> 00:24:03,680
Speaker 1: and you imagine things above that disc and blow that disk,

487
00:24:03,720 --> 00:24:05,960
Speaker 1: and you organize it in your mind. But you could

488
00:24:05,960 --> 00:24:08,600
Speaker 1: also spin that galaxy at an angle and tilt it

489
00:24:08,720 --> 00:24:11,080
Speaker 1: or look at it from another direction, and those are

490
00:24:11,280 --> 00:24:15,080
Speaker 1: just as good. They're equivalent. Right. There's no like fundamental

491
00:24:15,200 --> 00:24:18,480
Speaker 1: updirection out in the universe. There's no way to look

492
00:24:18,520 --> 00:24:21,920
Speaker 1: at the milky Way that's right or wrong, and there's

493
00:24:22,000 --> 00:24:24,919
Speaker 1: no way that the universe prefers any angle over another.

494
00:24:25,080 --> 00:24:27,840
Speaker 3: Yeah, astronauts report finding this very confusing when they get

495
00:24:27,880 --> 00:24:28,920
Speaker 3: up there, but they learn it quickly.

496
00:24:28,960 --> 00:24:32,560
Speaker 1: There's yeah, And that's really countertit because it's not part

497
00:24:32,560 --> 00:24:34,600
Speaker 1: of our experience because we live in a place where

498
00:24:34,640 --> 00:24:37,480
Speaker 1: there is a defined up and down. And so in

499
00:24:37,480 --> 00:24:39,239
Speaker 1: that same way, you might complain and say, well, your

500
00:24:39,280 --> 00:24:42,119
Speaker 1: experiment can have a different outcome in the middle of

501
00:24:42,160 --> 00:24:44,720
Speaker 1: deep space and near the surface of the Earth, And

502
00:24:44,760 --> 00:24:46,680
Speaker 1: that's true, but you've got to include the Earth in

503
00:24:46,720 --> 00:24:49,760
Speaker 1: your experiment, right. So if your experiment is like, how

504
00:24:49,840 --> 00:24:52,439
Speaker 1: much do I weigh on a scale when there's no

505
00:24:52,560 --> 00:24:54,600
Speaker 1: masses around me, the answer is going to be zero.

506
00:24:54,720 --> 00:24:56,320
Speaker 1: No matter where you are in the universe, there's no

507
00:24:56,640 --> 00:24:59,800
Speaker 1: part of space that depends on it. No angle matters

508
00:25:00,160 --> 00:25:03,280
Speaker 1: in the universe. But if you're including a planet in

509
00:25:03,320 --> 00:25:05,960
Speaker 1: your experiment, you know then you're going to measure the

510
00:25:06,000 --> 00:25:09,359
Speaker 1: same value on the scale no matter where you and

511
00:25:09,400 --> 00:25:12,080
Speaker 1: that planet are and the orientation of that planet. So

512
00:25:12,080 --> 00:25:14,480
Speaker 1: you got to include the planet in the experiment in

513
00:25:14,600 --> 00:25:16,200
Speaker 1: order to really get the symmetry.

514
00:25:16,560 --> 00:25:18,800
Speaker 3: Got it, Okay? Are there symmetries we should talk about?

515
00:25:18,840 --> 00:25:22,320
Speaker 1: There are so many fascinating symmetries. Like another important symmetry

516
00:25:22,320 --> 00:25:25,520
Speaker 1: is time. We don't think that the laws of physics

517
00:25:25,560 --> 00:25:28,520
Speaker 1: depend on time. We think, for example, the speed of

518
00:25:28,560 --> 00:25:30,240
Speaker 1: light is the speed of light, and it's the same

519
00:25:30,280 --> 00:25:33,080
Speaker 1: today as it's going to be tomorrow and a thousand

520
00:25:33,200 --> 00:25:35,520
Speaker 1: years ago and a billion years ago. We think the

521
00:25:35,560 --> 00:25:38,080
Speaker 1: speed of light is a constant. And this is sort

522
00:25:38,080 --> 00:25:40,240
Speaker 1: of a fundamental assumption we make in science all the time.

523
00:25:40,280 --> 00:25:43,680
Speaker 1: That's sometimes unspoken, that you can measure something and then

524
00:25:43,720 --> 00:25:46,159
Speaker 1: come back twenty years later and measured again and you

525
00:25:46,200 --> 00:25:49,199
Speaker 1: should get the same answer, right. I mean, you're measuring

526
00:25:49,240 --> 00:25:51,760
Speaker 1: the same universe. It's the same thing. But it's not

527
00:25:51,800 --> 00:25:54,080
Speaker 1: something that necessarily has to be right. It could be

528
00:25:54,119 --> 00:25:56,600
Speaker 1: we live in the universe that is evolving and changing.

529
00:25:56,920 --> 00:25:59,960
Speaker 1: We just sort of assume that the universe has physical law,

530
00:26:00,200 --> 00:26:02,959
Speaker 1: and then we can do experiments to reveal those laws,

531
00:26:03,400 --> 00:26:05,119
Speaker 1: and we can do it whenever we like. It doesn't

532
00:26:05,119 --> 00:26:08,159
Speaker 1: matter if it's Christmas or if it's summer or whatever.

533
00:26:08,200 --> 00:26:10,840
Speaker 1: And that's fascinating and very very useful. But that's like

534
00:26:10,880 --> 00:26:12,840
Speaker 1: another symmetry of the universe.

535
00:26:13,280 --> 00:26:16,560
Speaker 3: So I'm not really used to thinking of time as

536
00:26:16,600 --> 00:26:19,000
Speaker 3: a thing that you can call symmetrical, like you know,

537
00:26:19,040 --> 00:26:21,960
Speaker 3: for me, if something symmetrical are out, like the one

538
00:26:22,000 --> 00:26:23,680
Speaker 3: side of my head has a lot more gray hair

539
00:26:23,680 --> 00:26:25,240
Speaker 3: than the other. Thing is I'm thinking of like a

540
00:26:25,320 --> 00:26:27,200
Speaker 3: shape that is not exactly the same.

541
00:26:27,480 --> 00:26:29,000
Speaker 1: Yeah, So the way to think about it is this.

542
00:26:29,160 --> 00:26:33,919
Speaker 1: It's like imagine applying a transformation and then seeing if

543
00:26:33,960 --> 00:26:37,000
Speaker 1: there's a change. So, for example, you're thinking, the left

544
00:26:37,000 --> 00:26:38,520
Speaker 1: half of my face is the same as the right

545
00:26:38,560 --> 00:26:40,960
Speaker 1: half of my face. The transformation you're doing there is

546
00:26:41,000 --> 00:26:44,080
Speaker 1: you're reflecting it, right, So it's called a reflection symmetry.

547
00:26:44,480 --> 00:26:46,720
Speaker 1: If your face is symmetrical, then take your left side

548
00:26:46,760 --> 00:26:49,119
Speaker 1: and reflect it onto your right side and they should

549
00:26:49,119 --> 00:26:52,159
Speaker 1: look the same. Most people faces actually not that symmetrical.

550
00:26:52,560 --> 00:26:54,399
Speaker 1: And so if you do that, you look kind of weird.

551
00:26:54,960 --> 00:26:58,879
Speaker 1: But that's reflection symmetry, right, And so the concepts always

552
00:26:58,880 --> 00:27:02,000
Speaker 1: have a transformation, and then a question you ask, like

553
00:27:02,119 --> 00:27:05,880
Speaker 1: has this changed? So in your case, we're saying reflect

554
00:27:05,920 --> 00:27:08,199
Speaker 1: your face through a mirror, and we're asking do you

555
00:27:08,240 --> 00:27:11,680
Speaker 1: look different. In the case of time, for example, we're

556
00:27:11,720 --> 00:27:15,119
Speaker 1: asking shift time forward by ten seconds or by a

557
00:27:15,160 --> 00:27:18,240
Speaker 1: billion years? Do the laws of physics make any difference?

558
00:27:18,240 --> 00:27:22,080
Speaker 1: Do your experiments get the same results or not? And

559
00:27:22,160 --> 00:27:24,000
Speaker 1: so that's the sort of connection. You always have a

560
00:27:24,040 --> 00:27:27,679
Speaker 1: transformation you're applying, and then you're asking is something changed

561
00:27:27,760 --> 00:27:27,960
Speaker 1: or not?

562
00:27:28,840 --> 00:27:33,080
Speaker 3: Okay, so what kind of transformations could you apply that

563
00:27:33,119 --> 00:27:36,960
Speaker 3: are not symmetrical? Oh, I think that'll help me understand

564
00:27:37,720 --> 00:27:39,040
Speaker 3: why time is symmetrical.

565
00:27:39,560 --> 00:27:42,280
Speaker 1: Yeah, that's a great question. Something the universe is not

566
00:27:42,320 --> 00:27:47,240
Speaker 1: symmetrical to is acceleration. Like take your experiment, and now

567
00:27:47,280 --> 00:27:49,359
Speaker 1: take your experiment and put it on a rocket ship

568
00:27:49,680 --> 00:27:52,560
Speaker 1: so that there's a thrust. It's like accelerating through space.

569
00:27:53,000 --> 00:27:55,240
Speaker 1: You can get different answers, and you can think about

570
00:27:55,240 --> 00:27:58,080
Speaker 1: this very simply, like say you're just in a box

571
00:27:58,480 --> 00:28:00,760
Speaker 1: and your experiment is I have a ball on the floor,

572
00:28:00,880 --> 00:28:04,280
Speaker 1: and I'm just watching it. If you're not accelerating, you're

573
00:28:04,320 --> 00:28:06,639
Speaker 1: going to get one answer. If you are accelerating, then

574
00:28:06,680 --> 00:28:08,439
Speaker 1: the ball is going to roll to the back of

575
00:28:08,480 --> 00:28:11,159
Speaker 1: the box, right because it's not being accelerated and the

576
00:28:11,160 --> 00:28:13,600
Speaker 1: box is being accelerated. It's like a bowling ball in

577
00:28:13,600 --> 00:28:15,760
Speaker 1: the back of a truck. And so you're going to

578
00:28:15,800 --> 00:28:18,000
Speaker 1: get a different answer. And so the universe is not

579
00:28:18,160 --> 00:28:22,479
Speaker 1: symmetric to accelerations. Like, you accelerate your experiment, you're going

580
00:28:22,520 --> 00:28:25,520
Speaker 1: to get different answers. You move your experiment, you shouldn't

581
00:28:25,520 --> 00:28:27,960
Speaker 1: get a different answer. You spin your experiment to a

582
00:28:27,960 --> 00:28:30,760
Speaker 1: different direction, you shouldn't get a different answer. You delay

583
00:28:30,800 --> 00:28:33,200
Speaker 1: your experiment by a week, you shouldn't get a different answer.

584
00:28:33,320 --> 00:28:36,359
Speaker 1: But if you accelerate it, you're definitely getting a different answer.

585
00:28:36,640 --> 00:28:39,040
Speaker 1: So the universe not symmetric to acceleration.

586
00:28:39,560 --> 00:28:44,520
Speaker 3: And does Emmy's equation predict what should be symmetrical and

587
00:28:44,560 --> 00:28:46,720
Speaker 3: what shouldn't or that just requires some intuition.

588
00:28:47,200 --> 00:28:49,280
Speaker 1: Oh yeah, that's another great question. No, it doesn't tell

589
00:28:49,360 --> 00:28:52,480
Speaker 1: us what the symmetries are, but it does tell us

590
00:28:52,520 --> 00:28:54,880
Speaker 1: that if you find a symmetry, it has a big

591
00:28:54,920 --> 00:28:57,959
Speaker 1: consequences for how the universe behaves, and some of these

592
00:28:57,960 --> 00:29:01,800
Speaker 1: symmetries are easy to think about, like or location or direction.

593
00:29:01,920 --> 00:29:04,280
Speaker 1: They sort of make intuitive sense. By some of the

594
00:29:04,360 --> 00:29:08,320
Speaker 1: most important symmetries turn out to be weird quantum mechanical

595
00:29:08,440 --> 00:29:12,120
Speaker 1: quantities that we never really think about. We talked recently

596
00:29:12,200 --> 00:29:15,880
Speaker 1: about like electrons. Electrons are quant mechanical objects, and we

597
00:29:15,880 --> 00:29:19,040
Speaker 1: think of them as having like physical properties mass and

598
00:29:19,120 --> 00:29:21,880
Speaker 1: direction and spin and this kind of stuff, that they

599
00:29:21,920 --> 00:29:25,840
Speaker 1: also have weird quantum mechanical properties, like their wave functions

600
00:29:26,040 --> 00:29:29,000
Speaker 1: can have a complex piece to them. By complex, I

601
00:29:29,000 --> 00:29:31,680
Speaker 1: don't mean complicated. I mean like you know five plus

602
00:29:31,720 --> 00:29:34,560
Speaker 1: four I the way some numbers are real numbers and

603
00:29:34,600 --> 00:29:37,520
Speaker 1: some numbers are complex numbers. They have an imaginary component.

604
00:29:37,960 --> 00:29:40,640
Speaker 1: Electron wave functions can have an imaginary component, and this

605
00:29:41,000 --> 00:29:43,920
Speaker 1: isn't something you can measure, because whenever you measure the

606
00:29:43,960 --> 00:29:46,880
Speaker 1: wave function, you always take its amplitude square. The imaginary

607
00:29:46,880 --> 00:29:50,080
Speaker 1: part goes away. But it is a feature of the electron,

608
00:29:50,560 --> 00:29:52,520
Speaker 1: and so you can think of it as like an angle,

609
00:29:52,960 --> 00:29:55,360
Speaker 1: like you can rotate this thing through complex space. So

610
00:29:55,400 --> 00:29:59,800
Speaker 1: electrons have these weird complex internal quantum mechanical angle that

611
00:29:59,800 --> 00:30:02,520
Speaker 1: you can can't measure, and it turns out that the

612
00:30:02,600 --> 00:30:06,080
Speaker 1: universe respects that you can rotate electrons through this angle

613
00:30:06,240 --> 00:30:09,320
Speaker 1: and it doesn't change anything in the equations. So that's

614
00:30:09,320 --> 00:30:12,560
Speaker 1: like another weird symmetry that the universe has. And if

615
00:30:12,560 --> 00:30:14,280
Speaker 1: people want to read more about this, this is called

616
00:30:14,360 --> 00:30:18,720
Speaker 1: you one symmetry of the Lugrongen. So it's not just

617
00:30:18,880 --> 00:30:21,960
Speaker 1: like obvious physical symmetries that the universe has. We also

618
00:30:21,960 --> 00:30:25,160
Speaker 1: have these weird internal quantum mechanical symmetries that have very

619
00:30:25,200 --> 00:30:27,880
Speaker 1: deep consequences thanks to Nuther's theorem.

620
00:30:28,200 --> 00:30:30,680
Speaker 3: We were talking about these angles on the episode where

621
00:30:30,720 --> 00:30:34,240
Speaker 3: we were talking about charge and force. Isn't that right?

622
00:30:34,320 --> 00:30:36,000
Speaker 3: And what context did they come up in? I guess

623
00:30:36,000 --> 00:30:39,280
Speaker 3: they just came up in the wave function context.

624
00:30:39,400 --> 00:30:42,480
Speaker 1: Yeah, Well, we were talking about why we have photons,

625
00:30:43,040 --> 00:30:45,800
Speaker 1: and it turns out that you can't respect this weird

626
00:30:45,880 --> 00:30:49,240
Speaker 1: electron angle without having photons. Photons are the things that

627
00:30:49,360 --> 00:30:53,400
Speaker 1: make this weird electron angles symmetric in the equations of physics,

628
00:30:54,000 --> 00:30:56,800
Speaker 1: and that has the big consequence thanks to Nother's theorem.

629
00:30:57,080 --> 00:30:58,880
Speaker 1: But you have to have photons. You can't just do

630
00:30:58,960 --> 00:31:01,440
Speaker 1: this in the universe with just electrons, and so some

631
00:31:01,480 --> 00:31:04,880
Speaker 1: people like to say that the reason we have photons

632
00:31:05,360 --> 00:31:07,720
Speaker 1: is to respect this electron symmetry.

633
00:31:08,080 --> 00:31:10,959
Speaker 3: Okay, thanks, I'm expecting an honorary degree in physics one

634
00:31:11,000 --> 00:31:12,760
Speaker 3: of these days, so I have to make these connections

635
00:31:12,760 --> 00:31:13,600
Speaker 3: between episodes.

636
00:31:13,600 --> 00:31:15,760
Speaker 1: I'm gonna give you a pod in physics. Eventually.

637
00:31:15,960 --> 00:31:18,400
Speaker 3: This is the O stand for I went over my head.

638
00:31:19,200 --> 00:31:22,920
Speaker 3: Oh God, oh man for not catching that they're going

639
00:31:22,960 --> 00:31:25,920
Speaker 3: to take away the PhD I already have. I don't

640
00:31:25,960 --> 00:31:28,400
Speaker 3: know who they is, but someone's taken it away. The man.

641
00:31:29,200 --> 00:31:32,600
Speaker 3: All right, let's all take a break and ponder which

642
00:31:32,680 --> 00:31:35,720
Speaker 3: university should be giving me my honorary PhD. And when

643
00:31:35,720 --> 00:31:55,480
Speaker 3: we get back, we'll dive into the details of Notether's theorem.

644
00:31:55,560 --> 00:31:58,760
Speaker 3: All right, we're back, Daniel. You've been sort of giving

645
00:31:58,880 --> 00:32:02,560
Speaker 3: us tantalizing. It's about symmetries and what Notre taught us.

646
00:32:02,960 --> 00:32:04,800
Speaker 3: Let's talk more about what her theorem's all about.

647
00:32:05,080 --> 00:32:07,560
Speaker 1: Yes, so Notthern's theorem is really important. It tells us

648
00:32:08,000 --> 00:32:10,200
Speaker 1: what it means that there's a symmetry in the universe.

649
00:32:10,200 --> 00:32:13,280
Speaker 1: It tells us what the consequences are like. You might say, okay,

650
00:32:13,320 --> 00:32:15,160
Speaker 1: so I can do my experiment here, or I can

651
00:32:15,200 --> 00:32:16,400
Speaker 1: do it in the middle of deep space. I get

652
00:32:16,440 --> 00:32:18,600
Speaker 1: the same answer, who cares? What does that mean about

653
00:32:18,640 --> 00:32:22,440
Speaker 1: the universe? Well? Notther's theorem tells us what it means. Specifically,

654
00:32:22,480 --> 00:32:26,760
Speaker 1: it tells us that any symmetry implies a conservation law.

655
00:32:27,120 --> 00:32:29,480
Speaker 1: It means that there's something out there that the universe

656
00:32:29,520 --> 00:32:33,520
Speaker 1: respects that if you calculate it, that number never changes,

657
00:32:33,960 --> 00:32:36,680
Speaker 1: you know. So to think about what a conservation law is, like,

658
00:32:37,040 --> 00:32:39,080
Speaker 1: let's say you have a little economy and people are

659
00:32:39,080 --> 00:32:42,080
Speaker 1: spending money in trading on eggs for dollars or whatever.

660
00:32:42,560 --> 00:32:44,520
Speaker 1: You can spend those dollars, but this dollar is still

661
00:32:44,560 --> 00:32:47,680
Speaker 1: go somewhere, and they still are somewhere, right, So, like

662
00:32:47,720 --> 00:32:50,960
Speaker 1: the number of dollars in a closed economy is conserved

663
00:32:51,400 --> 00:32:53,440
Speaker 1: because you have a certain number of dollars and they're

664
00:32:53,480 --> 00:32:55,360
Speaker 1: just going to move around, but the number of them

665
00:32:55,480 --> 00:32:58,320
Speaker 1: doesn't change, right, So the total amount of money is

666
00:32:58,400 --> 00:33:01,000
Speaker 1: conserved there. And I know that in real economics the

667
00:33:01,040 --> 00:33:03,000
Speaker 1: total amount of money isn't conserved and value can be

668
00:33:03,000 --> 00:33:05,400
Speaker 1: created in whatever. But like say you have a simple

669
00:33:05,440 --> 00:33:08,360
Speaker 1: economy with a few dollars and they're just moving around,

670
00:33:08,560 --> 00:33:12,240
Speaker 1: the dollars can flow. There's a current of money, but overall,

671
00:33:12,400 --> 00:33:14,520
Speaker 1: there's a conservation of those dollars.

672
00:33:14,760 --> 00:33:19,160
Speaker 3: Right, Okay, assume a spherical economy exactly.

673
00:33:19,480 --> 00:33:21,680
Speaker 1: So another theorem tells us that all the symmetries we

674
00:33:21,720 --> 00:33:24,600
Speaker 1: talked about previously and will go through each one, imply

675
00:33:24,760 --> 00:33:27,720
Speaker 1: a conservation law in the universe. There's something that the

676
00:33:27,840 --> 00:33:31,720
Speaker 1: universe respects these Every symmetry has a conservation law, and

677
00:33:31,840 --> 00:33:35,120
Speaker 1: any conserved quantity implies that there's a symmetry there.

678
00:33:35,480 --> 00:33:37,280
Speaker 3: We start with that sphere example.

679
00:33:37,520 --> 00:33:39,680
Speaker 1: Yeah, so let's take a sphere and say we move

680
00:33:39,680 --> 00:33:42,560
Speaker 1: it somewhere else. It's still a sphere, right, that hasn't changed.

681
00:33:42,920 --> 00:33:46,840
Speaker 1: So what does that translation symmetry imply? It implies conservation

682
00:33:47,040 --> 00:33:51,600
Speaker 1: of momentum. Right. The reason that the universe conserves momentum

683
00:33:52,080 --> 00:33:55,080
Speaker 1: is because there is no special place in the universe.

684
00:33:55,280 --> 00:33:57,800
Speaker 1: There are no markings in space. It doesn't matter where

685
00:33:57,840 --> 00:34:00,440
Speaker 1: you do your experiment or where you take your measurement

686
00:34:00,840 --> 00:34:03,320
Speaker 1: that you should get the same answer. Noother's theorem says,

687
00:34:03,560 --> 00:34:07,080
Speaker 1: if that's true in your universe, then momentum is conserved.

688
00:34:07,720 --> 00:34:09,799
Speaker 1: And that's kind of like a big leap. You're like, what,

689
00:34:10,160 --> 00:34:12,680
Speaker 1: like I get there's a connection there. We have positions.

690
00:34:13,040 --> 00:34:15,960
Speaker 1: But now we're talking about momentums and velocities, and like

691
00:34:16,480 --> 00:34:20,160
Speaker 1: it's kind of crazy, right, Like what is momentum conservation anyway?

692
00:34:20,480 --> 00:34:23,440
Speaker 1: It just says that if you calculate the momentum of stuff,

693
00:34:23,480 --> 00:34:26,960
Speaker 1: which is mass times velocity, and then you let physics happen.

694
00:34:27,160 --> 00:34:29,759
Speaker 1: Like you have two balls and they bounce off each other,

695
00:34:30,360 --> 00:34:32,920
Speaker 1: and you measure their mass and their velocity beforehand, you

696
00:34:33,000 --> 00:34:34,920
Speaker 1: add it up, you get a number. You measure their

697
00:34:34,960 --> 00:34:37,520
Speaker 1: mass and velocity afterwards, and you calculate momentum and add

698
00:34:37,560 --> 00:34:39,920
Speaker 1: all up. You get the same number. It's like if

699
00:34:39,960 --> 00:34:42,279
Speaker 1: I buy eggs from you, I trade you dollars, the

700
00:34:42,360 --> 00:34:45,120
Speaker 1: total number of dollars in the universe hasn't changed. Well,

701
00:34:45,120 --> 00:34:47,280
Speaker 1: if we bounce balls off of each other, the amount

702
00:34:47,280 --> 00:34:50,440
Speaker 1: of momentum in the universe hasn't changed. And that's because

703
00:34:50,440 --> 00:34:53,840
Speaker 1: of notother's theorem. Another's theorem says we have momentum conservation

704
00:34:54,000 --> 00:34:57,879
Speaker 1: because space is the same everywhere. It doesn't matter where

705
00:34:57,920 --> 00:34:58,560
Speaker 1: you do your.

706
00:34:58,400 --> 00:35:01,839
Speaker 3: Experiment, okay, and so if you do your experiment at

707
00:35:01,840 --> 00:35:06,640
Speaker 3: different times, you get the same results. Because what is conserved.

708
00:35:06,400 --> 00:35:10,000
Speaker 1: Time symmetry means that there's a conservation of energy. The

709
00:35:10,080 --> 00:35:13,320
Speaker 1: reason we have conservation of energy is because of time symmetry,

710
00:35:13,719 --> 00:35:16,360
Speaker 1: and Nuther's theorem connects these things. It tells you exactly

711
00:35:16,440 --> 00:35:20,080
Speaker 1: what is conserved if you have a certain symmetry. And

712
00:35:20,120 --> 00:35:22,840
Speaker 1: so there's this pairing between energy and time. There's a

713
00:35:22,880 --> 00:35:27,799
Speaker 1: pairing between position and momentum, and Noutherar's theorem tells us that,

714
00:35:27,920 --> 00:35:32,800
Speaker 1: like translation symmetry, position symmetry gives us conservation momentum, time

715
00:35:32,880 --> 00:35:36,319
Speaker 1: symmetry gives us conservation of energy, and in fact it

716
00:35:36,320 --> 00:35:39,640
Speaker 1: goes even deeper than that. That's a really useful definition

717
00:35:39,840 --> 00:35:43,960
Speaker 1: of energy. Energy is the thing that's conserved if you

718
00:35:44,080 --> 00:35:47,280
Speaker 1: have time symmetry. That's the way a lot of physicists

719
00:35:47,360 --> 00:35:50,799
Speaker 1: think about energy now in terms of Nuther's theorem and

720
00:35:50,840 --> 00:35:53,880
Speaker 1: these conservation laws, and it's hard to sort of wrap

721
00:35:53,880 --> 00:35:56,400
Speaker 1: your mind around, like why is this? Can we understand

722
00:35:56,400 --> 00:35:58,640
Speaker 1: how Nutherar's theorem connects these things?

723
00:35:58,960 --> 00:36:00,600
Speaker 3: Can you give me an example of, like, if I

724
00:36:00,640 --> 00:36:03,879
Speaker 3: do the double slit experiment, maybe I'm making it at

725
00:36:03,880 --> 00:36:07,320
Speaker 3: two different times, how does that tell me about conservation

726
00:36:07,360 --> 00:36:07,840
Speaker 3: of energy?

727
00:36:08,520 --> 00:36:11,160
Speaker 1: Let's get to conservation of energy, because it's tricky, because

728
00:36:11,160 --> 00:36:13,680
Speaker 1: it turns out energy is not actually conserved in the universe,

729
00:36:13,840 --> 00:36:15,839
Speaker 1: which tells us something else about the universe. But let's

730
00:36:15,880 --> 00:36:18,880
Speaker 1: go back to simple momentum and thinking about balls and

731
00:36:18,920 --> 00:36:21,960
Speaker 1: thinking about what it tells us about the universe and

732
00:36:22,160 --> 00:36:24,120
Speaker 1: how space is the same. Right, it's interesting that you

733
00:36:24,120 --> 00:36:26,279
Speaker 1: could do the same experiment anywhere in the universe and

734
00:36:26,320 --> 00:36:28,759
Speaker 1: get the same answer. Why does that tell us something

735
00:36:28,760 --> 00:36:32,200
Speaker 1: about momentum. Well, imagine that we had a universe that

736
00:36:32,280 --> 00:36:35,279
Speaker 1: didn't have the same kind of space everywhere. Let's say

737
00:36:35,280 --> 00:36:37,359
Speaker 1: we had a universe that had an edge to it,

738
00:36:37,840 --> 00:36:40,680
Speaker 1: like a wall, you know, like a place where if

739
00:36:40,719 --> 00:36:43,920
Speaker 1: you tried to go there, you just bounced back. Right. Now,

740
00:36:43,920 --> 00:36:45,920
Speaker 1: we have a universe where you have most of the

741
00:36:45,920 --> 00:36:48,080
Speaker 1: same kind of space, normal space, but then you also

742
00:36:48,080 --> 00:36:50,400
Speaker 1: have an edge bit, and an edge bit has special

743
00:36:50,400 --> 00:36:53,319
Speaker 1: properties that if you hit it, you bounce back. Right.

744
00:36:53,840 --> 00:36:56,919
Speaker 1: So do we have a momentum conservation in that universe? No,

745
00:36:57,120 --> 00:36:59,200
Speaker 1: we don't, because what happens if you throw a ball

746
00:36:59,239 --> 00:37:03,160
Speaker 1: against the edge of the universe it bounces back, it

747
00:37:03,320 --> 00:37:07,520
Speaker 1: changes its momentum, and there's nothing to compensate for that. Usually,

748
00:37:07,560 --> 00:37:09,320
Speaker 1: if I want to change the momentum of something, I

749
00:37:09,440 --> 00:37:12,200
Speaker 1: bounce it against a wall, that wall pushes back and

750
00:37:12,239 --> 00:37:14,480
Speaker 1: it absorbs that momentum. The walls like pushed in the

751
00:37:14,520 --> 00:37:17,080
Speaker 1: other direction. But if I have the edge of the universe,

752
00:37:17,120 --> 00:37:19,520
Speaker 1: it's like special magical bit of space that can just

753
00:37:19,800 --> 00:37:22,840
Speaker 1: turn things around and change their momentum. Boom, I have

754
00:37:23,000 --> 00:37:26,719
Speaker 1: violated conservation of momentum. So there's an example of how

755
00:37:27,200 --> 00:37:30,280
Speaker 1: having the space not be the same everywhere will violate

756
00:37:30,320 --> 00:37:34,120
Speaker 1: conservation momentum. You can't have conservation and momentum in that universe.

757
00:37:34,400 --> 00:37:37,000
Speaker 1: And to me that's really deep because it tells us, hey,

758
00:37:37,160 --> 00:37:40,239
Speaker 1: if momentum is conserved, that means space is the same

759
00:37:40,280 --> 00:37:44,680
Speaker 1: everywhere and there isn't an edge to the universe. Boom.

760
00:37:44,760 --> 00:37:47,680
Speaker 1: It's like amazing these moments when you can do an

761
00:37:47,719 --> 00:37:51,000
Speaker 1: experiment here on Earth and from that concludes something about

762
00:37:51,120 --> 00:37:55,279
Speaker 1: deep space super far away. Like what I love it

763
00:37:55,320 --> 00:37:58,719
Speaker 1: when like the math clicks together and has these literally

764
00:37:58,800 --> 00:38:02,000
Speaker 1: far reaching consequences, is about what may be happening super

765
00:38:02,080 --> 00:38:05,720
Speaker 1: far away. You got moment That doesn't mean the universe

766
00:38:05,800 --> 00:38:08,319
Speaker 1: is infinite, right, It means there's no special space in

767
00:38:08,320 --> 00:38:10,640
Speaker 1: the universe. You could still have a finite universe, just

768
00:38:10,760 --> 00:38:13,200
Speaker 1: not one with an edge. If we have a finite

769
00:38:13,239 --> 00:38:15,120
Speaker 1: universe has to like wrap around it stuff. You can

770
00:38:15,160 --> 00:38:17,319
Speaker 1: have a finite universe where every bit of space is

771
00:38:17,400 --> 00:38:17,800
Speaker 1: the same.

772
00:38:18,040 --> 00:38:20,120
Speaker 3: I know just enough about physics now to get my

773
00:38:20,160 --> 00:38:22,919
Speaker 3: own way. So that's where we are in my learning career.

774
00:38:22,920 --> 00:38:23,239
Speaker 7: All right.

775
00:38:23,320 --> 00:38:26,680
Speaker 3: So we have talked about space bending or is it

776
00:38:26,719 --> 00:38:30,799
Speaker 3: space time bending? Okay, but that doesn't change momentum, and

777
00:38:30,880 --> 00:38:32,480
Speaker 3: so we still have conservation.

778
00:38:32,719 --> 00:38:35,080
Speaker 1: Yes, you can still have conservation of momentum even if

779
00:38:35,120 --> 00:38:37,920
Speaker 1: space time bends. Yeah, exactly, okay. And this is also

780
00:38:37,960 --> 00:38:42,120
Speaker 1: really fascinating because it connects us with quantum mechanics, Like

781
00:38:42,239 --> 00:38:44,279
Speaker 1: this is a general theory about the universe, but it

782
00:38:44,320 --> 00:38:48,120
Speaker 1: tells us there's a deep connection between position and momentum.

783
00:38:48,160 --> 00:38:50,480
Speaker 1: And we kind of already knew that because quantum mechanics

784
00:38:50,520 --> 00:38:54,359
Speaker 1: says you can't know position and momentum simultaneously, that these

785
00:38:54,400 --> 00:38:57,759
Speaker 1: two quantities are linked in a deep way, you know,

786
00:38:57,840 --> 00:38:59,560
Speaker 1: Like why is it that if you measure position, you

787
00:38:59,640 --> 00:39:02,360
Speaker 1: can't know momentum instead of if you measure position you

788
00:39:02,360 --> 00:39:06,359
Speaker 1: can't know like angle or energy or something. Because there's

789
00:39:06,400 --> 00:39:09,279
Speaker 1: a pairing between these two quantities, position and momentum, they're

790
00:39:09,320 --> 00:39:12,040
Speaker 1: deeply connected with each other. And if you know something

791
00:39:12,040 --> 00:39:15,719
Speaker 1: about like Fourya transforms, it's very natural to understand how

792
00:39:15,840 --> 00:39:19,840
Speaker 1: you transform something from physical space to momentum space. You

793
00:39:19,920 --> 00:39:23,080
Speaker 1: understand they're connected by these fourya transforms. They really are

794
00:39:23,120 --> 00:39:27,400
Speaker 1: not independent quantities. They're two different sides of the same coin,

795
00:39:28,200 --> 00:39:31,960
Speaker 1: and so Notther's theorem reveals that as well. So these

796
00:39:32,000 --> 00:39:34,160
Speaker 1: are deep connections. So now if you want, we can

797
00:39:34,200 --> 00:39:37,520
Speaker 1: talk about energy conservation and time translation invariance.

798
00:39:37,800 --> 00:39:40,120
Speaker 3: First I want to ask did she have like one

799
00:39:40,200 --> 00:39:42,600
Speaker 3: equation from which all of this popped out or was

800
00:39:42,640 --> 00:39:45,799
Speaker 3: it a different equation for each one of these connections.

801
00:39:45,880 --> 00:39:47,640
Speaker 1: It's a single equation. It tells you that if your

802
00:39:47,719 --> 00:39:51,880
Speaker 1: laws of physics are invariant under some transformation, then it

803
00:39:51,920 --> 00:39:55,279
Speaker 1: tells you what quantity is conserved. So you put in

804
00:39:55,320 --> 00:39:57,480
Speaker 1: your laws of physics, which we usually describe in terms

805
00:39:57,520 --> 00:40:00,480
Speaker 1: of a lagrangein, which is basically like kinetic energy minus

806
00:40:00,480 --> 00:40:03,279
Speaker 1: potential energy, and then you do your transformation. You say, well,

807
00:40:03,280 --> 00:40:06,040
Speaker 1: what happens if I change it by shifting it to

808
00:40:06,040 --> 00:40:08,160
Speaker 1: the left or shifting it to the right. And if

809
00:40:08,200 --> 00:40:10,400
Speaker 1: the answer is that you get the same lagrange in

810
00:40:10,480 --> 00:40:12,959
Speaker 1: out the same fundamental laws of physics, then it tells

811
00:40:13,000 --> 00:40:16,680
Speaker 1: you what quantity is conserved and as a single equation,

812
00:40:17,280 --> 00:40:20,080
Speaker 1: so you can change the symmetry you're exploring and it

813
00:40:20,120 --> 00:40:22,520
Speaker 1: will tell you what the conservation law is.

814
00:40:23,160 --> 00:40:25,800
Speaker 3: Okay, all right, awesome, Well let's move on to energy.

815
00:40:26,000 --> 00:40:29,680
Speaker 1: Yeah, so energy is super fascinating. And we were saying

816
00:40:29,680 --> 00:40:34,960
Speaker 1: earlier that if the universe has time translation symmetry, meaning

817
00:40:35,000 --> 00:40:37,880
Speaker 1: it doesn't matter when you do your experiment, then energy

818
00:40:37,920 --> 00:40:41,320
Speaker 1: is conserved in the universe. Cool, And everybody thinks energy

819
00:40:41,360 --> 00:40:43,640
Speaker 1: is conserved in the universe. You're taught energy is conserved

820
00:40:43,640 --> 00:40:46,279
Speaker 1: in the universe. Energy conservation is fundamental, and people think

821
00:40:46,320 --> 00:40:50,279
Speaker 1: about energy the way sort of we talk about dollars earlier, Like, yeah,

822
00:40:50,280 --> 00:40:52,799
Speaker 1: I have energy here and I can transform it, but

823
00:40:52,840 --> 00:40:56,040
Speaker 1: you can't create it or destroy it. Right, Like if

824
00:40:56,080 --> 00:40:58,520
Speaker 1: I'm going really really fast and I slam on the brakes,

825
00:40:58,560 --> 00:41:01,640
Speaker 1: where's my kinetic energy go It goes through friction into

826
00:41:01,680 --> 00:41:04,359
Speaker 1: the heat of the break pads, you know. Or if

827
00:41:04,400 --> 00:41:06,240
Speaker 1: you have a book on a shelf that has potential

828
00:41:06,320 --> 00:41:09,600
Speaker 1: energy you knock it off, that's transformed into kinetic energy.

829
00:41:09,840 --> 00:41:12,160
Speaker 1: Energy and mass can be transformed back and forth into

830
00:41:12,160 --> 00:41:14,360
Speaker 1: each other. All this kind of stuff. It's really intuitive

831
00:41:14,400 --> 00:41:17,000
Speaker 1: for people to think that energy is conserved in the universe.

832
00:41:17,400 --> 00:41:20,160
Speaker 1: But that's only true if the laws of physics actually

833
00:41:20,200 --> 00:41:23,760
Speaker 1: are invariant to time. And it turns out they're not quite.

834
00:41:24,080 --> 00:41:26,200
Speaker 3: Oh no, how are they not quite? Everything you know

835
00:41:26,320 --> 00:41:26,719
Speaker 3: is a line.

836
00:41:28,800 --> 00:41:30,560
Speaker 1: Well, what we include in the laws of physics are

837
00:41:30,560 --> 00:41:34,080
Speaker 1: the behavior of space time, and the expansion of space

838
00:41:34,280 --> 00:41:37,200
Speaker 1: breaks that. So the universe is not the same as

839
00:41:37,239 --> 00:41:40,080
Speaker 1: it was a billion years ago or five billion years ago.

840
00:41:40,320 --> 00:41:44,040
Speaker 1: The universe is expanding. Space is expanding. So it turns

841
00:41:44,040 --> 00:41:47,560
Speaker 1: out that space has to be static to satisfy this

842
00:41:47,719 --> 00:41:50,880
Speaker 1: time invariance. Because like the amount of dark energy in

843
00:41:50,880 --> 00:41:53,000
Speaker 1: the universe, the fraction of dark energy in the universe

844
00:41:53,200 --> 00:41:55,960
Speaker 1: is changing, the fraction of matter in the universe is changing.

845
00:41:56,680 --> 00:42:00,120
Speaker 1: So because we don't have time translation in VERYOCE, it's

846
00:42:00,120 --> 00:42:03,160
Speaker 1: because the universe isn't actually the same fundamentally as it

847
00:42:03,239 --> 00:42:05,840
Speaker 1: was five billion years ago. Energy is not conserved in

848
00:42:05,880 --> 00:42:08,800
Speaker 1: our universe. Wow, And we can understand that very easily.

849
00:42:08,880 --> 00:42:11,120
Speaker 1: But just by looking at the dark energy, like the

850
00:42:11,200 --> 00:42:15,360
Speaker 1: universe is expanding, that makes more space. Dark energy is

851
00:42:15,520 --> 00:42:19,000
Speaker 1: constant density, which means that as the universe expands, it

852
00:42:19,040 --> 00:42:22,600
Speaker 1: doesn't get diluted. It's not like matter, where you make

853
00:42:22,640 --> 00:42:24,920
Speaker 1: more space and you still have the same number of protons.

854
00:42:25,080 --> 00:42:27,560
Speaker 1: The density has gone down, the amount of matter has

855
00:42:27,600 --> 00:42:30,800
Speaker 1: stayed fixed. Dark energy is weird. As you make more space,

856
00:42:30,840 --> 00:42:33,440
Speaker 1: because the density is constant, you get more dark energy.

857
00:42:33,600 --> 00:42:36,920
Speaker 1: So dark energy is just increasing. Where is it coming from?

858
00:42:37,200 --> 00:42:40,440
Speaker 1: It doesn't have to come from anywhere because energy not

859
00:42:40,719 --> 00:42:44,239
Speaker 1: conserved in our universe. That's what Nother's theorem tells us.

860
00:42:44,440 --> 00:42:47,560
Speaker 1: It tells us energy doesn't just flow. It can be increased,

861
00:42:47,560 --> 00:42:50,160
Speaker 1: it can be created, and it can be destroyed. So

862
00:42:50,280 --> 00:42:52,839
Speaker 1: Nother's theorem is all about flow in currents. It says

863
00:42:52,840 --> 00:42:55,360
Speaker 1: that when you have a symmetry there's a current that's conserved,

864
00:42:55,360 --> 00:42:58,000
Speaker 1: things can't be created or destroyed. They can only flow.

865
00:42:58,560 --> 00:43:02,040
Speaker 1: But because time is not symmetric quantity in our universe,

866
00:43:02,719 --> 00:43:05,160
Speaker 1: energy is not conserved. It doesn't have to flow. It

867
00:43:05,160 --> 00:43:09,240
Speaker 1: can be created and destroyed. And that's a really deep

868
00:43:09,360 --> 00:43:11,960
Speaker 1: thing to understand about the universe, because boy, do we

869
00:43:12,000 --> 00:43:15,200
Speaker 1: have energy problems. And if we could just create energy, Wow,

870
00:43:15,239 --> 00:43:18,000
Speaker 1: that would change our experience, right, that would be a

871
00:43:18,040 --> 00:43:18,520
Speaker 1: big deal.

872
00:43:18,840 --> 00:43:22,040
Speaker 3: And was this a revelation when the theorem came out

873
00:43:22,160 --> 00:43:23,880
Speaker 3: or was this something we kind of had to handle on,

874
00:43:23,960 --> 00:43:24,880
Speaker 3: but now it was proven.

875
00:43:25,120 --> 00:43:28,319
Speaker 1: It was really troublesome actually, because Einstein didn't like to

876
00:43:28,360 --> 00:43:31,680
Speaker 1: imagine that there was something in the universe that violated

877
00:43:31,719 --> 00:43:35,399
Speaker 1: time translation in variance, and so he famously like rejected

878
00:43:35,800 --> 00:43:39,600
Speaker 1: adding this to the equations partially for that reason. And

879
00:43:39,640 --> 00:43:42,279
Speaker 1: it's only later when we discovered that the expansion of

880
00:43:42,320 --> 00:43:45,239
Speaker 1: the universe was accelerating that we realized we needed this,

881
00:43:45,840 --> 00:43:47,759
Speaker 1: and so yeah, that sort of blew up our whole

882
00:43:47,800 --> 00:43:50,480
Speaker 1: thinking about how the universe works. I know we've said

883
00:43:50,480 --> 00:43:52,560
Speaker 1: this on the podcast before, but it's hard for people

884
00:43:52,560 --> 00:43:54,440
Speaker 1: to think in because they still write in and say,

885
00:43:54,520 --> 00:43:56,560
Speaker 1: are you sure as an energy conserved? Like, it's not

886
00:43:56,640 --> 00:44:00,399
Speaker 1: conserved in our universe, folks, unfortunately, And Another's theorem tells

887
00:44:00,520 --> 00:44:02,799
Speaker 1: us what that means. It goes back and forth. Right,

888
00:44:03,160 --> 00:44:05,200
Speaker 1: if you have a symmetry, it tells you what's conserved,

889
00:44:05,239 --> 00:44:07,359
Speaker 1: and if you have a conservation, it tells you what

890
00:44:07,400 --> 00:44:11,239
Speaker 1: the symmetry is. And like that's deeply important because the

891
00:44:11,320 --> 00:44:13,480
Speaker 1: game of physics is to like figure out what is

892
00:44:13,520 --> 00:44:16,680
Speaker 1: the puzzle of the universe, and recognizing the symmetries or

893
00:44:16,719 --> 00:44:20,120
Speaker 1: the conservation laws is equivalent. It's like saying this is

894
00:44:20,160 --> 00:44:23,520
Speaker 1: something that's important to the universe. It's fundamental, it's deep.

895
00:44:23,560 --> 00:44:27,360
Speaker 1: Momentum is an important quantity in the universe for some reason,

896
00:44:27,480 --> 00:44:29,680
Speaker 1: and the reason is connected to the reason that space

897
00:44:29,800 --> 00:44:32,640
Speaker 1: is the same everywhere, the way that like the number

898
00:44:32,680 --> 00:44:35,600
Speaker 1: of podcasts in the universe not an important quantity. The

899
00:44:35,719 --> 00:44:39,080
Speaker 1: universe does not care. You can study podcasts and you

900
00:44:39,120 --> 00:44:42,160
Speaker 1: will not learn anything fundamental about the universe, except if

901
00:44:42,200 --> 00:44:44,160
Speaker 1: you listen to this podcast, you will learn a lot

902
00:44:44,160 --> 00:44:45,000
Speaker 1: about the universe.

903
00:44:45,200 --> 00:44:48,239
Speaker 3: The universe cares about this podcast, probably.

904
00:44:47,800 --> 00:44:49,840
Speaker 1: But it's not like every time a podcast is created,

905
00:44:49,880 --> 00:44:52,239
Speaker 1: another one is destroyed. If you discovered that that there

906
00:44:52,320 --> 00:44:54,880
Speaker 1: was like a conservation law podcast that would tell you

907
00:44:54,920 --> 00:44:58,040
Speaker 1: this some symmetry in the universe that's related to podcasting,

908
00:44:58,080 --> 00:45:00,359
Speaker 1: I don't know what that would be. And you're really

909
00:45:00,360 --> 00:45:02,440
Speaker 1: inside into how the universe works.

910
00:45:02,680 --> 00:45:06,880
Speaker 3: So was Emmy appreciated for this contribution in her time

911
00:45:07,280 --> 00:45:11,760
Speaker 3: or no? Because big people like Einstein were not willing

912
00:45:11,800 --> 00:45:12,720
Speaker 3: to accept the results.

913
00:45:12,760 --> 00:45:16,560
Speaker 1: People in the field definitely appreciated Nuther. Einstein said, quote

914
00:45:16,760 --> 00:45:21,080
Speaker 1: Nuther was the most significant creative mathematical genius thus far

915
00:45:21,200 --> 00:45:24,879
Speaker 1: produced since the higher education of women began, so there's

916
00:45:24,880 --> 00:45:27,520
Speaker 1: a qualifying there. He's like, she's the smartest lady I

917
00:45:27,520 --> 00:45:29,680
Speaker 1: ever met, and a lot of people since were like,

918
00:45:29,880 --> 00:45:33,040
Speaker 1: she's just the smartest mathematician period. You don't have to

919
00:45:33,040 --> 00:45:33,759
Speaker 1: put lady ye.

920
00:45:34,640 --> 00:45:38,680
Speaker 3: Well, and also qualifying since women were allowed in academia,

921
00:45:38,719 --> 00:45:41,160
Speaker 3: which was like seven years earlier or something like that. Right,

922
00:45:41,200 --> 00:45:42,160
Speaker 3: that's a pretty big quality.

923
00:45:42,160 --> 00:45:44,120
Speaker 1: It's a pretty big qualif But you know, Hilbert and

924
00:45:44,160 --> 00:45:46,120
Speaker 1: all these folks, they knew what they were dealing with.

925
00:45:46,280 --> 00:45:49,400
Speaker 1: They understood they were in the presence of genius. And

926
00:45:49,480 --> 00:45:52,920
Speaker 1: she made a lot of important contributions in abstract algebra,

927
00:45:53,120 --> 00:45:56,200
Speaker 1: like all huge contributions there. Like this is a small

928
00:45:56,320 --> 00:45:59,840
Speaker 1: part of her legacy, but it literally underlies all of physics.

929
00:46:00,000 --> 00:46:03,560
Speaker 1: Everything in physics is Nuther. There's a physicist, Ransom Stevens

930
00:46:03,600 --> 00:46:05,799
Speaker 1: who said, quote, you can make a strong case that

931
00:46:05,880 --> 00:46:09,200
Speaker 1: her theorem is the backbone on which all of modern

932
00:46:09,280 --> 00:46:13,480
Speaker 1: physics is built. Like boom. You know, Maxwell, he did

933
00:46:13,520 --> 00:46:15,799
Speaker 1: a little piece of it. Higgs, he found a little

934
00:46:15,800 --> 00:46:18,000
Speaker 1: piece of it. But all at rest on the foundation

935
00:46:18,440 --> 00:46:21,440
Speaker 1: of Nuther's theorem. All of our lagrongens. Every time we

936
00:46:21,480 --> 00:46:24,120
Speaker 1: talk about particle physics and how it works. It always

937
00:46:24,160 --> 00:46:27,479
Speaker 1: has to have symmetries and like symmetries and the group theory,

938
00:46:27,480 --> 00:46:30,360
Speaker 1: which is another kind of abstract algebra. It's like so

939
00:46:30,600 --> 00:46:34,120
Speaker 1: interwoven into the foundation of modern physics. It's like we're

940
00:46:34,160 --> 00:46:36,520
Speaker 1: all playing in Nuther's backyard.

941
00:46:36,960 --> 00:46:39,759
Speaker 3: So do you feel like she's being taught about in

942
00:46:39,800 --> 00:46:41,160
Speaker 3: classes more often?

943
00:46:41,239 --> 00:46:41,439
Speaker 2: Now?

944
00:46:41,520 --> 00:46:44,480
Speaker 3: Like are we making up for the fact that we

945
00:46:44,560 --> 00:46:47,960
Speaker 3: talked about you know, Einstein a lot, but those they

946
00:46:47,960 --> 00:46:50,680
Speaker 3: are not really at all? Or is she still I mean,

947
00:46:50,920 --> 00:46:53,239
Speaker 3: based on the audience responses, there's still plenty of folks

948
00:46:53,239 --> 00:46:54,040
Speaker 3: who don't know about her.

949
00:46:54,080 --> 00:46:55,719
Speaker 1: There's still plenty of folks that don't know about her,

950
00:46:55,800 --> 00:46:58,360
Speaker 1: So she's not talked about enough. And I think that,

951
00:46:58,440 --> 00:47:00,879
Speaker 1: you know, these things take time for somebody to get

952
00:47:00,920 --> 00:47:05,239
Speaker 1: to Einstein's level of like cultural impact. They have to

953
00:47:05,239 --> 00:47:07,359
Speaker 1: be celebrated in their time or there has to be

954
00:47:07,400 --> 00:47:11,400
Speaker 1: like a campaign after they die to resuscitate their legacy

955
00:47:11,400 --> 00:47:13,520
Speaker 1: and write books about them. And there just hasn't been

956
00:47:13,560 --> 00:47:16,920
Speaker 1: as much attention paid. And you know, it takes effort,

957
00:47:17,040 --> 00:47:18,880
Speaker 1: Like somebody's got to go out there and do the

958
00:47:18,920 --> 00:47:22,080
Speaker 1: research and write the books and make this argument in

959
00:47:22,200 --> 00:47:24,600
Speaker 1: order to have it rise above the level of noise

960
00:47:25,000 --> 00:47:28,239
Speaker 1: in this chaotic media landscape. So it's not easy to

961
00:47:28,320 --> 00:47:30,440
Speaker 1: sort of change the trajectory. But I think in this

962
00:47:30,560 --> 00:47:32,120
Speaker 1: case it's very well deserved.

963
00:47:32,960 --> 00:47:35,600
Speaker 3: Yep, sounds like there's a book project in there or

964
00:47:35,640 --> 00:47:36,160
Speaker 3: a movie.

965
00:47:36,480 --> 00:47:39,640
Speaker 1: Yeah, definitely, we need the Nether biopic for sure. Who's

966
00:47:39,640 --> 00:47:41,480
Speaker 1: going to plant her? Maybe Rachel Weiss or something.

967
00:47:41,800 --> 00:47:43,640
Speaker 3: Maybe I can't say I know what she looks like.

968
00:47:45,280 --> 00:47:46,120
Speaker 3: I should look it up.

969
00:47:46,200 --> 00:47:48,520
Speaker 1: And so, you know. Another's theorem tells us about the

970
00:47:48,600 --> 00:47:50,799
Speaker 1: symmetries in the universe, and it makes a lot of

971
00:47:50,800 --> 00:47:53,319
Speaker 1: sense when we think about translation symmetry. It gives us

972
00:47:53,480 --> 00:47:58,759
Speaker 1: momentum conservation. Rotation symmetry that gives us angular momentum conservation,

973
00:47:59,360 --> 00:48:01,800
Speaker 1: like the reason an angler momentum is conserving the universe,

974
00:48:01,840 --> 00:48:05,040
Speaker 1: the reason galaxies are discs, the reason the Earth still

975
00:48:05,080 --> 00:48:08,880
Speaker 1: spins is because the universe doesn't have a preferred direction.

976
00:48:09,560 --> 00:48:14,360
Speaker 1: Time translation symmetry gives us energy conservation that weird internal

977
00:48:14,400 --> 00:48:17,919
Speaker 1: electron angle symmetry we talked about earlier. Nuthu's theorem tells

978
00:48:18,040 --> 00:48:20,719
Speaker 1: us what that means, and what it means is conservation

979
00:48:20,840 --> 00:48:24,360
Speaker 1: of electric charge and that's pretty important in the universe.

980
00:48:24,480 --> 00:48:27,120
Speaker 1: Like you can transfer electric charge, but you can't create

981
00:48:27,160 --> 00:48:29,400
Speaker 1: it or destroy it. We have looked like we have

982
00:48:29,600 --> 00:48:32,520
Speaker 1: tried to create a destroy electric charge. Nobody's ever seen

983
00:48:32,520 --> 00:48:36,240
Speaker 1: a violation of that. That means that the universe really,

984
00:48:36,280 --> 00:48:41,720
Speaker 1: really really wants this weird internal electron angle to be preserved.

985
00:48:41,800 --> 00:48:44,560
Speaker 1: You know, it's fascinating, and this is like really deeply

986
00:48:44,600 --> 00:48:47,600
Speaker 1: interwoven into the way we structure all the quantum field

987
00:48:47,600 --> 00:48:49,040
Speaker 1: theories in physics.

988
00:48:49,400 --> 00:48:51,120
Speaker 3: All right, so we should all get Emmy on a

989
00:48:51,160 --> 00:48:54,360
Speaker 3: T shirt for starters, and we all need to have

990
00:48:54,400 --> 00:48:57,839
Speaker 3: a poster with things that Emmy maybe didn't actually say. Yeah,

991
00:48:58,760 --> 00:49:01,360
Speaker 3: because I heard a bunch of if Einstein posters do

992
00:49:01,520 --> 00:49:04,479
Speaker 3: have like quotes that you probably never actually is that true?

993
00:49:04,560 --> 00:49:07,279
Speaker 1: Yeah, And unfortunately, these days, if you google Einstein and

994
00:49:07,320 --> 00:49:10,160
Speaker 1: look for images, there's a bunch of AI generated nonsense.

995
00:49:10,200 --> 00:49:13,440
Speaker 1: It's not actually pictures of Einstein. So yeah, the information

996
00:49:13,520 --> 00:49:16,600
Speaker 1: landscape is deeply polluted. But I think somebody out there

997
00:49:16,640 --> 00:49:20,120
Speaker 1: who's like a Netflix executive should commission at like seven

998
00:49:20,239 --> 00:49:24,160
Speaker 1: part Emmy Nuther biopic miniseries. And I promise you if

999
00:49:24,160 --> 00:49:26,040
Speaker 1: you do that, you're going to win an Emmy for

1000
00:49:26,080 --> 00:49:27,000
Speaker 1: your Emmy series.

1001
00:49:27,760 --> 00:49:31,279
Speaker 3: Oh nice, nice, and we're available to hire to help out.

1002
00:49:31,400 --> 00:49:34,000
Speaker 1: Absolutely, Yes, I want to be on the set consulting.

1003
00:49:35,280 --> 00:49:37,440
Speaker 3: Yes, that sounds good. I'll play Emmy. I don't know

1004
00:49:37,480 --> 00:49:40,480
Speaker 3: what she looks like, but probably probably so did Emmy

1005
00:49:40,640 --> 00:49:42,480
Speaker 3: get to live a nice long life.

1006
00:49:42,840 --> 00:49:45,280
Speaker 1: So there were ups and downs, you know. She finally

1007
00:49:45,280 --> 00:49:48,120
Speaker 1: got a position after World War One, though she wasn't paid,

1008
00:49:48,640 --> 00:49:51,160
Speaker 1: and so she was working in Germany for a while.

1009
00:49:51,680 --> 00:49:54,680
Speaker 1: In nineteen thirty three, when the Nazis came to power, she,

1010
00:49:55,120 --> 00:49:58,920
Speaker 1: like many Jewish scientists, left. She went to Brent mahar

1011
00:49:59,280 --> 00:50:01,920
Speaker 1: and worked there and at the Institute for Advanced Studies,

1012
00:50:02,239 --> 00:50:06,240
Speaker 1: so in New Jersey. But later she died of complications

1013
00:50:06,280 --> 00:50:09,400
Speaker 1: of surgery on an ovarian syst So she got a

1014
00:50:09,440 --> 00:50:12,000
Speaker 1: very warm reception and she was very pleased to be

1015
00:50:12,200 --> 00:50:15,040
Speaker 1: in New Jersey. But she didn't last much longer. And

1016
00:50:15,080 --> 00:50:18,040
Speaker 1: so it's always a tragedy when somebody so smart dies

1017
00:50:18,080 --> 00:50:20,160
Speaker 1: so young, because I always imagine, like, what could they

1018
00:50:20,200 --> 00:50:23,280
Speaker 1: have contributed? What do we not know about the universe

1019
00:50:23,400 --> 00:50:26,560
Speaker 1: because this person died. You know, it's like thinking if

1020
00:50:26,560 --> 00:50:29,600
Speaker 1: Mozart had lived to seventy five, what music of his

1021
00:50:29,800 --> 00:50:32,680
Speaker 1: could we be enjoying today? We just don't know. It's

1022
00:50:32,719 --> 00:50:35,000
Speaker 1: just been deleted from the human experience.

1023
00:50:35,640 --> 00:50:38,560
Speaker 3: We're going to experience a similar feeling on our next

1024
00:50:38,719 --> 00:50:40,520
Speaker 3: episode when we talk about Nettie.

1025
00:50:40,239 --> 00:50:43,360
Speaker 1: Stevens, another female scientist.

1026
00:50:43,000 --> 00:50:46,479
Speaker 3: Another overlooked female scientist who tragically died young.

1027
00:50:46,560 --> 00:50:48,600
Speaker 1: All right, well, thanks to all the women out there

1028
00:50:48,640 --> 00:50:51,960
Speaker 1: making contributions to science. We hear you, We support you.

1029
00:50:52,200 --> 00:50:55,279
Speaker 1: We look forward to your biopic on Netflix, and.

1030
00:50:55,320 --> 00:50:56,480
Speaker 3: I'm available for hire.

1031
00:50:56,320 --> 00:50:58,799
Speaker 1: For those two.

1032
00:51:06,400 --> 00:51:10,239
Speaker 3: Daniel and Kelly's Extraordinary Universe is produced by iHeartRadio. We

1033
00:51:10,280 --> 00:51:12,680
Speaker 3: would love to hear from you, We really would.

1034
00:51:12,840 --> 00:51:15,600
Speaker 1: We want to know what questions you have about this

1035
00:51:15,800 --> 00:51:17,480
Speaker 1: Extraordinary Universe.

1036
00:51:17,680 --> 00:51:20,640
Speaker 3: Want to know your thoughts on recent shows, suggestions for

1037
00:51:20,719 --> 00:51:23,799
Speaker 3: future shows. If you contact us, we will get back

1038
00:51:23,840 --> 00:51:24,040
Speaker 3: to you.

1039
00:51:24,239 --> 00:51:27,759
Speaker 1: We really mean it. We answer every message. Email us

1040
00:51:27,800 --> 00:51:30,800
Speaker 1: at Questions at Danielandkelly dot org.

1041
00:51:30,800 --> 00:51:32,400
Speaker 3: Or you can find us on social media. We have

1042
00:51:32,440 --> 00:51:36,320
Speaker 3: accounts on x, Instagram, Blue Sky and on all of

1043
00:51:36,360 --> 00:51:40,000
Speaker 3: those platforms. You can find us at d and Kuniverse.

1044
00:51:40,120 --> 00:51:41,640
Speaker 1: Don't be shy write to us.