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Speaker 1: Hey, Dado, do you think podcasts obey the laws of physics? Oh?

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Speaker 1: I sure, hope. So I don't want to get some

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Speaker 1: sort of fine. What makes you worry about it? Well,

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Speaker 1: I've heard some people who use podcasts to fall asleep. Well,

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Speaker 1: I don't know. That sounds pretty harmless. How is that

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Speaker 1: violating the laws of physics? Well, isn't there something about

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Speaker 1: how bodies and motions stay in motion? I see where

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Speaker 1: you're going with this. That could be a problem if

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Speaker 1: the podcast puts bodies at rest that used to be

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Speaker 1: in motion. Yeah, yeah, that might be a problem, like

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Speaker 1: if they're driving or something. Maybe if you get in

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Speaker 1: bed and get comfortable before they, you know, put on

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Speaker 1: a podcast, then they could just continue being at the rest.

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Speaker 1: Then there might be asleep before we get to the

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Speaker 1: main topic of the podcast. Maybe we just put a

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Speaker 1: bunch of people to sleep. Wake up? Wake up? What

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Speaker 1: I put you to sleep? You're the physicist. I take

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Speaker 1: naps wherever I can find them. Hi am or handmake

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Speaker 1: cartoonist and the creator of PhD comics. Hi. I'm Daniel.

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Speaker 1: I'm a particle physicist and a professor at U c Irvine,

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Speaker 1: and I try to stay in motion is that hard

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Speaker 1: as a physicist, don't you sit in your couch or

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Speaker 1: your desk all the time and just think of solutions

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Speaker 1: to the questions about the universe. Yeah, but I find

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Speaker 1: that as I get older, a body at rest tends

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Speaker 1: to stay at rest, so it's harder and harder to

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Speaker 1: get out of that couch. I think a body at

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Speaker 1: rest also tends to get bigger. Unfortunately, with our age,

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Speaker 1: that's true, and we gravitationally attract more physicists onto the couch.

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Speaker 1: That's right, We expand spacetime or on our waist. It's

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Speaker 1: a weird law of the universe, the no diet theorem,

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Speaker 1: the law of general snack ativity. But anyways, welcome to

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Speaker 1: our podcast, Daniel and Jorge Explain the Universe, a production

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Speaker 1: of My Heart Radio in which we put your mind

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Speaker 1: into motion to understand the fundamental nature of the universe

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Speaker 1: around us, or at least to ask the deep questions

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Speaker 1: about how it works and try to observe the patterns,

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Speaker 1: the trends, the symmetries, the conservation laws, the fundamental rules

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Speaker 1: that seem to be organizing our universe. On this podcast,

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Speaker 1: we ask all of those big questions, and we don't

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Speaker 1: shy away from trying to find answers. Yeah, because the

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Speaker 1: universe is full of things to ask questions about, lots

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Speaker 1: of questions that we still haven't figured out despite hundreds

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Speaker 1: and maybe thousands of years of science and observing the universe,

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Speaker 1: and we try to talk about it and to increase

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Speaker 1: the gravity I guess in your brain, right, like information

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Speaker 1: causes gravity to increase, right, that's true. Yeah, Eventually our

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Speaker 1: goal is to turn your brain into a black hole.

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Speaker 1: Oh no, no, we want stuff to get out. That's true.

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Speaker 1: That would be undermining the fundamental purpose of our podcast.

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Speaker 1: That's right. It wouldn't go viral if I don't want

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Speaker 1: to turn into a black hole. But we do want

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Speaker 1: your brain to absorb information or to feel like you

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Speaker 1: are part of this centuries or maybe even millennial long

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Speaker 1: progress towards understanding the universe. When people look back on

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Speaker 1: the path of theoretical physics in a hundred years or

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Speaker 1: a thousand years, we will wonder how far along that

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Speaker 1: path we are. Have we just gotten started. Are we

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Speaker 1: around the corner from revealing the deepest secrets of the universe?

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Speaker 1: Only time will tell. Yeah, because it's amazing that the

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Speaker 1: universe is even understandable. Right, Like, we look at it,

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Speaker 1: it seems kind of chaotic, But the closer we look,

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Speaker 1: we start to notice patterns and trends that seems to

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Speaker 1: sort of govern how it works and what's going to happen.

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Speaker 1: It is amazing that the universe can be described by

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Speaker 1: sets of physical laws that don't seem to change in time. Right.

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Speaker 1: We take that for granted. I can do an experiment

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Speaker 1: and measure something about the universe, like the gravitational constant,

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Speaker 1: and then I can do that same experiment in fifty

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Speaker 1: years and get the same number. Why is that right?

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Speaker 1: Why do repeated experiments get the same answer. That's not

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Speaker 1: something we know, It's just something we've seen. It's just

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Speaker 1: something we basically assume as one of the foundational principles

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Speaker 1: of science. We don't know why it's true, but we

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Speaker 1: certainly do rely on it. Yeah, and you don't even

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Speaker 1: have to get that fancy to see how the universe

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Speaker 1: has these laws. Right, You can just toss an apple

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Speaker 1: in the air over and over and it will always

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Speaker 1: sort of come back to your head. But you can

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Speaker 1: also do it while being fancy. You can wear a

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Speaker 1: tuxedo and toss an apple into the air, nothing stopping

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Speaker 1: you from getting fancy? Are you anti fancy? Now? That's way.

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Speaker 1: I guess you could be tossing a kind of caviar

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Speaker 1: instead of an apple too. I mean, personally, I'm always

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Speaker 1: wearing a tuxedo while doing these podcasts. I thought we

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Speaker 1: had a dress code on this podcast. What are you wearing?

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Speaker 1: I'm wearing a pajama with a tuxedo printed on it. O. Man,

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Speaker 1: standards are sliding everywhere, folks, It's hard, that's right. We

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Speaker 1: don't have a dress code law here in the podcast.

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Speaker 1: That's right. And you're also allowed to wear whatever you

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Speaker 1: like when you're listening to this podcast. So if you've

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Speaker 1: been dutifully getting your txedo dry cleaned before you listen

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Speaker 1: to this podcast, you can now just wear pajama pants.

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Speaker 1: I'm pretty sure nobody was wearing a tuxedo while listening

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Speaker 1: to us, and that's maybe they're like a waiter maybe

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Speaker 1: at a fancy restaurant that you know, tunes out the

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Speaker 1: customers by listening to our podcast. I hope that we

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Speaker 1: have a pretty broad variety of what folks are wearing,

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Speaker 1: you know, all the way from athletic gear to tuxedos

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Speaker 1: with tails. And top hats. I'd just like to imagine

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Speaker 1: we're sampling all of the human experience the same way

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Speaker 1: we are trying to explore the entire range of physical

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Speaker 1: phenomena out there in the universe. Yeah, but it is

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Speaker 1: interesting that the universe has lost right, Like you can

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Speaker 1: imagine maybe a universe without laws? Is that even sort

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Speaker 1: of like a possible to a physicist. It's possible to

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Speaker 1: imagine that that universe exists, but it's hard to understand

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Speaker 1: how you would understand it. You know, the idea that

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Speaker 1: there are laws and that we can reveal them through experiment,

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Speaker 1: and that we can try to simplify them and use

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Speaker 1: them to predict the future. It's pretty basic to our

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Speaker 1: notion of understanding. It's sort of like goes to the

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Speaker 1: heart of storytelling, even well before like what we call

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Speaker 1: modern science. Indigenous culture is just learning about their environment

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Speaker 1: as they experience it, are telling stories, you know, like

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Speaker 1: you take this tree bark, you make a tea out

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Speaker 1: of it, you drink it, you feel better, and it's

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Speaker 1: a story, and it's sort of fundamental to the way

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Speaker 1: I think humans think. Yeah, that that is science as well, right, Absolutely,

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Speaker 1: it's accumulation of knowledge through experience. Yeah, Well, it's a

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Speaker 1: good thing that the universe does seem to have laws

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Speaker 1: because it allows us to kind of predict what's going

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Speaker 1: on and to build things to make our lives better,

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Speaker 1: and to have a little bit of context about where

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Speaker 1: we sit in the universe and why we're here. That's right,

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Speaker 1: and the patterns and trends that we notice in the universe,

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Speaker 1: they give us a lot of clues as to the

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Speaker 1: fundamental nature of the universe. Though we assume the universe

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Speaker 1: has laws, we don't make a lot of assumptions for

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Speaker 1: what those laws are. So we'd like to look around

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Speaker 1: and notice, like, what are the patterns that happened in

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Speaker 1: the universe, what are those laws that it seems to

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Speaker 1: follow in, what do those laws mean? And why do

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Speaker 1: we have those laws and not other laws. Yeah, And

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Speaker 1: probably one of the most important laws, or at least

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Speaker 1: the most useful laws we found and understanding the universe

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Speaker 1: and predicting what's going to happen, is the idea that

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Speaker 1: momentum is conserved. That's a law, right, that's like written

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Speaker 1: in the Statute of the universe. That is still a law.

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Speaker 1: A lot of things that you learned about in grade

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Speaker 1: school that you found were conserved in the universe, are

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Speaker 1: not mass, energy, energy plus mass, all of this stuff.

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Speaker 1: You thought that stuff was conserving universe. It turns out

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Speaker 1: it's not. But conservation and momentum still holds as far

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Speaker 1: as we know. Oh interesting, some laws have been repealed

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Speaker 1: that they made it all the way up to the

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Speaker 1: spraying cooard of the universen't they They got shut down? Well,

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Speaker 1: like Newtonian physics, some of these laws turned out to

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Speaker 1: be almost true, true in many many cases, but not

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Speaker 1: fundamentally true, not actually written in stone at the foundation

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Speaker 1: of the universe, just sort of like mostly working in

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Speaker 1: the scenarios we had tested them in so far, which

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Speaker 1: is a cool testament to how science progresses. You find

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Speaker 1: a pattern, it seems to be true everywhere, and then

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Speaker 1: a hundred years later people find exceptions. Exceptions reveal a

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Speaker 1: deeper truth. So when you say that momentum is conserved

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Speaker 1: is still a lot, it's it just means that it

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Speaker 1: hasn't been revealed yet kind of right, like, as far

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Speaker 1: as we know, that's the one that's still true. Yeah,

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Speaker 1: that's why we say it's still a law as of

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Speaker 1: the date of this podcast. But you know, in a

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Speaker 1: thousand years, when people are listening to this episode, they'll

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Speaker 1: laugh into their hands at our naivete right before they

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Speaker 1: fall asleep. But there is something really deep and fundamental

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Speaker 1: that we're doing when we find these conservation laws. You know,

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Speaker 1: we are looking around to trying to figure out, like

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Speaker 1: what is important in the universe, what's a meaningful thing?

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Speaker 1: Like when we think, oh, maybe energy is conserved in

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Speaker 1: the universe, we just look around. We notice that. We say, like, okay,

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Speaker 1: you have a bunch of energy in this configuration. You

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Speaker 1: let the universe do its thing, and you notice, oh,

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Speaker 1: there's the same amount of total energy. That suggests that

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Speaker 1: maybe energy is like important, it's fundamental, it's interesting, more

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Speaker 1: important than like, you know, the number of ice cream

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Speaker 1: cones in the universe, which changes a lot with time.

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Speaker 1: There's billions of years there was no ice cream and

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Speaker 1: then a brief flash of ice cream, and who knows

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Speaker 1: whether they'll be ice cream in the future. But nobody

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Speaker 1: expects the number of ice cream cones to be conserved

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Speaker 1: because nobody thinks that that's an important thing in the universe.

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Speaker 1: So if something is conserved, that suggests it is probably

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Speaker 1: important somehow to the universe. Well, Daniel, I think ice

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Speaker 1: cream is important about you, but it's an important part

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Speaker 1: of my diet for sure. Well, if only the things

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Speaker 1: that are important to you are also important to the universe,

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Speaker 1: I think ice cream is pretty important to a lot

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Speaker 1: of people. It's still around, it's it survived several lost

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Speaker 1: trying to ban But if ice cream was conserved, then

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Speaker 1: you could ask questions like, well, where did this ice

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Speaker 1: cream come from? More? Where does the ice cream go?

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Speaker 1: When you eat it? Right? It turns into something else

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Speaker 1: which is not ice cream. So that suggests that what's

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Speaker 1: conserved is not ice cream, but like some larger category

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Speaker 1: of things anyway, it's the same thing with energy and

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Speaker 1: with momentum. We discover whether these things are conserved by

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Speaker 1: the universe, and then we get to ask what does

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Speaker 1: that mean about the nature of the universe, right, because

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Speaker 1: I guess asking these questions is how we understand the universe, right, Like,

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Speaker 1: it's one thing to notice trends in it, but it's

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Speaker 1: another to sort of understand why the universe has these trends,

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Speaker 1: and like why do certain things that conserved and others don't?

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Speaker 1: You know, what does it mean about the universe? Can

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Speaker 1: we find some fundamental principle that tells us about all

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Speaker 1: these conservation laws where they come from. The wonderful thing

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Speaker 1: about science is that every answer leads to more questions.

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Speaker 1: You know, the question number one could be what's conserved

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Speaker 1: in the universe? Question number two is said, all right, well,

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Speaker 1: why these things and not other things? Always leads to

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Speaker 1: more questions which reveal a deeper truth of the universe.

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Speaker 1: That's the joy of science that the questions never do end. Well,

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Speaker 1: let's reveal some deeper truths today. So today on the podcast,

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Speaker 1: we'll be asking the question why is momentum conserved? Okay, so, Daniel,

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Speaker 1: you saying that energy is not conserved in the universe.

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Speaker 1: We have a podcast discussing that. But momentum is conserved.

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Speaker 1: Does that mean momentum is more important than energy? That's

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Speaker 1: a good question. Yeah. I would say that momentum conservation

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Speaker 1: tells us something fundamental about the nature of the universe

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Speaker 1: and the nature of space, which we'll get into. The

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Speaker 1: fact that energy is not conserved actually also tells us

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Speaker 1: something about the universe and the nature of time. I

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Speaker 1: think both of those facts, that momentum is conserved and

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Speaker 1: that energy is not do tell us something deep about

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Speaker 1: the nature of the universe. But yeah, I think momentum

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Speaker 1: fundamentally is more important. If you had like a competition

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Speaker 1: between quantities and physics, I would vote for momentum over energy.

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Speaker 1: Who would win in a fight, momentum or energy. Momentum

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Speaker 1: is a vector also, right, so it has multiple components.

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Speaker 1: It would definitely defeat energy, which is just a scale.

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Speaker 1: It's just a number. So momentum is a bigger army.

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Speaker 1: I see. Yeah. Also momentum has more momentum going for it.

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Speaker 1: You know that's important in a fight. Yeah, it's momentous, right,

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Speaker 1: but only in the moment. Maybe they should have called

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Speaker 1: it importum instead of momentum. Yeah, I'm not sure renaming

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Speaker 1: and would help there. But this is a fascinating question,

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Speaker 1: like why is momentum conserved? Because, as you were saying earlier,

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Speaker 1: does something you learn you know early on, like high school,

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Speaker 1: middle school, maybe even before, like the idea that if

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Speaker 1: something is in motion, it stays in motion, and if

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Speaker 1: something is address it it will stay in the rest

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Speaker 1: unless something changes m And I think that when people

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Speaker 1: learn about these conservation laws, the one that's most intuitive

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Speaker 1: is the one that's actually least true. You know, conservation

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Speaker 1: of mass, it sort of feels like it should make sense.

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Speaker 1: Like you have a chemical reaction. You start out with

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Speaker 1: a bunch of little lego brick chemical atoms and molecules,

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Speaker 1: and all you're doing is rearranging them, so of course

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Speaker 1: you should end up with the same amount of stuff

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Speaker 1: at the end. And that's the one that seems to

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Speaker 1: make the most sense to people. And I think that's

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Speaker 1: a revealing example because it makes sense because you think

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Speaker 1: of like stuff as being basic and fundamental to the universe.

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Speaker 1: Is that can be like created or destroyed, And you

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Speaker 1: hear that a lot in science fiction. Of course, now

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Speaker 1: we know that it's not and you can destroy mass

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Speaker 1: and turn into energy, and you can turn energy into

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Speaker 1: mass and all that kind of stuff. But you know,

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Speaker 1: the idea that a conservation law tells you about what's

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Speaker 1: important in the verse is sort of underlying all of this.

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Speaker 1: And I remember learning about conservation momentum and wondering, like, well,

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Speaker 1: what does that mean is conserved? Is like what does

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Speaker 1: that mean about the nature of the universe. Well, and

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Speaker 1: in the case of mass, I mean, you just kind

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Speaker 1: of have to figure that all mass is really energy, right,

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Speaker 1: And so then you're just it's like it's embedded in

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Speaker 1: the question of is energy conserved in the universe, which

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Speaker 1: it generally is, just to be clear, but we've recently

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Speaker 1: found that sometimes energy is not conserved. Yeah, it's a

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Speaker 1: nice idea to generalize the conservation and mass into the

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Speaker 1: conservation of energy and say mass is just one form

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Speaker 1: of energy. So when it disappears in the energy, that's okay,

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Speaker 1: because it's not true that mass is the fundamental stuff

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Speaker 1: in the universe. Energy is right. But then, as you say,

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Speaker 1: we discovered, actually the universe doesn't really care if energy

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Speaker 1: is conserved. It can just go away and we can

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Speaker 1: just sort of increase it. So dig into that podcast

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Speaker 1: if you're curious about that. But what that tells us

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Speaker 1: is that energy is not like the fundamental element of

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Speaker 1: the universe. It's more like ice cream cones. It's just

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Speaker 1: like something we came up with that makes sense to

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Speaker 1: us or is important to us. It's not deeply true.

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Speaker 1: It's not a deep feature of the universe. It's not

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Speaker 1: the chocolate ice cream of the universe. Maybe or are

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Speaker 1: the same momentum is a vanilla ice cream of the universe.

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Speaker 1: First of all, ice cream is not important to the

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Speaker 1: universe only and humans. But I guess we would be

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Speaker 1: saying that, you know, momentum is the dark chocolate at

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Speaker 1: the universe and energy is the white chocolate, well chocolate aside,

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Speaker 1: this is an interesting question why is momentum conserved? Because

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Speaker 1: we we all the field like it's true, and it

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Speaker 1: does seem to be true so far, But the question

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Speaker 1: is why does it get conserved in the universe. So,

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Speaker 1: as usual, we were wondering how many people out there

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Speaker 1: think they have an answer to this interesting and deep

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Speaker 1: question about how everything works. And thank you to our

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Speaker 1: volunteers who are willing to answer deep, difficult questions of

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Speaker 1: physics without any chance to prepare, so that we can

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Speaker 1: get a senswer what people out there are thinking. If

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Speaker 1: you'd like to participate, please you are very welcome right

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Speaker 1: to us to questions at Daniel and Jorge dot com.

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Speaker 1: So Daniel asked this question on the internet, why is

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Speaker 1: momentum conserved? And here's what people had to say. I'm

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Speaker 1: not really sure that momentum is preserved because momentum massive

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Speaker 1: velocity a product of mass and velocity and velocities relatives.

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Speaker 1: So if some velocities relative, I don't know how it

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Speaker 1: could be preserved, because if somebody else measures it, it's

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Speaker 1: going to be a different velocity. I was just took

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Speaker 1: that kind of as a given and never really questioned

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Speaker 1: why why. It's just because they tell us it's always conserved.

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Speaker 1: But it's related to, you know, a closed system of

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Speaker 1: matter and energy. None of that matter energy is created

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Speaker 1: or loss. It's just converted one way or the other.

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Speaker 1: And since momentum is in a way of function of

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Speaker 1: your mass and your energy, then it's just always there.

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Speaker 1: It can't it can't be bled off into another dimension

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Speaker 1: or something as far as I know, well, I guess

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Speaker 1: the reason momentum is conserved is because of Mutant said so,

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Speaker 1: and Einstein said so, maybe both of them. I think

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Speaker 1: all that we've been able to observe so far indicates

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Speaker 1: that momentum is conserved in terms of interactions that we've

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Speaker 1: measured those kinds of things. In terms of a conceptual

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Speaker 1: reason behind why momentum should be something that is conserved,

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Speaker 1: I don't know if there's any good explanation for that.

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Speaker 1: Thinking about a collision right now between let's say two objects,

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Speaker 1: and why is consu so an energy to another object

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Speaker 1: is transferred to the other one. So um is conserved

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Speaker 1: because nothing the energy, it's constantly nothing, It's wasted. Everything

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Speaker 1: gets transferred or transformed. Momentum may be described as mass

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Speaker 1: times velocity. It may further be described as the second

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Speaker 1: law of thermodynamics, or is it Newton's second law of motion?

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Speaker 1: I forget college was a long time ago. However, the

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Speaker 1: question of why is it preserved, I think is something

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Speaker 1: nobody knows yet. I think it just all has to

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Speaker 1: do with the way energy is transferred. So if I

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Speaker 1: were to be pushing something, for me to be pushing

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Speaker 1: that thing so it moves, I need to be adding

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Speaker 1: energy to the system. I need to be pushing it

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Speaker 1: and adding a force and therefore transferring energy from me

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Speaker 1: into it. But just due to the way Newton's laws work,

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Speaker 1: it too has to be pushing back on me. All right,

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Speaker 1: what do you think of the answer? I like the

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Speaker 1: because new And said so, and Einstein agreed. They're like

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Speaker 1: a council of physics, and they decide what's true. Oh,

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Speaker 1: maybe my kids should try that the next time. Their

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Speaker 1: parents don't know. But Newton said so, and Einstein agreed

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Speaker 1: that you should go to bed two out of two

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Speaker 1: seminal physicists agreed as if physicists have any voice and

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Speaker 1: anything relevant at all. You know, do you think physics

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Speaker 1: and general is sort of done by by polling and

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Speaker 1: kind of right, like, there's a little bit of sense

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Speaker 1: that in science it's about what the majority thinks is true. Right,

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Speaker 1: that's true. The consensus view is important, although you know,

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Speaker 1: one person against the world doesn't have to be wrong,

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Speaker 1: and in some cases, like one seminal physicists can persuade

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Speaker 1: a lot of folks. You know, if you say, well,

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Speaker 1: Einstein thought this, or Murray Gelman said that, or Feineman

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Speaker 1: put it this way, that can be pretty persuasive. But

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Speaker 1: I guess in general, none of the answers questioned that

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Speaker 1: idea that momentum is conserved, right, Nobody said, like, who

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Speaker 1: said momentum is conserved? Yeah, though some people thought that

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Speaker 1: we don't know the answer that we have no idea

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Speaker 1: why momentum is conserved, sort of like why is the

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Speaker 1: speed of light? What it is? We don't know, we

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Speaker 1: just measure it. Some people put it in that category.

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Speaker 1: I think they've been listening to our podcast and reading

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Speaker 1: our books too much. You know. Sometimes yes, is we

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Speaker 1: have no idea. You think they've become persuaded that physics

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Speaker 1: actually doesn't really know very much about the universe. Oh,

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Speaker 1: mission accomplished. We spoiled the ice cream. It just means

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Speaker 1: there's more ice cream of discovery left to eat for everybody. Well,

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Speaker 1: let's just recap it for people. So, momentum conservation means

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Speaker 1: that momentum is conservad Like, momentum is defined as what

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Speaker 1: mass times your velocity. Yes, so momentum for slow moving objects,

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Speaker 1: it's just mass times velocity. And when we say momentum

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Speaker 1: is conserved, we mean that if you have the momentum

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Speaker 1: of a bunch of stuff and then you let it

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Speaker 1: do its thing, follow the laws of physics, banging into

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Speaker 1: each other, bounce off of stuff, or just float through space,

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Speaker 1: and then later on you add up the momentum again

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Speaker 1: you should get the same number. And interestingly, momentum is

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Speaker 1: actually three different quantities. Is momentum and X momentum And

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Speaker 1: why momentum and z because we live in three dimensional

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Speaker 1: space and those are all independently conserved. The momentum conservation

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Speaker 1: is kind of three laws in one to deal Yeah, exactly.

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Speaker 1: For those of you who do like classical mechanics or

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Speaker 1: freshman physics. You know, that makes it very powerful because

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Speaker 1: you get three equations to constrain your answer rather than

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Speaker 1: just one from conservation of energy. Right, But you were

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Speaker 1: saying that it's only for slow moving things, like it's

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Speaker 1: different for other things. It turns out in relativity, the

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Speaker 1: definition of momentum is different from just mass times velocity.

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Speaker 1: There's this boost factor we call it the Gamma factor

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Speaker 1: or the Lorentz factor, which is one for slow moving

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Speaker 1: objects and approaches infinity as things get towards the speed

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Speaker 1: of light. So the real equation for momentum is mass

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Speaker 1: times velocity times this Gamma factor. We never noticed because

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Speaker 1: the Gama factor is close to one, so you can

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Speaker 1: ignore it for stuff that's less than you know, like

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Speaker 1: half the speed of light or a third at the

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Speaker 1: speed of light. But it becomes important as you get

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Speaker 1: near the speed of light. Oh, I said, you have

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Speaker 1: to do You have to adjust it because nothing can

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Speaker 1: go faster than the speed of light because it has

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Speaker 1: to have a limit, Like you can have momentum that's

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Speaker 1: greater than the speed of light. You have to adjust

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Speaker 1: in order to get conservation momentum, like the quantity that

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Speaker 1: is conserved is not mass times velocity. It's mass times

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Speaker 1: velocity times gamma. And you notice this as you get

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Speaker 1: to very high velocities. In order have conservation before and

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Speaker 1: after some interaction, for example, you have to use gamma

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Speaker 1: mass velocity, not just mass and velocity. And this is

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Speaker 1: actually the source of a lot of misunderstanding about relativistic physics.

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Speaker 1: People used to define gamma times mass as this weird

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Speaker 1: relativistic mass and say things like your mass gets really

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Speaker 1: large as you go towards high speeds because they wanted

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Speaker 1: to redefine momentum to be relativistic mass times velocity. Anyway,

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Speaker 1: we're gonna do a whole podcast about that question about

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Speaker 1: whether your mass actually does get larger as you approach

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Speaker 1: the speed of light. Sure answer is it doesn't. Right Right, Well,

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Speaker 1: I think at least for slow moving objects, it does

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Speaker 1: kind of match what people's intuition is about momentum, right,

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Speaker 1: like mass time velocity. We have something large, even if

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Speaker 1: it's moving slow, it has a lot of momentum and

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Speaker 1: it's hard to stop. But even something is small and

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Speaker 1: has a lot of velocity, it's also hard to stop.

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Speaker 1: Right like a bullet, it's pretty hard to stop if

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Speaker 1: it's coming towards you. It's so it's sort of like

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Speaker 1: it's a sense of how hard it is to stop

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Speaker 1: and wait. Yeah, and Newton's law force equals mass times

429
00:22:29,040 --> 00:22:32,680
Speaker 1: acceleration says exactly that. Another way to write Newton's law

430
00:22:32,720 --> 00:22:35,560
Speaker 1: instead of mass times acceleration is a change in momentum.

431
00:22:35,840 --> 00:22:38,360
Speaker 1: So Newton's law is force is the change in momentum.

432
00:22:38,400 --> 00:22:40,080
Speaker 1: If you want to change something's momentum by a lot,

433
00:22:40,160 --> 00:22:41,800
Speaker 1: it takes a big force. You want to change something

434
00:22:41,880 --> 00:22:44,919
Speaker 1: momentum by a little bit takes a smaller force. And

435
00:22:45,040 --> 00:22:47,560
Speaker 1: said another way, something with a lot of momentum takes

436
00:22:47,640 --> 00:22:50,520
Speaker 1: more force to stop. Something without a lot of momentum

437
00:22:50,720 --> 00:22:53,480
Speaker 1: doesn't take much force to stop, right, And the idea

438
00:22:53,520 --> 00:22:56,800
Speaker 1: that it's conserved means that it like it goes somewhere right,

439
00:22:56,880 --> 00:23:00,119
Speaker 1: or like if I try to stop a train and

440
00:23:00,119 --> 00:23:02,080
Speaker 1: may be able to stop it, but that momentum has

441
00:23:02,119 --> 00:23:04,920
Speaker 1: to go somewhere. That's right. If you throw a tennis ball,

442
00:23:04,960 --> 00:23:07,280
Speaker 1: for example, in front of a train, it will push

443
00:23:07,320 --> 00:23:09,639
Speaker 1: that tennis ball really really fast and slow down the

444
00:23:09,680 --> 00:23:12,280
Speaker 1: train a little bit. So the total momentum is the

445
00:23:12,320 --> 00:23:15,080
Speaker 1: same momentum can flow, as you say, from one object

446
00:23:15,080 --> 00:23:17,679
Speaker 1: to another, but the total momentum has to stay the

447
00:23:17,720 --> 00:23:21,639
Speaker 1: same before and after every physics process. Right. And the

448
00:23:21,680 --> 00:23:23,919
Speaker 1: weird thing is like like it's not like somebody's like

449
00:23:24,720 --> 00:23:29,000
Speaker 1: overseeing this transaction, right, Like it just happens, right when

450
00:23:29,000 --> 00:23:31,840
Speaker 1: things interact, somehow momentum is concerned. But it's not like

451
00:23:32,440 --> 00:23:35,080
Speaker 1: momentum actually flowed from one thing to do They just

452
00:23:35,119 --> 00:23:38,720
Speaker 1: pushed on each other and somehow momentum was conserved. Wow,

453
00:23:38,720 --> 00:23:41,280
Speaker 1: what a touch on like deep questions of philosophy. Does

454
00:23:41,280 --> 00:23:45,240
Speaker 1: the universe like calculate what's happening and follow some laws

455
00:23:45,240 --> 00:23:48,480
Speaker 1: like it's some big computer following a program, or does

456
00:23:48,520 --> 00:23:50,879
Speaker 1: it just happen and we're observing it and trying to

457
00:23:50,960 --> 00:23:54,120
Speaker 1: tell our own mathematical stories about it. We don't really know.

458
00:23:54,720 --> 00:23:56,840
Speaker 1: What we notice is that it does happen, and it

459
00:23:56,880 --> 00:24:00,240
Speaker 1: does tell us something about the nature of the universe. Yeah,

460
00:24:00,280 --> 00:24:02,680
Speaker 1: we don't really know sort of like how it happens.

461
00:24:02,960 --> 00:24:05,560
Speaker 1: All right, Well, we know it's conserved momentum, and so

462
00:24:05,680 --> 00:24:09,000
Speaker 1: let's ask the question why it's conserved, and let's get

463
00:24:09,040 --> 00:24:11,400
Speaker 1: into that, and we'll get into the person who actually

464
00:24:11,400 --> 00:24:14,440
Speaker 1: made this big breakthrough but first, let's take a quick break.

465
00:24:27,200 --> 00:24:29,800
Speaker 1: All right, we're talking about ice cream. It seems Daniel,

466
00:24:29,880 --> 00:24:33,400
Speaker 1: are you are you hungry dating some dessert right now?

467
00:24:34,760 --> 00:24:37,439
Speaker 1: That's for two reasons. One is because we record this

468
00:24:37,520 --> 00:24:40,520
Speaker 1: podcast around lunchtime, and the other reason is that today

469
00:24:40,720 --> 00:24:43,879
Speaker 1: is the birthday of the person who solved this riddle

470
00:24:44,119 --> 00:24:47,120
Speaker 1: and maybe one of the most important contributions in physics.

471
00:24:47,320 --> 00:24:51,400
Speaker 1: M that's right, Yeah, the person who discovered the basically

472
00:24:51,440 --> 00:24:54,560
Speaker 1: the answer to the question that we're asking today, why

473
00:24:54,760 --> 00:24:57,920
Speaker 1: is momentum conserved? So we talked about why that momentum

474
00:24:58,000 --> 00:25:01,480
Speaker 1: is conserved, what momentum is, and it just seems to

475
00:25:01,480 --> 00:25:04,640
Speaker 1: be conserved in the universe. And so Daniel, I guess

476
00:25:04,680 --> 00:25:08,000
Speaker 1: what's the answer wise, momentum conserved. It has something to

477
00:25:08,040 --> 00:25:11,879
Speaker 1: do with symmetries, that's right. So, I mean the mathematician

478
00:25:11,960 --> 00:25:14,640
Speaker 1: who just dabbled in physics about a hundred years ago,

479
00:25:14,960 --> 00:25:17,720
Speaker 1: she turns a hundred and forty today, the day we're

480
00:25:17,720 --> 00:25:20,720
Speaker 1: recording this podcast. She discovered that there's a really deep

481
00:25:20,760 --> 00:25:25,200
Speaker 1: connection between these conservation laws and symmetries of the universe.

482
00:25:25,640 --> 00:25:28,960
Speaker 1: So patterns that we see in the universe are connected

483
00:25:29,000 --> 00:25:32,040
Speaker 1: to these symmetries. So what do we mean by symmetries.

484
00:25:32,280 --> 00:25:34,280
Speaker 1: This is a case where we're using the totally normal

485
00:25:34,320 --> 00:25:36,560
Speaker 1: definition of a symmetry. We don't haven't like imbuted with

486
00:25:36,600 --> 00:25:39,840
Speaker 1: any special confusing meaning. It just means that, like you

487
00:25:40,040 --> 00:25:43,120
Speaker 1: change something and there's no impact, Like you could take

488
00:25:43,119 --> 00:25:46,800
Speaker 1: a ball and rotated and doesn't change the ball at all.

489
00:25:46,840 --> 00:25:49,080
Speaker 1: It still behaves the same way, it still looks the

490
00:25:49,119 --> 00:25:52,040
Speaker 1: same way. As an example of a symmetry where you

491
00:25:52,080 --> 00:25:54,439
Speaker 1: can take a road which is a straight line and

492
00:25:54,560 --> 00:25:57,080
Speaker 1: shifted by a hundreds and if it's a straight line,

493
00:25:57,160 --> 00:25:59,400
Speaker 1: it doesn't change it at all, or it's the same road.

494
00:25:59,800 --> 00:26:02,760
Speaker 1: The these kinds of symmetries turn out to be really

495
00:26:02,800 --> 00:26:05,640
Speaker 1: important in the nature of the universe and are connected

496
00:26:05,680 --> 00:26:08,920
Speaker 1: to these conservation laws, right right, But let's maybe take

497
00:26:08,920 --> 00:26:11,960
Speaker 1: a step back, right because I think the history of

498
00:26:12,000 --> 00:26:15,280
Speaker 1: this is that we knew that momentum was conserved, and

499
00:26:15,359 --> 00:26:18,680
Speaker 1: at the same time we're discovering something about the universe

500
00:26:18,720 --> 00:26:21,199
Speaker 1: that it is sort of symmetric in these weird and

501
00:26:21,280 --> 00:26:25,160
Speaker 1: interesting ways. And so maybe before we make that connection,

502
00:26:25,240 --> 00:26:28,040
Speaker 1: maybe step us through, like what exactly is a symmetry

503
00:26:28,280 --> 00:26:30,480
Speaker 1: in the universe? So there are lots of cool symmetries

504
00:26:30,480 --> 00:26:33,399
Speaker 1: in the universe. One of them is that space seems

505
00:26:33,440 --> 00:26:37,199
Speaker 1: to be the same everywhere, Like the nature of this

506
00:26:37,640 --> 00:26:40,760
Speaker 1: universe we find ourselves in doesn't change based on where

507
00:26:40,800 --> 00:26:44,080
Speaker 1: you are. You do an experiment to measure something fundamental

508
00:26:44,119 --> 00:26:47,280
Speaker 1: about the universe, it doesn't matter where in the universe

509
00:26:47,400 --> 00:26:50,800
Speaker 1: you measure it. Or said another way, if you shifted

510
00:26:50,840 --> 00:26:54,359
Speaker 1: the whole universe over by ten meters, no one would

511
00:26:54,359 --> 00:26:56,560
Speaker 1: be able to notice, right, the universe is the same,

512
00:26:56,640 --> 00:26:59,480
Speaker 1: no matter sort of where it is, right right. Yeah,

513
00:26:59,520 --> 00:27:01,600
Speaker 1: that's a pretty a cool idea. But I think maybe

514
00:27:01,640 --> 00:27:04,080
Speaker 1: I wonder what confuses people a lot sometimes is that

515
00:27:04,320 --> 00:27:07,199
Speaker 1: the name symmetry is a little bit different than what

516
00:27:07,280 --> 00:27:09,400
Speaker 1: you just describe, right, Like to I think the most

517
00:27:09,400 --> 00:27:11,879
Speaker 1: people that the word symmetry, it kind of means like

518
00:27:11,960 --> 00:27:15,280
Speaker 1: it's the mirror opposite, or like if I have a

519
00:27:15,320 --> 00:27:17,320
Speaker 1: pattern and a piece of paper, and then I have

520
00:27:17,480 --> 00:27:20,280
Speaker 1: the mirror image of the pattern right next to it,

521
00:27:20,320 --> 00:27:22,040
Speaker 1: then we would say the whole drawing is sort of

522
00:27:22,080 --> 00:27:25,399
Speaker 1: symmetric because it's the same left or right right, And

523
00:27:25,400 --> 00:27:28,680
Speaker 1: that's an example of what we consider a discrete symmetry. Right,

524
00:27:28,680 --> 00:27:31,120
Speaker 1: you can like flip the whole image and it looks

525
00:27:31,160 --> 00:27:34,199
Speaker 1: the same. Continuous symmetry is like take a piece of

526
00:27:34,200 --> 00:27:36,920
Speaker 1: paper and draw a circle. That circle is the same

527
00:27:37,080 --> 00:27:39,640
Speaker 1: no matter how much you rotated, and there's an infinite

528
00:27:39,720 --> 00:27:42,280
Speaker 1: number of ways you could rotate it and not change

529
00:27:42,320 --> 00:27:44,840
Speaker 1: the circle. Right. Or if you have an infinite sheet

530
00:27:44,880 --> 00:27:47,400
Speaker 1: of paper and you drew a picture, it wouldn't really

531
00:27:47,440 --> 00:27:49,480
Speaker 1: matter where you drew that picture. You can draw it

532
00:27:49,520 --> 00:27:51,520
Speaker 1: here or draw it there. It would be the same

533
00:27:51,600 --> 00:27:54,359
Speaker 1: because the paper is infinite. Right. But I guess maybe

534
00:27:54,480 --> 00:27:56,560
Speaker 1: I wonder like a more a better world would have been,

535
00:27:56,600 --> 00:28:01,000
Speaker 1: like you know, consistency or constancy of of things, right,

536
00:28:01,040 --> 00:28:03,879
Speaker 1: Because I think the reason you guys use symmetry. The

537
00:28:03,920 --> 00:28:05,800
Speaker 1: word symmetry is that it has to do with the

538
00:28:05,800 --> 00:28:09,320
Speaker 1: equations of motion of the universe, right, Like if you

539
00:28:09,359 --> 00:28:12,840
Speaker 1: apply like a mirror transformation or some kind of transformation

540
00:28:12,880 --> 00:28:14,960
Speaker 1: to the equations, and then it should stay the same. Yes,

541
00:28:15,040 --> 00:28:18,920
Speaker 1: So to totally generalize the word symmetry, what mathematicians mean

542
00:28:18,960 --> 00:28:21,320
Speaker 1: by it is that you make some kind of transformation

543
00:28:21,400 --> 00:28:24,040
Speaker 1: to the universe and then that doesn't change whatever it

544
00:28:24,080 --> 00:28:26,240
Speaker 1: is you're interested in. So, in the case of physics,

545
00:28:26,480 --> 00:28:28,919
Speaker 1: we make some sort of transformation to the universe, like

546
00:28:29,040 --> 00:28:31,960
Speaker 1: we shifted the left hun your feet, or we rotated

547
00:28:32,040 --> 00:28:34,280
Speaker 1: around some angle. And then the thing we're interested in

548
00:28:34,440 --> 00:28:37,000
Speaker 1: are are the laws of physics the same as you said,

549
00:28:37,000 --> 00:28:39,760
Speaker 1: like the equations of motion? Would you predict that Joorhes

550
00:28:39,840 --> 00:28:42,440
Speaker 1: apple flies through the air and lands in his hand

551
00:28:42,480 --> 00:28:45,320
Speaker 1: the same way if you put your access over here,

552
00:28:45,480 --> 00:28:47,560
Speaker 1: or if you said you know zero is over there,

553
00:28:48,000 --> 00:28:50,320
Speaker 1: or if you did the problem upside down, when you

554
00:28:50,360 --> 00:28:52,880
Speaker 1: get the same answer, If so, then there's a symmetry

555
00:28:52,960 --> 00:28:55,120
Speaker 1: to the problem. Or even like if I move the

556
00:28:55,160 --> 00:28:57,360
Speaker 1: Earth a few light years to the right, it should

557
00:28:57,400 --> 00:28:59,760
Speaker 1: still be the same, right, Yeah, if you the whole

558
00:28:59,800 --> 00:29:02,640
Speaker 1: universe right a few light years to the right, nobody

559
00:29:02,680 --> 00:29:05,280
Speaker 1: could do an experiment to determine that that's the case,

560
00:29:05,280 --> 00:29:08,840
Speaker 1: that that's happened, because no place in space is different. Right,

561
00:29:08,880 --> 00:29:11,240
Speaker 1: the rules should be the same everywhere. Right, So when

562
00:29:11,240 --> 00:29:13,640
Speaker 1: you hear the word symmetry in physics, really maybe in

563
00:29:13,720 --> 00:29:16,200
Speaker 1: your head you should be thinking like a constancy in

564
00:29:16,200 --> 00:29:19,320
Speaker 1: the universe, or like a invariability or something that doesn't

565
00:29:19,360 --> 00:29:22,560
Speaker 1: change when you move it or rotated or flipid. Right, right,

566
00:29:22,720 --> 00:29:25,080
Speaker 1: I like that there's no word in physics that you're

567
00:29:25,120 --> 00:29:28,800
Speaker 1: not up for redefining and improving. You know, science is

568
00:29:28,840 --> 00:29:31,479
Speaker 1: a constant project, and so we're always striving to improve.

569
00:29:31,600 --> 00:29:33,520
Speaker 1: But there is a bit of confusion there because if

570
00:29:33,520 --> 00:29:36,800
Speaker 1: you call it like an invariability, it comes close to

571
00:29:36,800 --> 00:29:40,120
Speaker 1: another word we use, which is invariance, which actually means

572
00:29:40,160 --> 00:29:44,560
Speaker 1: something quite different. Right. Invariance means no matter who's measuring it,

573
00:29:44,760 --> 00:29:47,440
Speaker 1: you always get the same answer. An example of an

574
00:29:47,480 --> 00:29:50,240
Speaker 1: invariant is like the speed of light. Everybody measures the

575
00:29:50,280 --> 00:29:52,640
Speaker 1: speed of light to be the same quantity, no matter

576
00:29:52,680 --> 00:29:56,880
Speaker 1: where you are or how fast you're traveling. Momentum is conserved,

577
00:29:56,960 --> 00:30:00,280
Speaker 1: we say, but it's not invariant because for examp people,

578
00:30:00,520 --> 00:30:03,800
Speaker 1: you are standing still, you measure your velocity be zero.

579
00:30:04,440 --> 00:30:07,360
Speaker 1: I'm moving past you. I measure your velocity to be

580
00:30:07,400 --> 00:30:10,400
Speaker 1: non zero, so I measure you'd have momentum. You measure

581
00:30:10,400 --> 00:30:13,440
Speaker 1: yourself to have no momentum. Momentum is not the same

582
00:30:13,480 --> 00:30:16,680
Speaker 1: for all observers, though it's always conserved. I will see

583
00:30:16,680 --> 00:30:19,760
Speaker 1: your momentum is conserved. You will see your momentum is conserved,

584
00:30:19,880 --> 00:30:23,760
Speaker 1: but it's not invariant. So invariant means something different in physics, yeah.

585
00:30:23,920 --> 00:30:25,600
Speaker 1: I mean, I'm not saying you should not use the

586
00:30:25,600 --> 00:30:28,160
Speaker 1: word symmetry. I'm just saying that it might be helpful

587
00:30:28,200 --> 00:30:30,240
Speaker 1: for people just kind of understand what's going on. If

588
00:30:30,240 --> 00:30:32,200
Speaker 1: if when they hear the words symmetry, they should sort

589
00:30:32,200 --> 00:30:34,560
Speaker 1: of be thinking more about like that things are the

590
00:30:34,600 --> 00:30:36,880
Speaker 1: same no matter if you move them over here, or

591
00:30:36,960 --> 00:30:39,280
Speaker 1: you do you throw the apple over here over there

592
00:30:39,320 --> 00:30:42,200
Speaker 1: or upside down, or if you rotate the whole universe

593
00:30:42,280 --> 00:30:44,720
Speaker 1: ninety degrees, it should still fall down back to my

594
00:30:44,760 --> 00:30:48,200
Speaker 1: head exactly. And those are a few examples of symmetries, right,

595
00:30:48,240 --> 00:30:50,920
Speaker 1: Like if you shift the whole universe over your experiment

596
00:30:50,960 --> 00:30:53,480
Speaker 1: should work the same way, you know, And that's true

597
00:30:53,720 --> 00:30:57,000
Speaker 1: if space is not different in different places in the universe.

598
00:30:57,040 --> 00:30:59,480
Speaker 1: If it were different, right, if space was like different

599
00:30:59,520 --> 00:31:01,320
Speaker 1: over there are and over here, if you have different

600
00:31:01,360 --> 00:31:03,160
Speaker 1: laws of physics over there and over here, you'll be

601
00:31:03,160 --> 00:31:05,640
Speaker 1: able to tell sort of like where the universe is

602
00:31:05,720 --> 00:31:09,120
Speaker 1: relative to those like different parts of space. That will

603
00:31:09,160 --> 00:31:12,400
Speaker 1: be fascinating. Um, but it seems to us so far

604
00:31:12,680 --> 00:31:15,000
Speaker 1: like space is the same everywhere. And that's a pretty

605
00:31:15,040 --> 00:31:18,160
Speaker 1: deep symmetry, right. It tells you something about the nature

606
00:31:18,160 --> 00:31:20,720
Speaker 1: of the universe itself, that the experiments are the same

607
00:31:20,800 --> 00:31:23,240
Speaker 1: everywhere you go, and the same seems to be true

608
00:31:23,240 --> 00:31:26,600
Speaker 1: for rotating, Like there's no up or down in the universe.

609
00:31:26,840 --> 00:31:29,360
Speaker 1: You could rotate the whole universe and you wouldn't be

610
00:31:29,360 --> 00:31:32,400
Speaker 1: able to notice that it had been rotated in the

611
00:31:32,440 --> 00:31:34,480
Speaker 1: sense that you mean that, you know, the laws of

612
00:31:34,520 --> 00:31:38,320
Speaker 1: physics don't change, and your experiments get the same results. Right,

613
00:31:38,440 --> 00:31:41,240
Speaker 1: But I wonder if that's sort of dependent on spacetime, right,

614
00:31:41,320 --> 00:31:44,080
Speaker 1: Like do you depend does that depend on flat space

615
00:31:44,160 --> 00:31:46,160
Speaker 1: time or you know, would that be still be the

616
00:31:46,160 --> 00:31:49,000
Speaker 1: same around close to the black hole or something where

617
00:31:49,040 --> 00:31:51,960
Speaker 1: spacetime is sort of bent or distorted. Yeah, it's a

618
00:31:52,000 --> 00:31:54,240
Speaker 1: good question, you know. So you might ask, like, I

619
00:31:54,320 --> 00:31:57,320
Speaker 1: do an experiment here and I notice my apple falls.

620
00:31:57,360 --> 00:32:00,320
Speaker 1: What if I move Jorge near a black hole, wouldn't

621
00:32:00,360 --> 00:32:02,920
Speaker 1: as apple fall differently? Yeah? Wouldn't you like that? Right?

622
00:32:04,520 --> 00:32:06,040
Speaker 1: You know? Then who would eat all the ice cream?

623
00:32:06,040 --> 00:32:07,240
Speaker 1: You know, I need somebody else to eat it so

624
00:32:07,240 --> 00:32:09,120
Speaker 1: I don't gain too much weight and become a black

625
00:32:09,160 --> 00:32:11,520
Speaker 1: hole myself. It would all fall into the black hole,

626
00:32:12,160 --> 00:32:13,720
Speaker 1: all right, So we can throw you into black hole

627
00:32:13,760 --> 00:32:16,080
Speaker 1: as long as we send a continuous stream of ice

628
00:32:16,120 --> 00:32:19,640
Speaker 1: cream scoops as well. Let's keep it as a thought experiment. No,

629
00:32:19,800 --> 00:32:22,880
Speaker 1: that's a good question, and you know, essentially the issue

630
00:32:22,920 --> 00:32:25,000
Speaker 1: there is that the black hole is sort of part

631
00:32:25,080 --> 00:32:30,480
Speaker 1: of your experiment, and so underlying space itself isn't change.

632
00:32:30,560 --> 00:32:33,200
Speaker 1: But the sort of laboratory of the experiment you're doing,

633
00:32:33,800 --> 00:32:36,640
Speaker 1: um includes a black hole in one scenario and doesn't

634
00:32:36,680 --> 00:32:38,880
Speaker 1: in the other scenario. That's why you get different outcomes

635
00:32:38,880 --> 00:32:42,120
Speaker 1: because you're sort of doing a different experiment. I see.

636
00:32:42,280 --> 00:32:45,360
Speaker 1: But so the theory still works no matter what what's

637
00:32:45,360 --> 00:32:48,000
Speaker 1: happening with space time. Yeah, although if it's not true

638
00:32:48,040 --> 00:32:51,280
Speaker 1: that space is the same everywhere, then the theory doesn't hold.

639
00:32:51,320 --> 00:32:54,160
Speaker 1: You know, for example, what if space was not like

640
00:32:54,520 --> 00:32:57,760
Speaker 1: continuous and infinite, what if it had a boundary, as

641
00:32:57,760 --> 00:32:59,960
Speaker 1: you've mentioned on several podcasts, there was like an edge

642
00:33:00,120 --> 00:33:02,480
Speaker 1: to it. Then you know, the laws of physics would

643
00:33:02,480 --> 00:33:04,800
Speaker 1: be different at the edge because space would be different

644
00:33:04,840 --> 00:33:07,080
Speaker 1: at the edge. Different things would have to happen. So

645
00:33:07,120 --> 00:33:09,320
Speaker 1: maybe the laws of physics would be different at the edge.

646
00:33:09,320 --> 00:33:11,920
Speaker 1: We don't actually know, right, is there a boundary to

647
00:33:12,040 --> 00:33:15,120
Speaker 1: space and doesn't go on forever? Another possible way that

648
00:33:15,160 --> 00:33:17,520
Speaker 1: it could not be true. Is like if space is

649
00:33:17,560 --> 00:33:21,840
Speaker 1: not continuous, if it's like pixelized or like a crystal,

650
00:33:21,960 --> 00:33:23,960
Speaker 1: then it might not have a continuous symmetry. You might

651
00:33:23,960 --> 00:33:27,520
Speaker 1: be like location is a symmetry up to a certain value.

652
00:33:27,600 --> 00:33:30,120
Speaker 1: You know, if you take like certain steps in space,

653
00:33:30,200 --> 00:33:31,640
Speaker 1: you get the same answer. But if you take like

654
00:33:31,680 --> 00:33:33,920
Speaker 1: a half step, maybe you get a different answer because

655
00:33:33,920 --> 00:33:36,720
Speaker 1: you're sort of like caught between two parts of the crystal. Yeah,

656
00:33:36,760 --> 00:33:40,160
Speaker 1: if it's quantum, then it maybe wouldn't be a symmetric,

657
00:33:40,360 --> 00:33:42,800
Speaker 1: But I guess to sort of generalize it though, as

658
00:33:42,800 --> 00:33:46,840
Speaker 1: far as we know, it's it is symmetric the laws

659
00:33:46,840 --> 00:33:49,479
Speaker 1: of physics throughout all of spacetime, as far as we know.

660
00:33:49,720 --> 00:33:52,920
Speaker 1: As far as we know, it's symmetric to translations, shifts,

661
00:33:52,960 --> 00:33:57,320
Speaker 1: and symmetric to rotations. And with a couple of exceptions,

662
00:33:57,400 --> 00:34:00,800
Speaker 1: it is symmetric two shifts in time. Like if you

663
00:34:00,840 --> 00:34:03,520
Speaker 1: do an experiment today and you experiment in a hundred years,

664
00:34:04,000 --> 00:34:06,160
Speaker 1: then you should get the same answer because the laws

665
00:34:06,160 --> 00:34:08,960
Speaker 1: of physics, we think don't change in time. Those are

666
00:34:08,960 --> 00:34:13,720
Speaker 1: three really basic symmetries that we've discovered in physics, right, translation, rotation,

667
00:34:13,760 --> 00:34:17,320
Speaker 1: and time, And that even applies to like moving backwards

668
00:34:17,360 --> 00:34:19,440
Speaker 1: in time, right, it does, Yeah, in the sense that

669
00:34:19,480 --> 00:34:22,160
Speaker 1: if you're comparing two experiments done at two different points

670
00:34:22,200 --> 00:34:24,040
Speaker 1: in time, one of them can be further back. But

671
00:34:24,080 --> 00:34:26,239
Speaker 1: I guess always one of them is further back, right,

672
00:34:26,360 --> 00:34:29,359
Speaker 1: It's it's not about time travel necessarily, all right. Well,

673
00:34:29,400 --> 00:34:31,520
Speaker 1: so that's the idea of symmetry in the universe. We

674
00:34:31,719 --> 00:34:35,319
Speaker 1: noticed that the equations of the universe have these symmetries

675
00:34:35,360 --> 00:34:37,000
Speaker 1: in them, but I guess we didn't know that they

676
00:34:37,000 --> 00:34:40,040
Speaker 1: were connected to the idea of conservation of momentum, right,

677
00:34:40,960 --> 00:34:42,640
Speaker 1: that's right, all right, So those are kind of like

678
00:34:42,680 --> 00:34:46,759
Speaker 1: the three main symmetries that the we've noticed about the

679
00:34:46,800 --> 00:34:48,560
Speaker 1: equations of the universe, and those are kind of like

680
00:34:48,600 --> 00:34:51,400
Speaker 1: the more intuitive one, but there are sort of deeper also,

681
00:34:51,840 --> 00:34:54,719
Speaker 1: symmetries kind of in that the quantum level. Right. Yeah.

682
00:34:54,760 --> 00:34:57,680
Speaker 1: We've talked about the podcast a few times about other

683
00:34:57,800 --> 00:35:01,319
Speaker 1: kinds of symmetries we've noticed in the universe. And these

684
00:35:01,320 --> 00:35:03,799
Speaker 1: are not things that are easy to grasp in your

685
00:35:03,800 --> 00:35:06,040
Speaker 1: mind because they're not things you see, but these are

686
00:35:06,280 --> 00:35:10,000
Speaker 1: like properties of quantum fields. And it turns out that

687
00:35:10,239 --> 00:35:13,800
Speaker 1: you can like rotate different quantum fields sort of into

688
00:35:13,880 --> 00:35:17,920
Speaker 1: each other. You can like swap in different colors of quarks,

689
00:35:18,080 --> 00:35:21,160
Speaker 1: turn red to green, and green to blue and blue

690
00:35:21,200 --> 00:35:24,520
Speaker 1: to red. Nothing changes in the universe, right, So we've

691
00:35:24,560 --> 00:35:26,719
Speaker 1: noticed these kinds of symmetries on the sort of like

692
00:35:26,840 --> 00:35:31,240
Speaker 1: quantum level that are very similar to these symmetries mathematically,

693
00:35:31,280 --> 00:35:34,760
Speaker 1: like they involved rotations, but not in a physical rotation

694
00:35:34,760 --> 00:35:36,680
Speaker 1: you know, like spinning anything. You're just sort of like

695
00:35:36,800 --> 00:35:40,200
Speaker 1: changing labels on quantum stuff. But these are just as

696
00:35:40,239 --> 00:35:44,080
Speaker 1: important and reveal also something really deeply true about the universe.

697
00:35:44,120 --> 00:35:46,680
Speaker 1: And we wouldn't have discovered the Higgs boson if we

698
00:35:46,719 --> 00:35:49,759
Speaker 1: hadn't noticed these symmetries. And again, these are like symmetries

699
00:35:49,880 --> 00:35:52,400
Speaker 1: or kind of invariant things you can do to the

700
00:35:52,440 --> 00:35:55,480
Speaker 1: equations that you're like, hey, wow, that's that's something strange

701
00:35:55,520 --> 00:35:58,359
Speaker 1: about the equations. They they are symmetric, They work no

702
00:35:58,400 --> 00:36:00,520
Speaker 1: matter what you do to it. Yeah, it just see

703
00:36:00,600 --> 00:36:03,680
Speaker 1: to matter in these cases, which gauge you choose. For

704
00:36:03,719 --> 00:36:06,200
Speaker 1: those of you who know like electrodynamics, you know that

705
00:36:06,239 --> 00:36:08,920
Speaker 1: there's sort of like an overall gauge you can choose

706
00:36:08,960 --> 00:36:11,799
Speaker 1: in electrodynamics and doesn't change the answers at all, just

707
00:36:11,840 --> 00:36:14,680
Speaker 1: like an arbitrary choice, just sort of like where you

708
00:36:14,800 --> 00:36:18,560
Speaker 1: choose your potential energy to be zero in classical mechanics problems.

709
00:36:18,560 --> 00:36:20,640
Speaker 1: It doesn't change the answer. It's just a choice. So

710
00:36:20,680 --> 00:36:22,680
Speaker 1: there's a symmetry there to the problem. You can change

711
00:36:22,719 --> 00:36:25,080
Speaker 1: these things and nothing changes and how you predict the

712
00:36:25,160 --> 00:36:27,520
Speaker 1: laws of physics, and that's in the same sense, you

713
00:36:27,520 --> 00:36:30,080
Speaker 1: can like change these things and how we describe these

714
00:36:30,160 --> 00:36:33,160
Speaker 1: quantum fields and doesn't make any difference for our predictions

715
00:36:33,200 --> 00:36:36,719
Speaker 1: for or how particles should interact with each other, right, right,

716
00:36:36,719 --> 00:36:38,400
Speaker 1: And I think we had a whole podcast about this

717
00:36:38,440 --> 00:36:40,719
Speaker 1: about this idea that you know, the word gauge here

718
00:36:41,040 --> 00:36:43,080
Speaker 1: it's sort of related to the idea of measuring something

719
00:36:43,200 --> 00:36:46,399
Speaker 1: or like having a reference you know, length or something. Yeah,

720
00:36:46,400 --> 00:36:48,799
Speaker 1: it actually comes from trains because back on the day,

721
00:36:48,840 --> 00:36:51,520
Speaker 1: people were building railroads all across the United States, and

722
00:36:51,520 --> 00:36:54,719
Speaker 1: they were building them of different gauges, and people thought like, Okay,

723
00:36:54,719 --> 00:36:57,200
Speaker 1: it's just sort of an arbitrary choice of train gauge.

724
00:36:57,360 --> 00:37:00,160
Speaker 1: So then when physicists were like making arbitrary choice in

725
00:37:00,200 --> 00:37:02,400
Speaker 1: their theories, they were trying to find a word that

726
00:37:02,560 --> 00:37:05,680
Speaker 1: captured that, like sort of sense of arbitrariness, as you say,

727
00:37:05,800 --> 00:37:08,120
Speaker 1: like to set a scale. So they chose the word

728
00:37:08,200 --> 00:37:10,759
Speaker 1: gauge because physicists love trains. I don't know why, like

729
00:37:10,800 --> 00:37:16,160
Speaker 1: in thought experiments, right yeah, well it's it's Europe, it's

730
00:37:16,160 --> 00:37:18,000
Speaker 1: full of trains, right, yeah. I suppose it was before

731
00:37:18,040 --> 00:37:20,719
Speaker 1: the air of the car that these things took over. So, yes,

732
00:37:20,800 --> 00:37:24,720
Speaker 1: that's right. You would just call them ubers today or lives.

733
00:37:26,320 --> 00:37:27,839
Speaker 1: All right. Well, so that's kind of where we were

734
00:37:27,880 --> 00:37:30,400
Speaker 1: in the history of physics. Like we knew that momentum

735
00:37:30,480 --> 00:37:33,080
Speaker 1: was conserved, like we could see it with simple experiments.

736
00:37:33,080 --> 00:37:35,120
Speaker 1: It seemed to work with with Newtonian physics. But at

737
00:37:35,120 --> 00:37:37,520
Speaker 1: the same time we had these more complex equations of

738
00:37:37,520 --> 00:37:40,680
Speaker 1: the universe and we noticed kind of these special symmetries

739
00:37:40,719 --> 00:37:43,839
Speaker 1: mathematical symmetries about them. But I guess people hadn't put

740
00:37:43,840 --> 00:37:46,279
Speaker 1: the two together right to make the connection. That's right.

741
00:37:46,400 --> 00:37:49,640
Speaker 1: We had noticed these properties of the universe that things

742
00:37:49,640 --> 00:37:52,600
Speaker 1: seem to be conserved, and we also noticed mathematically that

743
00:37:52,640 --> 00:37:56,400
Speaker 1: there were symmetries to our equations. Until we got a

744
00:37:56,520 --> 00:37:59,439
Speaker 1: very special physicist on the scene. And so let's talk

745
00:37:59,440 --> 00:38:02,040
Speaker 1: about her and how she put the two together and

746
00:38:02,120 --> 00:38:05,520
Speaker 1: answered the question basically, why is momentum conserved? But first

747
00:38:05,560 --> 00:38:20,239
Speaker 1: let's take another quick break. All right, we're asking the

748
00:38:20,320 --> 00:38:23,319
Speaker 1: question why is momentum conserved? And we know it has

749
00:38:23,360 --> 00:38:26,160
Speaker 1: something to do with symmetries, but um, we know nobody

750
00:38:26,160 --> 00:38:28,480
Speaker 1: had put the two and two together until is his

751
00:38:28,600 --> 00:38:33,120
Speaker 1: name there? That's right. Actually, she's a mathematician, Emmanuther, and

752
00:38:33,520 --> 00:38:37,239
Speaker 1: she was an expert in abstract algebra and really kind

753
00:38:37,320 --> 00:38:40,520
Speaker 1: of a genius, and she sort of got pulled into

754
00:38:40,560 --> 00:38:43,400
Speaker 1: a question in physics just very briefly wrote like, you know,

755
00:38:43,480 --> 00:38:45,480
Speaker 1: one paper on it and then moved back to a

756
00:38:45,600 --> 00:38:48,720
Speaker 1: real interest in math. But this one paper is basically

757
00:38:48,760 --> 00:38:52,440
Speaker 1: now the foundations of all of theoretical physics. Her, like

758
00:38:52,560 --> 00:38:55,160
Speaker 1: you know, side hustle turned out to be, you know,

759
00:38:55,239 --> 00:38:58,480
Speaker 1: the most important thing anybody's ever done. Man, does it

760
00:38:58,600 --> 00:39:00,880
Speaker 1: feel like you know, you guys, like the entire field

761
00:39:00,880 --> 00:39:03,560
Speaker 1: of physics was stuck and then they just like you know,

762
00:39:03,640 --> 00:39:05,839
Speaker 1: one mathematician had to take like a five minute break

763
00:39:05,880 --> 00:39:08,799
Speaker 1: from from their important work can come and saved all

764
00:39:08,800 --> 00:39:11,480
Speaker 1: of you. Yeah, And it's even more tragic than that

765
00:39:11,560 --> 00:39:13,520
Speaker 1: because due to the fact that she was a woman,

766
00:39:13,600 --> 00:39:16,920
Speaker 1: she wasn't even really allowed to participate in academia and

767
00:39:17,040 --> 00:39:20,280
Speaker 1: in research, even in mathematics, not necessarily just in physics.

768
00:39:20,400 --> 00:39:22,719
Speaker 1: And then when the history of all this stuff was written,

769
00:39:22,760 --> 00:39:25,959
Speaker 1: she was largely sidelined. So people, a lot of people

770
00:39:25,960 --> 00:39:28,279
Speaker 1: have never heard of Emmy Nuther, even though she's like

771
00:39:28,600 --> 00:39:33,359
Speaker 1: more influential than Einstein. WHOA All right, well, maybe take

772
00:39:33,440 --> 00:39:35,879
Speaker 1: us back. So she was around in the nineteen hundreds, right,

773
00:39:35,920 --> 00:39:38,680
Speaker 1: she was born before the nineteen hundreds. Yeah, she was

774
00:39:38,719 --> 00:39:41,279
Speaker 1: born in eighteen eighty two. You know, the end of

775
00:39:41,280 --> 00:39:45,520
Speaker 1: that century had like important mathematical work by like Rieman

776
00:39:45,760 --> 00:39:50,040
Speaker 1: and Mankowski, laying really the foundations for relativity that Einstein

777
00:39:50,080 --> 00:39:53,000
Speaker 1: would later pull together in the early nineteen hundreds and

778
00:39:53,040 --> 00:39:55,520
Speaker 1: teach us a whole new way to think about space

779
00:39:55,640 --> 00:39:57,799
Speaker 1: and time. So she was around during a sort of

780
00:39:57,880 --> 00:40:01,279
Speaker 1: very exciting time when mathematics was really informing physics. And

781
00:40:01,360 --> 00:40:05,200
Speaker 1: she came from a wealthy family and had academic background.

782
00:40:05,200 --> 00:40:08,640
Speaker 1: She professors in her family. But because she was a woman,

783
00:40:08,680 --> 00:40:12,239
Speaker 1: she was not even allowed to enroll in university. Like

784
00:40:12,400 --> 00:40:15,440
Speaker 1: it's just not a thing that women could do back then, Right,

785
00:40:15,480 --> 00:40:18,840
Speaker 1: this is like before Mary Curie became the first woman

786
00:40:18,880 --> 00:40:20,799
Speaker 1: in France to get a PhD. You know, it's just

787
00:40:20,840 --> 00:40:23,239
Speaker 1: like not something that women were allowed to do. Its

788
00:40:23,280 --> 00:40:25,919
Speaker 1: mind boggling now, but it was sort of the way

789
00:40:25,960 --> 00:40:28,719
Speaker 1: things were back then. Yeah, it's pretty tragic. And she

790
00:40:28,920 --> 00:40:32,200
Speaker 1: was born in Germany or yeah, she's German. She was

791
00:40:32,239 --> 00:40:35,640
Speaker 1: born in Bavaria, and she wanted to study in Gottingen

792
00:40:35,960 --> 00:40:38,840
Speaker 1: and they just didn't allow it until nineteen o three

793
00:40:39,239 --> 00:40:42,200
Speaker 1: when they finally allowed women to enroll. She'd been sitting

794
00:40:42,200 --> 00:40:45,280
Speaker 1: in on lectures of course for a while, not officially enrolled,

795
00:40:45,320 --> 00:40:47,279
Speaker 1: but then she was allowed to enroll, and then in

796
00:40:47,440 --> 00:40:50,719
Speaker 1: nineteen o seven she was only the second woman ever

797
00:40:50,880 --> 00:40:56,239
Speaker 1: to earn a PhD in mathematics in the world, right, basically, yeah,

798
00:40:56,280 --> 00:40:59,680
Speaker 1: in the world. And you know, they're famous folks out there, Hilbert,

799
00:41:00,000 --> 00:41:02,880
Speaker 1: I'm Minkowski Shortschild. All these folks knew her, and they

800
00:41:02,920 --> 00:41:06,560
Speaker 1: all knew and said that she was smarter than they were. Wow,

801
00:41:06,880 --> 00:41:11,960
Speaker 1: these are like, you know, seminal you know, mathematicians in physics. Yeah, absolutely,

802
00:41:12,280 --> 00:41:14,879
Speaker 1: and yet there were a lot of institutional barriers. For

803
00:41:14,960 --> 00:41:17,680
Speaker 1: eight years after she got her PhD, she was doing

804
00:41:17,719 --> 00:41:20,600
Speaker 1: teaching and research and she was not being paid. She

805
00:41:20,800 --> 00:41:24,280
Speaker 1: just sort of like volunteering. Nobody would hire her because

806
00:41:24,320 --> 00:41:27,439
Speaker 1: she was a woman, even though she was making important contributions.

807
00:41:27,480 --> 00:41:30,920
Speaker 1: It's you know, it's really ridiculous. Yeah, that's pretty tragic,

808
00:41:30,960 --> 00:41:33,520
Speaker 1: pretty crazy. And she actually had to sort of practice

809
00:41:33,520 --> 00:41:35,560
Speaker 1: physics and teach it for free kind of right, because

810
00:41:35,560 --> 00:41:38,680
Speaker 1: they wouldn't hire her. Yeah, exactly, despite her like glowing

811
00:41:38,719 --> 00:41:42,120
Speaker 1: recommendations from seminal folks in the field, she's rejected from

812
00:41:42,120 --> 00:41:45,280
Speaker 1: position after position just because she was a woman. Hilbert

813
00:41:45,360 --> 00:41:48,720
Speaker 1: is a famous mathematician. He wanted her to teach because

814
00:41:48,719 --> 00:41:51,200
Speaker 1: she was also a great teacher, but they refused to

815
00:41:51,200 --> 00:41:53,359
Speaker 1: give her the position. So what he did was he

816
00:41:53,400 --> 00:41:55,400
Speaker 1: signed up to teach the class and then he hired

817
00:41:55,440 --> 00:41:57,480
Speaker 1: her basically to be his t a and then he

818
00:41:57,560 --> 00:42:00,279
Speaker 1: just never showed up, So she taught the class enough.

819
00:42:00,320 --> 00:42:04,719
Speaker 1: That's noble or lazy or both somehow both, I'm not sure.

820
00:42:04,760 --> 00:42:06,719
Speaker 1: But you know, she came from a wealthy background, so

821
00:42:06,760 --> 00:42:09,080
Speaker 1: she was able to just keep working even though she

822
00:42:09,080 --> 00:42:12,040
Speaker 1: didn't have a salary. And after World War One, she

823
00:42:12,160 --> 00:42:14,840
Speaker 1: finally was able to get an academic position, but they

824
00:42:14,880 --> 00:42:17,880
Speaker 1: wouldn't pay her. So they're like finally letting her in

825
00:42:17,920 --> 00:42:19,680
Speaker 1: the door, but like, yeah, but we're drawing the line

826
00:42:19,680 --> 00:42:22,719
Speaker 1: at providing you any funding or any money for your work.

827
00:42:23,000 --> 00:42:27,160
Speaker 1: Talk about like unequal pay. That's the ultimate inequality. And

828
00:42:27,239 --> 00:42:30,080
Speaker 1: around the time that Einstein was developed in general relativity,

829
00:42:30,239 --> 00:42:32,399
Speaker 1: people were trying to understand, like what did it mean?

830
00:42:32,680 --> 00:42:34,920
Speaker 1: You know, Einstein had these equations and it took decades

831
00:42:34,960 --> 00:42:38,080
Speaker 1: for people to really understand what it means. And one

832
00:42:38,120 --> 00:42:40,600
Speaker 1: of the questions about general relativity was like, what does

833
00:42:40,640 --> 00:42:43,920
Speaker 1: it mean for energy conservation? People thought energy was conserved

834
00:42:43,920 --> 00:42:46,279
Speaker 1: back then, but in general relativity they were like, hold

835
00:42:46,280 --> 00:42:49,240
Speaker 1: on a second, it's not clear if energy is conserved

836
00:42:49,239 --> 00:42:52,360
Speaker 1: in general relativity. What's going on. People knew that Nuther

837
00:42:52,680 --> 00:42:56,040
Speaker 1: was an expert in algebra and in mathematics, a lot

838
00:42:56,040 --> 00:42:58,799
Speaker 1: of which was really important underlying general relativity, so they

839
00:42:58,840 --> 00:43:01,120
Speaker 1: asked her to look at this question, right, because I

840
00:43:01,120 --> 00:43:03,239
Speaker 1: think at this point in the history of physics, like

841
00:43:03,280 --> 00:43:06,200
Speaker 1: we were at the point where basically Newtonian physics were

842
00:43:06,239 --> 00:43:09,200
Speaker 1: being upturned, right, Like we had relied on Newtonian physics

843
00:43:09,280 --> 00:43:11,840
Speaker 1: all the time. People thought they were the thing that

844
00:43:11,960 --> 00:43:14,480
Speaker 1: told us the momentum was conserved. But now they had

845
00:43:14,520 --> 00:43:17,080
Speaker 1: this whole new sort of class of physics, this whole

846
00:43:17,080 --> 00:43:20,759
Speaker 1: new sort of level of quantum and relativity, and so

847
00:43:20,840 --> 00:43:22,600
Speaker 1: people were like, wait a minute, what's going on. Is

848
00:43:22,680 --> 00:43:26,560
Speaker 1: momentum still conserved according to these new sort of equations, right,

849
00:43:26,600 --> 00:43:28,200
Speaker 1: that's kind of where we were. That's where we were.

850
00:43:28,280 --> 00:43:30,359
Speaker 1: People like, well, we think general relativity makes a lot

851
00:43:30,400 --> 00:43:32,759
Speaker 1: of sense. There's a lot to like about it. But

852
00:43:32,840 --> 00:43:35,160
Speaker 1: now we get to ask new questions about it, like

853
00:43:35,520 --> 00:43:38,360
Speaker 1: why does it seem that in general relativity energy is

854
00:43:38,400 --> 00:43:41,840
Speaker 1: not necessarily conserved? Under what conditions would you be conserved?

855
00:43:41,880 --> 00:43:44,240
Speaker 1: What does that mean? This is like a big question

856
00:43:44,520 --> 00:43:47,520
Speaker 1: about the nature of these new mathematical and physical discoveries.

857
00:43:47,800 --> 00:43:49,879
Speaker 1: And so she looked into it and she figured out

858
00:43:49,960 --> 00:43:53,080
Speaker 1: something really interesting and very deep about the nature of

859
00:43:53,080 --> 00:43:55,960
Speaker 1: the universe. Wow. She took a little coffee break and

860
00:43:56,040 --> 00:43:59,120
Speaker 1: she came and figured everything out for everybody. I know,

861
00:43:59,200 --> 00:44:01,960
Speaker 1: all these folks who were like paid and had full professorships,

862
00:44:02,360 --> 00:44:04,280
Speaker 1: you know, and this is their job. They like asked

863
00:44:04,320 --> 00:44:08,759
Speaker 1: the volunteer mathematician who they excluded from academic positions to

864
00:44:08,800 --> 00:44:10,839
Speaker 1: come and solve their problem. And she did, and then

865
00:44:10,840 --> 00:44:13,960
Speaker 1: she went back into mathematics. Right, that's wild and it's

866
00:44:14,040 --> 00:44:16,640
Speaker 1: interesting too. Because she was surrounded by all these like

867
00:44:16,760 --> 00:44:19,800
Speaker 1: famous mathematicians, right, she worked with them, Hilbert Schwartshell. I

868
00:44:19,840 --> 00:44:22,000
Speaker 1: mean these are big names, even not just in math

869
00:44:22,080 --> 00:44:25,920
Speaker 1: but also in physics, like you know the Shortschild radius

870
00:44:25,920 --> 00:44:28,560
Speaker 1: of a black hole. Right, Absolutely all these folks knew

871
00:44:28,560 --> 00:44:30,759
Speaker 1: her and had great respect for her. And it's a

872
00:44:30,760 --> 00:44:34,040
Speaker 1: little sad that in the telling of these stories later on,

873
00:44:34,680 --> 00:44:37,319
Speaker 1: she was mostly omitted from it. Even though she made

874
00:44:37,320 --> 00:44:39,719
Speaker 1: this really seminal contribution, which we'll talk about in just

875
00:44:39,760 --> 00:44:42,080
Speaker 1: a moment, history has largely forgotten about her. And like

876
00:44:42,080 --> 00:44:44,040
Speaker 1: I think, if you ask people who made the most

877
00:44:44,040 --> 00:44:47,239
Speaker 1: important contributions to physics in the last century, you'd get Einstein,

878
00:44:47,320 --> 00:44:49,919
Speaker 1: you might get Shortinger, but like, no, there is up there,

879
00:44:50,280 --> 00:44:53,840
Speaker 1: maybe even more important than Einstein, and yet almost nobody

880
00:44:53,880 --> 00:44:57,000
Speaker 1: knows about her. Wow, up there with Einstein. All right, Well,

881
00:44:57,080 --> 00:44:59,920
Speaker 1: let's get into what exactly she did, Like, what was

882
00:45:00,080 --> 00:45:01,840
Speaker 1: the breakthrough that she had, What was the connection that

883
00:45:01,880 --> 00:45:04,400
Speaker 1: she made? So it sounds very simple, but the connection

884
00:45:04,440 --> 00:45:07,799
Speaker 1: she made was that any symmetry you have in your

885
00:45:07,800 --> 00:45:11,960
Speaker 1: equations will generate a conservation law. What that means is

886
00:45:11,960 --> 00:45:14,880
Speaker 1: that any conservation you see in the universe any time

887
00:45:15,239 --> 00:45:18,359
Speaker 1: you see something being conserved, you don't understand it. What

888
00:45:18,400 --> 00:45:21,719
Speaker 1: it means is that it comes from some symmetry. Right,

889
00:45:21,760 --> 00:45:25,359
Speaker 1: there's always some symmetry which produces a conservation law. So,

890
00:45:25,440 --> 00:45:29,279
Speaker 1: for example, conservation of momentum comes from the fact that

891
00:45:29,400 --> 00:45:32,600
Speaker 1: space is the same everywhere. If you shift your experiment

892
00:45:32,680 --> 00:45:35,120
Speaker 1: from here to over there, you don't get a different answer.

893
00:45:35,520 --> 00:45:38,200
Speaker 1: That's why momentum is concerned. Can you maybe go a

894
00:45:38,239 --> 00:45:40,520
Speaker 1: little bit into more detail, like why is that? Why

895
00:45:40,719 --> 00:45:42,839
Speaker 1: is it that having the equations be the same here

896
00:45:42,960 --> 00:45:47,440
Speaker 1: or there results or gives us conservation of momentum. We'll

897
00:45:47,440 --> 00:45:50,520
Speaker 1: remember that what we're talking about is that physics doesn't change. Right,

898
00:45:50,520 --> 00:45:52,640
Speaker 1: So you shift your whole experiment from here to there,

899
00:45:52,960 --> 00:45:56,040
Speaker 1: you get the same equations of motion, and the equations

900
00:45:56,040 --> 00:45:58,360
Speaker 1: of motion if you know anything about like Hamiltonian or

901
00:45:58,440 --> 00:46:02,400
Speaker 1: Lagrange and mechanics, these equations only depend on the derivatives

902
00:46:02,520 --> 00:46:06,120
Speaker 1: of your position, how your position changes with time, not

903
00:46:06,239 --> 00:46:09,719
Speaker 1: the actual value of the position. Right, And so if

904
00:46:09,760 --> 00:46:12,440
Speaker 1: you take your position and you add a constant to it,

905
00:46:12,960 --> 00:46:15,600
Speaker 1: you know x goes to x plus a, then the

906
00:46:15,600 --> 00:46:19,000
Speaker 1: derivatives don't change because when you take the derivative a disappears.

907
00:46:19,400 --> 00:46:22,280
Speaker 1: The equations emotions you get when you shift your position

908
00:46:22,560 --> 00:46:25,440
Speaker 1: don't change because the equations of emotion only depend on

909
00:46:25,480 --> 00:46:29,560
Speaker 1: the derivative, and the derivative of your position is your velocity,

910
00:46:29,840 --> 00:46:33,040
Speaker 1: which is closely connected to your momentum. That's sort of

911
00:46:33,080 --> 00:46:36,839
Speaker 1: like a sketch for why the symmetry in position gives

912
00:46:36,880 --> 00:46:40,239
Speaker 1: you conservation of momentum, because the equations of motion only

913
00:46:40,280 --> 00:46:44,000
Speaker 1: depend on the derivative of the position, not the position themselves.

914
00:46:44,880 --> 00:46:46,400
Speaker 1: I think what you're saying is that the equations of

915
00:46:46,480 --> 00:46:49,319
Speaker 1: motion of the universe basically don't have pocisition in them.

916
00:46:49,320 --> 00:46:51,880
Speaker 1: They just have velocities in them. Yeah. Another way to

917
00:46:51,920 --> 00:46:54,400
Speaker 1: think about it is that they only have relative positions.

918
00:46:54,960 --> 00:46:57,960
Speaker 1: You shift everything over, nothing changes. It's only changes in

919
00:46:58,040 --> 00:47:00,920
Speaker 1: position are important. That's what the equation of motion are about,

920
00:47:01,200 --> 00:47:05,239
Speaker 1: and changes the position is velocity, and velocity is basically momentum. Right.

921
00:47:05,239 --> 00:47:08,040
Speaker 1: But I guess the question then, is why this the

922
00:47:08,080 --> 00:47:10,759
Speaker 1: fact that it's the same here or there? Well, why

923
00:47:10,800 --> 00:47:13,920
Speaker 1: does that mean that? You know? Objects in motion stay

924
00:47:13,920 --> 00:47:16,800
Speaker 1: in motion, and objects and address stay and rest. It

925
00:47:16,880 --> 00:47:19,960
Speaker 1: might seem weird to connect these two quantities momentum, right

926
00:47:20,080 --> 00:47:23,160
Speaker 1: and position, but you know, there's another great advance in

927
00:47:23,200 --> 00:47:25,680
Speaker 1: the early part of this century that connected momentum position,

928
00:47:25,680 --> 00:47:27,879
Speaker 1: that told us that there was a close relationship between

929
00:47:27,920 --> 00:47:31,200
Speaker 1: these two quantities, And that's quantum mechanics, which, like the

930
00:47:31,239 --> 00:47:34,560
Speaker 1: Heisenberg and certainty principle, tells you that momentum and position

931
00:47:34,600 --> 00:47:37,440
Speaker 1: are closely related to each other because one is basically

932
00:47:37,480 --> 00:47:40,520
Speaker 1: like the foury transform of the other one. And so

933
00:47:40,600 --> 00:47:43,960
Speaker 1: these two quantities are like really coupled together. And so

934
00:47:44,040 --> 00:47:47,279
Speaker 1: the fact that you can shift your experiment over by

935
00:47:47,400 --> 00:47:50,280
Speaker 1: ten meters or by light year and it doesn't change

936
00:47:50,280 --> 00:47:54,120
Speaker 1: the answer tells you something about the relationship between momentum

937
00:47:54,200 --> 00:47:57,319
Speaker 1: and position, and so that's sort of where it originates.

938
00:47:58,560 --> 00:48:03,720
Speaker 1: To help at all, let's try this. Maybe, let's assume

939
00:48:03,800 --> 00:48:07,239
Speaker 1: that the equations of the universe were not symmetric, right, Like,

940
00:48:07,320 --> 00:48:10,280
Speaker 1: let's say that you know, you didn't have these equations.

941
00:48:10,320 --> 00:48:14,799
Speaker 1: How would that translate to momentum not being conserved? All right, So,

942
00:48:14,840 --> 00:48:19,359
Speaker 1: if the equations of motion of the universe depended on position, right,

943
00:48:19,400 --> 00:48:23,080
Speaker 1: not just changes of position, like if if equals and

944
00:48:23,160 --> 00:48:26,799
Speaker 1: may here and if equals three m A and Mars

945
00:48:27,360 --> 00:48:29,520
Speaker 1: not in Mars, but like near than in the neighborhood

946
00:48:29,520 --> 00:48:31,560
Speaker 1: of Mars. Like, let's say the equations of the universe

947
00:48:32,080 --> 00:48:35,040
Speaker 1: change from here to there, How would that affect whether

948
00:48:35,200 --> 00:48:37,360
Speaker 1: or not a ball of ice cream right throughout Mars

949
00:48:37,520 --> 00:48:40,080
Speaker 1: is going to change velocity. If you're a particle and

950
00:48:40,120 --> 00:48:43,759
Speaker 1: you're moving through a universe where the rules are changing

951
00:48:43,960 --> 00:48:48,320
Speaker 1: as you move, right, then your trajectory might change because

952
00:48:48,320 --> 00:48:50,880
Speaker 1: the rules are the things that govern your trajectory, that

953
00:48:50,960 --> 00:48:53,800
Speaker 1: tell your trajectory how it moves. So if over here

954
00:48:53,800 --> 00:48:55,879
Speaker 1: in our part of the universe, it requires a force

955
00:48:55,960 --> 00:48:58,919
Speaker 1: to change momentum, but over there it doesn't, right, then

956
00:48:59,200 --> 00:49:01,719
Speaker 1: your momentum might change without anybody applying a force to

957
00:49:01,800 --> 00:49:04,040
Speaker 1: it in that part of the universe. And so your

958
00:49:04,080 --> 00:49:06,960
Speaker 1: momentum might be changed just by the fact of moving

959
00:49:07,000 --> 00:49:10,440
Speaker 1: from here to there where where the rules are different. Right,

960
00:49:10,480 --> 00:49:12,640
Speaker 1: But what if nothing interacts with my ice cream wall

961
00:49:12,680 --> 00:49:15,560
Speaker 1: from here to there, why would it change or how

962
00:49:15,600 --> 00:49:18,000
Speaker 1: could it change velocity? You know what I mean? How

963
00:49:18,040 --> 00:49:20,239
Speaker 1: could the momentum change? Or maybe like, are you saying

964
00:49:20,239 --> 00:49:23,160
Speaker 1: that maybe the definition of momentum would change, You're assuming

965
00:49:23,200 --> 00:49:26,400
Speaker 1: implicitly there that you need to interact with somebody to

966
00:49:26,480 --> 00:49:29,560
Speaker 1: change its momentum, which is assuming conservation of momentum. But

967
00:49:29,640 --> 00:49:32,319
Speaker 1: in this example, we're talking about a universe where the

968
00:49:32,400 --> 00:49:34,560
Speaker 1: rules are different from one place to another, and so

969
00:49:34,640 --> 00:49:37,799
Speaker 1: you don't have conservation and momentum, and so it would

970
00:49:37,880 --> 00:49:41,479
Speaker 1: break pretty basic fundamental things like that things could change

971
00:49:41,560 --> 00:49:45,399
Speaker 1: momentum without anything interacting with it. That would break Well,

972
00:49:45,520 --> 00:49:48,000
Speaker 1: let's say like here on Earth or in our neighborhood,

973
00:49:48,080 --> 00:49:50,279
Speaker 1: it's E equals they may, but near Mars it's e

974
00:49:50,560 --> 00:49:53,400
Speaker 1: equals three m A. Right, like, if I apply a force,

975
00:49:53,520 --> 00:49:55,160
Speaker 1: I need three times the amount of force to get

976
00:49:55,160 --> 00:49:58,400
Speaker 1: something to accelerate. Would that break the laws of conservation

977
00:49:58,440 --> 00:50:01,200
Speaker 1: momentum or not? Yeah, absolute, it would because remember force

978
00:50:01,360 --> 00:50:04,480
Speaker 1: is a change of momentum, and so it's talking about

979
00:50:04,960 --> 00:50:07,960
Speaker 1: is having a different change in momentum over here and

980
00:50:08,160 --> 00:50:10,960
Speaker 1: over there. So you'd have to have some like gradual

981
00:50:11,080 --> 00:50:13,680
Speaker 1: change in the laws between here and there, and then

982
00:50:14,040 --> 00:50:17,240
Speaker 1: you know the same acceleration would require a different force

983
00:50:17,640 --> 00:50:20,279
Speaker 1: here and over there, and so that would mean a

984
00:50:20,280 --> 00:50:23,120
Speaker 1: different change in momentum. So absolutely, what are you saying,

985
00:50:23,200 --> 00:50:25,000
Speaker 1: or are you saying the ball would slow down or

986
00:50:25,000 --> 00:50:26,960
Speaker 1: the ball would speed up? In that case, it would

987
00:50:27,000 --> 00:50:30,120
Speaker 1: slow down because effectively you'd be increasing its mass to

988
00:50:30,280 --> 00:50:33,880
Speaker 1: like three m without changing its momentum, so its velocity

989
00:50:33,880 --> 00:50:36,399
Speaker 1: would drop. Are you're saying because there's no force, then

990
00:50:37,320 --> 00:50:40,000
Speaker 1: because we sort of change the mass kind of, then

991
00:50:40,120 --> 00:50:43,919
Speaker 1: the velocity would change. Yeah. Um, it gets pretty hard

992
00:50:43,960 --> 00:50:47,640
Speaker 1: to do these calculations because your intuition really assumes that

993
00:50:47,719 --> 00:50:50,319
Speaker 1: these things are conserved. Right. Well, I guess what I'm

994
00:50:50,320 --> 00:50:52,640
Speaker 1: trying to do is get a you know, kind of

995
00:50:52,640 --> 00:50:55,200
Speaker 1: an in twitest sense of what you mean when you say,

996
00:50:55,239 --> 00:50:58,520
Speaker 1: like symmetries equals conservation of of something. I think maybe

997
00:50:58,560 --> 00:51:01,080
Speaker 1: an intuitive way to understand it is to think about

998
00:51:01,160 --> 00:51:04,080
Speaker 1: just the relative sense of these quantities. You know, like,

999
00:51:04,480 --> 00:51:06,840
Speaker 1: we know that no place in the universe is different

1000
00:51:06,880 --> 00:51:09,359
Speaker 1: from any other place. We also know that the only

1001
00:51:09,360 --> 00:51:13,120
Speaker 1: important thing is not your position, but your relative velocity. Right,

1002
00:51:13,160 --> 00:51:15,640
Speaker 1: those two really are saying the same thing, that what

1003
00:51:15,719 --> 00:51:18,000
Speaker 1: matters is not where you are in the universe, but

1004
00:51:18,040 --> 00:51:22,480
Speaker 1: your velocity relative to that stuff. So momentum is important

1005
00:51:22,640 --> 00:51:25,440
Speaker 1: and not position. That's why momentum is conserved and not

1006
00:51:25,480 --> 00:51:28,120
Speaker 1: like location. So I think that's the most intuitive way

1007
00:51:28,120 --> 00:51:31,000
Speaker 1: to think about it. You know that underlying you, there's

1008
00:51:31,040 --> 00:51:34,360
Speaker 1: no fixed grid where somebody is measuring your position is

1009
00:51:34,400 --> 00:51:37,240
Speaker 1: just about how you're moving relative to stuff that's important,

1010
00:51:37,400 --> 00:51:40,319
Speaker 1: not your location. One way to say that is while

1011
00:51:40,360 --> 00:51:42,080
Speaker 1: you can move your experiment somewhere else and get the

1012
00:51:42,080 --> 00:51:44,560
Speaker 1: same answer. Another way to say that is, actually the

1013
00:51:44,600 --> 00:51:48,840
Speaker 1: important thing is motion, not position, and that's conservation and momentum.

1014
00:51:48,960 --> 00:51:50,840
Speaker 1: I think maybe you're telling me that you sort of

1015
00:51:50,840 --> 00:51:53,280
Speaker 1: have to go into the math to really understand that connection,

1016
00:51:53,960 --> 00:51:55,719
Speaker 1: Like it sort of comes comes from the math. But

1017
00:51:55,800 --> 00:51:57,880
Speaker 1: it's kind of hard to really see it from an

1018
00:51:57,920 --> 00:52:00,880
Speaker 1: intuitive point of view because maybe we are so ingrain

1019
00:52:00,960 --> 00:52:03,439
Speaker 1: in this idea of conservation, but we can't think of

1020
00:52:03,440 --> 00:52:05,400
Speaker 1: of things not being conservad Yeah, I used to think

1021
00:52:05,440 --> 00:52:07,239
Speaker 1: I had intuitive understanding of it until you ask me

1022
00:52:07,239 --> 00:52:08,680
Speaker 1: a bunch of questions about it, and now I'm not

1023
00:52:08,719 --> 00:52:13,319
Speaker 1: so sure. I've destroyed the conservation of knowledge in your brain.

1024
00:52:13,480 --> 00:52:17,279
Speaker 1: But it is very simple mathematically and very deep and fascinating.

1025
00:52:17,440 --> 00:52:20,879
Speaker 1: You can take this example that translations in space lead

1026
00:52:20,920 --> 00:52:23,640
Speaker 1: to conservation momentum and apply to lots of other things,

1027
00:52:23,719 --> 00:52:25,719
Speaker 1: and it also holds. That's why I know if the

1028
00:52:25,840 --> 00:52:29,400
Speaker 1: theorem is so powerful, it doesn't just explain conservation momentum,

1029
00:52:29,440 --> 00:52:32,480
Speaker 1: it also explains other conservation laws that we see in

1030
00:52:32,520 --> 00:52:35,759
Speaker 1: the universe. For example, you can apply the same thing

1031
00:52:35,800 --> 00:52:39,840
Speaker 1: to rotation. Right. We don't care about the orientation of

1032
00:52:39,920 --> 00:52:42,120
Speaker 1: anything in the universe because there's no up or down.

1033
00:52:42,120 --> 00:52:45,040
Speaker 1: There's no preferred direction. The same way there's no preferred location.

1034
00:52:45,560 --> 00:52:49,040
Speaker 1: That's why we have conservation of angular momentum because rotation

1035
00:52:49,120 --> 00:52:54,759
Speaker 1: is not fundamental, but relative rotations are. Rotational velocity is important,

1036
00:52:54,840 --> 00:52:58,160
Speaker 1: and so we have conservation of angular momentum because the

1037
00:52:58,280 --> 00:53:00,799
Speaker 1: universe can be rotated through in our during angle and

1038
00:53:00,880 --> 00:53:03,640
Speaker 1: nothing changes. Right. I think what you're saying is that

1039
00:53:03,680 --> 00:53:07,839
Speaker 1: she sort of drew that connection between these mathematical symmetries

1040
00:53:08,080 --> 00:53:11,520
Speaker 1: and these sort of physical ideas of conservation of things,

1041
00:53:11,600 --> 00:53:13,640
Speaker 1: like things overall, if you look at them at the system,

1042
00:53:13,640 --> 00:53:16,640
Speaker 1: they don't change. And she said, hey, that's because you

1043
00:53:16,719 --> 00:53:20,200
Speaker 1: have these symmetries in these equations like they're they're they're

1044
00:53:20,239 --> 00:53:22,120
Speaker 1: sort of one and the same exactly, not just a

1045
00:53:22,160 --> 00:53:25,279
Speaker 1: symmetry and the equation a symmetry in the universe. Right,

1046
00:53:25,320 --> 00:53:29,440
Speaker 1: conservation momentum tells you that space is the same everywhere.

1047
00:53:29,680 --> 00:53:32,320
Speaker 1: That's a big conclusion. Right, If momentum really is conserved

1048
00:53:32,360 --> 00:53:34,760
Speaker 1: everywhere in the universe. It tells you there's no different

1049
00:53:34,760 --> 00:53:37,560
Speaker 1: place in space. Every place in space is the same.

1050
00:53:37,600 --> 00:53:40,520
Speaker 1: It's not just the equations. It's like the universe, man,

1051
00:53:41,480 --> 00:53:45,319
Speaker 1: the universe, man. So what exactly is the theorem? Like,

1052
00:53:45,360 --> 00:53:48,120
Speaker 1: how do you de verbalize that theorem? The theorem is

1053
00:53:48,160 --> 00:53:53,000
Speaker 1: that every continuous symmetry of the lagrange in which describes

1054
00:53:53,080 --> 00:53:56,919
Speaker 1: the motion and interaction of particles, leads to a conservation law.

1055
00:53:57,040 --> 00:54:01,080
Speaker 1: So continuous symmetry like translation in space, a rotation in space,

1056
00:54:01,480 --> 00:54:04,799
Speaker 1: or shifting in time. The original question she was trying

1057
00:54:04,800 --> 00:54:08,960
Speaker 1: to ask is is energy conserved in generalativity? And if not,

1058
00:54:09,200 --> 00:54:12,120
Speaker 1: why not? And so this was her answer. Her answer was,

1059
00:54:12,239 --> 00:54:14,920
Speaker 1: if space doesn't change with time, if the laws of

1060
00:54:14,920 --> 00:54:18,319
Speaker 1: the universe don't change in time, then energy is conserved.

1061
00:54:18,640 --> 00:54:20,680
Speaker 1: If the laws in the universe do change in time,

1062
00:54:20,880 --> 00:54:24,280
Speaker 1: then energy is not conserved. Sort of blew everybody's minds

1063
00:54:24,280 --> 00:54:27,879
Speaker 1: when she discovered that. WHOA, So she sort of made

1064
00:54:27,920 --> 00:54:31,160
Speaker 1: a bridge between the new physics and the old physics,

1065
00:54:31,200 --> 00:54:33,960
Speaker 1: right or she provided kind of the answer that said, hey,

1066
00:54:34,000 --> 00:54:36,040
Speaker 1: they're all sort of one and the same. Yeah, she

1067
00:54:36,280 --> 00:54:39,960
Speaker 1: helped us understand why these conservation laws appear and under

1068
00:54:40,040 --> 00:54:42,840
Speaker 1: what conditions they do, and of course, for decades afterwards

1069
00:54:42,840 --> 00:54:46,000
Speaker 1: people were like, well, obviously energy is conserved in the universe,

1070
00:54:46,040 --> 00:54:48,239
Speaker 1: and so therefore the rules of physics must be the

1071
00:54:48,280 --> 00:54:50,360
Speaker 1: same as a function of time. Now, of course, we

1072
00:54:50,440 --> 00:54:52,920
Speaker 1: know the universe is expanding, and that means that energy

1073
00:54:52,960 --> 00:54:56,080
Speaker 1: is not conserved because space is changing with time. Right,

1074
00:54:56,120 --> 00:54:58,359
Speaker 1: So you know, if the theorem is still teaching us

1075
00:54:58,400 --> 00:55:00,759
Speaker 1: things about the nature of the universe, the fact that

1076
00:55:00,760 --> 00:55:03,520
Speaker 1: the universe is expanding means that energy is not conserved.

1077
00:55:03,640 --> 00:55:06,680
Speaker 1: And we know why because it sort of breaks her theorem,

1078
00:55:06,800 --> 00:55:09,480
Speaker 1: or it's outside of her theorem, because there isn't a

1079
00:55:09,480 --> 00:55:12,960
Speaker 1: symmetry with time, which is why we don't have energy conservation.

1080
00:55:13,360 --> 00:55:16,400
Speaker 1: If the universe was symmetric in time, if space was

1081
00:55:16,440 --> 00:55:18,920
Speaker 1: the same size and not expanding, then we would have

1082
00:55:19,040 --> 00:55:22,400
Speaker 1: energy conservation. So we know why we don't have energy

1083
00:55:22,400 --> 00:55:24,600
Speaker 1: conservation just the same way we know why we do

1084
00:55:24,880 --> 00:55:27,680
Speaker 1: have momentum conservation. All right, Well, I think that sort

1085
00:55:27,680 --> 00:55:30,359
Speaker 1: of answer is the main question of the episode, which

1086
00:55:30,400 --> 00:55:32,840
Speaker 1: is wise momentum conserved, And it seems like the answer

1087
00:55:33,000 --> 00:55:35,399
Speaker 1: is that it's it's sort of like baked into the

1088
00:55:35,440 --> 00:55:38,840
Speaker 1: equations of the universe, like it's because the equations of

1089
00:55:38,880 --> 00:55:42,360
Speaker 1: the universe don't change no matter where you put them. Yeah,

1090
00:55:42,440 --> 00:55:45,719
Speaker 1: it's because space is the same everywhere in the universe.

1091
00:55:46,120 --> 00:55:49,160
Speaker 1: That's why momentum is conserved. Well, it's everywhere. It's the

1092
00:55:49,200 --> 00:55:51,800
Speaker 1: same everywhere in the universe, but not everywhere in time,

1093
00:55:51,920 --> 00:55:54,840
Speaker 1: like it's it's changing, but it's changing everywhere at the

1094
00:55:54,880 --> 00:55:57,680
Speaker 1: same time. I think it's what you're saying. Space is expanding,

1095
00:55:57,719 --> 00:56:00,520
Speaker 1: it is changing, but the rules of the universe are

1096
00:56:00,520 --> 00:56:03,040
Speaker 1: the same at every location in space. Yeah, there's no

1097
00:56:03,120 --> 00:56:05,760
Speaker 1: different parts of space. Is like vanilla space and chocolate

1098
00:56:05,800 --> 00:56:08,839
Speaker 1: space and strawberry space. It's all the same space. That's

1099
00:56:08,840 --> 00:56:14,040
Speaker 1: all the same swirl exactly. You only get one option,

1100
00:56:14,280 --> 00:56:17,240
Speaker 1: and that's one kind of space swirl in this universe.

1101
00:56:17,480 --> 00:56:20,279
Speaker 1: I see. But if we do maybe find out some

1102
00:56:20,520 --> 00:56:23,279
Speaker 1: time in the future that space is different, like at

1103
00:56:23,280 --> 00:56:25,520
Speaker 1: the borders or at the edges, or maybe in the

1104
00:56:25,600 --> 00:56:29,640
Speaker 1: next universe over, then maybe momentum wouldn't be conserved. Yeah, exactly.

1105
00:56:29,719 --> 00:56:33,200
Speaker 1: Maybe momentum will be dethroned the way energy was, or

1106
00:56:33,239 --> 00:56:35,800
Speaker 1: at least, you know, not dethroned. But just like hey,

1107
00:56:35,960 --> 00:56:39,560
Speaker 1: it would confirm there's theorem actually in a way right. Yeah,

1108
00:56:39,680 --> 00:56:42,239
Speaker 1: And if you're interested in other weird quantum applications in

1109
00:56:42,360 --> 00:56:45,200
Speaker 1: other's theorem, check out our episode about gauge symmetry, which

1110
00:56:45,239 --> 00:56:48,520
Speaker 1: relies heavily on this idea and which promised to have

1111
00:56:48,560 --> 00:56:51,279
Speaker 1: a whole episode diving into another's theorem. So here it is.

1112
00:56:51,400 --> 00:56:54,960
Speaker 1: But Another's theorem also explains why we have like conserved

1113
00:56:55,040 --> 00:56:57,880
Speaker 1: electric charges in the universe that comes from an internal

1114
00:56:58,000 --> 00:57:01,680
Speaker 1: quantum symmetry and also to they're weird, conservation laws in

1115
00:57:01,760 --> 00:57:06,320
Speaker 1: particle physics come from symmetries we see in the equations

1116
00:57:06,320 --> 00:57:09,120
Speaker 1: of particle physics and are powered by Neuthers theorem. Well,

1117
00:57:09,160 --> 00:57:11,239
Speaker 1: I feel like there are two big lessons here. One

1118
00:57:11,440 --> 00:57:13,799
Speaker 1: is that sometimes even that like the things that seem

1119
00:57:13,840 --> 00:57:16,320
Speaker 1: intuitive and the universe have a deep sort of mathematical

1120
00:57:16,960 --> 00:57:19,040
Speaker 1: route in the in how the universe works. And then

1121
00:57:19,080 --> 00:57:22,920
Speaker 1: you should always ask mathematicians for help with your physics problems. Yeah,

1122
00:57:23,320 --> 00:57:25,240
Speaker 1: they're like the nine one one of the physics world.

1123
00:57:25,680 --> 00:57:28,160
Speaker 1: Like we've been trying for centuries. Can you guys, you know,

1124
00:57:28,360 --> 00:57:31,400
Speaker 1: take a break and help us out. Yeah. Well, that

1125
00:57:31,440 --> 00:57:34,640
Speaker 1: part of history is really rich with fascinating mathematics that

1126
00:57:34,760 --> 00:57:37,400
Speaker 1: was developed for decades just had a pure interest in

1127
00:57:37,440 --> 00:57:40,080
Speaker 1: mathematics and then oh it turns out to be really

1128
00:57:40,080 --> 00:57:42,760
Speaker 1: helpful and solve important problems in physics. Yeah. And I

1129
00:57:42,800 --> 00:57:45,040
Speaker 1: guess the other interesting thing is here is that you know,

1130
00:57:45,440 --> 00:57:47,240
Speaker 1: I mean, you know, there was someone who is sort

1131
00:57:47,240 --> 00:57:51,160
Speaker 1: of outside of academa right, kind of unjustly so and

1132
00:57:51,280 --> 00:57:55,120
Speaker 1: justly so. She's excluded, but she still made this amazing contribution.

1133
00:57:55,360 --> 00:57:58,320
Speaker 1: Like you know, these breakthroughs can come from anywhere. Yeah, exactly,

1134
00:57:58,400 --> 00:58:00,400
Speaker 1: And we really should have much more different city in

1135
00:58:00,480 --> 00:58:03,680
Speaker 1: physics and in mathematics and in academia because we need

1136
00:58:03,760 --> 00:58:06,680
Speaker 1: all sorts to solve the tough problems that are facing us.

1137
00:58:07,080 --> 00:58:09,080
Speaker 1: So happy birthday, I mean author, and thank you for

1138
00:58:09,120 --> 00:58:11,880
Speaker 1: all your contributions. Yeah for sure, thank you. Let's all

1139
00:58:11,920 --> 00:58:14,760
Speaker 1: have a scoop of space Sworld ice cream and to

1140
00:58:14,840 --> 00:58:19,840
Speaker 1: celebrate her birthday. Yeah, and expand the space around our

1141
00:58:19,840 --> 00:58:22,520
Speaker 1: waistload's a little bit and know our minds with what

1142
00:58:22,640 --> 00:58:25,160
Speaker 1: it all means. All right, Well, I think that um

1143
00:58:25,200 --> 00:58:27,680
Speaker 1: answers a question and it tells us some pretty deep

1144
00:58:27,680 --> 00:58:30,320
Speaker 1: things about the universe. We hope you enjoyed that. Thanks

1145
00:58:30,320 --> 00:58:40,880
Speaker 1: for joining us, See you next time. Thanks for listening

1146
00:58:40,880 --> 00:58:43,600
Speaker 1: and remember that. Daniel and Jorge Explain the Universe is

1147
00:58:43,640 --> 00:58:47,120
Speaker 1: a production of I heart Radio. Or more podcast from

1148
00:58:47,160 --> 00:58:50,920
Speaker 1: my heart Radio. Visit the i heart Radio app, Apple Podcasts,

1149
00:58:51,040 --> 00:59:03,600
Speaker 1: or wherever you listen to your favorite shows.