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Speaker 4: Hey dadil do you think podcasts obey the laws of physics?

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Speaker 1: Oh?

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Speaker 5: Why?

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Speaker 1: Sure? Hope? So I don't want to get some sort

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

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Speaker 4: Well, I've first some people who use podcasts to fall asleep.

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

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Speaker 1: that violating the laws of physics?

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Speaker 4: Well, isn't there something about how bodies and motions stay

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Speaker 4: in motion?

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Speaker 1: I see where you're going with this. That could be

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Speaker 1: a problem if the podcast puts bodies at rest that

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Speaker 1: used to be in motion.

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Speaker 4: Yeah, yeah, that might be a problem, like driving or something.

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Speaker 4: Maybe they should get in bed and get comfortable before they,

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Speaker 4: you know, put on a podcast. Then they could just

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Speaker 4: continue being in the rest.

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

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Speaker 1: main topic of the podcast.

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Speaker 4: Maybe we just put a bunch of people to sleep.

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Speaker 4: Wake up, Wake up? What I put you to sleep?

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Speaker 4: You're the physicists.

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Speaker 6: I take naps wherever I can find them.

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Speaker 4: Hi, am pre handmade cartoonists and the creator of PhD Comics.

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Speaker 1: Hi, I'm Daniel. I'm a particle physicist and a professor

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Speaker 1: at U See Irvine, and I try to stay in motion.

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Speaker 4: Is that hard as a physicist? Don't you sit in

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Speaker 4: your couch or your desk all the time and just

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Speaker 4: think up solutions to the questions about the universe.

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Speaker 7: Yeah?

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Speaker 1: But I find that as I get older, a body

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Speaker 1: at rest to stay at rest, so it gets harder

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Speaker 1: and harder to get out of that couch.

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Speaker 4: I think a body at rest also thanks to get bigger.

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Speaker 4: 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 4: That's right. We expand space time or on our waste.

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Speaker 4: It's the weird law of the universe, the no diet theorem.

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Speaker 1: The law of general snack aativity.

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Speaker 4: But anyways, welcome to our podcast, Daniel and Jorge Explain

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Speaker 4: the Universe, a production of iHeartRadio.

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Speaker 1: In which we put your mind into motion to understand

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Speaker 1: the fundamental nature of the universe around us, or at

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Speaker 1: least to ask the deep questions about how it works

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Speaker 1: and try to observe the patterns the trends, the symmetries,

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Speaker 1: the conservation laws, the fundamental rules that seem to be

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Speaker 1: organizing our universe. On this podcast, we ask all of

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Speaker 1: those big questions, and we don't shy away from trying

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Speaker 1: to find answers.

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Speaker 4: Yeah, because the universe is full of things to ask

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Speaker 4: questions about, lots of questions that we still haven't figured

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Speaker 4: out despite hundreds and maybe thousands of years of science

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Speaker 4: and observing the universe, and we try to talk about

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Speaker 4: it and to increase the gravity I guess in your brain, right,

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Speaker 4: Like information causes gravity to increase.

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Speaker 1: Right, that's true. Yeah, Eventually our goal is to turn

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Speaker 1: your brain into a black hole.

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Speaker 4: Oh no, no, we want stuff to get out too.

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Speaker 1: That's true. Oh, that would be undermining the fundamental purpose

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Speaker 1: of our podcast.

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Speaker 4: That's right. It wouldn't go viral if everyone turned into

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Speaker 4: a black hole.

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Speaker 1: But we do want your brain to absorb information or

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Speaker 1: to feel like you are part of this centuries or

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Speaker 1: maybe even millennial long progress towards understanding the universe. When

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Speaker 1: people look back on the path of theoretical physics in

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Speaker 1: one hundred years or in a thousand years, we'll wonder

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Speaker 1: how far along that path we are have we just

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Speaker 1: gotten started. Are we around the corner from revealing the

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Speaker 1: deepest secrets of the universe? Only time will tell.

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Speaker 4: Yeah, because it's amazing that the universe is even understandable. Right, Like,

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Speaker 4: we look at it, it seems kind of chaotic, but

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Speaker 4: the closer we look, we start to notice patterns and

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Speaker 4: trends that seem to sort of govern how it works

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Speaker 4: 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.

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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.

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Speaker 4: Yeah, you don't even have to get that fancy to

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Speaker 4: see how the universe has these laws, right, You can

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Speaker 4: just toss an apple in the air over and over

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Speaker 4: and it will always sort of come back to your head.

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Speaker 1: But you can also do it while being fancy. You

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Speaker 1: can wear a tuxedo and toss an apple into the air.

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Speaker 1: Nothing's stopping you from getting fancy. Are you anti fancy? Now?

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Speaker 4: That's ry. I guess you could be tossing a count

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Speaker 4: of caviaar instead of an apple too.

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Speaker 1: I mean, personally, I'm always wearing a tuxedo while doing

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Speaker 1: these podcasts. I thought we had a dress code on

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Speaker 1: this podcast. What are you wearing?

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Speaker 4: I'm wearing a pajama with a tuxedo printed on it.

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Speaker 1: Oh man, standards are sliding everywhere, folks.

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Speaker 4: It's that's right. We don't have a dress code law

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Speaker 4: 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 tuxedo 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 4: I'm pretty sure nobody was wearing a tuxedo while listening

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Speaker 4: to us, unless maybe they're like a waiter maybe at

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Speaker 4: a fancy restaurant you go that you know, tunes out

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Speaker 4: the customers by listening to our podcast, I hope.

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Speaker 1: That we have a pretty broad variety of what folks

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Speaker 1: are wearing, you know, all the way from athletic gear

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Speaker 1: to tuxedos with tails and top hats. I'd just like

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Speaker 1: to imagine we're sampling all of the human experience the

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Speaker 1: same way we are trying to explore the entire range

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Speaker 1: of physical phenomena out there in the universe.

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Speaker 4: Yeah, but it is interesting that the universe has lost right,

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Speaker 4: Like you can imagine maybe a universe with that laws.

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Speaker 4: Is that even sort of like possible to a physicist.

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Speaker 1: It's possible to imagine that that universe exists, but it's

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Speaker 1: hard to understand how you would understand it. You know,

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Speaker 1: the idea that there are laws and that we can

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Speaker 1: reveal them through experiment, and that we can try to

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Speaker 1: simplify them and use them to predict the future. It's

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Speaker 1: pretty basic to our notion of understanding it sort of

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Speaker 1: like goes to the heart of storytelling, even well before

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Speaker 1: like what we call modern science. Indigenous cultures just learning

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Speaker 1: about their environment as they experience it, are telling stories,

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Speaker 1: you know, like you take this tree bark, you make

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Speaker 1: a tea out of it, you drink it you feel better,

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

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Speaker 1: the way I think humans think.

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Speaker 4: Yeah, that is science as well, right.

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

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Speaker 4: Well, it's a good thing that the universe does seem

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Speaker 4: to have laws because it allows us to kind of

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Speaker 4: predict what's going on and to build things to make

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Speaker 4: our lives better, and to have a little bit of

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Speaker 4: context about where we sit in the universe and why

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Speaker 4: we're here.

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Speaker 1: That's right, And the patterns and trends that we notice

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Speaker 1: in the universe they give us a lot of clues

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Speaker 1: as to the fundamental nature of the universe. Though we

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Speaker 1: assume the universe has laws, we don't make a lot

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Speaker 1: of assumptions for what those laws are. So we'd like

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Speaker 1: to look around and notice, like, what are the patterns

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Speaker 1: that happen in the universe, what are those laws that

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Speaker 1: it seems to follow in, what do those laws mean?

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Speaker 1: And why do we have those laws and not other laws?

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Speaker 4: Yeah, And probably one of the most important laws, or

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Speaker 4: at least the most useful laws that we found in

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Speaker 4: understanding the universe and preticuting what's going to happen, is

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Speaker 4: the idea that momentum is conserved. That's a law, right,

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Speaker 4: that's like written in the Statute of the Universe.

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Speaker 1: That is still a law. A lot of things that

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Speaker 1: you learned about in grade school that you thought were

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Speaker 1: conserved in the universe are not mass, energy, energy plus mass,

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Speaker 1: all of this stuff. You thought that stuff was conserved

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Speaker 1: in the universe. It turns out it's not. But conservation

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Speaker 1: and momentum still holds as far as we know. Oh.

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Speaker 4: Interesting, some laws have been repealed. They made it all

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Speaker 4: the way up to the Supreme Court of the universe,

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Speaker 4: and the end they got shut down.

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Speaker 1: Yeah. Well, like Newtonian physics, some of these laws turned

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Speaker 1: out to be almost true, true in many many cases,

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

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Speaker 1: the foundation of the universe, just sort of like mostly

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

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Speaker 1: which is a cool testament to like how science progresses.

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Speaker 1: You find a pattern, it seems to be true everywhere,

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Speaker 1: and then one hundred years later people find exceptions, exceptions

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Speaker 1: that reveal a deeper truth.

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Speaker 4: So when you say that momentum is conserve is still

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Speaker 4: a law, it just means that it hasn't been revealed

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Speaker 4: yet kind of right, like, as far as we know,

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Speaker 4: that's the one that's still true.

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

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

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Speaker 1: a thousand years, when people are listening to this episode,

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Speaker 1: they'll laugh into their hands at our naivete.

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Speaker 4: Right before they fall asleep.

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Speaker 1: But there is something really deep and fundamental that we're

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

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Speaker 1: are looking around to try to figure out, like what

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

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Speaker 1: when we think, oh, maybe energy conserved in the universe,

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Speaker 1: 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 when there was no ice cream

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

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Speaker 1: knows whether they'll be ice cream in the future, But

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Speaker 1: nobody expects the number of ice cream cones to be

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Speaker 1: conserved because nobody thinks that that's an important thing in

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Speaker 1: the universe. So if something is conserved, that suggests that

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Speaker 1: it's probably important somehow to the universe.

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Speaker 4: Well, Daniel, I think ice cream is important. I don't

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Speaker 4: know about you, but it's an important part of my

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Speaker 4: diet for sure.

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Speaker 1: Well, if only the things that are important to you

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Speaker 1: were also important to the universe, I.

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Speaker 4: Think ice cream is pretty important to a lot of people.

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Speaker 4: It's still around, It survives several lost trying to ban it.

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Speaker 1: If ice cream was conserved, then you could ask questions like, well,

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Speaker 1: where did this ice cream come from? Or where does

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Speaker 1: the ice cream go? When you eat it? Right, it

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Speaker 1: turns into something else which is not ice cream. So

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Speaker 1: that suggests that what's conserved is not ice cream, but

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Speaker 1: like some larger category of things anyway, it's the same

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Speaker 1: thing with energy and with momentum. We discover whether these

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Speaker 1: things are conserved by the universe, and then we get

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Speaker 1: to ask what does that mean about the nature of

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Speaker 1: the universe?

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Speaker 4: Right, Because I guess asking these questions is how we

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Speaker 4: understand the universe, right, Like, it's one thing to notice

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Speaker 4: trends in it, but it's another to sort of understand

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Speaker 4: why the universe has these trends, and like why do

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Speaker 4: certain things they conserve 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, question number one could be what's conserved in

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

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

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Speaker 1: questions which reveal a deeper truth of the universe. That's

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Speaker 1: the joy of science that the questions never do end.

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Speaker 4: Well, let's reveal some deeper truth today. So today on

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Speaker 4: the podcast, we'll be asking the question why is momentum conserved? Okay, so, Daniel,

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Speaker 4: you're saying that energy is not conserved in the universe.

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Speaker 4: We have a podcast discussing that, but momentum is conserved.

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Speaker 4: Does that mean momentum is more important than energy?

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Speaker 1: That's a good question. Yeah. I would say that momentum

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

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

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

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

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Speaker 1: So I think both of those facts, that momentum is

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Speaker 1: conserved and that energy is not do tell us something

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Speaker 1: deep about the nature of the universe. But yeah, I

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Speaker 1: think momentum fundamentally is more important. If you had like

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Speaker 1: a competition between quantities and physics, I would vote for

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Speaker 1: momentum over energy.

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Speaker 4: Who would win in a fight, momentum or energy?

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Speaker 1: Well, momentum is a vector also, right, so it has

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Speaker 1: multiple components. It would definitely defeat energy, which is just

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Speaker 1: a scale, it's just a number. So momentum is a

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Speaker 1: bigger army.

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Speaker 4: I see. Yeah. Also momentum has more or momentum going

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Speaker 4: for it. You know, that's important in a fight.

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Speaker 1: Yeah, it's momentous, right, but only in the moment. Maybe

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Speaker 1: they should have called it importum instead of momentum.

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Speaker 4: Yeah, yeah, I'm not sure renaming it would help there.

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Speaker 4: But this is a fascinating question, like why is momentum conserved? Because,

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Speaker 4: as you were saying earlier, this is something you learn

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Speaker 4: you know early on, like high school, middle school, maybe

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Speaker 4: even before, like the idea that if something is in motion,

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Speaker 4: it stays in motion, and if something's at rest, it

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Speaker 4: will stay in the rest unless something changes.

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Speaker 1: And I think that when people learn about these conservation laws,

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Speaker 1: the one that's most intuitive is the one that's actually

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Speaker 1: least true. You know, conservation of mass. It sort of

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Speaker 1: feels like it should make sense, like you have a

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Speaker 1: chemical reaction. You start out with a bunch of little

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Speaker 1: lego brick chemical atoms and molecules, and all you're doing

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Speaker 1: is rearranging them, so of course you should end up

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Speaker 1: with the same amount of stuff at the end. The

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Speaker 1: one that seems to make the most sense to people.

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Speaker 1: And I think that's a revealing example because it makes

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Speaker 1: sense because you think of like stuff as being basic

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Speaker 1: and fundamental to the universe, as it can't be like

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Speaker 1: created or destroyed, and you hear that a lot in

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Speaker 1: science fiction. Of course, now we know that it's not

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Speaker 1: and you can destroy mass and turn it into energy,

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Speaker 1: and you can turn energy into mass and all that

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Speaker 1: kind of stuff. But you know, the idea that a

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Speaker 1: conservation law tells you about what's important in the universe

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Speaker 1: is sort of underlying all of this. And I remember

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Speaker 1: learning about conservation momentum and wondering, like, well, what does

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

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Speaker 1: about the nature of the universe.

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Speaker 4: Well, and in the case of mass, I mean, you

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Speaker 4: just kind of have to figure that all mass is

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Speaker 4: really energy, right, and so then you're just it's like

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Speaker 4: it's embedded in the question of is energy conserved in

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Speaker 4: the universe, which it generally is, just to be clear,

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Speaker 4: but we've recently found that sometimes energy is not conserved.

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Speaker 1: Yeah, it's a nice idea to generalize the conservation of

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Speaker 1: mass into the conservation of energy and say, mass is

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Speaker 1: just one form of energy, so when it disappears in

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Speaker 1: the energy, that's okay, because it's not true that mass

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Speaker 1: is the fundamental stuff in the universe. Energy is right,

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Speaker 1: But then, as you say, we discovered, actually the universe

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Speaker 1: doesn't really care if energy is conserved. It can just

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Speaker 1: go away and we can just sort of increase it.

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Speaker 1: So dig into that podcast if you're curious about that.

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Speaker 1: But what that tells us is that energy is not

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Speaker 1: like the fundamental element of the universe. It's more like

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Speaker 1: ice cream cones. It's just like something we came up

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Speaker 1: with that makes sense to us or is important to us.

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Speaker 1: It's not deeply true it's not a deep feature of

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Speaker 1: the universe.

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Speaker 4: It's not the chocolate ice cream of the universe. Maybe,

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Speaker 4: or are momentum is a vanilla ice cream.

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Speaker 1: Of the universe. First of all, ice cream is not

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Speaker 1: important to the universe, only to you as humans. But

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Speaker 1: I guess we would be saying that, you know, momentum

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Speaker 1: is the dark chocolate of the universe and energy is

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Speaker 1: the white chocolate.

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Speaker 4: Well chocolate aside, this is an interesting question why is

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Speaker 4: momentum conserved? Because we we all the field like gets true,

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Speaker 4: and it does seem to be true so far, But

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Speaker 4: the question is why does it get conserved than the universe? So,

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Speaker 4: as usual, we were wondering how many people out there

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Speaker 4: think they have an answer to this interesting and deep

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Speaker 4: question about how everything works.

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Speaker 1: And thank you to our volunteers who are willing to

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Speaker 1: answer deep, difficult questions of physics without any chance to prepare,

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Speaker 1: so that we can get a sense for what people

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Speaker 1: out there are thinking. If you'd like to participate, please

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Speaker 1: you are very welcome write to us to questions at

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Speaker 1: Danielandjorge dot com.

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Speaker 4: So Daniel asked this question on the internet, why is

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Speaker 4: momentum conserved? And here's what people have to say.

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Speaker 5: I'm not really sure that momentum is preserved because momentum

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Speaker 5: massive velocity a product of massive velocity, and velocity is relative.

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Speaker 5: So if if velocity is relative, I don't know how

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Speaker 5: it could be preserved because if somebody else measures it.

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Speaker 6: It's going to be a different velocity.

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Speaker 8: I just took that kind of as a given and

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Speaker 8: never really question why why. It's just because they tell

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Speaker 8: us it's always conserved. But it's related to you a

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Speaker 8: closed system of matter and energy. None of that matter

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Speaker 8: energy is created or loss. It's just converted one way

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Speaker 8: or the other. And since momentum is in a way

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Speaker 8: of function of your mass and your energy, then it's

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Speaker 8: just always there. It can't be bled off into another

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Speaker 8: dimension or something as far as I know.

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Speaker 5: Well, I guess the reason that momentum is conserved is

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Speaker 5: because of Newton said so, and Einstein said so, maybe

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Speaker 5: both of them.

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Speaker 9: I think all that we've been able to observe so

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Speaker 9: far indicates that momentum is conserved in terms of interactions

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Speaker 9: that we've measured those kinds of things. In terms of

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Speaker 9: a conceptual reason behind why momentum should be something that

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Speaker 9: is conserved, I don't know if there's any good explanation

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Speaker 9: for that.

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Speaker 10: Get about a collision right now between let's say two objects,

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Speaker 10: and why it's so. An energy to another object is

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Speaker 10: transferred to data one. So it's concerned because nothing and

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Speaker 10: the energy it's constant, nothing, it's wasted. Everything gets transferred

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Speaker 10: or transformed.

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Speaker 11: Momentum may be described as mass time's velocity. It may

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Speaker 11: further be described as the second law of thermodynamics, or

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Speaker 11: is it Newton's second law of motion? I forget College

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Speaker 11: was a long time ago. However, the question of why

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Speaker 11: is it preserved, I think is something nobody knows yet.

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Speaker 12: I think it just all has to do with the

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Speaker 12: way energy is transferred. So if I were to be

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Speaker 12: pushing something, for me to be pushing that thing so

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Speaker 12: it moves, I need to be adding energy to the system.

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Speaker 12: I need to be pushing it and adding a force

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Speaker 12: and therefore transferring energy from me into it. But just

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Speaker 12: due to the way Newton's laws work, it too has

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Speaker 12: to be pushing back on me.

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Speaker 4: All right, what do you think of the answers?

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Speaker 1: I like the because Newton said so in Einstein agreed.

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Speaker 1: They're like a council of physics and they decide what's true.

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Speaker 4: Oh, maybe my kids should try that the next time.

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Speaker 4: Their parents don't know. But Newton said so, and Einstein.

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Speaker 1: Agreed that you should go to bed.

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Speaker 4: Two out of two seminal physicists agreed.

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Speaker 1: As if physicists have any voice in anything relevant at all,

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Speaker 1: You know.

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Speaker 4: Do you think physics in general is sort of done

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Speaker 4: by by polling and kind of right, like, there is

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Speaker 4: a little bit of sense that in science it's about

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Speaker 4: what the majority thinks is true.

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

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

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Speaker 1: in some cases, like one seminal physicist can persuade a

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

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Speaker 1: thought this, or Murray Gellman said that, or Fineman put

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

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Speaker 4: But I guess in general, none of the answers questioned

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Speaker 4: that idea that momentum is conserved, right, Nobody said, like,

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Speaker 4: who said momentum is conserved?

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Speaker 1: Yeah, though some people thought that we don't know the answer,

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Speaker 1: that we have no idea why momentum is conserved, sort

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Speaker 1: of like why is the speed of light what it is?

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Speaker 1: We don't know. We just measure it. Some people put

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Speaker 1: it in that category.

440
00:21:31,880 --> 00:21:34,040
Speaker 4: I think they've been listening to our podcast and reading

441
00:21:34,040 --> 00:21:35,800
Speaker 4: our books too much.

442
00:21:36,119 --> 00:21:36,320
Speaker 1: You know.

443
00:21:36,359 --> 00:21:38,440
Speaker 4: Sometimes the answer is we have no idea.

444
00:21:38,600 --> 00:21:40,960
Speaker 1: You think they've become persuaded that physics actually doesn't really

445
00:21:41,040 --> 00:21:44,680
Speaker 1: know very much about the universe. Oh, mission accomplished.

446
00:21:45,359 --> 00:21:47,000
Speaker 4: Uh oh, we spoiled the ice cream.

447
00:21:48,560 --> 00:21:51,080
Speaker 1: It just means there's more ice cream of discovery left

448
00:21:51,119 --> 00:21:52,080
Speaker 1: to eat for everybody.

449
00:21:52,320 --> 00:21:55,480
Speaker 4: Well, let's just recap it for people. So, momentum conservation

450
00:21:55,600 --> 00:21:59,080
Speaker 4: means that momentum is conserved. Like momentum is defined as

451
00:21:59,160 --> 00:22:01,160
Speaker 4: what mass time your velocity.

452
00:22:01,440 --> 00:22:04,919
Speaker 1: Yeah, so momentum for slow moving objects is just mass

453
00:22:04,920 --> 00:22:08,960
Speaker 1: times velocity. And when we say momentum is conserved, we

454
00:22:09,080 --> 00:22:11,560
Speaker 1: mean that if you have the menum of a bunch

455
00:22:11,560 --> 00:22:13,720
Speaker 1: of stuff and then you let it do its thing,

456
00:22:13,840 --> 00:22:16,760
Speaker 1: follow the laws of physics, bang into each other, bounce

457
00:22:16,800 --> 00:22:19,400
Speaker 1: off of stuff, or just float through space, and then

458
00:22:19,480 --> 00:22:22,399
Speaker 1: later on you add up the momentum again you should

459
00:22:22,440 --> 00:22:26,080
Speaker 1: get the same number. And interestingly, momentum is actually three

460
00:22:26,160 --> 00:22:29,240
Speaker 1: different quantities. It's momentum and x momentum and hy momentum

461
00:22:29,280 --> 00:22:31,600
Speaker 1: and z. Because we live in three dimensional space, and

462
00:22:31,640 --> 00:22:35,840
Speaker 1: those are all independently conserved, So momentum conservation is kind

463
00:22:35,880 --> 00:22:37,280
Speaker 1: of three laws in one.

464
00:22:37,680 --> 00:22:38,840
Speaker 4: Ooh, it's the deal.

465
00:22:39,280 --> 00:22:41,680
Speaker 1: Yeah, exactly for those of you who do like classical

466
00:22:41,720 --> 00:22:44,200
Speaker 1: mechanics or freshman physics, you know, that makes it very

467
00:22:44,240 --> 00:22:47,119
Speaker 1: powerful because you get three equations to constrain your answer

468
00:22:47,359 --> 00:22:49,480
Speaker 1: rather than just one from conservation of energy.

469
00:22:49,840 --> 00:22:52,240
Speaker 4: Right, But you were saying that it's only for slow

470
00:22:52,280 --> 00:22:54,680
Speaker 4: moving things, like it's different for other things.

471
00:22:54,840 --> 00:22:58,119
Speaker 1: Yeah, it turns out in relativity, the definition of momentum

472
00:22:58,200 --> 00:23:02,000
Speaker 1: is different from just mass times velocity. There's this boost

473
00:23:02,040 --> 00:23:05,520
Speaker 1: factor we call it the Gamma factor or the Lorentz factor,

474
00:23:05,880 --> 00:23:09,240
Speaker 1: which is one for slow moving objects and approaches infinity

475
00:23:09,240 --> 00:23:11,760
Speaker 1: as things get towards the speed of light. So the

476
00:23:11,800 --> 00:23:16,239
Speaker 1: real equation for momentum is mass times velocity times this

477
00:23:16,320 --> 00:23:19,119
Speaker 1: gamma factor. We never noticed because the Gamma factor is

478
00:23:19,160 --> 00:23:21,679
Speaker 1: close to one, so you can ignore it for stuff

479
00:23:21,760 --> 00:23:23,520
Speaker 1: that's less than you know, like half the speed of

480
00:23:23,560 --> 00:23:25,399
Speaker 1: light or a third of the speed of light. But

481
00:23:25,440 --> 00:23:28,240
Speaker 1: it becomes important as you get near the speed of light.

482
00:23:28,440 --> 00:23:30,960
Speaker 4: Oh, I see, you have to adjust it because nothing

483
00:23:31,000 --> 00:23:33,040
Speaker 4: can go faster than the speed of light because it

484
00:23:33,480 --> 00:23:35,560
Speaker 4: has to have a limit, like you can't have momentum

485
00:23:35,560 --> 00:23:37,080
Speaker 4: that's greater than the speed of light.

486
00:23:37,160 --> 00:23:39,359
Speaker 1: You have to adjust it in order to get conservation momentum, Like,

487
00:23:39,359 --> 00:23:43,040
Speaker 1: the quantity that is conserved is not mass times velocity,

488
00:23:43,040 --> 00:23:46,280
Speaker 1: it's mass times velocity times gamma. And you notice this

489
00:23:46,400 --> 00:23:48,440
Speaker 1: as you get to very high velocities. In order to

490
00:23:48,520 --> 00:23:51,919
Speaker 1: have conservation before and after some interaction, for example, you

491
00:23:51,960 --> 00:23:55,440
Speaker 1: have to use gamma mass velocity, not just mass and velocity.

492
00:23:55,800 --> 00:23:56,200
Speaker 3: And this is.

493
00:23:56,119 --> 00:23:59,720
Speaker 1: Actually the source of a lot of misunderstanding about relativistic physics.

494
00:24:00,000 --> 00:24:03,679
Speaker 1: People used to define gamma times mass as this weird

495
00:24:03,920 --> 00:24:07,639
Speaker 1: relativistic mass and say things like your mask gets really

496
00:24:07,800 --> 00:24:11,280
Speaker 1: large as you go towards high speeds because they wanted

497
00:24:11,280 --> 00:24:15,720
Speaker 1: to redefine momentum to be relativistic mass times velocity. Anyway,

498
00:24:15,720 --> 00:24:17,480
Speaker 1: we're going to do a whole podcast about that question

499
00:24:17,520 --> 00:24:20,520
Speaker 1: about whether your mass actually does get larger as you

500
00:24:20,560 --> 00:24:23,359
Speaker 1: approach the speed of light. Short answer is no, it doesn't.

501
00:24:23,600 --> 00:24:26,359
Speaker 4: Right right, Well, I think at least for slow moving objects,

502
00:24:26,440 --> 00:24:30,400
Speaker 4: it does kind of match what people's intuition is about momentum, right,

503
00:24:30,440 --> 00:24:33,800
Speaker 4: like mass times velocity. If we have something large even

504
00:24:33,800 --> 00:24:36,199
Speaker 4: if it's moving slow, it has a lot of momentum

505
00:24:36,240 --> 00:24:39,440
Speaker 4: and it's hard to stop. But even something is small

506
00:24:39,520 --> 00:24:42,040
Speaker 4: and has a lot of velocity, it's also hard to stop, right,

507
00:24:42,080 --> 00:24:44,720
Speaker 4: Like a bullet is pretty hard to stop if it's

508
00:24:44,760 --> 00:24:47,480
Speaker 4: coming towards you. It's sort of like it's a sense

509
00:24:47,520 --> 00:24:49,000
Speaker 4: of how hard it is to stop.

510
00:24:48,800 --> 00:24:51,600
Speaker 1: In a way. Yeah, and Newton's law force equals mass

511
00:24:51,640 --> 00:24:55,320
Speaker 1: times acceleration says exactly that. Another way to write Newton's

512
00:24:55,359 --> 00:24:58,520
Speaker 1: law instead of mass times acceleration is a change in momentum.

513
00:24:58,640 --> 00:25:01,200
Speaker 1: So Newton's law is forced is the change in momentum.

514
00:25:01,240 --> 00:25:02,920
Speaker 1: If you want to change something's momentum by a lot,

515
00:25:03,000 --> 00:25:04,720
Speaker 1: it takes a big force. You want to change something's

516
00:25:04,760 --> 00:25:07,119
Speaker 1: momentum by a little bit, it takes a smaller force.

517
00:25:07,680 --> 00:25:10,080
Speaker 1: And said another way, something with a lot of momentum

518
00:25:10,119 --> 00:25:12,840
Speaker 1: takes more force to stop. Something without a lot of

519
00:25:12,840 --> 00:25:15,480
Speaker 1: momentum doesn't take much force to stop.

520
00:25:15,440 --> 00:25:17,920
Speaker 4: Right, And the idea that it's conserved means that it

521
00:25:18,080 --> 00:25:20,480
Speaker 4: like it goes somewhere right, or like if I try

522
00:25:20,520 --> 00:25:23,840
Speaker 4: to stop a train and may be able to stop it,

523
00:25:23,880 --> 00:25:26,080
Speaker 4: but that momentum has to go somewhere.

524
00:25:25,720 --> 00:25:28,240
Speaker 1: That's right. If you throw a tennis ball, for example,

525
00:25:28,280 --> 00:25:30,600
Speaker 1: in front of a train, it will push that tennis

526
00:25:30,600 --> 00:25:33,000
Speaker 1: ball really really fast and slow down the train a

527
00:25:33,040 --> 00:25:35,639
Speaker 1: little bit. So the total momentum is the same. The

528
00:25:35,640 --> 00:25:38,399
Speaker 1: momentum can flow, as you say, from one object to another,

529
00:25:38,720 --> 00:25:41,399
Speaker 1: but the total momentum has to stay the same before

530
00:25:41,480 --> 00:25:43,440
Speaker 1: and after every physics process.

531
00:25:43,880 --> 00:25:44,240
Speaker 5: Right.

532
00:25:44,280 --> 00:25:46,439
Speaker 4: And the weird thing is like it's not like somebody

533
00:25:46,520 --> 00:25:50,680
Speaker 4: is like overseeing this transaction, right, Like it just happens.

534
00:25:51,200 --> 00:25:54,440
Speaker 4: Right when things interact somehow, momentum is conserved. But it's

535
00:25:54,440 --> 00:25:57,560
Speaker 4: not like momentum actually flowed from one thing to do

536
00:25:57,640 --> 00:26:01,200
Speaker 4: They just pushed on each other and momentum was conserved.

537
00:26:01,320 --> 00:26:03,800
Speaker 1: Wow, what a touch on like deep questions of philosophy.

538
00:26:03,920 --> 00:26:08,040
Speaker 1: Does the universe like calculate what's happening and follow some laws,

539
00:26:08,119 --> 00:26:11,320
Speaker 1: like it's some big computer following a program or does

540
00:26:11,359 --> 00:26:13,760
Speaker 1: it just happen and we're observing it and trying to

541
00:26:13,800 --> 00:26:16,919
Speaker 1: tell our own mathematical stories about it. We don't really know.

542
00:26:17,560 --> 00:26:19,679
Speaker 1: What we notice is that it does happen, and it

543
00:26:19,720 --> 00:26:23,040
Speaker 1: does tell us something about the nature of the universe. Yeah,

544
00:26:23,040 --> 00:26:26,040
Speaker 1: we don't really know sort of like how it happens.

545
00:26:25,800 --> 00:26:28,320
Speaker 4: All right, well, we know it's conserved momentum, and so

546
00:26:28,480 --> 00:26:31,840
Speaker 4: let's ask the question why it's conserved, and let's get

547
00:26:31,880 --> 00:26:34,240
Speaker 4: into that, and we'll get into the person who actually

548
00:26:34,280 --> 00:26:37,320
Speaker 4: made this big breakthrough. But first let's take a quick break.

549
00:26:42,040 --> 00:26:44,960
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599
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Speaker 1: spoonful of Greek yogurt, you're probably not thinking about the

600
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Speaker 1: environmental impact of each and every bite, But the people

601
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Speaker 1: in the dairy industry are US. Dairy has set themselves

602
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603
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Speaker 1: twenty to fifty. That's why they're working hard every day

604
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605
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606
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Speaker 1: most dairy farms reuse water up to four times. The

607
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608
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609
00:29:48,560 --> 00:29:51,560
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612
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614
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617
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Speaker 4: All right, we're talking about ice cream. It seems daniel

618
00:30:21,840 --> 00:30:24,920
Speaker 4: a lot are you? Are you hungry dating some dessert

619
00:30:25,000 --> 00:30:25,360
Speaker 4: right now?

620
00:30:26,720 --> 00:30:29,400
Speaker 1: That's for two reasons. One is because we record this

621
00:30:29,440 --> 00:30:32,440
Speaker 1: podcast around lunchtime, and the other reason is that today

622
00:30:32,640 --> 00:30:35,880
Speaker 1: is the birthday of the person who solved this riddle

623
00:30:36,080 --> 00:30:39,080
Speaker 1: and made one of the most important contributions in physics.

624
00:30:39,280 --> 00:30:39,600
Speaker 13: Mmmm.

625
00:30:39,800 --> 00:30:43,440
Speaker 4: That's right. Yeah, the person who discovered the basically the

626
00:30:43,560 --> 00:30:46,800
Speaker 4: answer to the question that we're asking today, why is

627
00:30:46,880 --> 00:30:50,560
Speaker 4: momentum conserved? So we talked about why that momentum is conserved,

628
00:30:50,560 --> 00:30:53,960
Speaker 4: what momentum is, and it just seems to be conserved

629
00:30:53,960 --> 00:30:57,000
Speaker 4: in the universe. And so Daniel, I guess what's the

630
00:30:57,040 --> 00:31:00,040
Speaker 4: answer why is momentum conserved? It has something to do

631
00:31:00,120 --> 00:31:01,400
Speaker 4: with symmetries.

632
00:31:00,920 --> 00:31:04,120
Speaker 1: That's right. So I mean that they're a mathematician who

633
00:31:04,200 --> 00:31:07,000
Speaker 1: just dabbled in physics about one hundred years ago. She

634
00:31:07,000 --> 00:31:10,040
Speaker 1: turns one hundred and forty today, the day we're recording

635
00:31:10,080 --> 00:31:13,120
Speaker 1: this podcast. She discovered that there's a really deep connection

636
00:31:13,200 --> 00:31:17,719
Speaker 1: between these conservation laws and symmetries of the universe. So

637
00:31:17,880 --> 00:31:21,040
Speaker 1: patterns that we see in the universe are connected to

638
00:31:21,080 --> 00:31:24,320
Speaker 1: these symmetries. So what do we mean by symmetries. This

639
00:31:24,400 --> 00:31:26,720
Speaker 1: is a case where we're using the totally normal definition

640
00:31:26,760 --> 00:31:28,520
Speaker 1: of a symmetry. We don't have it like imbuted with

641
00:31:28,560 --> 00:31:31,760
Speaker 1: any special confusing meaning. It just means that like you

642
00:31:31,960 --> 00:31:35,080
Speaker 1: change something and there's no impact, Like you could take

643
00:31:35,080 --> 00:31:38,400
Speaker 1: a ball and rotate it and doesn't change the ball

644
00:31:38,440 --> 00:31:40,520
Speaker 1: at all, It still behaves the same way, it still

645
00:31:40,560 --> 00:31:43,320
Speaker 1: looks the same way. It's an example of a symmetry.

646
00:31:43,800 --> 00:31:45,680
Speaker 1: Or you can take a road which is a straight

647
00:31:45,720 --> 00:31:48,320
Speaker 1: line and shift it by one hundred meters and if

648
00:31:48,320 --> 00:31:50,240
Speaker 1: it's a straight line, it doesn't change it at all,

649
00:31:50,360 --> 00:31:53,800
Speaker 1: or it's the same road. These kinds of symmetries turn

650
00:31:53,840 --> 00:31:56,400
Speaker 1: out to be really important in the nature of the

651
00:31:56,480 --> 00:31:59,280
Speaker 1: universe and are connected to these conservation laws.

652
00:31:59,080 --> 00:32:01,760
Speaker 4: Right, right, But let's maybe take a step back, right

653
00:32:01,840 --> 00:32:05,000
Speaker 4: because I think the history of this is that we

654
00:32:05,120 --> 00:32:07,960
Speaker 4: knew that momentum was conserved, and at the same time

655
00:32:08,080 --> 00:32:11,480
Speaker 4: we're discovering something about the universe that it is sort

656
00:32:11,480 --> 00:32:15,000
Speaker 4: of symmetric in these weird and interesting ways. And so

657
00:32:15,240 --> 00:32:18,080
Speaker 4: maybe before we make that connection, maybe step us through

658
00:32:18,160 --> 00:32:20,920
Speaker 4: like what exactly is a symmetry in the universe.

659
00:32:21,080 --> 00:32:23,040
Speaker 1: So there are lots of cool symmetries in the universe.

660
00:32:23,200 --> 00:32:25,760
Speaker 1: One of them is that space seems to be the

661
00:32:25,800 --> 00:32:30,360
Speaker 1: same everywhere, Like the nature of this universe we find

662
00:32:30,400 --> 00:32:33,880
Speaker 1: ourselves in doesn't change based on where you are. You

663
00:32:33,920 --> 00:32:36,920
Speaker 1: do an experiment to measure something fundamental about the universe,

664
00:32:37,200 --> 00:32:40,040
Speaker 1: it doesn't matter where in the universe you measure it.

665
00:32:40,600 --> 00:32:43,680
Speaker 1: Or said another way, if you shifted the whole universe

666
00:32:43,760 --> 00:32:47,480
Speaker 1: over by ten meters, no one would be able to notice, right,

667
00:32:47,480 --> 00:32:49,640
Speaker 1: the universe is the same, no matter sort of where

668
00:32:49,680 --> 00:32:51,160
Speaker 1: it is right right.

669
00:32:51,240 --> 00:32:53,560
Speaker 4: Yeah, that's a pretty cool idea. But I think maybe

670
00:32:53,560 --> 00:32:56,400
Speaker 4: I wonder what confuses people a lot sometimes is that

671
00:32:56,440 --> 00:32:59,160
Speaker 4: the name symmetry is a little bit different than what

672
00:32:59,200 --> 00:33:01,600
Speaker 4: you just described. Like to I think the most people,

673
00:33:01,600 --> 00:33:04,320
Speaker 4: the word symmetry, it kind of means like it's the

674
00:33:04,360 --> 00:33:07,960
Speaker 4: mirror opposite, Or like if I have a pattern and

675
00:33:07,960 --> 00:33:09,960
Speaker 4: a piece of paper, and then I have the mirror

676
00:33:10,520 --> 00:33:12,520
Speaker 4: image of the pattern right next to it, then we

677
00:33:12,520 --> 00:33:14,680
Speaker 4: would say the whole drawing is sort of symmetric because

678
00:33:14,720 --> 00:33:16,720
Speaker 4: it's the same left or right right.

679
00:33:17,240 --> 00:33:20,600
Speaker 1: And that's an example of what we consider a discrete symmetry. Right,

680
00:33:20,640 --> 00:33:23,040
Speaker 1: you can like flip the whole image and it looks

681
00:33:23,080 --> 00:33:26,160
Speaker 1: the same. Continuous symmetry is like take a piece of

682
00:33:26,160 --> 00:33:28,920
Speaker 1: paper and draw a circle. That circle is the same

683
00:33:29,000 --> 00:33:31,600
Speaker 1: no matter how much you rotated, and there's an infinite

684
00:33:31,680 --> 00:33:34,240
Speaker 1: number of ways you could rotate it and not change

685
00:33:34,240 --> 00:33:36,760
Speaker 1: the circle. Right, Or if you have an infinite sheet

686
00:33:36,800 --> 00:33:39,360
Speaker 1: of paper and you drew a picture, it wouldn't really

687
00:33:39,360 --> 00:33:41,360
Speaker 1: matter where you drew that picture, you could draw it

688
00:33:41,440 --> 00:33:43,440
Speaker 1: here or draw it there. It would be the same

689
00:33:43,560 --> 00:33:44,920
Speaker 1: because the paper is infinite.

690
00:33:45,240 --> 00:33:47,400
Speaker 4: Right. But I guess maybe I wonder like a more

691
00:33:47,440 --> 00:33:50,600
Speaker 4: a better word would have been, like, you know, consistency

692
00:33:50,720 --> 00:33:54,520
Speaker 4: or constancy of things, right, because I think the reason

693
00:33:54,520 --> 00:33:57,120
Speaker 4: you guys use symmetry. The word symmetry is that it

694
00:33:57,120 --> 00:34:00,440
Speaker 4: has to do with the equations of motion of the universe,

695
00:34:00,520 --> 00:34:03,680
Speaker 4: right Like, if you apply like an a mirror transformation

696
00:34:03,840 --> 00:34:05,640
Speaker 4: or some kind of transformation to the equations, then it

697
00:34:05,680 --> 00:34:06,600
Speaker 4: should stay the same.

698
00:34:06,720 --> 00:34:10,640
Speaker 1: Yes, So to totally generalize the word symmetry, what mathematicians

699
00:34:10,680 --> 00:34:12,359
Speaker 1: mean by it is that you make some kind of

700
00:34:12,520 --> 00:34:15,880
Speaker 1: transformation to the universe and then that doesn't change whatever

701
00:34:15,880 --> 00:34:17,520
Speaker 1: it is you're interested in. And so, in the case

702
00:34:17,560 --> 00:34:20,680
Speaker 1: of physics, we make some sort of transformation to the universe,

703
00:34:20,760 --> 00:34:22,960
Speaker 1: like we shift it to the left one hundred feet,

704
00:34:23,040 --> 00:34:25,279
Speaker 1: or we rotate it around some angle, and then the

705
00:34:25,320 --> 00:34:28,239
Speaker 1: thing we're interested in are the laws of physics, the

706
00:34:28,239 --> 00:34:30,600
Speaker 1: same as you said, like the equations of motion. Would

707
00:34:30,640 --> 00:34:33,520
Speaker 1: you predict that horages apple flies through the air and

708
00:34:33,600 --> 00:34:35,759
Speaker 1: lands in his hand the same way if you put

709
00:34:35,800 --> 00:34:38,279
Speaker 1: your axis over here, or if you said, you know

710
00:34:38,440 --> 00:34:41,000
Speaker 1: zero is over there, or if you did the problem

711
00:34:41,080 --> 00:34:43,600
Speaker 1: upside down, would you get the same answer. If so,

712
00:34:43,800 --> 00:34:45,640
Speaker 1: then there's a symmetry to the problem.

713
00:34:45,920 --> 00:34:47,799
Speaker 4: Or even like if I move the Earth a few

714
00:34:47,880 --> 00:34:50,600
Speaker 4: light years to the right, it should still be the same, right.

715
00:34:50,719 --> 00:34:53,200
Speaker 1: Yeah, if you knew the whole universe right a few

716
00:34:53,239 --> 00:34:55,640
Speaker 1: light years to the right, nobody could do an experiment

717
00:34:55,760 --> 00:34:58,680
Speaker 1: to determine that that's the case, that that's happened, because

718
00:34:58,680 --> 00:35:01,479
Speaker 1: no place in space is different, right, The rules should

719
00:35:01,520 --> 00:35:02,560
Speaker 1: be the same everywhere.

720
00:35:02,719 --> 00:35:02,879
Speaker 13: Right.

721
00:35:02,920 --> 00:35:05,160
Speaker 4: So when you hear the word symmetry in physics, really

722
00:35:05,200 --> 00:35:07,200
Speaker 4: maybe in your head you should be thinking like a

723
00:35:07,360 --> 00:35:10,840
Speaker 4: constancy in the universe, or like an invariability, or something

724
00:35:10,840 --> 00:35:13,200
Speaker 4: that doesn't change when you move it or rotate it

725
00:35:13,320 --> 00:35:13,839
Speaker 4: or flip it.

726
00:35:13,920 --> 00:35:16,680
Speaker 1: Right, right, I like that there's no word in physics

727
00:35:16,719 --> 00:35:20,239
Speaker 1: that you're not up for redefining and improving. You know,

728
00:35:20,320 --> 00:35:22,920
Speaker 1: science is a constant project, and so we're always striving

729
00:35:22,920 --> 00:35:24,960
Speaker 1: to improve. But there is a bit of confusion there

730
00:35:25,000 --> 00:35:28,359
Speaker 1: because if you call it like an invariability, it comes

731
00:35:28,360 --> 00:35:31,439
Speaker 1: close to another word we use, which is invariance, which

732
00:35:31,480 --> 00:35:35,560
Speaker 1: actually means something quite different. Right. Invariance means no matter

733
00:35:35,640 --> 00:35:38,719
Speaker 1: who's measuring it, you always get the same answer. An

734
00:35:38,800 --> 00:35:41,080
Speaker 1: example of an invariant is like the speed of light.

735
00:35:41,320 --> 00:35:44,000
Speaker 1: Everybody measures the speed of light to be the same quantity,

736
00:35:44,200 --> 00:35:46,680
Speaker 1: no matter where you are or how fast you're traveling.

737
00:35:46,840 --> 00:35:51,560
Speaker 1: Momentum is conserved, we say, but it's not invariant because

738
00:35:51,600 --> 00:35:55,200
Speaker 1: for example, you are standing still, you measure your velocity

739
00:35:55,280 --> 00:35:59,080
Speaker 1: be zero. I'm moving past you. I measure your velocity

740
00:35:59,120 --> 00:36:00,799
Speaker 1: to be non zero. So if I measure you to

741
00:36:00,840 --> 00:36:04,640
Speaker 1: have momentum, you measure yourself to have no momentum. Momentum

742
00:36:04,680 --> 00:36:07,960
Speaker 1: is not the same for all observers, though it's always conserved.

743
00:36:08,120 --> 00:36:10,480
Speaker 1: I will see your momentum is conserved. You will see

744
00:36:10,480 --> 00:36:13,640
Speaker 1: your momentum is conserved, but it's not invariant. So invariant

745
00:36:13,680 --> 00:36:15,240
Speaker 1: means something different in physics.

746
00:36:15,480 --> 00:36:17,480
Speaker 4: Yeah, I mean, I'm not saying you should not use

747
00:36:17,480 --> 00:36:19,680
Speaker 4: the word symmetry. I'm just saying that it might be

748
00:36:19,760 --> 00:36:21,839
Speaker 4: helpful for people to just kind of understand what's going

749
00:36:21,880 --> 00:36:23,680
Speaker 4: on if if when they hear the word symmetry, they

750
00:36:23,680 --> 00:36:26,200
Speaker 4: should sort of be thinking more about like that things

751
00:36:26,239 --> 00:36:28,640
Speaker 4: are the same no matter if you move them over here,

752
00:36:28,760 --> 00:36:31,200
Speaker 4: or you do you throw the apple over here, over there,

753
00:36:31,280 --> 00:36:34,160
Speaker 4: or upside down, or if you rotate the whole universe

754
00:36:34,200 --> 00:36:36,560
Speaker 4: ninety degrees, it should still fall down back to.

755
00:36:36,560 --> 00:36:39,920
Speaker 1: My head exactly. And those are a few examples of symmetries,

756
00:36:39,960 --> 00:36:42,359
Speaker 1: right Like, if you shift the whole universe over, your

757
00:36:42,400 --> 00:36:45,080
Speaker 1: experiment should work the same way, you know, and that's

758
00:36:45,160 --> 00:36:48,400
Speaker 1: true if space is not different in different places in

759
00:36:48,440 --> 00:36:50,480
Speaker 1: the universe. If it were different, right, if space was

760
00:36:50,560 --> 00:36:52,880
Speaker 1: like different over there and over here, if you have

761
00:36:52,960 --> 00:36:55,040
Speaker 1: different laws of physics over there and over here, you'll

762
00:36:55,040 --> 00:36:57,400
Speaker 1: be able to tell sort of like where the universe

763
00:36:57,480 --> 00:37:00,880
Speaker 1: is relative to those like different parts of space, that

764
00:37:00,880 --> 00:37:04,319
Speaker 1: would be fascinating. But it seems to us so far

765
00:37:04,680 --> 00:37:06,920
Speaker 1: like space is the same everywhere. And that's a pretty

766
00:37:06,960 --> 00:37:10,080
Speaker 1: deep symmetry, right It tells you something about the nature

767
00:37:10,120 --> 00:37:12,680
Speaker 1: of the universe itself, that the experiments are the same

768
00:37:12,760 --> 00:37:15,200
Speaker 1: everywhere you go. And the same seems to be true

769
00:37:15,200 --> 00:37:17,880
Speaker 1: for rotating, right, Like, there's no up or down in

770
00:37:17,920 --> 00:37:20,840
Speaker 1: the universe. You could rotate the whole universe and you

771
00:37:20,880 --> 00:37:24,080
Speaker 1: wouldn't be able to notice that it had been rotated. WHOA,

772
00:37:24,160 --> 00:37:25,960
Speaker 1: in the sense that you mean that, you know, the

773
00:37:26,120 --> 00:37:28,880
Speaker 1: laws of physics don't change and your experiments get the

774
00:37:28,880 --> 00:37:30,600
Speaker 1: same results, right.

775
00:37:30,360 --> 00:37:33,400
Speaker 4: But I wonder if that sort of dependent on space time, right, Like,

776
00:37:33,719 --> 00:37:36,359
Speaker 4: do you depend does that depend on flat space time

777
00:37:36,560 --> 00:37:38,359
Speaker 4: or you know, would that be still be the same

778
00:37:38,400 --> 00:37:41,320
Speaker 4: around close to a black hole or something where space

779
00:37:41,400 --> 00:37:43,360
Speaker 4: time is sort of bent or distorted.

780
00:37:43,480 --> 00:37:46,000
Speaker 1: Yeah, it's a good question, you know. So you might ask, like,

781
00:37:46,120 --> 00:37:49,280
Speaker 1: I do an experiment here, and I notice my apple falls.

782
00:37:49,280 --> 00:37:52,200
Speaker 1: What if I move Jorge near a black hole? Wouldn't

783
00:37:52,200 --> 00:37:53,799
Speaker 1: this apple fall differently? Yeah?

784
00:37:53,840 --> 00:37:54,560
Speaker 4: Wouldn't you like that?

785
00:37:54,680 --> 00:37:54,839
Speaker 12: Right?

786
00:37:56,560 --> 00:37:56,600
Speaker 6: No?

787
00:37:56,680 --> 00:37:58,120
Speaker 1: Then who would eat all the ice cream? You know,

788
00:37:58,120 --> 00:37:59,399
Speaker 1: I need somebody else to eat it so I don't

789
00:37:59,440 --> 00:38:01,760
Speaker 1: gain too much and become a black hole myself.

790
00:38:01,840 --> 00:38:03,479
Speaker 4: It would all fall into the black hole.

791
00:38:04,080 --> 00:38:05,480
Speaker 1: All right, So we can throw you into a black

792
00:38:05,520 --> 00:38:07,840
Speaker 1: hole as long as we send a continuous stream of

793
00:38:07,840 --> 00:38:09,080
Speaker 1: ice cream scoops as well.

794
00:38:09,880 --> 00:38:11,400
Speaker 4: Let's keep it as a thought experiment.

795
00:38:11,520 --> 00:38:14,480
Speaker 1: No, that's a good question, And you know, essentially the

796
00:38:14,520 --> 00:38:16,600
Speaker 1: issue there is that the black hole is sort of

797
00:38:16,680 --> 00:38:22,440
Speaker 1: part of your experiment, and so underlying space itself isn't change.

798
00:38:22,520 --> 00:38:25,200
Speaker 1: But the sort of laboratory of the experiment you're doing

799
00:38:26,040 --> 00:38:28,719
Speaker 1: includes a black hole in one scenario and doesn't in

800
00:38:28,760 --> 00:38:31,040
Speaker 1: the other scenario. That's why you get different outcomes because

801
00:38:31,040 --> 00:38:33,040
Speaker 1: you're sort of doing a different experiment.

802
00:38:33,640 --> 00:38:36,640
Speaker 4: I see. But so the theory still works no matter

803
00:38:36,719 --> 00:38:38,239
Speaker 4: what's happening with space time.

804
00:38:38,400 --> 00:38:40,719
Speaker 1: Yeah, although if it's not true that space is the

805
00:38:40,760 --> 00:38:44,120
Speaker 1: same everywhere, then the theory doesn't hold. You know, for example,

806
00:38:44,520 --> 00:38:48,560
Speaker 1: what if space was not like continuous and infinite. What

807
00:38:48,680 --> 00:38:51,080
Speaker 1: if it had a boundary, as you've mentioned on several podcasts,

808
00:38:51,200 --> 00:38:53,319
Speaker 1: there was like an edge to it. Then you know,

809
00:38:53,400 --> 00:38:55,520
Speaker 1: the laws of physics would be different at the edge

810
00:38:55,560 --> 00:38:57,879
Speaker 1: because space would be different at the edge. Different things

811
00:38:57,920 --> 00:39:00,000
Speaker 1: would have to happen. So maybe the laws of physics

812
00:39:00,080 --> 00:39:02,759
Speaker 1: would be different at the edge. We don't actually know, right,

813
00:39:02,880 --> 00:39:04,880
Speaker 1: is there a boundary to space? And does it go

814
00:39:04,960 --> 00:39:07,640
Speaker 1: on forever? Another possible way that it could not be

815
00:39:07,719 --> 00:39:11,359
Speaker 1: true is like if space is not continuous, if it's

816
00:39:11,480 --> 00:39:14,400
Speaker 1: like pixelized or like a crystal, then it might not

817
00:39:14,440 --> 00:39:17,279
Speaker 1: have a continuous symmetry. It might be like location is

818
00:39:17,280 --> 00:39:19,839
Speaker 1: a symmetry up to a certain value. You know, if

819
00:39:19,840 --> 00:39:22,480
Speaker 1: you take like certain steps in space, you get the

820
00:39:22,480 --> 00:39:24,280
Speaker 1: same answer, But if you take like a half step,

821
00:39:24,320 --> 00:39:26,279
Speaker 1: maybe you get a different answer because you're sort of

822
00:39:26,280 --> 00:39:28,200
Speaker 1: like caught between two parts of the crystal.

823
00:39:28,480 --> 00:39:31,520
Speaker 4: Yeah, if it's quantum, then it maybe wouldn't be a

824
00:39:31,560 --> 00:39:34,520
Speaker 4: symmetric but I guess to sort of generalize it though,

825
00:39:34,560 --> 00:39:38,759
Speaker 4: as far as we know, it is symmetric the laws

826
00:39:38,760 --> 00:39:41,200
Speaker 4: of physics throughout all of space time, as far as

827
00:39:41,200 --> 00:39:41,400
Speaker 4: we know.

828
00:39:41,640 --> 00:39:44,840
Speaker 1: As far as we know, it's symmetric to translations, shifts,

829
00:39:44,920 --> 00:39:49,279
Speaker 1: and symmetric to rotations. And with a couple of exceptions,

830
00:39:49,320 --> 00:39:52,759
Speaker 1: it is symmetric to shifts in time. Like if you

831
00:39:52,800 --> 00:39:55,520
Speaker 1: do an experiment today, you experiment in one hundred years,

832
00:39:55,920 --> 00:39:58,080
Speaker 1: then you should get the same answer because the laws

833
00:39:58,080 --> 00:40:00,719
Speaker 1: of physics, we think don't change in t time. Those

834
00:40:00,719 --> 00:40:04,360
Speaker 1: are three really basic symmetries that we've discovered in physics.

835
00:40:04,239 --> 00:40:07,279
Speaker 4: Right, translation, rotation, and time. And that even applies to

836
00:40:07,400 --> 00:40:09,640
Speaker 4: like moving backwards in time.

837
00:40:09,719 --> 00:40:11,680
Speaker 1: Right it does. Yeah, in the sense that if you're

838
00:40:11,680 --> 00:40:14,480
Speaker 1: comparing two experiments done at two different points in time,

839
00:40:14,560 --> 00:40:16,279
Speaker 1: one of them could be further back. But I guess

840
00:40:16,320 --> 00:40:18,799
Speaker 1: always one of them is further back. Right, It's not

841
00:40:18,880 --> 00:40:21,080
Speaker 1: about time travel necessarily.

842
00:40:20,840 --> 00:40:22,799
Speaker 4: All right, Well, so that's the idea of symmetry in

843
00:40:22,840 --> 00:40:25,840
Speaker 4: the universe. We noticed that the equations of the universe

844
00:40:25,880 --> 00:40:28,560
Speaker 4: have these symmetries in them, but I guess we didn't

845
00:40:28,600 --> 00:40:31,160
Speaker 4: know that they were connected to the idea of conservation

846
00:40:31,200 --> 00:40:33,759
Speaker 4: of momentum, right, mm hmmm, that's right, all right. So

847
00:40:33,760 --> 00:40:37,719
Speaker 4: those are kind of like the three main symmetries that

848
00:40:37,800 --> 00:40:39,920
Speaker 4: we've noticed about the equations of the universe, and those

849
00:40:39,920 --> 00:40:42,120
Speaker 4: are kind of like the more intuitive one, but there

850
00:40:42,120 --> 00:40:45,279
Speaker 4: are sort of deeper also, symmetries kind of in the

851
00:40:45,320 --> 00:40:46,200
Speaker 4: quantum level. Right.

852
00:40:46,440 --> 00:40:49,320
Speaker 1: Yeah, We've talked on the podcast a few times about

853
00:40:49,360 --> 00:40:53,040
Speaker 1: other kinds of symmetries we've noticed in the universe. And

854
00:40:53,080 --> 00:40:55,600
Speaker 1: these are not things that are easy to grasp in

855
00:40:55,600 --> 00:40:57,759
Speaker 1: your mind because they're not things you see. But these

856
00:40:57,840 --> 00:41:01,680
Speaker 1: are like properties of quantum fields. And it turns out

857
00:41:01,719 --> 00:41:05,440
Speaker 1: that you can like rotate different quantum fields sort of

858
00:41:05,480 --> 00:41:09,319
Speaker 1: into each other. You can like swap different colors of

859
00:41:09,440 --> 00:41:12,799
Speaker 1: quarks turn red to green, and green to blue and

860
00:41:12,840 --> 00:41:16,239
Speaker 1: blue to red. Nothing changes in the universe. Right, So

861
00:41:16,280 --> 00:41:18,600
Speaker 1: we've noticed these kinds of symmetries on the sort of

862
00:41:18,600 --> 00:41:23,160
Speaker 1: like quantum level that are very similar to these symmetries mathematically,

863
00:41:23,239 --> 00:41:26,680
Speaker 1: like they involve rotations, but not in a physical rotation,

864
00:41:26,719 --> 00:41:28,640
Speaker 1: you know, like spinning anything. You're just sort of like

865
00:41:28,719 --> 00:41:32,120
Speaker 1: changing labels on quantum stuff. But these are just as

866
00:41:32,200 --> 00:41:36,000
Speaker 1: important and reveal also something really deeply true about the universe.

867
00:41:36,040 --> 00:41:38,640
Speaker 1: And we wouldn't have discovered the Higgs boson if we

868
00:41:38,680 --> 00:41:40,000
Speaker 1: hadn't noticed these symmetries.

869
00:41:40,120 --> 00:41:43,319
Speaker 4: And again, these are like symmetries or kind of invariant

870
00:41:43,360 --> 00:41:45,959
Speaker 4: things you can do to the equations that you're like, hey, wow,

871
00:41:46,040 --> 00:41:49,879
Speaker 4: that's something strange about the equations. They're symmetric. They work

872
00:41:50,200 --> 00:41:51,319
Speaker 4: no matter what do you do to it.

873
00:41:51,520 --> 00:41:54,680
Speaker 1: Yeah, it just to matter in these cases which gauge

874
00:41:54,760 --> 00:41:57,520
Speaker 1: you choose. For those of you who know like electrodynamics,

875
00:41:57,760 --> 00:41:59,919
Speaker 1: you know that there's sort of like an overall gay

876
00:42:00,200 --> 00:42:03,280
Speaker 1: you can choose in electrodynamics and doesn't change the answers

877
00:42:03,280 --> 00:42:05,880
Speaker 1: at all, just like an arbitrary choice, just sort of

878
00:42:05,920 --> 00:42:08,560
Speaker 1: like where you choose your potential energy to be zero

879
00:42:08,920 --> 00:42:11,799
Speaker 1: in classical mechanics problems. It doesn't change the answer. It's

880
00:42:11,800 --> 00:42:13,960
Speaker 1: just a choice. So there's a symmetry there to the problem.

881
00:42:14,040 --> 00:42:16,440
Speaker 1: You can change these things and nothing changes in how

882
00:42:16,480 --> 00:42:18,759
Speaker 1: you predict the laws of physics. And that's in the

883
00:42:18,840 --> 00:42:21,319
Speaker 1: same sense you can like change these things and how

884
00:42:21,360 --> 00:42:24,160
Speaker 1: we describe these quantum fields and doesn't make any difference

885
00:42:24,200 --> 00:42:27,440
Speaker 1: for our predictions or for how particles should interact with

886
00:42:27,520 --> 00:42:28,719
Speaker 1: each other, right, right, And.

887
00:42:28,760 --> 00:42:30,600
Speaker 4: I think we had a whole podcast about this about

888
00:42:30,640 --> 00:42:33,120
Speaker 4: this idea that you know, the word gauge here, it's

889
00:42:33,120 --> 00:42:35,239
Speaker 4: sort of related to the idea of measuring something or

890
00:42:35,280 --> 00:42:37,960
Speaker 4: like having a reference you know, length or something.

891
00:42:38,120 --> 00:42:40,759
Speaker 1: Yeah, it actually comes from trains because back in the day,

892
00:42:40,760 --> 00:42:43,440
Speaker 1: people were building railroads all across the United States, and

893
00:42:43,480 --> 00:42:46,640
Speaker 1: they were building them of different gauges, and people thought like, okay,

894
00:42:46,640 --> 00:42:49,240
Speaker 1: it's just sort of an arbitrary choice of train gauge.

895
00:42:49,320 --> 00:42:52,080
Speaker 1: So then when physicists were like making arbitrary choices in

896
00:42:52,120 --> 00:42:54,400
Speaker 1: their theories, they were trying to find a word that

897
00:42:54,520 --> 00:42:57,640
Speaker 1: captured that like sort of sense of arbitrariness, as you say,

898
00:42:57,760 --> 00:42:59,960
Speaker 1: like to set a scale. So they chose the word

899
00:43:00,160 --> 00:43:02,719
Speaker 1: gauge because physicists loved trains. I don't know why, like

900
00:43:02,760 --> 00:43:03,719
Speaker 1: in thought experiments.

901
00:43:03,800 --> 00:43:09,080
Speaker 4: Right, yeah, well it's Europe, it's full trains, right, Yeah.

902
00:43:09,080 --> 00:43:10,680
Speaker 1: I suppose it was before the air of the car

903
00:43:10,840 --> 00:43:11,799
Speaker 1: that these things took over.

904
00:43:11,920 --> 00:43:13,799
Speaker 4: So yeah, yes, that's right. You would just call them

905
00:43:13,880 --> 00:43:19,200
Speaker 4: ubers today or lifts. All right, Well, so that's kind

906
00:43:19,239 --> 00:43:21,160
Speaker 4: of where we were in the history of physics. Like

907
00:43:21,200 --> 00:43:24,040
Speaker 4: we knew that momentum was conserved, like we could see

908
00:43:24,040 --> 00:43:26,880
Speaker 4: it with simple experiments. It seemed to work with Newtonian physics.

909
00:43:26,880 --> 00:43:28,719
Speaker 4: But at the same time, we had these more complex

910
00:43:28,800 --> 00:43:31,120
Speaker 4: equations of the universe and we noticed kind of these

911
00:43:31,160 --> 00:43:35,239
Speaker 4: special symmetries mathematical symmetries about them. But I guess people

912
00:43:35,320 --> 00:43:37,600
Speaker 4: hadn't put the two together right to make the connection.

913
00:43:37,800 --> 00:43:41,200
Speaker 1: That's right. We had noticed these properties of the universe

914
00:43:41,200 --> 00:43:43,480
Speaker 1: that things seemed to be conserved, and we also noticed

915
00:43:43,520 --> 00:43:47,720
Speaker 1: mathematically that there were symmetries to our equations.

916
00:43:47,360 --> 00:43:50,520
Speaker 4: Until we got a very special physicist on the scene.

917
00:43:50,600 --> 00:43:53,120
Speaker 4: And so let's talk about her and how she put

918
00:43:53,160 --> 00:43:55,680
Speaker 4: the two together and answer the question basically, why is

919
00:43:55,719 --> 00:43:58,760
Speaker 4: momentum conserved? But first, let's take another quick break.

920
00:44:03,680 --> 00:44:05,480
Speaker 1: When you pop a piece of cheese into your mouth

921
00:44:05,560 --> 00:44:08,719
Speaker 1: or enjoy a rich spoonful of Greek yogurt, you're probably

922
00:44:08,760 --> 00:44:12,840
Speaker 1: not thinking about the environmental impact of each and every bite,

923
00:44:12,840 --> 00:44:15,440
Speaker 1: But the people in the dairy industry are us. Dairy

924
00:44:15,480 --> 00:44:19,799
Speaker 1: has set themselves some ambitious sustainability goals, including being greenhouse

925
00:44:19,840 --> 00:44:22,399
Speaker 1: gas neutral by twenty to fifty. That's why they're working

926
00:44:22,440 --> 00:44:24,800
Speaker 1: hard every day to find new ways to reduce waste,

927
00:44:24,840 --> 00:44:29,040
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928
00:44:29,120 --> 00:44:32,680
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929
00:44:32,719 --> 00:44:36,120
Speaker 1: The same water cools the milk, cleans equipment, washes the barn,

930
00:44:36,200 --> 00:44:39,920
Speaker 1: and irrigates the crops. How is US dairy tackling greenhouse gases?

931
00:44:39,960 --> 00:44:42,960
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932
00:44:43,000 --> 00:44:46,360
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933
00:44:46,440 --> 00:44:48,680
Speaker 1: electric cars. So the next time you grab a slice

934
00:44:48,680 --> 00:44:50,560
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935
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936
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937
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939
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940
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941
00:45:09,440 --> 00:45:10,239
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942
00:45:10,160 --> 00:45:10,960
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943
00:45:11,160 --> 00:45:14,560
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944
00:45:14,640 --> 00:45:18,040
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945
00:45:17,600 --> 00:45:21,360
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946
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974
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Speaker 4: All right, we're asking the question why is momentum conserved?

975
00:46:58,600 --> 00:47:00,680
Speaker 4: And we know it has something to do with symmetries,

976
00:47:00,719 --> 00:47:03,240
Speaker 4: but we know nobody had put the two into together

977
00:47:03,360 --> 00:47:05,160
Speaker 4: until a physicis name not there?

978
00:47:05,280 --> 00:47:09,040
Speaker 1: That's right. Actually she's a mathematician. AMI knew her, and

979
00:47:09,440 --> 00:47:13,239
Speaker 1: she was an expert in abstract algebra and really kind

980
00:47:13,239 --> 00:47:16,440
Speaker 1: of a genius, and she sort of got pulled into

981
00:47:16,480 --> 00:47:19,360
Speaker 1: a question in physics just very briefly wrote like, you know,

982
00:47:19,400 --> 00:47:21,520
Speaker 1: one paper on it and then moved back to her

983
00:47:21,520 --> 00:47:24,680
Speaker 1: real interest in math. But this one paper is basically

984
00:47:24,719 --> 00:47:28,440
Speaker 1: now the foundations of all of theoretical physics. Her like

985
00:47:28,480 --> 00:47:31,080
Speaker 1: you know, side hustle turned out to be, you know,

986
00:47:31,160 --> 00:47:33,279
Speaker 1: the most important thing anybody's ever done.

987
00:47:33,520 --> 00:47:35,920
Speaker 4: Oh man, does it feel like you know, you guys

988
00:47:35,960 --> 00:47:38,279
Speaker 4: liked the entire field of physics was stuck, and then

989
00:47:38,320 --> 00:47:40,799
Speaker 4: they just like, you know, one mathematician had to take

990
00:47:40,840 --> 00:47:43,319
Speaker 4: like a five minute break from from their important word

991
00:47:43,680 --> 00:47:44,960
Speaker 4: and come and save all of you.

992
00:47:45,640 --> 00:47:45,879
Speaker 7: Yeah.

993
00:47:45,920 --> 00:47:48,239
Speaker 1: And it's even more tragic than that because due to

994
00:47:48,320 --> 00:47:50,200
Speaker 1: the fact that she was a woman, she wasn't even

995
00:47:50,239 --> 00:47:54,080
Speaker 1: really allowed to participate in academia and in research, even

996
00:47:54,120 --> 00:47:56,799
Speaker 1: in mathematics, not necessarily just in physics. And then when

997
00:47:56,840 --> 00:47:59,040
Speaker 1: the history of all this stuff was written, she was

998
00:47:59,120 --> 00:48:02,239
Speaker 1: largely sideline. So people a lot of people have never

999
00:48:02,280 --> 00:48:04,799
Speaker 1: heard of, I mean nuthor, even though she's like more

1000
00:48:04,840 --> 00:48:06,520
Speaker 1: influential than Einstein.

1001
00:48:06,680 --> 00:48:09,920
Speaker 4: WHOA all right, well, maybe take us back. So she

1002
00:48:10,080 --> 00:48:12,319
Speaker 4: was around in the nineteen hundreds, right, she was born

1003
00:48:12,400 --> 00:48:13,920
Speaker 4: before the nineteen hundreds.

1004
00:48:14,120 --> 00:48:16,719
Speaker 1: Yeah, she was born in eighteen eighty two, and you know,

1005
00:48:16,760 --> 00:48:20,319
Speaker 1: the end of that century had like important mathematical work

1006
00:48:20,360 --> 00:48:24,440
Speaker 1: by like Riemont and Minkowski laying really the foundations for

1007
00:48:24,640 --> 00:48:27,919
Speaker 1: relativity that Einstein would later pull together in the early

1008
00:48:28,000 --> 00:48:30,319
Speaker 1: nineteen hundreds and teach us a whole new way to

1009
00:48:30,400 --> 00:48:33,359
Speaker 1: think about space and time. So she was around during

1010
00:48:33,400 --> 00:48:35,960
Speaker 1: a sort of very exciting time when mathematics was really

1011
00:48:36,000 --> 00:48:39,520
Speaker 1: informing physics. And she came from a wealthy family and

1012
00:48:39,840 --> 00:48:42,720
Speaker 1: that had academic background. She's like professors in her family.

1013
00:48:42,960 --> 00:48:45,359
Speaker 1: But because she was a woman, she was not even

1014
00:48:45,400 --> 00:48:49,000
Speaker 1: allowed to enroll in university. Like, it's just not a

1015
00:48:49,000 --> 00:48:51,680
Speaker 1: thing that women could do back then, Right, this is

1016
00:48:51,760 --> 00:48:55,280
Speaker 1: like before Mary Curie became the first woman in France

1017
00:48:55,320 --> 00:48:57,160
Speaker 1: to get a PhD. You know, it's just like not

1018
00:48:57,360 --> 00:49:00,200
Speaker 1: something that women were allowed to do. It's mind boggling now,

1019
00:49:00,640 --> 00:49:02,879
Speaker 1: but it was sort of the way things were back then.

1020
00:49:03,200 --> 00:49:06,520
Speaker 4: Yeah, it's pretty tragic. And she was born in Germany or.

1021
00:49:06,719 --> 00:49:09,520
Speaker 1: Yeah, she's German. She was born in Bavaria, and she

1022
00:49:10,000 --> 00:49:12,959
Speaker 1: wanted to study in Gottingen and they just didn't allow

1023
00:49:13,000 --> 00:49:16,720
Speaker 1: it until nineteen oh three when they finally allowed women

1024
00:49:16,760 --> 00:49:19,480
Speaker 1: to enroll. She'd been sitting in on lectures of course

1025
00:49:19,520 --> 00:49:21,799
Speaker 1: for a while, not officially enrolled, but then she was

1026
00:49:21,840 --> 00:49:24,799
Speaker 1: allowed to enroll, and then in nineteen oh seven she

1027
00:49:25,000 --> 00:49:28,000
Speaker 1: was only the second woman ever to earn a PhD

1028
00:49:28,160 --> 00:49:29,120
Speaker 1: in mathematics.

1029
00:49:29,280 --> 00:49:32,480
Speaker 4: Wow, in the world, right, basically, yeah.

1030
00:49:32,200 --> 00:49:35,000
Speaker 1: In the world, and you know, they're famous folks out there.

1031
00:49:35,160 --> 00:49:38,680
Speaker 1: Hilbert kleinb Minkowski shortsiled. All these folks knew her, and

1032
00:49:38,719 --> 00:49:41,359
Speaker 1: they all knew and said that she was smarter than

1033
00:49:41,440 --> 00:49:41,839
Speaker 1: they were.

1034
00:49:42,160 --> 00:49:45,480
Speaker 4: Wow. And these are like, you know, seminole you know,

1035
00:49:45,520 --> 00:49:46,800
Speaker 4: mathematicians and physics.

1036
00:49:47,000 --> 00:49:50,440
Speaker 1: Yeah. Absolutely, and yet there were a lot of institutional barriers.

1037
00:49:50,640 --> 00:49:53,360
Speaker 1: For eight years after she got her PhD, she was

1038
00:49:53,400 --> 00:49:56,439
Speaker 1: doing teaching and research and she was not being paid.

1039
00:49:56,520 --> 00:49:59,719
Speaker 1: She just sort of like volunteering. Nobody would hire her

1040
00:49:59,800 --> 00:50:01,799
Speaker 1: because because she was a woman, even though she was

1041
00:50:01,840 --> 00:50:05,200
Speaker 1: making important contributions. It's you know, it's really ridiculous.

1042
00:50:05,480 --> 00:50:08,440
Speaker 4: Yeah, that's pretty tragic, pretty crazy. And she actually had

1043
00:50:08,440 --> 00:50:10,839
Speaker 4: to sort of practice physics and teach it for free

1044
00:50:10,920 --> 00:50:12,399
Speaker 4: kind of right, because they wouldn't hire her.

1045
00:50:12,520 --> 00:50:16,360
Speaker 1: Yeah, exactly. Despite her like glowing recommendations from seminal folks

1046
00:50:16,360 --> 00:50:19,520
Speaker 1: in the field, she's rejected from position after position just

1047
00:50:19,560 --> 00:50:22,520
Speaker 1: because she was a woman. Hilbert, who's a famous mathematician,

1048
00:50:22,880 --> 00:50:25,200
Speaker 1: he wanted her to teach because she was also a

1049
00:50:25,239 --> 00:50:27,920
Speaker 1: great teacher, but they refused to give her the position.

1050
00:50:28,040 --> 00:50:30,080
Speaker 1: So what he did was he signed up to teach

1051
00:50:30,080 --> 00:50:32,279
Speaker 1: the class, and then he hired her basically to be

1052
00:50:32,320 --> 00:50:34,759
Speaker 1: his TA and then he just never showed up, so

1053
00:50:34,800 --> 00:50:35,720
Speaker 1: she taught the class.

1054
00:50:35,800 --> 00:50:38,239
Speaker 4: I don't know if that's noble or lazy. I can't

1055
00:50:38,320 --> 00:50:40,279
Speaker 4: touch were both somehow both.

1056
00:50:40,160 --> 00:50:41,600
Speaker 1: I'm not sure, but you know, she came from a

1057
00:50:41,640 --> 00:50:44,440
Speaker 1: wealthy background, so she was able to just keep working

1058
00:50:44,560 --> 00:50:47,320
Speaker 1: even though she didn't have a salary. And after World

1059
00:50:47,360 --> 00:50:50,240
Speaker 1: War One she finally was able to get an academic position,

1060
00:50:50,520 --> 00:50:53,719
Speaker 1: but they wouldn't pay her. They're like finally letting her

1061
00:50:53,760 --> 00:50:55,400
Speaker 1: in the door, but like, yeah, but we're drawing the

1062
00:50:55,400 --> 00:50:58,040
Speaker 1: line that providing you any funding or any money for

1063
00:50:58,160 --> 00:50:58,680
Speaker 1: your work.

1064
00:50:58,960 --> 00:51:02,600
Speaker 4: Talk about like unequal that's the ultimate inequality.

1065
00:51:02,920 --> 00:51:06,040
Speaker 1: And around the time that Einstein was developed in general relativity,

1066
00:51:06,200 --> 00:51:08,359
Speaker 1: people were trying to understand like what did it mean?

1067
00:51:08,640 --> 00:51:10,880
Speaker 1: You know, Einstein had these equations and it took decades

1068
00:51:10,880 --> 00:51:13,759
Speaker 1: for people to like really understand what it means. And

1069
00:51:13,840 --> 00:51:16,359
Speaker 1: one of the questions about general relativity was like what

1070
00:51:16,400 --> 00:51:19,400
Speaker 1: does it mean for energy conservation? People thought energy was

1071
00:51:19,440 --> 00:51:22,000
Speaker 1: conserved back then, but in general relativity they were like,

1072
00:51:22,000 --> 00:51:24,680
Speaker 1: hold on a second, it's not clear if energy is

1073
00:51:24,719 --> 00:51:27,960
Speaker 1: conserved in general relativity. What's going on. People knew that

1074
00:51:28,040 --> 00:51:31,759
Speaker 1: Nuther was an expert in algebra and in mathematics, a

1075
00:51:31,800 --> 00:51:34,640
Speaker 1: lot of which was really important underlying general relativity. So

1076
00:51:34,680 --> 00:51:36,400
Speaker 1: they asked her to look at this question.

1077
00:51:36,440 --> 00:51:38,360
Speaker 4: Right, because I think at this point in the history

1078
00:51:38,400 --> 00:51:40,800
Speaker 4: of physics, like we were at the point where basically

1079
00:51:40,840 --> 00:51:44,080
Speaker 4: Newtonian physics were being upturned, right, Like, we had relied

1080
00:51:44,080 --> 00:51:47,120
Speaker 4: on Newtonian physics all the time. People thought that the

1081
00:51:47,160 --> 00:51:49,839
Speaker 4: thing that told us a momentum was conserved. But now

1082
00:51:50,080 --> 00:51:52,680
Speaker 4: they had this whole new sort of class of physics,

1083
00:51:52,680 --> 00:51:56,440
Speaker 4: this whole new sort of level of quantum and relativity,

1084
00:51:56,480 --> 00:51:58,359
Speaker 4: and so people were like, wait a minute, what's going on?

1085
00:51:58,520 --> 00:52:02,520
Speaker 4: Is momentum still conserved according to these new sort of equations, right,

1086
00:52:02,560 --> 00:52:03,359
Speaker 4: That's kind of where we were.

1087
00:52:03,520 --> 00:52:05,359
Speaker 1: That's where we were. People like, well, we think general

1088
00:52:05,360 --> 00:52:07,719
Speaker 1: relativity makes a lot of sense, there's a lot to

1089
00:52:07,840 --> 00:52:09,759
Speaker 1: like about it. But now we get to ask new

1090
00:52:09,880 --> 00:52:12,880
Speaker 1: questions about it, like why does it seem that in

1091
00:52:12,960 --> 00:52:16,680
Speaker 1: general relativity energy is not necessarily conserved? Under what conditions

1092
00:52:16,880 --> 00:52:19,200
Speaker 1: would it be conserved? What does that mean? This is

1093
00:52:19,239 --> 00:52:21,600
Speaker 1: like a big question about the nature of these new

1094
00:52:21,640 --> 00:52:24,799
Speaker 1: mathematical and physical discoveries, And so she looked into it

1095
00:52:24,840 --> 00:52:28,000
Speaker 1: and she figured out something really interesting and very deep

1096
00:52:28,320 --> 00:52:29,600
Speaker 1: about the nature of the universe.

1097
00:52:29,840 --> 00:52:32,919
Speaker 4: Wow, she took a little coffee break and she came

1098
00:52:33,000 --> 00:52:34,640
Speaker 4: and figured everything out for everybody.

1099
00:52:34,840 --> 00:52:36,680
Speaker 1: I know, all these folks who were like paid and

1100
00:52:36,680 --> 00:52:39,560
Speaker 1: had full professorships, you know, and this is their job.

1101
00:52:39,640 --> 00:52:43,239
Speaker 1: They like asked the volunteer mathematician who they'd excluded from

1102
00:52:43,320 --> 00:52:46,359
Speaker 1: academic positions to come and solve their problem. And she did.

1103
00:52:46,520 --> 00:52:48,200
Speaker 1: And then she went back into mathematics.

1104
00:52:48,440 --> 00:52:51,360
Speaker 4: Right. That's wild and it's interesting too, because she was

1105
00:52:51,440 --> 00:52:54,520
Speaker 4: surrounded by all these like famous mathematicians, right, she worked

1106
00:52:54,520 --> 00:52:56,800
Speaker 4: with them. Hilbert S. Warshaw. I mean, these are big names,

1107
00:52:56,920 --> 00:52:59,200
Speaker 4: even not just in math but also in physics, like

1108
00:52:59,280 --> 00:53:02,799
Speaker 4: you know the Shortshi radius of a black hole. Right.

1109
00:53:02,840 --> 00:53:05,760
Speaker 1: Absolutely, all these folks knew her and had great respect

1110
00:53:05,760 --> 00:53:07,759
Speaker 1: for her. And it's a little sad that in the

1111
00:53:08,160 --> 00:53:11,760
Speaker 1: telling of these stories later on, she was mostly omitted

1112
00:53:11,800 --> 00:53:14,520
Speaker 1: from it. Even though she made this really seminal contribution,

1113
00:53:14,560 --> 00:53:16,680
Speaker 1: which we'll talk about in just a moment, history has

1114
00:53:16,760 --> 00:53:18,759
Speaker 1: largely forgotten about her. Like I think if you ask

1115
00:53:18,800 --> 00:53:21,360
Speaker 1: people who made the most important contributions to physics in

1116
00:53:21,400 --> 00:53:24,239
Speaker 1: the last century, you'd get Einstein, you might get Schrodinger,

1117
00:53:24,520 --> 00:53:27,000
Speaker 1: but like, no, there is up there, maybe even more

1118
00:53:27,040 --> 00:53:30,439
Speaker 1: important than Einstein, and yet almost nobody knows about her.

1119
00:53:30,560 --> 00:53:33,399
Speaker 4: Wow, up there with Einstein. All right, Well, let's get

1120
00:53:33,440 --> 00:53:36,480
Speaker 4: into what exactly she did, Like, what was the breakthrough

1121
00:53:36,480 --> 00:53:38,280
Speaker 4: that she had? What was the connection that she made?

1122
00:53:38,320 --> 00:53:40,920
Speaker 1: So it sounds very simple, but the connection she made

1123
00:53:41,000 --> 00:53:44,879
Speaker 1: was that any symmetry you have in your equations will

1124
00:53:44,960 --> 00:53:48,319
Speaker 1: generate a conservation law. What that means is that any

1125
00:53:48,400 --> 00:53:51,960
Speaker 1: conservation you see in the universe, anytime you see something

1126
00:53:52,000 --> 00:53:55,000
Speaker 1: being conserved, you don't understand it. What it means is

1127
00:53:55,000 --> 00:53:58,400
Speaker 1: that it comes from some symmetry. Right, there's always some

1128
00:53:58,440 --> 00:54:03,000
Speaker 1: symmetry which produces a conservation law. So, for example, conservation

1129
00:54:03,080 --> 00:54:06,160
Speaker 1: of momentum comes from the fact that space is the

1130
00:54:06,200 --> 00:54:09,120
Speaker 1: same everywhere. If you shift your experiment from here to

1131
00:54:09,200 --> 00:54:12,040
Speaker 1: over there, you don't get a different answer. That's why

1132
00:54:12,080 --> 00:54:13,280
Speaker 1: momentum is concerned.

1133
00:54:13,400 --> 00:54:15,360
Speaker 4: Can you maybe go a little bit into more detail,

1134
00:54:15,400 --> 00:54:17,640
Speaker 4: like why is that? Why is it that having the

1135
00:54:17,640 --> 00:54:21,040
Speaker 4: equations be the same here or there results or it

1136
00:54:21,120 --> 00:54:23,240
Speaker 4: gives us conservation of momentum.

1137
00:54:23,280 --> 00:54:25,600
Speaker 1: Well, remember that what we're talking about is the physics

1138
00:54:25,600 --> 00:54:27,920
Speaker 1: doesn't change. Right, So you shift your whole experiment from

1139
00:54:27,920 --> 00:54:30,720
Speaker 1: here to there, you get the same equations of motion,

1140
00:54:31,280 --> 00:54:33,200
Speaker 1: and the equations of motion if you know anything about

1141
00:54:33,239 --> 00:54:37,080
Speaker 1: like Hamiltonian or Lagrange and mechanics, these equations only depend

1142
00:54:37,160 --> 00:54:41,040
Speaker 1: on the derivatives of your position, how your position changes

1143
00:54:41,120 --> 00:54:44,680
Speaker 1: with time, not the actual value of the position. Right,

1144
00:54:44,760 --> 00:54:47,359
Speaker 1: And so if you take your position and you add

1145
00:54:47,400 --> 00:54:50,440
Speaker 1: a constant to it, you know, x goes to x

1146
00:54:50,480 --> 00:54:53,040
Speaker 1: plus a, then the derivatives don't change because when you

1147
00:54:53,080 --> 00:54:55,920
Speaker 1: take the derivative a disappears. I mean, the equations of

1148
00:54:55,960 --> 00:54:59,280
Speaker 1: motions you get when you shift your position don't change

1149
00:54:59,480 --> 00:55:02,520
Speaker 1: because thequations of motion only depend on the derivative, and

1150
00:55:02,560 --> 00:55:06,080
Speaker 1: the derivative of your position is your velocity, which is

1151
00:55:06,120 --> 00:55:09,200
Speaker 1: closely connected to your momentum. That's sort of like a

1152
00:55:09,239 --> 00:55:13,600
Speaker 1: sketch for why the symmetry in position gives you conservation

1153
00:55:13,760 --> 00:55:16,759
Speaker 1: of momentum, because the equations of motion only depend on

1154
00:55:16,840 --> 00:55:19,960
Speaker 1: the derivative of the position, not the position themselves.

1155
00:55:20,800 --> 00:55:22,360
Speaker 4: I think what you're saying is that the equations of

1156
00:55:22,440 --> 00:55:25,200
Speaker 4: motion of the universe basically don't have position in them.

1157
00:55:25,280 --> 00:55:27,000
Speaker 4: They just have velocities in them.

1158
00:55:27,080 --> 00:55:28,600
Speaker 1: Yeah, Another way to think about it is that they

1159
00:55:28,680 --> 00:55:32,680
Speaker 1: only have relative positions. You shift everything over, nothing changes,

1160
00:55:32,800 --> 00:55:35,480
Speaker 1: so only changes in position are important. That's what the

1161
00:55:35,480 --> 00:55:38,920
Speaker 1: equations of motion are about, and changes the position is velocity,

1162
00:55:38,920 --> 00:55:40,880
Speaker 1: and velocity is basically momentum.

1163
00:55:40,960 --> 00:55:43,799
Speaker 4: Right. But I guess the question then is why does

1164
00:55:43,880 --> 00:55:46,400
Speaker 4: the fact that it's the same here or there, well,

1165
00:55:46,480 --> 00:55:49,200
Speaker 4: why does that mean that? You know, objects and motion

1166
00:55:49,600 --> 00:55:52,560
Speaker 4: stay in motion, and objects and address stay at rest.

1167
00:55:52,680 --> 00:55:55,919
Speaker 1: It might seem weird to connect these two quantities momentum, right,

1168
00:55:56,000 --> 00:55:59,080
Speaker 1: and position, But you know, there's another great advance in

1169
00:55:59,120 --> 00:56:01,279
Speaker 1: the early part of this centry, the connected momentum and

1170
00:56:01,320 --> 00:56:03,560
Speaker 1: position that told us that there was a close relationship

1171
00:56:03,560 --> 00:56:07,040
Speaker 1: between these two quantities. And that's quantum mechanics, which, like

1172
00:56:07,040 --> 00:56:10,080
Speaker 1: the Heisenberg and certainty principle, tells you that momentum and

1173
00:56:10,120 --> 00:56:12,880
Speaker 1: position are closely related to each other because one is

1174
00:56:12,880 --> 00:56:16,239
Speaker 1: basically like the Foyer transform of the other one. And

1175
00:56:16,320 --> 00:56:19,759
Speaker 1: so these two quantities are like really coupled together. And

1176
00:56:19,800 --> 00:56:22,799
Speaker 1: so the fact that you can shift your experiment over

1177
00:56:23,040 --> 00:56:25,840
Speaker 1: by ten meters or by light year and it doesn't

1178
00:56:25,920 --> 00:56:29,400
Speaker 1: change the answer tells you something about the relationship between

1179
00:56:29,520 --> 00:56:33,239
Speaker 1: momentum and position, and so that's sort of where it originates.

1180
00:56:35,880 --> 00:56:40,880
Speaker 4: No, let's try this. Maybe, let's assume that the equations

1181
00:56:40,880 --> 00:56:43,680
Speaker 4: of the universe were not symmetric, right, Like, let's say

1182
00:56:43,719 --> 00:56:46,640
Speaker 4: that you know you didn't have these equations. How would

1183
00:56:46,640 --> 00:56:50,040
Speaker 4: that translate to momentum not being concerned?

1184
00:56:50,280 --> 00:56:52,160
Speaker 1: All right? So, if the equations of motion of the

1185
00:56:52,239 --> 00:56:58,200
Speaker 1: universe depended on position, right, not just changes of position.

1186
00:56:58,000 --> 00:57:01,320
Speaker 4: Like if equals the may hear f equals three m

1187
00:57:01,360 --> 00:57:04,640
Speaker 4: a in Mars, not in Mars, but like near than

1188
00:57:04,760 --> 00:57:06,920
Speaker 4: in the neighborhood of Mars. Like, let's say the equations

1189
00:57:06,920 --> 00:57:09,799
Speaker 4: of the universe change from here to there, how would

1190
00:57:09,840 --> 00:57:12,480
Speaker 4: that affect whether or not a ball of ice cream

1191
00:57:12,520 --> 00:57:14,840
Speaker 4: might throw at Mars is going to change velocity.

1192
00:57:15,040 --> 00:57:17,640
Speaker 1: If you're a particle and you're moving through a universe

1193
00:57:17,960 --> 00:57:22,160
Speaker 1: where the rules are changing as you move, right, then

1194
00:57:22,240 --> 00:57:25,640
Speaker 1: your trajectory might change because the rules are the things

1195
00:57:25,640 --> 00:57:28,680
Speaker 1: that govern your trajectory, that tell your trajectory how it moves.

1196
00:57:28,880 --> 00:57:30,840
Speaker 1: So if over here in our part of the universe,

1197
00:57:31,000 --> 00:57:33,240
Speaker 1: it requires a force to change your momentum, but over

1198
00:57:33,280 --> 00:57:36,479
Speaker 1: there it doesn't, right, then your momentum might change without

1199
00:57:36,480 --> 00:57:39,040
Speaker 1: anybody applying a force. To it in that part of

1200
00:57:39,040 --> 00:57:41,600
Speaker 1: the universe, and so your momentum might be changed just

1201
00:57:41,640 --> 00:57:44,760
Speaker 1: by the fact of moving from here to there where

1202
00:57:44,800 --> 00:57:45,800
Speaker 1: the rules are different.

1203
00:57:46,200 --> 00:57:48,360
Speaker 4: Right, But what if nothing interacts with my ice cream

1204
00:57:48,400 --> 00:57:51,360
Speaker 4: ball from here to there? Why would it change? Or

1205
00:57:51,360 --> 00:57:53,800
Speaker 4: how could it change velocity? You know what I mean?

1206
00:57:53,840 --> 00:57:55,880
Speaker 4: How could the momentum change? Or maybe like, are you

1207
00:57:55,920 --> 00:57:58,320
Speaker 4: saying that maybe the definition of momentum would change.

1208
00:57:58,520 --> 00:58:01,880
Speaker 1: You're assuming implicitly there that you need to interact with

1209
00:58:01,960 --> 00:58:05,400
Speaker 1: somebody to change its momentum, which is assuming conservation of momentum.

1210
00:58:05,440 --> 00:58:08,160
Speaker 1: But in this example, we're talking about a universe where

1211
00:58:08,200 --> 00:58:10,400
Speaker 1: the rules are different from one place to another, and

1212
00:58:10,440 --> 00:58:13,480
Speaker 1: so you don't have conservation and momentum, and so it

1213
00:58:13,480 --> 00:58:17,160
Speaker 1: would break pretty basic fundamental things like that things could

1214
00:58:17,200 --> 00:58:19,560
Speaker 1: change momentum without anything interacting with it.

1215
00:58:20,200 --> 00:58:22,920
Speaker 4: That would break Well, let's say like here on Earth

1216
00:58:23,000 --> 00:58:25,560
Speaker 4: or in our neighborhood, it's F equals maa, but near

1217
00:58:25,600 --> 00:58:28,600
Speaker 4: Mars it's f equals three ma Right, Like, if I

1218
00:58:28,640 --> 00:58:30,800
Speaker 4: apply a force, I need three tize amount of force

1219
00:58:30,880 --> 00:58:33,680
Speaker 4: to get something to accelerate. Would that break the laws

1220
00:58:33,720 --> 00:58:35,080
Speaker 4: of conservation and momentum or not?

1221
00:58:35,360 --> 00:58:38,000
Speaker 1: Yeah, absolutely it would because Remember, force is a change

1222
00:58:38,000 --> 00:58:41,400
Speaker 1: of momentum, and so it's talking about is having a

1223
00:58:41,440 --> 00:58:45,120
Speaker 1: different change in momentum over here and over there. So

1224
00:58:45,160 --> 00:58:47,520
Speaker 1: you'd have to have some like gradual change in the

1225
00:58:47,600 --> 00:58:50,280
Speaker 1: laws between here and there, and then you know, the

1226
00:58:50,320 --> 00:58:54,800
Speaker 1: same acceleration would require a different force here and over there,

1227
00:58:55,240 --> 00:58:57,800
Speaker 1: and so that would mean a different change in momentum.

1228
00:58:57,840 --> 00:58:59,680
Speaker 4: So absolutely what he's saying, are are you saying the

1229
00:58:59,680 --> 00:59:02,000
Speaker 4: ball slow down or the ball would speed up?

1230
00:59:02,120 --> 00:59:04,439
Speaker 1: In that case, it would slow down because effectively you'd

1231
00:59:04,480 --> 00:59:08,280
Speaker 1: be increasing its mass to like three m without changing

1232
00:59:08,280 --> 00:59:10,320
Speaker 1: its momentum, so its velocity would drop.

1233
00:59:10,440 --> 00:59:14,120
Speaker 4: You're saying, because there's no force, then because we sort

1234
00:59:14,160 --> 00:59:17,400
Speaker 4: of change the mass kind of, then the velocity would change.

1235
00:59:17,600 --> 00:59:21,280
Speaker 1: Yeah, it gets pretty hard to do these calculations because

1236
00:59:21,320 --> 00:59:24,920
Speaker 1: your intuition really assumes that these things are conserved.

1237
00:59:25,240 --> 00:59:26,920
Speaker 4: Right. Well, I guess what I'm trying to do is

1238
00:59:27,440 --> 00:59:29,360
Speaker 4: get us, you know, kind of an into a sense

1239
00:59:29,440 --> 00:59:32,480
Speaker 4: of what you mean when you say, like symmetries equals

1240
00:59:32,520 --> 00:59:33,880
Speaker 4: conservation of something.

1241
00:59:34,000 --> 00:59:36,360
Speaker 1: I think maybe an intuitive way to understand it is

1242
00:59:36,400 --> 00:59:39,160
Speaker 1: to think about just the relative sense of these quantities.

1243
00:59:39,480 --> 00:59:41,960
Speaker 1: You know, like we know that no place in the

1244
00:59:42,040 --> 00:59:44,680
Speaker 1: universe is different from any other place. We also know

1245
00:59:44,800 --> 00:59:47,160
Speaker 1: that the only important thing is not your position, but

1246
00:59:47,200 --> 00:59:50,360
Speaker 1: your relative velocity. Right, those two really are saying the

1247
00:59:50,400 --> 00:59:53,120
Speaker 1: same thing, that what matters is not where you are

1248
00:59:53,120 --> 00:59:56,360
Speaker 1: in the universe, but your velocity relative to that stuff.

1249
00:59:56,760 --> 01:00:00,520
Speaker 1: So momentum is important and not position. That's why momentum

1250
01:00:00,560 --> 01:00:03,080
Speaker 1: is conserved and not like location. So I think that's

1251
01:00:03,120 --> 01:00:05,280
Speaker 1: the most intuitive way to think about it. You know

1252
01:00:05,360 --> 01:00:09,200
Speaker 1: that underlying you, there's no fixed grid where somebody's measuring.

1253
01:00:09,240 --> 01:00:12,160
Speaker 1: Your position is just about how you're moving relative to

1254
01:00:12,200 --> 01:00:15,160
Speaker 1: stuff that's important, not your location. So one way to

1255
01:00:15,200 --> 01:00:17,520
Speaker 1: say that is, well, you can move your experiment somewhere

1256
01:00:17,560 --> 01:00:19,400
Speaker 1: else and get the same answer. Another way to say

1257
01:00:19,440 --> 01:00:22,920
Speaker 1: that is, actually, the important thing is motion, not position,

1258
01:00:23,240 --> 01:00:24,840
Speaker 1: and that's conservation and momentum.

1259
01:00:24,920 --> 01:00:26,800
Speaker 4: I think maybe you're telling me that you sort of

1260
01:00:26,800 --> 01:00:29,120
Speaker 4: have to go into the math to really understand that connection,

1261
01:00:29,920 --> 01:00:31,880
Speaker 4: Like it sort of comes from the math, But it's

1262
01:00:31,960 --> 01:00:34,320
Speaker 4: kind of hard to really see it from an intuitive

1263
01:00:34,320 --> 01:00:37,000
Speaker 4: point of view, because maybe we are so ingrained in

1264
01:00:37,040 --> 01:00:39,840
Speaker 4: this idea of conservation that we can't think of things

1265
01:00:39,840 --> 01:00:40,640
Speaker 4: not being conserved.

1266
01:00:40,720 --> 01:00:42,440
Speaker 1: Yeah, I used to think I had intuitive understanding of

1267
01:00:42,480 --> 01:00:44,160
Speaker 1: it until you asked me a bunch of questions about it,

1268
01:00:44,200 --> 01:00:45,240
Speaker 1: And now I'm not so sure.

1269
01:00:46,800 --> 01:00:49,240
Speaker 4: I've destroyed the conservation of knowledge in your brain.

1270
01:00:49,440 --> 01:00:53,200
Speaker 1: But it is very simple mathematically and very deep and fascinating.

1271
01:00:53,400 --> 01:00:56,840
Speaker 1: You can take this example that translations in space lead

1272
01:00:56,880 --> 01:00:59,080
Speaker 1: to conservation and momentum and apply it to lots of

1273
01:00:59,120 --> 01:01:01,400
Speaker 1: other things in it all also holds. That's why I

1274
01:01:01,400 --> 01:01:03,640
Speaker 1: not if this's theorem is so powerful. It doesn't just

1275
01:01:03,760 --> 01:01:07,880
Speaker 1: explain conservation and momentum. It also explains other conservation laws

1276
01:01:07,920 --> 01:01:10,880
Speaker 1: that we see in the universe. For example, you can

1277
01:01:10,920 --> 01:01:12,280
Speaker 1: apply the same thing to rotation.

1278
01:01:12,760 --> 01:01:12,960
Speaker 7: Right.

1279
01:01:13,160 --> 01:01:16,360
Speaker 1: We don't care about the orientation of anything in the

1280
01:01:16,400 --> 01:01:19,240
Speaker 1: universe because there's no up or down. There's no preferred direction.

1281
01:01:19,280 --> 01:01:22,000
Speaker 1: The same way there's no preferred location. That's why we

1282
01:01:22,080 --> 01:01:25,880
Speaker 1: have conservation of angular momentum because rotation is not fundamental,

1283
01:01:26,240 --> 01:01:31,000
Speaker 1: but relative rotations are. Rotational velocity is important, and so

1284
01:01:31,040 --> 01:01:34,880
Speaker 1: we have conservation of angular momentum because the universe can

1285
01:01:34,920 --> 01:01:37,720
Speaker 1: be rotated through an arbitrary angle and nothing changes.

1286
01:01:38,240 --> 01:01:40,040
Speaker 4: Right. I think what you're saying is that she sort

1287
01:01:40,040 --> 01:01:44,560
Speaker 4: of drew that connection between these mathematical symmetries and these

1288
01:01:44,600 --> 01:01:48,480
Speaker 4: sort of physical ideas of conservation of things, like things overall,

1289
01:01:48,480 --> 01:01:50,400
Speaker 4: if you look at them at a system, they don't change.

1290
01:01:50,680 --> 01:01:53,880
Speaker 4: And she said, hey, that's because you have these symmetries

1291
01:01:54,000 --> 01:01:57,280
Speaker 4: in these equations, like they're sort of one and the same.

1292
01:01:57,200 --> 01:01:59,040
Speaker 1: Exactly, and not just the symmetry in the equation, a

1293
01:01:59,120 --> 01:02:03,439
Speaker 1: symmetry in the universe. Right, conservation momentum tells you that

1294
01:02:03,520 --> 01:02:06,960
Speaker 1: space is the same everywhere. That's a big conclusion, right,

1295
01:02:06,960 --> 01:02:09,320
Speaker 1: If momentum really is conserved everywhere in the universe, it

1296
01:02:09,360 --> 01:02:12,440
Speaker 1: tells you there's no different place in space. Every place

1297
01:02:12,480 --> 01:02:14,720
Speaker 1: in space is the same. It's not just the equations.

1298
01:02:14,760 --> 01:02:18,040
Speaker 4: It's like the universe, man, the universe.

1299
01:02:18,080 --> 01:02:18,400
Speaker 11: Man.

1300
01:02:18,640 --> 01:02:18,840
Speaker 9: Huh.

1301
01:02:19,360 --> 01:02:21,720
Speaker 4: So what exactly is the theorem? Like, how do you

1302
01:02:21,960 --> 01:02:23,320
Speaker 4: how do you verbalize that theorem?

1303
01:02:23,400 --> 01:02:28,080
Speaker 1: The theorem is that every continuous symmetry of the Lagrangen,

1304
01:02:28,160 --> 01:02:31,800
Speaker 1: which describes the motion and interaction of particles, leads to

1305
01:02:31,840 --> 01:02:35,760
Speaker 1: a conservation law. So continuous symmetry like translation in space

1306
01:02:35,880 --> 01:02:39,800
Speaker 1: or rotation in space or shifting in time. The original

1307
01:02:39,880 --> 01:02:43,080
Speaker 1: question she was trying to ask is is energy conserved

1308
01:02:43,400 --> 01:02:46,200
Speaker 1: in general relativity? And if not, why not? And so

1309
01:02:46,280 --> 01:02:49,400
Speaker 1: this was her answer. Her answer was, if space doesn't

1310
01:02:49,480 --> 01:02:51,520
Speaker 1: change with time, if the laws of the universe don't

1311
01:02:51,560 --> 01:02:55,160
Speaker 1: change in time, then energy is conserved. If the laws

1312
01:02:55,160 --> 01:02:57,560
Speaker 1: in the universe do change in time, then energy is

1313
01:02:57,600 --> 01:03:01,120
Speaker 1: not conserved. Sort of blew everybody's mind when she discovered that.

1314
01:03:01,400 --> 01:03:05,360
Speaker 4: Whoa, So she sort of made a bridge between the

1315
01:03:05,400 --> 01:03:08,120
Speaker 4: new physics and the old physics, right, or she provided

1316
01:03:08,200 --> 01:03:10,520
Speaker 4: kind of the answer that said, hey, they're all sort

1317
01:03:10,520 --> 01:03:11,400
Speaker 4: of one and the same.

1318
01:03:11,600 --> 01:03:15,320
Speaker 1: Yeah, she helped us understand why these conservation laws appear

1319
01:03:15,400 --> 01:03:18,000
Speaker 1: and under what conditions they do. And of course, for

1320
01:03:18,040 --> 01:03:21,320
Speaker 1: decades afterwards people were like, well, obviously energy is conserved

1321
01:03:21,320 --> 01:03:23,760
Speaker 1: in the universe, and so therefore the rules of physics

1322
01:03:23,800 --> 01:03:25,840
Speaker 1: must be the same as a function of time. Now,

1323
01:03:25,840 --> 01:03:28,040
Speaker 1: of course, we know the universe is expanding, and that

1324
01:03:28,080 --> 01:03:31,120
Speaker 1: means that energy is not conserved because space is changing

1325
01:03:31,160 --> 01:03:34,080
Speaker 1: with time. Right, so, if this theorem is still teaching

1326
01:03:34,160 --> 01:03:36,600
Speaker 1: us things about the nature of the universe, the fact

1327
01:03:36,600 --> 01:03:38,920
Speaker 1: that the universe is expanding means that energy is not

1328
01:03:38,960 --> 01:03:40,240
Speaker 1: conserved and we know.

1329
01:03:40,320 --> 01:03:43,160
Speaker 4: Why because it sort of breaks her theorem or it's

1330
01:03:43,200 --> 01:03:44,200
Speaker 4: outside of her theorem.

1331
01:03:44,320 --> 01:03:47,080
Speaker 1: Yeah, because there isn't a symmetry with time, which is

1332
01:03:47,080 --> 01:03:50,240
Speaker 1: why we don't have energy conservation. If the universe was

1333
01:03:50,320 --> 01:03:53,200
Speaker 1: symmetric in time, if space was the same size and

1334
01:03:53,240 --> 01:03:56,640
Speaker 1: not expanding, then we would have energy conservation. So we

1335
01:03:56,720 --> 01:03:59,280
Speaker 1: know why we don't have energy conservation just the same

1336
01:03:59,280 --> 01:04:02,040
Speaker 1: way we know why we do have momentum conservation.

1337
01:04:02,160 --> 01:04:04,200
Speaker 4: All right, Well, I think that sort of answer is

1338
01:04:04,240 --> 01:04:06,720
Speaker 4: the main question of the episode, which is why is

1339
01:04:06,720 --> 01:04:09,160
Speaker 4: momentum conserved? And it seems like the answer is that

1340
01:04:09,240 --> 01:04:13,160
Speaker 4: it's sort of like baked into the equations of the universe,

1341
01:04:13,240 --> 01:04:16,080
Speaker 4: Like it's because the equations of the universe don't change

1342
01:04:16,240 --> 01:04:17,880
Speaker 4: no matter where you put them.

1343
01:04:17,960 --> 01:04:21,680
Speaker 1: Yeah, it's because space is the same everywhere in the universe.

1344
01:04:22,040 --> 01:04:23,960
Speaker 1: That's why momentum is conserved.

1345
01:04:24,080 --> 01:04:26,240
Speaker 4: Well, it's everywhere. It's the same everywhere in the universe,

1346
01:04:26,280 --> 01:04:29,680
Speaker 4: but not everywhere in time, Like it's changing, but it's

1347
01:04:29,720 --> 01:04:31,840
Speaker 4: changing everywhere at the same time, I think is what

1348
01:04:31,880 --> 01:04:32,320
Speaker 4: you're saying.

1349
01:04:32,480 --> 01:04:35,720
Speaker 1: Space is expanding, it is changing, but the rules of

1350
01:04:35,760 --> 01:04:38,600
Speaker 1: the universe are the same at every location in space. Yeah,

1351
01:04:38,640 --> 01:04:40,880
Speaker 1: there's no different parts of space. There's no like vanilla

1352
01:04:40,920 --> 01:04:43,760
Speaker 1: space and chocolate space and strawberry space. It's all the

1353
01:04:43,760 --> 01:04:44,400
Speaker 1: same space.

1354
01:04:44,560 --> 01:04:47,960
Speaker 4: That's all the same swirl exactly.

1355
01:04:48,680 --> 01:04:51,560
Speaker 1: You only get one option, and that's one kind of

1356
01:04:51,600 --> 01:04:53,200
Speaker 1: space swirl in this universe.

1357
01:04:53,440 --> 01:04:56,680
Speaker 4: I see. But if we do maybe find out sometime

1358
01:04:56,720 --> 01:04:59,680
Speaker 4: in the future that space is different, like at the border,

1359
01:05:00,160 --> 01:05:02,479
Speaker 4: at the edges, or maybe in the next universe over,

1360
01:05:02,920 --> 01:05:04,720
Speaker 4: then maybe momentum wouldn't be conserved.

1361
01:05:04,840 --> 01:05:08,520
Speaker 1: Yeah, exactly, Maybe momentum will be dethroned the way energy was.

1362
01:05:09,080 --> 01:05:11,640
Speaker 4: Or at least, you know, not dethrone But just like, hey,

1363
01:05:11,880 --> 01:05:15,200
Speaker 4: it would confirm Nother's theorem actually in a way, right.

1364
01:05:15,280 --> 01:05:18,120
Speaker 1: Yeah. And if you're interested in other weird quantum applications

1365
01:05:18,160 --> 01:05:20,800
Speaker 1: in Other's theorem, check out our episode about gauge symmetry,

1366
01:05:20,920 --> 01:05:24,240
Speaker 1: which relies heavily on this idea and which promised to

1367
01:05:24,400 --> 01:05:26,920
Speaker 1: have a whole episode diving into Nother's theorem. So here

1368
01:05:26,960 --> 01:05:29,840
Speaker 1: it is. But Nother's theorem also explains why we have

1369
01:05:30,040 --> 01:05:33,160
Speaker 1: like conserved electric charges in the universe that comes from

1370
01:05:33,160 --> 01:05:37,080
Speaker 1: an internal quantum symmetry, and also to other weird conservation

1371
01:05:37,200 --> 01:05:41,520
Speaker 1: laws in particle physics come from symmetries we see in

1372
01:05:41,560 --> 01:05:44,000
Speaker 1: the equations of particle physics and are powered by a

1373
01:05:44,040 --> 01:05:44,720
Speaker 1: Noather's theorem.

1374
01:05:44,920 --> 01:05:46,840
Speaker 4: Well, I feel like there are two big Lessons zero

1375
01:05:46,960 --> 01:05:49,480
Speaker 4: one is that sometimes even that, like the things that

1376
01:05:49,520 --> 01:05:51,520
Speaker 4: seem intuitive in the universe have a deep sort of

1377
01:05:51,560 --> 01:05:54,720
Speaker 4: mathematical root the in how the universe works.

1378
01:05:54,800 --> 01:05:56,840
Speaker 1: And then you should always ask mathematicians for help with

1379
01:05:56,880 --> 01:05:57,800
Speaker 1: your physics problems.

1380
01:05:58,600 --> 01:06:01,160
Speaker 4: Yeah, they're like the nine one one of the physics world.

1381
01:06:01,760 --> 01:06:04,120
Speaker 4: We've been trying for centuries. Can you guys, you know,

1382
01:06:04,320 --> 01:06:06,520
Speaker 4: take a break and help us out?

1383
01:06:06,880 --> 01:06:09,240
Speaker 1: Yeah, Well, that part of history is really rich with

1384
01:06:09,320 --> 01:06:12,640
Speaker 1: fascinating mathematics that was developed for decades just out of

1385
01:06:12,680 --> 01:06:15,200
Speaker 1: pure interest in mathematics. And then oh, it turns out

1386
01:06:15,200 --> 01:06:18,440
Speaker 1: to be really helpful and solve important problems in physics. Yeah.

1387
01:06:18,480 --> 01:06:20,440
Speaker 4: And I guess the other interesting thing is here is

1388
01:06:20,480 --> 01:06:22,479
Speaker 4: that you know, I mean, you know, there was someone

1389
01:06:22,520 --> 01:06:25,280
Speaker 4: who was sort of outside of academia right, kind of

1390
01:06:25,880 --> 01:06:29,680
Speaker 4: unjustly so in justly so she's excluded, but she still

1391
01:06:29,680 --> 01:06:32,640
Speaker 4: made this amazing contribution. Like you know, these breakthroughs can

1392
01:06:32,720 --> 01:06:33,400
Speaker 4: come from anywhere.

1393
01:06:33,480 --> 01:06:36,200
Speaker 1: Yeah, exactly. And we really should have much more diversity

1394
01:06:36,240 --> 01:06:39,440
Speaker 1: in physics and in mathematics and in academia because we

1395
01:06:39,480 --> 01:06:42,080
Speaker 1: need all sorts to solve the tough problems that are

1396
01:06:42,080 --> 01:06:44,880
Speaker 1: facing us. So happy birthday, I mean and thank you

1397
01:06:44,920 --> 01:06:46,040
Speaker 1: for all your contributions.

1398
01:06:46,280 --> 01:06:47,320
Speaker 4: Yeah, for sure, thank you.

1399
01:06:47,480 --> 01:06:49,960
Speaker 1: Let's all have a scoop of space Sworld ice cream

1400
01:06:50,520 --> 01:06:52,480
Speaker 1: and to celebrate her birthday.

1401
01:06:52,600 --> 01:06:56,400
Speaker 4: Yeah, and the expand the space around our waistlines a

1402
01:06:56,400 --> 01:06:56,960
Speaker 4: little bit.

1403
01:06:56,960 --> 01:06:59,280
Speaker 1: And blow our minds with what it all means.

1404
01:06:59,480 --> 01:07:02,240
Speaker 4: All right, Well, I think that answers a question and

1405
01:07:02,320 --> 01:07:04,520
Speaker 4: it tells us some pretty deep things about the universe.

1406
01:07:04,800 --> 01:07:07,800
Speaker 4: We hope you enjoyed that. Thanks for joining us, See

1407
01:07:07,840 --> 01:07:08,320
Speaker 4: you next time.

1408
01:07:16,040 --> 01:07:18,840
Speaker 1: Thanks for listening, and remember that Daniel and Jorge Explain

1409
01:07:18,920 --> 01:07:22,919
Speaker 1: the Universe is a production of iHeartRadio. For more podcasts

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01:07:22,920 --> 01:07:27,560
Speaker 1: from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever

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