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Why is momentum conserved? · Daniel and Kelly’s Extraordinary Universe

• 0:08
  Speaker 1: Hey, Dado, do you think podcasts obey the laws of physics? Oh?
• 0:13
  Speaker 1: I sure, hope. So I don't want to get some
• 0:14
  Speaker 1: sort of fine. What makes you worry about it? Well,
• 0:18
  Speaker 1: I've heard some people who use podcasts to fall asleep. Well,
• 0:21
  Speaker 1: I don't know. That sounds pretty harmless. How is that
• 0:23
  Speaker 1: violating the laws of physics? Well, isn't there something about
• 0:26
  Speaker 1: how bodies and motions stay in motion? I see where
• 0:29
  Speaker 1: you're going with this. That could be a problem if
• 0:31
  Speaker 1: the podcast puts bodies at rest that used to be
• 0:34
  Speaker 1: in motion. Yeah, yeah, that might be a problem, like
• 0:36
  Speaker 1: if they're driving or something. Maybe if you get in
• 0:40
  Speaker 1: bed and get comfortable before they, you know, put on
• 0:42
  Speaker 1: a podcast, then they could just continue being at the rest.
• 0:46
  Speaker 1: Then there might be asleep before we get to the
• 0:48
  Speaker 1: main topic of the podcast. Maybe we just put a
• 0:50
  Speaker 1: bunch of people to sleep. Wake up? Wake up? What
• 0:55
  Speaker 1: I put you to sleep? You're the physicist. I take
• 0:58
  Speaker 1: naps wherever I can find them. Hi am or handmake
• 1:16
  Speaker 1: cartoonist and the creator of PhD comics. Hi. I'm Daniel.
• 1:19
  Speaker 1: I'm a particle physicist and a professor at U c Irvine,
• 1:22
  Speaker 1: and I try to stay in motion is that hard
• 1:27
  Speaker 1: as a physicist, don't you sit in your couch or
• 1:29
  Speaker 1: your desk all the time and just think of solutions
• 1:31
  Speaker 1: to the questions about the universe. Yeah, but I find
• 1:35
  Speaker 1: that as I get older, a body at rest tends
• 1:37
  Speaker 1: to stay at rest, so it's harder and harder to
• 1:39
  Speaker 1: get out of that couch. I think a body at
• 1:42
  Speaker 1: rest also tends to get bigger. Unfortunately, with our age,
• 1:47
  Speaker 1: that's true, and we gravitationally attract more physicists onto the couch.
• 1:51
  Speaker 1: That's right, We expand spacetime or on our waist. It's
• 1:55
  Speaker 1: a weird law of the universe, the no diet theorem,
• 1:59
  Speaker 1: the law of general snack ativity. But anyways, welcome to
• 2:02
  Speaker 1: our podcast, Daniel and Jorge Explain the Universe, a production
• 2:05
  Speaker 1: of My Heart Radio in which we put your mind
• 2:08
  Speaker 1: into motion to understand the fundamental nature of the universe
• 2:12
  Speaker 1: around us, or at least to ask the deep questions
• 2:16
  Speaker 1: about how it works and try to observe the patterns,
• 2:19
  Speaker 1: the trends, the symmetries, the conservation laws, the fundamental rules
• 2:23
  Speaker 1: that seem to be organizing our universe. On this podcast,
• 2:27
  Speaker 1: we ask all of those big questions, and we don't
• 2:29
  Speaker 1: shy away from trying to find answers. Yeah, because the
• 2:33
  Speaker 1: universe is full of things to ask questions about, lots
• 2:35
  Speaker 1: of questions that we still haven't figured out despite hundreds
• 2:38
  Speaker 1: and maybe thousands of years of science and observing the universe,
• 2:41
  Speaker 1: and we try to talk about it and to increase
• 2:44
  Speaker 1: the gravity I guess in your brain, right, like information
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  Speaker 1: causes gravity to increase, right, that's true. Yeah, Eventually our
• 2:51
  Speaker 1: goal is to turn your brain into a black hole.
• 2:54
  Speaker 1: Oh no, no, we want stuff to get out. That's true.
• 2:59
  Speaker 1: That would be undermining the fundamental purpose of our podcast.
• 3:02
  Speaker 1: That's right. It wouldn't go viral if I don't want
• 3:04
  Speaker 1: to turn into a black hole. But we do want
• 3:07
  Speaker 1: your brain to absorb information or to feel like you
• 3:10
  Speaker 1: are part of this centuries or maybe even millennial long
• 3:14
  Speaker 1: progress towards understanding the universe. When people look back on
• 3:18
  Speaker 1: the path of theoretical physics in a hundred years or
• 3:21
  Speaker 1: a thousand years, we will wonder how far along that
• 3:24
  Speaker 1: path we are. Have we just gotten started. Are we
• 3:27
  Speaker 1: around the corner from revealing the deepest secrets of the universe?
• 3:31
  Speaker 1: Only time will tell. Yeah, because it's amazing that the
• 3:33
  Speaker 1: universe is even understandable. Right, Like, we look at it,
• 3:36
  Speaker 1: it seems kind of chaotic, But the closer we look,
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  Speaker 1: we start to notice patterns and trends that seems to
• 3:41
  Speaker 1: sort of govern how it works and what's going to happen.
• 3:44
  Speaker 1: It is amazing that the universe can be described by
• 3:47
  Speaker 1: sets of physical laws that don't seem to change in time. Right.
• 3:52
  Speaker 1: We take that for granted. I can do an experiment
• 3:54
  Speaker 1: and measure something about the universe, like the gravitational constant,
• 3:58
  Speaker 1: and then I can do that same experiment in fifty
• 4:00
  Speaker 1: years and get the same number. Why is that right?
• 4:03
  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
• 4:12
  Speaker 1: of science. We don't know why it's true, but we
• 4:15
  Speaker 1: certainly do rely on it. Yeah, and you don't even
• 4:17
  Speaker 1: have to get that fancy to see how the universe
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  Speaker 1: has these laws. Right, You can just toss an apple
• 4:21
  Speaker 1: in the air over and over and it will always
• 4:23
  Speaker 1: sort of come back to your head. But you can
• 4:25
  Speaker 1: also do it while being fancy. You can wear a
• 4:26
  Speaker 1: tuxedo and toss an apple into the air, nothing stopping
• 4:29
  Speaker 1: you from getting fancy? Are you anti fancy? Now? That's way.
• 4:32
  Speaker 1: I guess you could be tossing a kind of caviar
• 4:34
  Speaker 1: instead of an apple too. I mean, personally, I'm always
• 4:37
  Speaker 1: wearing a tuxedo while doing these podcasts. I thought we
• 4:40
  Speaker 1: had a dress code on this podcast. What are you wearing?
• 4:42
  Speaker 1: I'm wearing a pajama with a tuxedo printed on it. O. Man,
• 4:46
  Speaker 1: standards are sliding everywhere, folks, It's hard, that's right. We
• 4:51
  Speaker 1: don't have a dress code law here in the podcast.
• 4:54
  Speaker 1: That's right. And you're also allowed to wear whatever you
• 4:56
  Speaker 1: like when you're listening to this podcast. So if you've
• 4:58
  Speaker 1: been dutifully getting your txedo dry cleaned before you listen
• 5:02
  Speaker 1: to this podcast, you can now just wear pajama pants.
• 5:05
  Speaker 1: I'm pretty sure nobody was wearing a tuxedo while listening
• 5:08
  Speaker 1: to us, and that's maybe they're like a waiter maybe
• 5:10
  Speaker 1: at a fancy restaurant that you know, tunes out the
• 5:13
  Speaker 1: customers by listening to our podcast. I hope that we
• 5:16
  Speaker 1: have a pretty broad variety of what folks are wearing,
• 5:19
  Speaker 1: you know, all the way from athletic gear to tuxedos
• 5:22
  Speaker 1: with tails. And top hats. I'd just like to imagine
• 5:24
  Speaker 1: we're sampling all of the human experience the same way
• 5:27
  Speaker 1: we are trying to explore the entire range of physical
• 5:30
  Speaker 1: phenomena out there in the universe. Yeah, but it is
• 5:33
  Speaker 1: interesting that the universe has lost right, Like you can
• 5:35
  Speaker 1: imagine maybe a universe without laws? Is that even sort
• 5:38
  Speaker 1: of like a possible to a physicist. It's possible to
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  Speaker 1: imagine that that universe exists, but it's hard to understand
• 5:44
  Speaker 1: how you would understand it. You know, the idea that
• 5:48
  Speaker 1: there are laws and that we can reveal them through experiment,
• 5:51
  Speaker 1: and that we can try to simplify them and use
• 5:52
  Speaker 1: them to predict the future. It's pretty basic to our
• 5:55
  Speaker 1: notion of understanding. It's sort of like goes to the
• 5:58
  Speaker 1: heart of storytelling, even well before like what we call
• 6:01
  Speaker 1: modern science. Indigenous culture is just learning about their environment
• 6:05
  Speaker 1: as they experience it, are telling stories, you know, like
• 6:08
  Speaker 1: you take this tree bark, you make a tea out
• 6:10
  Speaker 1: of it, you drink it, you feel better, and it's
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  Speaker 1: a story, and it's sort of fundamental to the way
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  Speaker 1: I think humans think. Yeah, that that is science as well, right, Absolutely,
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  Speaker 1: it's accumulation of knowledge through experience. Yeah, Well, it's a
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  Speaker 1: good thing that the universe does seem to have laws
• 6:23
  Speaker 1: because it allows us to kind of predict what's going
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  Speaker 1: on and to build things to make our lives better,
• 6:28
  Speaker 1: and to have a little bit of context about where
• 6:31
  Speaker 1: we sit in the universe and why we're here. That's right,
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  Speaker 1: and the patterns and trends that we notice in the universe,
• 6:36
  Speaker 1: they give us a lot of clues as to the
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  Speaker 1: fundamental nature of the universe. Though we assume the universe
• 6:41
  Speaker 1: has laws, we don't make a lot of assumptions for
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  Speaker 1: what those laws are. So we'd like to look around
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  Speaker 1: and notice, like, what are the patterns that happened in
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  Speaker 1: the universe, what are those laws that it seems to
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  Speaker 1: follow in, what do those laws mean? And why do
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  Speaker 1: we have those laws and not other laws. Yeah, And
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  Speaker 1: probably one of the most important laws, or at least
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  Speaker 1: the most useful laws we found and understanding the universe
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  Speaker 1: and predicting what's going to happen, is the idea that
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  Speaker 1: momentum is conserved. That's a law, right, that's like written
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  Speaker 1: in the Statute of the universe. That is still a law.
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  Speaker 1: A lot of things that you learned about in grade
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  Speaker 1: school that you found were conserved in the universe, are
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  Speaker 1: not mass, energy, energy plus mass, all of this stuff.
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  Speaker 1: You thought that stuff was conserving universe. It turns out
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  Speaker 1: it's not. But conservation and momentum still holds as far
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  Speaker 1: as we know. Oh interesting, some laws have been repealed
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  Speaker 1: that they made it all the way up to the
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  Speaker 1: spraying cooard of the universen't they They got shut down? Well,
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  Speaker 1: like Newtonian physics, some of these laws turned out to
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  Speaker 1: be almost true, true in many many cases, but not
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  Speaker 1: fundamentally true, not actually written in stone at the foundation
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  Speaker 1: of the universe, just sort of like mostly working in
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  Speaker 1: the scenarios we had tested them in so far, which
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  Speaker 1: is a cool testament to how science progresses. You find
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  Speaker 1: a pattern, it seems to be true everywhere, and then
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  Speaker 1: a hundred years later people find exceptions. Exceptions reveal a
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  Speaker 1: deeper truth. So when you say that momentum is conserved
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  Speaker 1: is still a lot, it's it just means that it
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  Speaker 1: hasn't been revealed yet kind of right, like, as far
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  Speaker 1: as we know, that's the one that's still true. Yeah,
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  Speaker 1: that's why we say it's still a law as of
• 8:13
  Speaker 1: the date of this podcast. But you know, in a
• 8:15
  Speaker 1: thousand years, when people are listening to this episode, they'll
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  Speaker 1: laugh into their hands at our naivete right before they
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  Speaker 1: fall asleep. But there is something really deep and fundamental
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  Speaker 1: that we're doing when we find these conservation laws. You know,
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  Speaker 1: we are looking around to trying to figure out, like
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  Speaker 1: what is important in the universe, what's a meaningful thing?
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  Speaker 1: Like when we think, oh, maybe energy is conserved in
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  Speaker 1: the universe, we just look around. We notice that. We say, like, okay,
• 8:41
  Speaker 1: you have a bunch of energy in this configuration. You
• 8:43
  Speaker 1: let the universe do its thing, and you notice, oh,
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  Speaker 1: there's the same amount of total energy. That suggests that
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  Speaker 1: maybe energy is like important, it's fundamental, it's interesting, more
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  Speaker 1: important than like, you know, the number of ice cream
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  Speaker 1: cones in the universe, which changes a lot with time.
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  Speaker 1: There's billions of years there was no ice cream and
• 9:01
  Speaker 1: then a brief flash of ice cream, and who knows
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  Speaker 1: whether they'll be ice cream in the future. But nobody
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  Speaker 1: expects the number of ice cream cones to be conserved
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  Speaker 1: because nobody thinks that that's an important thing in the universe.
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  Speaker 1: So if something is conserved, that suggests it is probably
• 9:15
  Speaker 1: important somehow to the universe. Well, Daniel, I think ice
• 9:18
  Speaker 1: cream is important about you, but it's an important part
• 9:21
  Speaker 1: of my diet for sure. Well, if only the things
• 9:24
  Speaker 1: that are important to you are also important to the universe,
• 9:29
  Speaker 1: I think ice cream is pretty important to a lot
• 9:30
  Speaker 1: of people. It's still around, it's it survived several lost
• 9:35
  Speaker 1: trying to ban But if ice cream was conserved, then
• 9:38
  Speaker 1: you could ask questions like, well, where did this ice
• 9:41
  Speaker 1: cream come from? More? Where does the ice cream go?
• 9:43
  Speaker 1: When you eat it? Right? It turns into something else
• 9:46
  Speaker 1: which is not ice cream. So that suggests that what's
• 9:48
  Speaker 1: conserved is not ice cream, but like some larger category
• 9:51
  Speaker 1: of things anyway, it's the same thing with energy and
• 9:54
  Speaker 1: with momentum. We discover whether these things are conserved by
• 9:57
  Speaker 1: the universe, and then we get to ask what does
• 9:59
  Speaker 1: that mean about the nature of the universe, right, because
• 10:02
  Speaker 1: I guess asking these questions is how we understand the universe, right, Like,
• 10:05
  Speaker 1: it's one thing to notice trends in it, but it's
• 10:07
  Speaker 1: another to sort of understand why the universe has these trends,
• 10:10
  Speaker 1: and like why do certain things that conserved and others don't?
• 10:14
  Speaker 1: You know, what does it mean about the universe? Can
• 10:16
  Speaker 1: we find some fundamental principle that tells us about all
• 10:19
  Speaker 1: these conservation laws where they come from. The wonderful thing
• 10:22
  Speaker 1: about science is that every answer leads to more questions.
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  Speaker 1: You know, the question number one could be what's conserved
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  Speaker 1: in the universe? Question number two is said, all right, well,
• 10:28
  Speaker 1: why these things and not other things? Always leads to
• 10:31
  Speaker 1: more questions which reveal a deeper truth of the universe.
• 10:34
  Speaker 1: That's the joy of science that the questions never do end. Well,
• 10:37
  Speaker 1: let's reveal some deeper truths today. So today on the podcast,
• 10:40
  Speaker 1: we'll be asking the question why is momentum conserved? Okay, so, Daniel,
• 10:50
  Speaker 1: you saying that energy is not conserved in the universe.
• 10:53
  Speaker 1: We have a podcast discussing that. But momentum is conserved.
• 10:55
  Speaker 1: Does that mean momentum is more important than energy? That's
• 10:59
  Speaker 1: a good question. Yeah. I would say that momentum conservation
• 11:02
  Speaker 1: tells us something fundamental about the nature of the universe
• 11:05
  Speaker 1: and the nature of space, which we'll get into. The
• 11:08
  Speaker 1: fact that energy is not conserved actually also tells us
• 11:11
  Speaker 1: something about the universe and the nature of time. I
• 11:15
  Speaker 1: think both of those facts, that momentum is conserved and
• 11:17
  Speaker 1: that energy is not do tell us something deep about
• 11:20
  Speaker 1: the nature of the universe. But yeah, I think momentum
• 11:23
  Speaker 1: fundamentally is more important. If you had like a competition
• 11:26
  Speaker 1: between quantities and physics, I would vote for momentum over energy.
• 11:30
  Speaker 1: Who would win in a fight, momentum or energy. Momentum
• 11:34
  Speaker 1: is a vector also, right, so it has multiple components.
• 11:37
  Speaker 1: It would definitely defeat energy, which is just a scale.
• 11:39
  Speaker 1: It's just a number. So momentum is a bigger army.
• 11:42
  Speaker 1: I see. Yeah. Also momentum has more momentum going for it.
• 11:46
  Speaker 1: You know that's important in a fight. Yeah, it's momentous, right,
• 11:48
  Speaker 1: but only in the moment. Maybe they should have called
• 11:51
  Speaker 1: it importum instead of momentum. Yeah, I'm not sure renaming
• 11:55
  Speaker 1: and would help there. But this is a fascinating question,
• 11:58
  Speaker 1: like why is momentum conserved? Because, as you were saying earlier,
• 12:01
  Speaker 1: does something you learn you know early on, like high school,
• 12:05
  Speaker 1: middle school, maybe even before, like the idea that if
• 12:08
  Speaker 1: something is in motion, it stays in motion, and if
• 12:11
  Speaker 1: something is address it it will stay in the rest
• 12:13
  Speaker 1: unless something changes m And I think that when people
• 12:16
  Speaker 1: learn about these conservation laws, the one that's most intuitive
• 12:20
  Speaker 1: is the one that's actually least true. You know, conservation
• 12:23
  Speaker 1: of mass, it sort of feels like it should make sense.
• 12:26
  Speaker 1: Like you have a chemical reaction. You start out with
• 12:29
  Speaker 1: a bunch of little lego brick chemical atoms and molecules,
• 12:32
  Speaker 1: and all you're doing is rearranging them, so of course
• 12:34
  Speaker 1: you should end up with the same amount of stuff
• 12:35
  Speaker 1: at the end. And that's the one that seems to
• 12:38
  Speaker 1: make the most sense to people. And I think that's
• 12:40
  Speaker 1: a revealing example because it makes sense because you think
• 12:42
  Speaker 1: of like stuff as being basic and fundamental to the universe.
• 12:46
  Speaker 1: Is that can be like created or destroyed, And you
• 12:48
  Speaker 1: hear that a lot in science fiction. Of course, now
• 12:50
  Speaker 1: we know that it's not and you can destroy mass
• 12:53
  Speaker 1: and turn into energy, and you can turn energy into
• 12:55
  Speaker 1: mass and all that kind of stuff. But you know,
• 12:56
  Speaker 1: the idea that a conservation law tells you about what's
• 12:59
  Speaker 1: important in the verse is sort of underlying all of this.
• 13:02
  Speaker 1: And I remember learning about conservation momentum and wondering, like, well,
• 13:05
  Speaker 1: what does that mean is conserved? Is like what does
• 13:07
  Speaker 1: that mean about the nature of the universe. Well, and
• 13:10
  Speaker 1: in the case of mass, I mean, you just kind
• 13:12
  Speaker 1: of have to figure that all mass is really energy, right,
• 13:15
  Speaker 1: And so then you're just it's like it's embedded in
• 13:18
  Speaker 1: the question of is energy conserved in the universe, which
• 13:21
  Speaker 1: it generally is, just to be clear, but we've recently
• 13:25
  Speaker 1: found that sometimes energy is not conserved. Yeah, it's a
• 13:28
  Speaker 1: nice idea to generalize the conservation and mass into the
• 13:31
  Speaker 1: conservation of energy and say mass is just one form
• 13:34
  Speaker 1: of energy. So when it disappears in the energy, that's okay,
• 13:36
  Speaker 1: because it's not true that mass is the fundamental stuff
• 13:40
  Speaker 1: in the universe. Energy is right. But then, as you say,
• 13:42
  Speaker 1: we discovered, actually the universe doesn't really care if energy
• 13:46
  Speaker 1: is conserved. It can just go away and we can
• 13:49
  Speaker 1: just sort of increase it. So dig into that podcast
• 13:52
  Speaker 1: if you're curious about that. But what that tells us
• 13:54
  Speaker 1: is that energy is not like the fundamental element of
• 13:57
  Speaker 1: the universe. It's more like ice cream cones. It's just
• 13:59
  Speaker 1: like something we came up with that makes sense to
• 14:02
  Speaker 1: us or is important to us. It's not deeply true.
• 14:05
  Speaker 1: It's not a deep feature of the universe. It's not
• 14:07
  Speaker 1: the chocolate ice cream of the universe. Maybe or are
• 14:10
  Speaker 1: the same momentum is a vanilla ice cream of the universe.
• 14:14
  Speaker 1: First of all, ice cream is not important to the
• 14:16
  Speaker 1: universe only and humans. But I guess we would be
• 14:19
  Speaker 1: saying that, you know, momentum is the dark chocolate at
• 14:21
  Speaker 1: the universe and energy is the white chocolate, well chocolate aside,
• 14:27
  Speaker 1: this is an interesting question why is momentum conserved? Because
• 14:30
  Speaker 1: we we all the field like it's true, and it
• 14:33
  Speaker 1: does seem to be true so far, But the question
• 14:35
  Speaker 1: is why does it get conserved in the universe. So,
• 14:38
  Speaker 1: as usual, we were wondering how many people out there
• 14:40
  Speaker 1: think they have an answer to this interesting and deep
• 14:43
  Speaker 1: question about how everything works. And thank you to our
• 14:46
  Speaker 1: volunteers who are willing to answer deep, difficult questions of
• 14:50
  Speaker 1: physics without any chance to prepare, so that we can
• 14:53
  Speaker 1: get a senswer what people out there are thinking. If
• 14:55
  Speaker 1: you'd like to participate, please you are very welcome right
• 14:58
  Speaker 1: to us to questions at Daniel and Jorge dot com.
• 15:01
  Speaker 1: So Daniel asked this question on the internet, why is
• 15:04
  Speaker 1: momentum conserved? And here's what people had to say. I'm
• 15:07
  Speaker 1: not really sure that momentum is preserved because momentum massive
• 15:13
  Speaker 1: velocity a product of mass and velocity and velocities relatives.
• 15:17
  Speaker 1: So if some velocities relative, I don't know how it
• 15:20
  Speaker 1: could be preserved, because if somebody else measures it, it's
• 15:24
  Speaker 1: going to be a different velocity. I was just took
• 15:26
  Speaker 1: that kind of as a given and never really questioned
• 15:29
  Speaker 1: why why. It's just because they tell us it's always conserved.
• 15:33
  Speaker 1: But it's related to, you know, a closed system of
• 15:37
  Speaker 1: matter and energy. None of that matter energy is created
• 15:43
  Speaker 1: or loss. It's just converted one way or the other.
• 15:45
  Speaker 1: And since momentum is in a way of function of
• 15:49
  Speaker 1: your mass and your energy, then it's just always there.
• 15:53
  Speaker 1: It can't it can't be bled off into another dimension
• 15:56
  Speaker 1: or something as far as I know, well, I guess
• 16:00
  Speaker 1: the reason momentum is conserved is because of Mutant said so,
• 16:05
  Speaker 1: and Einstein said so, maybe both of them. I think
• 16:11
  Speaker 1: all that we've been able to observe so far indicates
• 16:16
  Speaker 1: that momentum is conserved in terms of interactions that we've
• 16:20
  Speaker 1: measured those kinds of things. In terms of a conceptual
• 16:27
  Speaker 1: reason behind why momentum should be something that is conserved,
• 16:32
  Speaker 1: I don't know if there's any good explanation for that.
• 16:37
  Speaker 1: Thinking about a collision right now between let's say two objects,
• 16:43
  Speaker 1: and why is consu so an energy to another object
• 16:49
  Speaker 1: is transferred to the other one. So um is conserved
• 16:57
  Speaker 1: because nothing the energy, it's constantly nothing, It's wasted. Everything
• 17:04
  Speaker 1: gets transferred or transformed. Momentum may be described as mass
• 17:11
  Speaker 1: times velocity. It may further be described as the second
• 17:17
  Speaker 1: law of thermodynamics, or is it Newton's second law of motion?
• 17:22
  Speaker 1: I forget college was a long time ago. However, the
• 17:26
  Speaker 1: question of why is it preserved, I think is something
• 17:30
  Speaker 1: nobody knows yet. I think it just all has to
• 17:33
  Speaker 1: do with the way energy is transferred. So if I
• 17:36
  Speaker 1: were to be pushing something, for me to be pushing
• 17:39
  Speaker 1: that thing so it moves, I need to be adding
• 17:42
  Speaker 1: energy to the system. I need to be pushing it
• 17:45
  Speaker 1: and adding a force and therefore transferring energy from me
• 17:48
  Speaker 1: into it. But just due to the way Newton's laws work,
• 17:53
  Speaker 1: it too has to be pushing back on me. All right,
• 17:56
  Speaker 1: what do you think of the answer? I like the
• 17:59
  Speaker 1: because new And said so, and Einstein agreed. They're like
• 18:02
  Speaker 1: a council of physics, and they decide what's true. Oh,
• 18:06
  Speaker 1: maybe my kids should try that the next time. Their
• 18:09
  Speaker 1: parents don't know. But Newton said so, and Einstein agreed
• 18:13
  Speaker 1: that you should go to bed two out of two
• 18:16
  Speaker 1: seminal physicists agreed as if physicists have any voice and
• 18:21
  Speaker 1: anything relevant at all. You know, do you think physics
• 18:24
  Speaker 1: and general is sort of done by by polling and
• 18:27
  Speaker 1: kind of right, like, there's a little bit of sense
• 18:29
  Speaker 1: that in science it's about what the majority thinks is true. Right,
• 18:33
  Speaker 1: that's true. The consensus view is important, although you know,
• 18:36
  Speaker 1: one person against the world doesn't have to be wrong,
• 18:39
  Speaker 1: and in some cases, like one seminal physicists can persuade
• 18:43
  Speaker 1: a lot of folks. You know, if you say, well,
• 18:45
  Speaker 1: Einstein thought this, or Murray Gelman said that, or Feineman
• 18:48
  Speaker 1: put it this way, that can be pretty persuasive. But
• 18:51
  Speaker 1: I guess in general, none of the answers questioned that
• 18:53
  Speaker 1: idea that momentum is conserved, right, Nobody said, like, who
• 18:56
  Speaker 1: said momentum is conserved? Yeah, though some people thought that
• 18:59
  Speaker 1: we don't know the answer that we have no idea
• 19:02
  Speaker 1: why momentum is conserved, sort of like why is the
• 19:04
  Speaker 1: speed of light? What it is? We don't know, we
• 19:06
  Speaker 1: just measure it. Some people put it in that category.
• 19:09
  Speaker 1: I think they've been listening to our podcast and reading
• 19:11
  Speaker 1: our books too much. You know. Sometimes yes, is we
• 19:14
  Speaker 1: have no idea. You think they've become persuaded that physics
• 19:17
  Speaker 1: actually doesn't really know very much about the universe. Oh,
• 19:20
  Speaker 1: mission accomplished. We spoiled the ice cream. It just means
• 19:26
  Speaker 1: there's more ice cream of discovery left to eat for everybody. Well,
• 19:29
  Speaker 1: let's just recap it for people. So, momentum conservation means
• 19:33
  Speaker 1: that momentum is conservad Like, momentum is defined as what
• 19:36
  Speaker 1: mass times your velocity. Yes, so momentum for slow moving objects,
• 19:41
  Speaker 1: it's just mass times velocity. And when we say momentum
• 19:45
  Speaker 1: is conserved, we mean that if you have the momentum
• 19:48
  Speaker 1: of a bunch of stuff and then you let it
• 19:50
  Speaker 1: do its thing, follow the laws of physics, banging into
• 19:52
  Speaker 1: each other, bounce off of stuff, or just float through space,
• 19:56
  Speaker 1: and then later on you add up the momentum again
• 19:59
  Speaker 1: you should get the same number. And interestingly, momentum is
• 20:02
  Speaker 1: actually three different quantities. Is momentum and X momentum And
• 20:05
  Speaker 1: why momentum and z because we live in three dimensional
• 20:08
  Speaker 1: space and those are all independently conserved. The momentum conservation
• 20:12
  Speaker 1: is kind of three laws in one to deal Yeah, exactly.
• 20:17
  Speaker 1: For those of you who do like classical mechanics or
• 20:19
  Speaker 1: freshman physics. You know, that makes it very powerful because
• 20:22
  Speaker 1: you get three equations to constrain your answer rather than
• 20:24
  Speaker 1: just one from conservation of energy. Right, But you were
• 20:28
  Speaker 1: saying that it's only for slow moving things, like it's
• 20:30
  Speaker 1: different for other things. It turns out in relativity, the
• 20:34
  Speaker 1: definition of momentum is different from just mass times velocity.
• 20:38
  Speaker 1: There's this boost factor we call it the Gamma factor
• 20:41
  Speaker 1: or the Lorentz factor, which is one for slow moving
• 20:44
  Speaker 1: objects and approaches infinity as things get towards the speed
• 20:47
  Speaker 1: of light. So the real equation for momentum is mass
• 20:51
  Speaker 1: times velocity times this Gamma factor. We never noticed because
• 20:55
  Speaker 1: the Gama factor is close to one, so you can
• 20:57
  Speaker 1: ignore it for stuff that's less than you know, like
• 21:00
  Speaker 1: half the speed of light or a third at the
• 21:01
  Speaker 1: speed of light. But it becomes important as you get
• 21:04
  Speaker 1: near the speed of light. Oh, I said, you have
• 21:06
  Speaker 1: to do You have to adjust it because nothing can
• 21:08
  Speaker 1: go faster than the speed of light because it has
• 21:10
  Speaker 1: to have a limit, Like you can have momentum that's
• 21:12
  Speaker 1: greater than the speed of light. You have to adjust
• 21:14
  Speaker 1: in order to get conservation momentum, like the quantity that
• 21:17
  Speaker 1: is conserved is not mass times velocity. It's mass times
• 21:21
  Speaker 1: velocity times gamma. And you notice this as you get
• 21:24
  Speaker 1: to very high velocities. In order have conservation before and
• 21:27
  Speaker 1: after some interaction, for example, you have to use gamma
• 21:30
  Speaker 1: mass velocity, not just mass and velocity. And this is
• 21:33
  Speaker 1: actually the source of a lot of misunderstanding about relativistic physics.
• 21:37
  Speaker 1: People used to define gamma times mass as this weird
• 21:41
  Speaker 1: relativistic mass and say things like your mass gets really
• 21:44
  Speaker 1: large as you go towards high speeds because they wanted
• 21:48
  Speaker 1: to redefine momentum to be relativistic mass times velocity. Anyway,
• 21:52
  Speaker 1: we're gonna do a whole podcast about that question about
• 21:54
  Speaker 1: whether your mass actually does get larger as you approach
• 21:58
  Speaker 1: the speed of light. Sure answer is it doesn't. Right Right, Well,
• 22:01
  Speaker 1: I think at least for slow moving objects, it does
• 22:04
  Speaker 1: kind of match what people's intuition is about momentum, right,
• 22:07
  Speaker 1: like mass time velocity. We have something large, even if
• 22:11
  Speaker 1: it's moving slow, it has a lot of momentum and
• 22:13
  Speaker 1: it's hard to stop. But even something is small and
• 22:16
  Speaker 1: has a lot of velocity, it's also hard to stop.
• 22:19
  Speaker 1: Right like a bullet, it's pretty hard to stop if
• 22:21
  Speaker 1: it's coming towards you. It's so it's sort of like
• 22:24
  Speaker 1: it's a sense of how hard it is to stop
• 22:25
  Speaker 1: and wait. Yeah, and Newton's law force equals mass times
• 22:29
  Speaker 1: acceleration says exactly that. Another way to write Newton's law
• 22:32
  Speaker 1: instead of mass times acceleration is a change in momentum.
• 22:35
  Speaker 1: So Newton's law is force is the change in momentum.
• 22:38
  Speaker 1: If you want to change something's momentum by a lot,
• 22:40
  Speaker 1: it takes a big force. You want to change something
• 22:41
  Speaker 1: momentum by a little bit takes a smaller force. And
• 22:45
  Speaker 1: said another way, something with a lot of momentum takes
• 22:47
  Speaker 1: more force to stop. Something without a lot of momentum
• 22:50
  Speaker 1: doesn't take much force to stop, right, And the idea
• 22:53
  Speaker 1: that it's conserved means that it like it goes somewhere right,
• 22:56
  Speaker 1: or like if I try to stop a train and
• 23:00
  Speaker 1: may be able to stop it, but that momentum has
• 23:02
  Speaker 1: to go somewhere. That's right. If you throw a tennis ball,
• 23:04
  Speaker 1: for example, in front of a train, it will push
• 23:07
  Speaker 1: that tennis ball really really fast and slow down the
• 23:09
  Speaker 1: train a little bit. So the total momentum is the
• 23:12
  Speaker 1: same momentum can flow, as you say, from one object
• 23:15
  Speaker 1: to another, but the total momentum has to stay the
• 23:17
  Speaker 1: same before and after every physics process. Right. And the
• 23:21
  Speaker 1: weird thing is like like it's not like somebody's like
• 23:24
  Speaker 1: overseeing this transaction, right, Like it just happens, right when
• 23:29
  Speaker 1: things interact, somehow momentum is concerned. But it's not like
• 23:32
  Speaker 1: momentum actually flowed from one thing to do They just
• 23:35
  Speaker 1: pushed on each other and somehow momentum was conserved. Wow,
• 23:38
  Speaker 1: what a touch on like deep questions of philosophy. Does
• 23:41
  Speaker 1: the universe like calculate what's happening and follow some laws
• 23:45
  Speaker 1: like it's some big computer following a program, or does
• 23:48
  Speaker 1: it just happen and we're observing it and trying to
• 23:50
  Speaker 1: tell our own mathematical stories about it. We don't really know.
• 23:54
  Speaker 1: What we notice is that it does happen, and it
• 23:56
  Speaker 1: does tell us something about the nature of the universe. Yeah,
• 24:00
  Speaker 1: we don't really know sort of like how it happens.
• 24:02
  Speaker 1: All right, Well, we know it's conserved momentum, and so
• 24:05
  Speaker 1: let's ask the question why it's conserved, and let's get
• 24:09
  Speaker 1: into that, and we'll get into the person who actually
• 24:11
  Speaker 1: made this big breakthrough but first, let's take a quick break.
• 24:27
  Speaker 1: All right, we're talking about ice cream. It seems Daniel,
• 24:29
  Speaker 1: are you are you hungry dating some dessert right now?
• 24:34
  Speaker 1: That's for two reasons. One is because we record this
• 24:37
  Speaker 1: podcast around lunchtime, and the other reason is that today
• 24:40
  Speaker 1: is the birthday of the person who solved this riddle
• 24:44
  Speaker 1: and maybe one of the most important contributions in physics.
• 24:47
  Speaker 1: M that's right, Yeah, the person who discovered the basically
• 24:51
  Speaker 1: the answer to the question that we're asking today, why
• 24:54
  Speaker 1: is momentum conserved? So we talked about why that momentum
• 24:58
  Speaker 1: is conserved, what momentum is, and it just seems to
• 25:01
  Speaker 1: be conserved in the universe. And so Daniel, I guess
• 25:04
  Speaker 1: what's the answer wise, momentum conserved. It has something to
• 25:08
  Speaker 1: do with symmetries, that's right. So, I mean the mathematician
• 25:11
  Speaker 1: who just dabbled in physics about a hundred years ago,
• 25:14
  Speaker 1: she turns a hundred and forty today, the day we're
• 25:17
  Speaker 1: recording this podcast. She discovered that there's a really deep
• 25:20
  Speaker 1: connection between these conservation laws and symmetries of the universe.
• 25:25
  Speaker 1: So patterns that we see in the universe are connected
• 25:29
  Speaker 1: to these symmetries. So what do we mean by symmetries.
• 25:32
  Speaker 1: This is a case where we're using the totally normal
• 25:34
  Speaker 1: definition of a symmetry. We don't haven't like imbuted with
• 25:36
  Speaker 1: any special confusing meaning. It just means that, like you
• 25:40
  Speaker 1: change something and there's no impact, Like you could take
• 25:43
  Speaker 1: a ball and rotated and doesn't change the ball at all.
• 25:46
  Speaker 1: It still behaves the same way, it still looks the
• 25:49
  Speaker 1: same way. As an example of a symmetry where you
• 25:52
  Speaker 1: can take a road which is a straight line and
• 25:54
  Speaker 1: shifted by a hundreds and if it's a straight line,
• 25:57
  Speaker 1: it doesn't change it at all, or it's the same road.
• 25:59
  Speaker 1: The these kinds of symmetries turn out to be really
• 26:02
  Speaker 1: important in the nature of the universe and are connected
• 26:05
  Speaker 1: to these conservation laws, right right, But let's maybe take
• 26:08
  Speaker 1: a step back, right because I think the history of
• 26:12
  Speaker 1: this is that we knew that momentum was conserved, and
• 26:15
  Speaker 1: at the same time we're discovering something about the universe
• 26:18
  Speaker 1: that it is sort of symmetric in these weird and
• 26:21
  Speaker 1: interesting ways. And so maybe before we make that connection,
• 26:25
  Speaker 1: maybe step us through, like what exactly is a symmetry
• 26:28
  Speaker 1: in the universe? So there are lots of cool symmetries
• 26:30
  Speaker 1: in the universe. One of them is that space seems
• 26:33
  Speaker 1: to be the same everywhere, Like the nature of this
• 26:37
  Speaker 1: universe we find ourselves in doesn't change based on where
• 26:40
  Speaker 1: you are. You do an experiment to measure something fundamental
• 26:44
  Speaker 1: about the universe, it doesn't matter where in the universe
• 26:47
  Speaker 1: you measure it. Or said another way, if you shifted
• 26:50
  Speaker 1: the whole universe over by ten meters, no one would
• 26:54
  Speaker 1: be able to notice, right, the universe is the same,
• 26:56
  Speaker 1: no matter sort of where it is, right right. Yeah,
• 26:59
  Speaker 1: that's a pretty a cool idea. But I think maybe
• 27:01
  Speaker 1: I wonder what confuses people a lot sometimes is that
• 27:04
  Speaker 1: the name symmetry is a little bit different than what
• 27:07
  Speaker 1: you just describe, right, Like to I think the most
• 27:09
  Speaker 1: people that the word symmetry, it kind of means like
• 27:11
  Speaker 1: it's the mirror opposite, or like if I have a
• 27:15
  Speaker 1: pattern and a piece of paper, and then I have
• 27:17
  Speaker 1: the mirror image of the pattern right next to it,
• 27:20
  Speaker 1: then we would say the whole drawing is sort of
• 27:22
  Speaker 1: symmetric because it's the same left or right right, And
• 27:25
  Speaker 1: that's an example of what we consider a discrete symmetry. Right,
• 27:28
  Speaker 1: you can like flip the whole image and it looks
• 27:31
  Speaker 1: the same. Continuous symmetry is like take a piece of
• 27:34
  Speaker 1: paper and draw a circle. That circle is the same
• 27:37
  Speaker 1: no matter how much you rotated, and there's an infinite
• 27:39
  Speaker 1: number of ways you could rotate it and not change
• 27:42
  Speaker 1: the circle. Right. Or if you have an infinite sheet
• 27:44
  Speaker 1: of paper and you drew a picture, it wouldn't really
• 27:47
  Speaker 1: matter where you drew that picture. You can draw it
• 27:49
  Speaker 1: here or draw it there. It would be the same
• 27:51
  Speaker 1: because the paper is infinite. Right. But I guess maybe
• 27:54
  Speaker 1: I wonder like a more a better world would have been,
• 27:56
  Speaker 1: like you know, consistency or constancy of of things, right,
• 28:01
  Speaker 1: Because I think the reason you guys use symmetry. The
• 28:03
  Speaker 1: word symmetry is that it has to do with the
• 28:05
  Speaker 1: equations of motion of the universe, right, Like if you
• 28:09
  Speaker 1: apply like a mirror transformation or some kind of transformation
• 28:12
  Speaker 1: to the equations, and then it should stay the same. Yes,
• 28:15
  Speaker 1: So to totally generalize the word symmetry, what mathematicians mean
• 28:18
  Speaker 1: by it is that you make some kind of transformation
• 28:21
  Speaker 1: to the universe and then that doesn't change whatever it
• 28:24
  Speaker 1: is you're interested in. So, in the case of physics,
• 28:26
  Speaker 1: we make some sort of transformation to the universe, like
• 28:29
  Speaker 1: we shifted the left hun your feet, or we rotated
• 28:32
  Speaker 1: around some angle. And then the thing we're interested in
• 28:34
  Speaker 1: are are the laws of physics the same as you said,
• 28:37
  Speaker 1: like the equations of motion? Would you predict that Joorhes
• 28:39
  Speaker 1: apple flies through the air and lands in his hand
• 28:42
  Speaker 1: the same way if you put your access over here,
• 28:45
  Speaker 1: or if you said you know zero is over there,
• 28:48
  Speaker 1: or if you did the problem upside down, when you
• 28:50
  Speaker 1: get the same answer, If so, then there's a symmetry
• 28:52
  Speaker 1: to the problem. Or even like if I move the
• 28:55
  Speaker 1: Earth a few light years to the right, it should
• 28:57
  Speaker 1: still be the same, right, Yeah, if you the whole
• 28:59
  Speaker 1: universe right a few light years to the right, nobody
• 29:02
  Speaker 1: could do an experiment to determine that that's the case,
• 29:05
  Speaker 1: that that's happened, because no place in space is different. Right,
• 29:08
  Speaker 1: the rules should be the same everywhere. Right, So when
• 29:11
  Speaker 1: you hear the word symmetry in physics, really maybe in
• 29:13
  Speaker 1: your head you should be thinking like a constancy in
• 29:16
  Speaker 1: the universe, or like a invariability or something that doesn't
• 29:19
  Speaker 1: change when you move it or rotated or flipid. Right, right,
• 29:22
  Speaker 1: I like that there's no word in physics that you're
• 29:25
  Speaker 1: not up for redefining and improving. You know, science is
• 29:28
  Speaker 1: a constant project, and so we're always striving to improve.
• 29:31
  Speaker 1: But there is a bit of confusion there because if
• 29:33
  Speaker 1: you call it like an invariability, it comes close to
• 29:36
  Speaker 1: another word we use, which is invariance, which actually means
• 29:40
  Speaker 1: something quite different. Right. Invariance means no matter who's measuring it,
• 29:44
  Speaker 1: you always get the same answer. An example of an
• 29:47
  Speaker 1: invariant is like the speed of light. Everybody measures the
• 29:50
  Speaker 1: speed of light to be the same quantity, no matter
• 29:52
  Speaker 1: where you are or how fast you're traveling. Momentum is conserved,
• 29:56
  Speaker 1: we say, but it's not invariant because for examp people,
• 30:00
  Speaker 1: you are standing still, you measure your velocity be zero.
• 30:04
  Speaker 1: I'm moving past you. I measure your velocity to be
• 30:07
  Speaker 1: non zero, so I measure you'd have momentum. You measure
• 30:10
  Speaker 1: yourself to have no momentum. Momentum is not the same
• 30:13
  Speaker 1: for all observers, though it's always conserved. I will see
• 30:16
  Speaker 1: your momentum is conserved. You will see your momentum is conserved,
• 30:19
  Speaker 1: but it's not invariant. So invariant means something different in physics, yeah.
• 30:23
  Speaker 1: I mean, I'm not saying you should not use the
• 30:25
  Speaker 1: word symmetry. I'm just saying that it might be helpful
• 30:28
  Speaker 1: for people just kind of understand what's going on. If
• 30:30
  Speaker 1: if when they hear the words symmetry, they should sort
• 30:32
  Speaker 1: of be thinking more about like that things are the
• 30:34
  Speaker 1: same no matter if you move them over here, or
• 30:36
  Speaker 1: you do you throw the apple over here over there
• 30:39
  Speaker 1: or upside down, or if you rotate the whole universe
• 30:42
  Speaker 1: ninety degrees, it should still fall down back to my
• 30:44
  Speaker 1: head exactly. And those are a few examples of symmetries, right,
• 30:48
  Speaker 1: Like if you shift the whole universe over your experiment
• 30:50
  Speaker 1: should work the same way, you know, And that's true
• 30:53
  Speaker 1: if space is not different in different places in the universe.
• 30:57
  Speaker 1: If it were different, right, if space was like different
• 30:59
  Speaker 1: over there are and over here, if you have different
• 31:01
  Speaker 1: laws of physics over there and over here, you'll be
• 31:03
  Speaker 1: able to tell sort of like where the universe is
• 31:05
  Speaker 1: relative to those like different parts of space. That will
• 31:09
  Speaker 1: be fascinating. Um, but it seems to us so far
• 31:12
  Speaker 1: like space is the same everywhere. And that's a pretty
• 31:15
  Speaker 1: deep symmetry, right. It tells you something about the nature
• 31:18
  Speaker 1: of the universe itself, that the experiments are the same
• 31:20
  Speaker 1: everywhere you go, and the same seems to be true
• 31:23
  Speaker 1: for rotating, Like there's no up or down in the universe.
• 31:26
  Speaker 1: You could rotate the whole universe and you wouldn't be
• 31:29
  Speaker 1: able to notice that it had been rotated in the
• 31:32
  Speaker 1: sense that you mean that, you know, the laws of
• 31:34
  Speaker 1: physics don't change, and your experiments get the same results. Right,
• 31:38
  Speaker 1: But I wonder if that's sort of dependent on spacetime, right,
• 31:41
  Speaker 1: Like do you depend does that depend on flat space
• 31:44
  Speaker 1: time or you know, would that be still be the
• 31:46
  Speaker 1: same around close to the black hole or something where
• 31:49
  Speaker 1: spacetime is sort of bent or distorted. Yeah, it's a
• 31:52
  Speaker 1: good question, you know. So you might ask, like, I
• 31:54
  Speaker 1: do an experiment here and I notice my apple falls.
• 31:57
  Speaker 1: What if I move Jorge near a black hole, wouldn't
• 32:00
  Speaker 1: as apple fall differently? Yeah? Wouldn't you like that? Right?
• 32:04
  Speaker 1: You know? Then who would eat all the ice cream?
• 32:06
  Speaker 1: You know, I need somebody else to eat it so
• 32:07
  Speaker 1: I don't gain too much weight and become a black
• 32:09
  Speaker 1: hole myself. It would all fall into the black hole,
• 32:12
  Speaker 1: all right, So we can throw you into black hole
• 32:13
  Speaker 1: as long as we send a continuous stream of ice
• 32:16
  Speaker 1: cream scoops as well. Let's keep it as a thought experiment. No,
• 32:19
  Speaker 1: that's a good question, and you know, essentially the issue
• 32:22
  Speaker 1: there is that the black hole is sort of part
• 32:25
  Speaker 1: of your experiment, and so underlying space itself isn't change.
• 32:30
  Speaker 1: But the sort of laboratory of the experiment you're doing,
• 32:33
  Speaker 1: um includes a black hole in one scenario and doesn't
• 32:36
  Speaker 1: in the other scenario. That's why you get different outcomes
• 32:38
  Speaker 1: because you're sort of doing a different experiment. I see.
• 32:42
  Speaker 1: But so the theory still works no matter what what's
• 32:45
  Speaker 1: happening with space time. Yeah, although if it's not true
• 32:48
  Speaker 1: that space is the same everywhere, then the theory doesn't hold.
• 32:51
  Speaker 1: You know, for example, what if space was not like
• 32:54
  Speaker 1: continuous and infinite, what if it had a boundary, as
• 32:57
  Speaker 1: you've mentioned on several podcasts, there was like an edge
• 33:00
  Speaker 1: to it. Then you know, the laws of physics would
• 33:02
  Speaker 1: be different at the edge because space would be different
• 33:04
  Speaker 1: at the edge. Different things would have to happen. So
• 33:07
  Speaker 1: maybe the laws of physics would be different at the edge.
• 33:09
  Speaker 1: We don't actually know, right, is there a boundary to
• 33:12
  Speaker 1: space and doesn't go on forever? Another possible way that
• 33:15
  Speaker 1: it could not be true. Is like if space is
• 33:17
  Speaker 1: not continuous, if it's like pixelized or like a crystal,
• 33:21
  Speaker 1: then it might not have a continuous symmetry. You might
• 33:23
  Speaker 1: be like location is a symmetry up to a certain value.
• 33:27
  Speaker 1: You know, if you take like certain steps in space,
• 33:30
  Speaker 1: you get the same answer. But if you take like
• 33:31
  Speaker 1: a half step, maybe you get a different answer because
• 33:33
  Speaker 1: you're sort of like caught between two parts of the crystal. Yeah,
• 33:36
  Speaker 1: if it's quantum, then it maybe wouldn't be a symmetric,
• 33:40
  Speaker 1: But I guess to sort of generalize it though, as
• 33:42
  Speaker 1: far as we know, it's it is symmetric the laws
• 33:46
  Speaker 1: of physics throughout all of spacetime, as far as we know.
• 33:49
  Speaker 1: As far as we know, it's symmetric to translations, shifts,
• 33:52
  Speaker 1: and symmetric to rotations. And with a couple of exceptions,
• 33:57
  Speaker 1: it is symmetric two shifts in time. Like if you
• 34:00
  Speaker 1: do an experiment today and you experiment in a hundred years,
• 34:04
  Speaker 1: then you should get the same answer because the laws
• 34:06
  Speaker 1: of physics, we think don't change in time. Those are
• 34:08
  Speaker 1: three really basic symmetries that we've discovered in physics, right, translation, rotation,
• 34:13
  Speaker 1: and time, And that even applies to like moving backwards
• 34:17
  Speaker 1: in time, right, it does, Yeah, in the sense that
• 34:19
  Speaker 1: if you're comparing two experiments done at two different points
• 34:22
  Speaker 1: in time, one of them can be further back. But
• 34:24
  Speaker 1: I guess always one of them is further back, right,
• 34:26
  Speaker 1: It's it's not about time travel necessarily, all right. Well,
• 34:29
  Speaker 1: so that's the idea of symmetry in the universe. We
• 34:31
  Speaker 1: noticed that the equations of the universe have these symmetries
• 34:35
  Speaker 1: in them, but I guess we didn't know that they
• 34:37
  Speaker 1: were connected to the idea of conservation of momentum, right,
• 34:40
  Speaker 1: that's right, all right, So those are kind of like
• 34:42
  Speaker 1: the three main symmetries that the we've noticed about the
• 34:46
  Speaker 1: equations of the universe, and those are kind of like
• 34:48
  Speaker 1: the more intuitive one, but there are sort of deeper also,
• 34:51
  Speaker 1: symmetries kind of in that the quantum level. Right. Yeah.
• 34:54
  Speaker 1: We've talked about the podcast a few times about other
• 34:57
  Speaker 1: kinds of symmetries we've noticed in the universe. And these
• 35:01
  Speaker 1: are not things that are easy to grasp in your
• 35:03
  Speaker 1: mind because they're not things you see, but these are
• 35:06
  Speaker 1: like properties of quantum fields. And it turns out that
• 35:10
  Speaker 1: you can like rotate different quantum fields sort of into
• 35:13
  Speaker 1: each other. You can like swap in different colors of quarks,
• 35:18
  Speaker 1: turn red to green, and green to blue and blue
• 35:21
  Speaker 1: to red. Nothing changes in the universe, right, So we've
• 35:24
  Speaker 1: noticed these kinds of symmetries on the sort of like
• 35:26
  Speaker 1: quantum level that are very similar to these symmetries mathematically,
• 35:31
  Speaker 1: like they involved rotations, but not in a physical rotation
• 35:34
  Speaker 1: you know, like spinning anything. You're just sort of like
• 35:36
  Speaker 1: changing labels on quantum stuff. But these are just as
• 35:40
  Speaker 1: important and reveal also something really deeply true about the universe.
• 35:44
  Speaker 1: And we wouldn't have discovered the Higgs boson if we
• 35:46
  Speaker 1: hadn't noticed these symmetries. And again, these are like symmetries
• 35:49
  Speaker 1: or kind of invariant things you can do to the
• 35:52
  Speaker 1: equations that you're like, hey, wow, that's that's something strange
• 35:55
  Speaker 1: about the equations. They they are symmetric, They work no
• 35:58
  Speaker 1: matter what you do to it. Yeah, it just see
• 36:00
  Speaker 1: to matter in these cases, which gauge you choose. For
• 36:03
  Speaker 1: those of you who know like electrodynamics, you know that
• 36:06
  Speaker 1: there's sort of like an overall gauge you can choose
• 36:08
  Speaker 1: in electrodynamics and doesn't change the answers at all, just
• 36:11
  Speaker 1: like an arbitrary choice, just sort of like where you
• 36:14
  Speaker 1: choose your potential energy to be zero in classical mechanics problems.
• 36:18
  Speaker 1: It doesn't change the answer. It's just a choice. So
• 36:20
  Speaker 1: there's a symmetry there to the problem. You can change
• 36:22
  Speaker 1: these things and nothing changes and how you predict the
• 36:25
  Speaker 1: laws of physics, and that's in the same sense, you
• 36:27
  Speaker 1: can like change these things and how we describe these
• 36:30
  Speaker 1: quantum fields and doesn't make any difference for our predictions
• 36:33
  Speaker 1: for or how particles should interact with each other, right, right,
• 36:36
  Speaker 1: And I think we had a whole podcast about this
• 36:38
  Speaker 1: about this idea that you know, the word gauge here
• 36:41
  Speaker 1: it's sort of related to the idea of measuring something
• 36:43
  Speaker 1: or like having a reference you know, length or something. Yeah,
• 36:46
  Speaker 1: it actually comes from trains because back on the day,
• 36:48
  Speaker 1: people were building railroads all across the United States, and
• 36:51
  Speaker 1: they were building them of different gauges, and people thought like, Okay,
• 36:54
  Speaker 1: it's just sort of an arbitrary choice of train gauge.
• 36:57
  Speaker 1: So then when physicists were like making arbitrary choice in
• 37:00
  Speaker 1: their theories, they were trying to find a word that
• 37:02
  Speaker 1: captured that, like sort of sense of arbitrariness, as you say,
• 37:05
  Speaker 1: like to set a scale. So they chose the word
• 37:08
  Speaker 1: gauge because physicists love trains. I don't know why, like
• 37:10
  Speaker 1: in thought experiments, right yeah, well it's it's Europe, it's
• 37:16
  Speaker 1: full of trains, right, yeah. I suppose it was before
• 37:18
  Speaker 1: the air of the car that these things took over. So, yes,
• 37:20
  Speaker 1: that's right. You would just call them ubers today or lives.
• 37:26
  Speaker 1: All right. Well, so that's kind of where we were
• 37:27
  Speaker 1: in the history of physics. Like we knew that momentum
• 37:30
  Speaker 1: was conserved, like we could see it with simple experiments.
• 37:33
  Speaker 1: It seemed to work with with Newtonian physics. But at
• 37:35
  Speaker 1: the same time we had these more complex equations of
• 37:37
  Speaker 1: the universe and we noticed kind of these special symmetries
• 37:40
  Speaker 1: mathematical symmetries about them. But I guess people hadn't put
• 37:43
  Speaker 1: the two together right to make the connection. That's right.
• 37:46
  Speaker 1: We had noticed these properties of the universe that things
• 37:49
  Speaker 1: seem to be conserved, and we also noticed mathematically that
• 37:52
  Speaker 1: there were symmetries to our equations. Until we got a
• 37:56
  Speaker 1: very special physicist on the scene. And so let's talk
• 37:59
  Speaker 1: about her and how she put the two together and
• 38:02
  Speaker 1: answered the question basically, why is momentum conserved? But first
• 38:05
  Speaker 1: let's take another quick break. All right, we're asking the
• 38:20
  Speaker 1: question why is momentum conserved? And we know it has
• 38:23
  Speaker 1: something to do with symmetries, but um, we know nobody
• 38:26
  Speaker 1: had put the two and two together until is his
• 38:28
  Speaker 1: name there? That's right. Actually, she's a mathematician, Emmanuther, and
• 38:33
  Speaker 1: she was an expert in abstract algebra and really kind
• 38:37
  Speaker 1: of a genius, and she sort of got pulled into
• 38:40
  Speaker 1: a question in physics just very briefly wrote like, you know,
• 38:43
  Speaker 1: one paper on it and then moved back to a
• 38:45
  Speaker 1: real interest in math. But this one paper is basically
• 38:48
  Speaker 1: now the foundations of all of theoretical physics. Her, like
• 38:52
  Speaker 1: you know, side hustle turned out to be, you know,
• 38:55
  Speaker 1: the most important thing anybody's ever done. Man, does it
• 38:58
  Speaker 1: feel like you know, you guys, like the entire field
• 39:00
  Speaker 1: of physics was stuck and then they just like you know,
• 39:03
  Speaker 1: one mathematician had to take like a five minute break
• 39:05
  Speaker 1: from from their important work can come and saved all
• 39:08
  Speaker 1: of you. Yeah, And it's even more tragic than that
• 39:11
  Speaker 1: because due to the fact that she was a woman,
• 39:13
  Speaker 1: she wasn't even really allowed to participate in academia and
• 39:17
  Speaker 1: in research, even in mathematics, not necessarily just in physics.
• 39:20
  Speaker 1: And then when the history of all this stuff was written,
• 39:22
  Speaker 1: she was largely sidelined. So people, a lot of people
• 39:25
  Speaker 1: have never heard of Emmy Nuther, even though she's like
• 39:28
  Speaker 1: more influential than Einstein. WHOA All right, well, maybe take
• 39:33
  Speaker 1: us back. So she was around in the nineteen hundreds, right,
• 39:35
  Speaker 1: she was born before the nineteen hundreds. Yeah, she was
• 39:38
  Speaker 1: born in eighteen eighty two. You know, the end of
• 39:41
  Speaker 1: that century had like important mathematical work by like Rieman
• 39:45
  Speaker 1: and Mankowski, laying really the foundations for relativity that Einstein
• 39:50
  Speaker 1: would later pull together in the early nineteen hundreds and
• 39:53
  Speaker 1: teach us a whole new way to think about space
• 39:55
  Speaker 1: and time. So she was around during a sort of
• 39:57
  Speaker 1: very exciting time when mathematics was really informing physics. And
• 40:01
  Speaker 1: she came from a wealthy family and had academic background.
• 40:05
  Speaker 1: She professors in her family. But because she was a woman,
• 40:08
  Speaker 1: she was not even allowed to enroll in university. Like
• 40:12
  Speaker 1: it's just not a thing that women could do back then, Right,
• 40:15
  Speaker 1: this is like before Mary Curie became the first woman
• 40:18
  Speaker 1: in France to get a PhD. You know, it's just
• 40:20
  Speaker 1: like not something that women were allowed to do. Its
• 40:23
  Speaker 1: mind boggling now, but it was sort of the way
• 40:25
  Speaker 1: things were back then. Yeah, it's pretty tragic. And she
• 40:28
  Speaker 1: was born in Germany or yeah, she's German. She was
• 40:32
  Speaker 1: born in Bavaria, and she wanted to study in Gottingen
• 40:35
  Speaker 1: and they just didn't allow it until nineteen o three
• 40:39
  Speaker 1: when they finally allowed women to enroll. She'd been sitting
• 40:42
  Speaker 1: in on lectures of course for a while, not officially enrolled,
• 40:45
  Speaker 1: but then she was allowed to enroll, and then in
• 40:47
  Speaker 1: nineteen o seven she was only the second woman ever
• 40:50
  Speaker 1: to earn a PhD in mathematics in the world, right, basically, yeah,
• 40:56
  Speaker 1: in the world. And you know, they're famous folks out there, Hilbert,
• 41:00
  Speaker 1: I'm Minkowski Shortschild. All these folks knew her, and they
• 41:02
  Speaker 1: all knew and said that she was smarter than they were. Wow,
• 41:06
  Speaker 1: these are like, you know, seminal you know, mathematicians in physics. Yeah, absolutely,
• 41:12
  Speaker 1: and yet there were a lot of institutional barriers. For
• 41:14
  Speaker 1: eight years after she got her PhD, she was doing
• 41:17
  Speaker 1: teaching and research and she was not being paid. She
• 41:20
  Speaker 1: just sort of like volunteering. Nobody would hire her because
• 41:24
  Speaker 1: she was a woman, even though she was making important contributions.
• 41:27
  Speaker 1: It's you know, it's really ridiculous. Yeah, that's pretty tragic,
• 41:30
  Speaker 1: pretty crazy. And she actually had to sort of practice
• 41:33
  Speaker 1: physics and teach it for free kind of right, because
• 41:35
  Speaker 1: they wouldn't hire her. Yeah, exactly, despite her like glowing
• 41:38
  Speaker 1: recommendations from seminal folks in the field, she's rejected from
• 41:42
  Speaker 1: position after position just because she was a woman. Hilbert
• 41:45
  Speaker 1: is a famous mathematician. He wanted her to teach because
• 41:48
  Speaker 1: she was also a great teacher, but they refused to
• 41:51
  Speaker 1: give her the position. So what he did was he
• 41:53
  Speaker 1: signed up to teach the class and then he hired
• 41:55
  Speaker 1: her basically to be his t a and then he
• 41:57
  Speaker 1: just never showed up, So she taught the class enough.
• 42:00
  Speaker 1: That's noble or lazy or both somehow both, I'm not sure.
• 42:04
  Speaker 1: But you know, she came from a wealthy background, so
• 42:06
  Speaker 1: she was able to just keep working even though she
• 42:09
  Speaker 1: didn't have a salary. And after World War One, she
• 42:12
  Speaker 1: finally was able to get an academic position, but they
• 42:14
  Speaker 1: wouldn't pay her. So they're like finally letting her in
• 42:17
  Speaker 1: the door, but like, yeah, but we're drawing the line
• 42:19
  Speaker 1: at providing you any funding or any money for your work.
• 42:23
  Speaker 1: Talk about like unequal pay. That's the ultimate inequality. And
• 42:27
  Speaker 1: around the time that Einstein was developed in general relativity,
• 42:30
  Speaker 1: people were trying to understand, like what did it mean?
• 42:32
  Speaker 1: You know, Einstein had these equations and it took decades
• 42:34
  Speaker 1: for people to really understand what it means. And one
• 42:38
  Speaker 1: of the questions about general relativity was like, what does
• 42:40
  Speaker 1: it mean for energy conservation? People thought energy was conserved
• 42:43
  Speaker 1: back then, but in general relativity they were like, hold
• 42:46
  Speaker 1: on a second, it's not clear if energy is conserved
• 42:49
  Speaker 1: in general relativity. What's going on. People knew that Nuther
• 42:52
  Speaker 1: was an expert in algebra and in mathematics, a lot
• 42:56
  Speaker 1: of which was really important underlying general relativity, so they
• 42:58
  Speaker 1: asked her to look at this question, right, because I
• 43:01
  Speaker 1: think at this point in the history of physics, like
• 43:03
  Speaker 1: we were at the point where basically Newtonian physics were
• 43:06
  Speaker 1: being upturned, right, Like we had relied on Newtonian physics
• 43:09
  Speaker 1: all the time. People thought they were the thing that
• 43:11
  Speaker 1: told us the momentum was conserved. But now they had
• 43:14
  Speaker 1: this whole new sort of class of physics, this whole
• 43:17
  Speaker 1: new sort of level of quantum and relativity, and so
• 43:20
  Speaker 1: people were like, wait a minute, what's going on. Is
• 43:22
  Speaker 1: momentum still conserved according to these new sort of equations, right,
• 43:26
  Speaker 1: that's kind of where we were. That's where we were.
• 43:28
  Speaker 1: People like, well, we think general relativity makes a lot
• 43:30
  Speaker 1: of sense. There's a lot to like about it. But
• 43:32
  Speaker 1: now we get to ask new questions about it, like
• 43:35
  Speaker 1: why does it seem that in general relativity energy is
• 43:38
  Speaker 1: not necessarily conserved? Under what conditions would you be conserved?
• 43:41
  Speaker 1: What does that mean? This is like a big question
• 43:44
  Speaker 1: about the nature of these new mathematical and physical discoveries.
• 43:47
  Speaker 1: And so she looked into it and she figured out
• 43:49
  Speaker 1: something really interesting and very deep about the nature of
• 43:53
  Speaker 1: the universe. Wow. She took a little coffee break and
• 43:56
  Speaker 1: she came and figured everything out for everybody. I know,
• 43:59
  Speaker 1: all these folks who were like paid and had full professorships,
• 44:02
  Speaker 1: you know, and this is their job. They like asked
• 44:04
  Speaker 1: the volunteer mathematician who they excluded from academic positions to
• 44:08
  Speaker 1: come and solve their problem. And she did, and then
• 44:10
  Speaker 1: she went back into mathematics. Right, that's wild and it's
• 44:14
  Speaker 1: interesting too. Because she was surrounded by all these like
• 44:16
  Speaker 1: famous mathematicians, right, she worked with them, Hilbert Schwartshell. I
• 44:19
  Speaker 1: mean these are big names, even not just in math
• 44:22
  Speaker 1: but also in physics, like you know the Shortschild radius
• 44:25
  Speaker 1: of a black hole. Right, Absolutely all these folks knew
• 44:28
  Speaker 1: her and had great respect for her. And it's a
• 44:30
  Speaker 1: little sad that in the telling of these stories later on,
• 44:34
  Speaker 1: she was mostly omitted from it. Even though she made
• 44:37
  Speaker 1: this really seminal contribution, which we'll talk about in just
• 44:39
  Speaker 1: a moment, history has largely forgotten about her. And like
• 44:42
  Speaker 1: I think, if you ask people who made the most
• 44:44
  Speaker 1: important contributions to physics in the last century, you'd get Einstein,
• 44:47
  Speaker 1: you might get Shortinger, but like, no, there is up there,
• 44:50
  Speaker 1: maybe even more important than Einstein, and yet almost nobody
• 44:53
  Speaker 1: knows about her. Wow, up there with Einstein. All right, Well,
• 44:57
  Speaker 1: let's get into what exactly she did, Like, what was
• 45:00
  Speaker 1: the breakthrough that she had, What was the connection that
• 45:01
  Speaker 1: she made? So it sounds very simple, but the connection
• 45:04
  Speaker 1: she made was that any symmetry you have in your
• 45:07
  Speaker 1: equations will generate a conservation law. What that means is
• 45:11
  Speaker 1: that any conservation you see in the universe any time
• 45:15
  Speaker 1: you see something being conserved, you don't understand it. What
• 45:18
  Speaker 1: it means is that it comes from some symmetry. Right,
• 45:21
  Speaker 1: there's always some symmetry which produces a conservation law. So,
• 45:25
  Speaker 1: for example, conservation of momentum comes from the fact that
• 45:29
  Speaker 1: space is the same everywhere. If you shift your experiment
• 45:32
  Speaker 1: from here to over there, you don't get a different answer.
• 45:35
  Speaker 1: That's why momentum is concerned. Can you maybe go a
• 45:38
  Speaker 1: little bit into more detail, like why is that? Why
• 45:40
  Speaker 1: is it that having the equations be the same here
• 45:42
  Speaker 1: or there results or gives us conservation of momentum. We'll
• 45:47
  Speaker 1: remember that what we're talking about is that physics doesn't change. Right,
• 45:50
  Speaker 1: So you shift your whole experiment from here to there,
• 45:52
  Speaker 1: you get the same equations of motion, and the equations
• 45:56
  Speaker 1: of motion if you know anything about like Hamiltonian or
• 45:58
  Speaker 1: Lagrange and mechanics, these equations only depend on the derivatives
• 46:02
  Speaker 1: of your position, how your position changes with time, not
• 46:06
  Speaker 1: the actual value of the position. Right, And so if
• 46:09
  Speaker 1: you take your position and you add a constant to it,
• 46:12
  Speaker 1: you know x goes to x plus a, then the
• 46:15
  Speaker 1: derivatives don't change because when you take the derivative a disappears.
• 46:19
  Speaker 1: The equations emotions you get when you shift your position
• 46:22
  Speaker 1: don't change because the equations of emotion only depend on
• 46:25
  Speaker 1: the derivative, and the derivative of your position is your velocity,
• 46:29
  Speaker 1: which is closely connected to your momentum. That's sort of
• 46:33
  Speaker 1: like a sketch for why the symmetry in position gives
• 46:36
  Speaker 1: you conservation of momentum, because the equations of motion only
• 46:40
  Speaker 1: depend on the derivative of the position, not the position themselves.
• 46:44
  Speaker 1: I think what you're saying is that the equations of
• 46:46
  Speaker 1: motion of the universe basically don't have pocisition in them.
• 46:49
  Speaker 1: They just have velocities in them. Yeah. Another way to
• 46:51
  Speaker 1: think about it is that they only have relative positions.
• 46:54
  Speaker 1: You shift everything over, nothing changes. It's only changes in
• 46:58
  Speaker 1: position are important. That's what the equation of motion are about,
• 47:01
  Speaker 1: and changes the position is velocity, and velocity is basically momentum. Right.
• 47:05
  Speaker 1: But I guess the question then, is why this the
• 47:08
  Speaker 1: fact that it's the same here or there? Well, why
• 47:10
  Speaker 1: does that mean that? You know? Objects in motion stay
• 47:13
  Speaker 1: in motion, and objects and address stay and rest. It
• 47:16
  Speaker 1: might seem weird to connect these two quantities momentum, right
• 47:20
  Speaker 1: and position, but you know, there's another great advance in
• 47:23
  Speaker 1: the early part of this century that connected momentum position,
• 47:25
  Speaker 1: that told us that there was a close relationship between
• 47:27
  Speaker 1: these two quantities, And that's quantum mechanics, which, like the
• 47:31
  Speaker 1: Heisenberg and certainty principle, tells you that momentum and position
• 47:34
  Speaker 1: are closely related to each other because one is basically
• 47:37
  Speaker 1: like the foury transform of the other one. And so
• 47:40
  Speaker 1: these two quantities are like really coupled together. And so
• 47:44
  Speaker 1: the fact that you can shift your experiment over by
• 47:47
  Speaker 1: ten meters or by light year and it doesn't change
• 47:50
  Speaker 1: the answer tells you something about the relationship between momentum
• 47:54
  Speaker 1: and position, and so that's sort of where it originates.
• 47:58
  Speaker 1: To help at all, let's try this. Maybe, let's assume
• 48:03
  Speaker 1: that the equations of the universe were not symmetric, right, Like,
• 48:07
  Speaker 1: let's say that you know, you didn't have these equations.
• 48:10
  Speaker 1: How would that translate to momentum not being conserved? All right, So,
• 48:14
  Speaker 1: if the equations of motion of the universe depended on position, right,
• 48:19
  Speaker 1: not just changes of position, like if if equals and
• 48:23
  Speaker 1: may here and if equals three m A and Mars
• 48:27
  Speaker 1: not in Mars, but like near than in the neighborhood
• 48:29
  Speaker 1: of Mars. Like, let's say the equations of the universe
• 48:32
  Speaker 1: change from here to there, How would that affect whether
• 48:35
  Speaker 1: or not a ball of ice cream right throughout Mars
• 48:37
  Speaker 1: is going to change velocity. If you're a particle and
• 48:40
  Speaker 1: you're moving through a universe where the rules are changing
• 48:43
  Speaker 1: as you move, right, then your trajectory might change because
• 48:48
  Speaker 1: the rules are the things that govern your trajectory, that
• 48:50
  Speaker 1: tell your trajectory how it moves. So if over here
• 48:53
  Speaker 1: in our part of the universe, it requires a force
• 48:55
  Speaker 1: to change momentum, but over there it doesn't, right, then
• 48:59
  Speaker 1: your momentum might change without anybody applying a force to
• 49:01
  Speaker 1: it in that part of the universe. And so your
• 49:04
  Speaker 1: momentum might be changed just by the fact of moving
• 49:07
  Speaker 1: from here to there where where the rules are different. Right,
• 49:10
  Speaker 1: But what if nothing interacts with my ice cream wall
• 49:12
  Speaker 1: from here to there, why would it change or how
• 49:15
  Speaker 1: could it change velocity? You know what I mean? How
• 49:18
  Speaker 1: could the momentum change? Or maybe like, are you saying
• 49:20
  Speaker 1: that maybe the definition of momentum would change, You're assuming
• 49:23
  Speaker 1: implicitly there that you need to interact with somebody to
• 49:26
  Speaker 1: change its momentum, which is assuming conservation of momentum. But
• 49:29
  Speaker 1: in this example, we're talking about a universe where the
• 49:32
  Speaker 1: rules are different from one place to another, and so
• 49:34
  Speaker 1: you don't have conservation and momentum, and so it would
• 49:37
  Speaker 1: break pretty basic fundamental things like that things could change
• 49:41
  Speaker 1: momentum without anything interacting with it. That would break Well,
• 49:45
  Speaker 1: let's say like here on Earth or in our neighborhood,
• 49:48
  Speaker 1: it's E equals they may, but near Mars it's e
• 49:50
  Speaker 1: equals three m A. Right, like, if I apply a force,
• 49:53
  Speaker 1: I need three times the amount of force to get
• 49:55
  Speaker 1: something to accelerate. Would that break the laws of conservation
• 49:58
  Speaker 1: momentum or not? Yeah, absolute, it would because remember force
• 50:01
  Speaker 1: is a change of momentum, and so it's talking about
• 50:04
  Speaker 1: is having a different change in momentum over here and
• 50:08
  Speaker 1: over there. So you'd have to have some like gradual
• 50:11
  Speaker 1: change in the laws between here and there, and then
• 50:14
  Speaker 1: you know the same acceleration would require a different force
• 50:17
  Speaker 1: here and over there, and so that would mean a
• 50:20
  Speaker 1: different change in momentum. So absolutely, what are you saying,
• 50:23
  Speaker 1: or are you saying the ball would slow down or
• 50:25
  Speaker 1: the ball would speed up? In that case, it would
• 50:27
  Speaker 1: slow down because effectively you'd be increasing its mass to
• 50:30
  Speaker 1: like three m without changing its momentum, so its velocity
• 50:33
  Speaker 1: would drop. Are you're saying because there's no force, then
• 50:37
  Speaker 1: because we sort of change the mass kind of, then
• 50:40
  Speaker 1: the velocity would change. Yeah. Um, it gets pretty hard
• 50:43
  Speaker 1: to do these calculations because your intuition really assumes that
• 50:47
  Speaker 1: these things are conserved. Right. Well, I guess what I'm
• 50:50
  Speaker 1: trying to do is get a you know, kind of
• 50:52
  Speaker 1: an in twitest sense of what you mean when you say,
• 50:55
  Speaker 1: like symmetries equals conservation of of something. I think maybe
• 50:58
  Speaker 1: an intuitive way to understand it is to think about
• 51:01
  Speaker 1: just the relative sense of these quantities. You know, like,
• 51:04
  Speaker 1: we know that no place in the universe is different
• 51:06
  Speaker 1: from any other place. We also know that the only
• 51:09
  Speaker 1: important thing is not your position, but your relative velocity. Right,
• 51:13
  Speaker 1: those two really are saying the same thing, that what
• 51:15
  Speaker 1: matters is not where you are in the universe, but
• 51:18
  Speaker 1: your velocity relative to that stuff. So momentum is important
• 51:22
  Speaker 1: and not position. That's why momentum is conserved and not
• 51:25
  Speaker 1: like location. So I think that's the most intuitive way
• 51:28
  Speaker 1: to think about it. You know that underlying you, there's
• 51:31
  Speaker 1: no fixed grid where somebody is measuring your position is
• 51:34
  Speaker 1: just about how you're moving relative to stuff that's important,
• 51:37
  Speaker 1: not your location. One way to say that is while
• 51:40
  Speaker 1: you can move your experiment somewhere else and get the
• 51:42
  Speaker 1: same answer. Another way to say that is, actually the
• 51:44
  Speaker 1: important thing is motion, not position, and that's conservation and momentum.
• 51:48
  Speaker 1: I think maybe you're telling me that you sort of
• 51:50
  Speaker 1: have to go into the math to really understand that connection,
• 51:53
  Speaker 1: Like it sort of comes comes from the math. But
• 51:55
  Speaker 1: it's kind of hard to really see it from an
• 51:57
  Speaker 1: intuitive point of view because maybe we are so ingrain
• 52:00
  Speaker 1: in this idea of conservation, but we can't think of
• 52:03
  Speaker 1: of things not being conservad Yeah, I used to think
• 52:05
  Speaker 1: I had intuitive understanding of it until you ask me
• 52:07
  Speaker 1: a bunch of questions about it, and now I'm not
• 52:08
  Speaker 1: so sure. I've destroyed the conservation of knowledge in your brain.
• 52:13
  Speaker 1: But it is very simple mathematically and very deep and fascinating.
• 52:17
  Speaker 1: You can take this example that translations in space lead
• 52:20
  Speaker 1: to conservation momentum and apply to lots of other things,
• 52:23
  Speaker 1: and it also holds. That's why I know if the
• 52:25
  Speaker 1: theorem is so powerful, it doesn't just explain conservation momentum,
• 52:29
  Speaker 1: it also explains other conservation laws that we see in
• 52:32
  Speaker 1: the universe. For example, you can apply the same thing
• 52:35
  Speaker 1: to rotation. Right. We don't care about the orientation of
• 52:39
  Speaker 1: anything in the universe because there's no up or down.
• 52:42
  Speaker 1: There's no preferred direction. The same way there's no preferred location.
• 52:45
  Speaker 1: That's why we have conservation of angular momentum because rotation
• 52:49
  Speaker 1: is not fundamental, but relative rotations are. Rotational velocity is important,
• 52:54
  Speaker 1: and so we have conservation of angular momentum because the
• 52:58
  Speaker 1: universe can be rotated through in our during angle and
• 53:00
  Speaker 1: nothing changes. Right. I think what you're saying is that
• 53:03
  Speaker 1: she sort of drew that connection between these mathematical symmetries
• 53:08
  Speaker 1: and these sort of physical ideas of conservation of things,
• 53:11
  Speaker 1: like things overall, if you look at them at the system,
• 53:13
  Speaker 1: they don't change. And she said, hey, that's because you
• 53:16
  Speaker 1: have these symmetries in these equations like they're they're they're
• 53:20
  Speaker 1: sort of one and the same exactly, not just a
• 53:22
  Speaker 1: symmetry and the equation a symmetry in the universe. Right,
• 53:25
  Speaker 1: conservation momentum tells you that space is the same everywhere.
• 53:29
  Speaker 1: That's a big conclusion. Right, If momentum really is conserved
• 53:32
  Speaker 1: everywhere in the universe. It tells you there's no different
• 53:34
  Speaker 1: place in space. Every place in space is the same.
• 53:37
  Speaker 1: It's not just the equations. It's like the universe, man,
• 53:41
  Speaker 1: the universe, man. So what exactly is the theorem? Like,
• 53:45
  Speaker 1: how do you de verbalize that theorem? The theorem is
• 53:48
  Speaker 1: that every continuous symmetry of the lagrange in which describes
• 53:53
  Speaker 1: the motion and interaction of particles, leads to a conservation law.
• 53:57
  Speaker 1: So continuous symmetry like translation in space, a rotation in space,
• 54:01
  Speaker 1: or shifting in time. The original question she was trying
• 54:04
  Speaker 1: to ask is is energy conserved in generalativity? And if not,
• 54:09
  Speaker 1: why not? And so this was her answer. Her answer was,
• 54:12
  Speaker 1: if space doesn't change with time, if the laws of
• 54:14
  Speaker 1: the universe don't change in time, then energy is conserved.
• 54:18
  Speaker 1: If the laws in the universe do change in time,
• 54:20
  Speaker 1: then energy is not conserved. Sort of blew everybody's minds
• 54:24
  Speaker 1: when she discovered that. WHOA, So she sort of made
• 54:27
  Speaker 1: a bridge between the new physics and the old physics,
• 54:31
  Speaker 1: right or she provided kind of the answer that said, hey,
• 54:34
  Speaker 1: they're all sort of one and the same. Yeah, she
• 54:36
  Speaker 1: helped us understand why these conservation laws appear and under
• 54:40
  Speaker 1: what conditions they do, and of course, for decades afterwards
• 54:42
  Speaker 1: people were like, well, obviously energy is conserved in the universe,
• 54:46
  Speaker 1: and so therefore the rules of physics must be the
• 54:48
  Speaker 1: same as a function of time. Now, of course, we
• 54:50
  Speaker 1: know the universe is expanding, and that means that energy
• 54:52
  Speaker 1: is not conserved because space is changing with time. Right,
• 54:56
  Speaker 1: So you know, if the theorem is still teaching us
• 54:58
  Speaker 1: things about the nature of the universe, the fact that
• 55:00
  Speaker 1: the universe is expanding means that energy is not conserved.
• 55:03
  Speaker 1: And we know why because it sort of breaks her theorem,
• 55:06
  Speaker 1: or it's outside of her theorem, because there isn't a
• 55:09
  Speaker 1: symmetry with time, which is why we don't have energy conservation.
• 55:13
  Speaker 1: If the universe was symmetric in time, if space was
• 55:16
  Speaker 1: the same size and not expanding, then we would have
• 55:19
  Speaker 1: energy conservation. So we know why we don't have energy
• 55:22
  Speaker 1: conservation just the same way we know why we do
• 55:24
  Speaker 1: have momentum conservation. All right, Well, I think that sort
• 55:27
  Speaker 1: of answer is the main question of the episode, which
• 55:30
  Speaker 1: is wise momentum conserved, And it seems like the answer
• 55:33
  Speaker 1: is that it's it's sort of like baked into the
• 55:35
  Speaker 1: equations of the universe, like it's because the equations of
• 55:38
  Speaker 1: the universe don't change no matter where you put them. Yeah,
• 55:42
  Speaker 1: it's because space is the same everywhere in the universe.
• 55:46
  Speaker 1: That's why momentum is conserved. Well, it's everywhere. It's the
• 55:49
  Speaker 1: same everywhere in the universe, but not everywhere in time,
• 55:51
  Speaker 1: like it's it's changing, but it's changing everywhere at the
• 55:54
  Speaker 1: same time. I think it's what you're saying. Space is expanding,
• 55:57
  Speaker 1: it is changing, but the rules of the universe are
• 56:00
  Speaker 1: the same at every location in space. Yeah, there's no
• 56:03
  Speaker 1: different parts of space. Is like vanilla space and chocolate
• 56:05
  Speaker 1: space and strawberry space. It's all the same space. That's
• 56:08
  Speaker 1: all the same swirl exactly. You only get one option,
• 56:14
  Speaker 1: and that's one kind of space swirl in this universe.
• 56:17
  Speaker 1: I see. But if we do maybe find out some
• 56:20
  Speaker 1: time in the future that space is different, like at
• 56:23
  Speaker 1: the borders or at the edges, or maybe in the
• 56:25
  Speaker 1: next universe over, then maybe momentum wouldn't be conserved. Yeah, exactly.
• 56:29
  Speaker 1: Maybe momentum will be dethroned the way energy was, or
• 56:33
  Speaker 1: at least, you know, not dethroned. But just like hey,
• 56:35
  Speaker 1: it would confirm there's theorem actually in a way right. Yeah,
• 56:39
  Speaker 1: And if you're interested in other weird quantum applications in
• 56:42
  Speaker 1: other's theorem, check out our episode about gauge symmetry, which
• 56:45
  Speaker 1: relies heavily on this idea and which promised to have
• 56:48
  Speaker 1: a whole episode diving into another's theorem. So here it is.
• 56:51
  Speaker 1: But Another's theorem also explains why we have like conserved
• 56:55
  Speaker 1: electric charges in the universe that comes from an internal
• 56:58
  Speaker 1: quantum symmetry and also to they're weird, conservation laws in
• 57:01
  Speaker 1: particle physics come from symmetries we see in the equations
• 57:06
  Speaker 1: of particle physics and are powered by Neuthers theorem. Well,
• 57:09
  Speaker 1: I feel like there are two big lessons here. One
• 57:11
  Speaker 1: is that sometimes even that like the things that seem
• 57:13
  Speaker 1: intuitive and the universe have a deep sort of mathematical
• 57:16
  Speaker 1: route in the in how the universe works. And then
• 57:19
  Speaker 1: you should always ask mathematicians for help with your physics problems. Yeah,
• 57:23
  Speaker 1: they're like the nine one one of the physics world.
• 57:25
  Speaker 1: Like we've been trying for centuries. Can you guys, you know,
• 57:28
  Speaker 1: take a break and help us out. Yeah. Well, that
• 57:31
  Speaker 1: part of history is really rich with fascinating mathematics that
• 57:34
  Speaker 1: was developed for decades just had a pure interest in
• 57:37
  Speaker 1: mathematics and then oh it turns out to be really
• 57:40
  Speaker 1: helpful and solve important problems in physics. Yeah. And I
• 57:42
  Speaker 1: guess the other interesting thing is here is that you know,
• 57:45
  Speaker 1: I mean, you know, there was someone who is sort
• 57:47
  Speaker 1: of outside of academa right, kind of unjustly so and
• 57:51
  Speaker 1: justly so. She's excluded, but she still made this amazing contribution.
• 57:55
  Speaker 1: Like you know, these breakthroughs can come from anywhere. Yeah, exactly,
• 57:58
  Speaker 1: And we really should have much more different city in
• 58:00
  Speaker 1: physics and in mathematics and in academia because we need
• 58:03
  Speaker 1: all sorts to solve the tough problems that are facing us.
• 58:07
  Speaker 1: So happy birthday, I mean author, and thank you for
• 58:09
  Speaker 1: all your contributions. Yeah for sure, thank you. Let's all
• 58:11
  Speaker 1: have a scoop of space Sworld ice cream and to
• 58:14
  Speaker 1: celebrate her birthday. Yeah, and expand the space around our
• 58:19
  Speaker 1: waistload's a little bit and know our minds with what
• 58:22
  Speaker 1: it all means. All right, Well, I think that um
• 58:25
  Speaker 1: answers a question and it tells us some pretty deep
• 58:27
  Speaker 1: things about the universe. We hope you enjoyed that. Thanks
• 58:30
  Speaker 1: for joining us, See you next time. Thanks for listening
• 58:40
  Speaker 1: and remember that. Daniel and Jorge Explain the Universe is
• 58:43
  Speaker 1: a production of I heart Radio. Or more podcast from
• 58:47
  Speaker 1: my heart Radio. Visit the i heart Radio app, Apple Podcasts,
• 58:51
  Speaker 1: or wherever you listen to your favorite shows.