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