Speaker 1: Physics has set itself quite the task. The job is
Speaker 1: to explain the whole universe, everything inside of it, and
Speaker 1: all of its doing and throwing. Usually we think of
Speaker 1: that in terms of the matter, the stuff, and the
Speaker 1: forces how that stuff interacts. So when we count our
Speaker 1: progress towards the big goal of physics, we sometimes think
Speaker 1: about the number of particles and the number of forces.
Speaker 1: We reduce that number when we break open matter to
Speaker 1: see what it's made out of, or when we unify
Speaker 1: forces like we be merged electricity and magnetism into electromagnetism
Speaker 1: and then later added the weak force to make the
Speaker 1: electroweak force sorry magnetism. Eventually, we hope we'll get down
Speaker 1: to one particle and one force that explains everything that happens.
Speaker 1: But what if there there is a better way. Maybe
Speaker 1: forces are intuitive to us, part of the stories we
Speaker 1: tell about what we see with a simple intuitive analog
Speaker 1: in our experience. But what if they aren't a natural
Speaker 1: fit to the real mechanisms of the universe itself? What
Speaker 1: if forces emerged from something else. Today on the pod,
Speaker 1: we'll talk about something we've mentioned many times in many contexts.
Speaker 1: It's time to dive in and talk about the mysterious
Speaker 1: quantity that has no analog in our intuitive experience, but
Speaker 1: seems to dominate in the events of the universe, action,
Speaker 1: and specifically, why the universe seems to minimize it. Welcome
Speaker 1: to Daniel and Kelly's Extraordinary Minimal Universe.
Speaker 2: Hello.
Speaker 3: I'm Kelly Wintersmith.
Speaker 4: I study parasites and space and it's winter right now,
Speaker 4: so it is my season of least action.
Speaker 1: Hi. I'm Daniel. I'm a particle physicist. It's winter here
Speaker 1: in southern California, though I can hardly tell.
Speaker 3: So we're.
Speaker 4: We're talking about potential energy and kinetic energy a little
Speaker 4: bit today, which reminds me of my intro physics class,
Speaker 4: which makes me wonder, what is the coolest demonstration you
Speaker 4: have done for your students as a teacher.
Speaker 1: Ooh, that's a good question. I think the coolest demonstration
Speaker 1: I've ever done doesn't actually relate to kinetic or potential energy.
Speaker 1: I know, there's like those famous ones where you like
Speaker 1: push a bowling ball away from your nose and then
Speaker 1: you stand there all cool as it comes back and
Speaker 1: doesn't crunch you in the face. But I think the
Speaker 1: most interesting ones are the ones that reveals something about
Speaker 1: the universe you can't otherwise see. So I once brought
Speaker 1: in a homemade cloud chamber. This is something you can
Speaker 1: actually build yourself in your garage with pretty simple ingredients
Speaker 1: that could show you muons flying through the air. It
Speaker 1: reveals to you that the world around you is filled
Speaker 1: with these invisible particles flying at high speeds, and you
Speaker 1: can build the device using fairly simple ingredients to reveal them.
Speaker 1: These cloud chambers have like super saturated air, and as
Speaker 1: the muons fly through, they create these droplets which become visible.
Speaker 1: You probably have seen them at science museums. I just
Speaker 1: think that's awesome because it shows you that the world
Speaker 1: is so much more complex than your senses can reveal.
Speaker 4: Did we discover muons pretty early on? Because they're so
Speaker 4: easy to see?
Speaker 1: We discovered the muon years and years ago using cloud
Speaker 1: chambers actually, and then you can spot them also using
Speaker 1: big blocks of emulsion. Emulsion is sort of like a
Speaker 1: three dimensional bit of photographic plate that you later like
Speaker 1: slice up and develop as photographs. And we put them
Speaker 1: on the tops of mountains and we saw a lot
Speaker 1: of particles shooting through them, and that was the first
Speaker 1: clue about muons.
Speaker 4: Yeah, who did we know what they were immediately or
Speaker 4: did it take a while to work that out?
Speaker 2: No?
Speaker 1: Actually, it's sort of a famous surprise because we had
Speaker 1: the idea of like atomic structure and it was all
Speaker 1: very nice and neat. We had protons and neutrons and electrons,
Speaker 1: and then we discovered the muon which wasn't part of
Speaker 1: the atom. And a famous physicist I Robbie said, who
Speaker 1: ordered that, like, we don't need this. We're you know,
Speaker 1: we have a pretty good thing going, like get out
Speaker 1: to hear universe with your pesky facts.
Speaker 2: Yeah.
Speaker 4: No, I've been there running experiments and you're like, no, please,
Speaker 4: don't do that, universe.
Speaker 3: But it does it anyway exactly.
Speaker 1: And you know, the universe is under no obligation to
Speaker 1: make sense to us, or to do what we expect,
Speaker 1: or to follow rules that sort of connect with our
Speaker 1: intuitive way of thinking. Which is why I'm so excited
Speaker 1: today to finally get to talk about this concept we've
Speaker 1: been mentioning and referring to for months and months and
Speaker 1: months now, and we're going to do a deep dive
Speaker 1: and an explanation of it today. And what is it
Speaker 1: called called action and the principle of least action, and
Speaker 1: it's a completely different way to think about motion in
Speaker 1: the universe and why things fall down, or why things
Speaker 1: slide the way they do, or even how quantum fields oscillate. Really,
Speaker 1: it's the most basic principle we've discovered, but it's also
Speaker 1: kind of counterintuitive, so it takes a little bit of
Speaker 1: a mental mind shift to think about the universe in
Speaker 1: terms of action. It's also a terribly terribly named word
Speaker 1: because it has nothing to do with the word action
Speaker 1: we use in English.
Speaker 4: Well, it is a physics concept, so it would have
Speaker 4: to have a bad name.
Speaker 1: Why did they do this? You know, they should have
Speaker 1: just come up with a new name, plasma, cagical or
Speaker 1: something and use that so that when you hear it,
Speaker 1: you're like, Okay, this is something new. I have to
Speaker 1: make a new space in my brain. But if you
Speaker 1: use an existing word, that has to like share that
Speaker 1: room in your brain with that other concept which has
Speaker 1: the same word.
Speaker 4: Well, I think somebody needs to hold on to plasmacajigle
Speaker 4: or whatever it was that you said. Thing needs to
Speaker 4: be named that, and you should be in charge of
Speaker 4: naming things in physics from here on out.
Speaker 1: All right, Well, I guess I just need to discover
Speaker 1: something and then I can name it flasmaca jiggle, and
Speaker 1: then we'll be all set. You know, I've done the
Speaker 1: hard part already, and you know, just the pesky bit
Speaker 1: about actually discovering something in the universe.
Speaker 3: Yeah, right, yeah, that tiny bit.
Speaker 4: And so we asked the extraordinaries, why does the universe
Speaker 4: flazmaca jiggle?
Speaker 2: No, we didn't. No.
Speaker 1: I went out there and I asked folks what they
Speaker 1: knew about action, because this is something we get requests
Speaker 1: about a lot, and we've mentioned occasionally on the podcast
Speaker 1: and people ask us, ooh, would you go into more
Speaker 1: depth about that? And it's something I love doing on
Speaker 1: the pod, is explaining something on a depth beyond what's
Speaker 1: typically out there in popular science, but I hope in
Speaker 1: an actual, approachable way that'll make people really appreciate the
Speaker 1: way physics is done on the cutting edge. But of course,
Speaker 1: before we dig into it, I wanted to know what
Speaker 1: people already knew about this concept, So I asked, folks,
Speaker 1: why does the universe verse minimize action as usual? If
Speaker 1: you would like to join this crew of people who
Speaker 1: respond to these questions without the opportunity to google them.
Speaker 1: Please write to us questions at Danielankelly dot org. We
Speaker 1: would love to add your voice in the meantime. Think
Speaker 1: about it. Why do you think the universe minimizes action?
Speaker 3: Why does it flasmacajicle.
Speaker 1: Here's what people have to say. Since I have no
Speaker 1: idea what this means, I'm forced to fall back on
Speaker 1: a template answer of.
Speaker 5: Entropy, because the universe is just bound to follow laws
Speaker 5: with no shortcuts and no long cuts. So I think
Speaker 5: that minimizing action is probably another way of saying minimizing
Speaker 5: divergence from laws.
Speaker 1: For every action, there's an equal and opposite reaction, So
Speaker 1: I guess the universe minimizes reactions as well.
Speaker 4: To safe energy and to minimize possible outcomes.
Speaker 2: To know, is the universe lazy? Is it just chilled out?
Speaker 1: It is the world likes to be in its lowest
Speaker 1: energy state.
Speaker 2: Because actions speak louder than words, and there's far too
Speaker 2: much noise pollution.
Speaker 1: Because anything that happens, or any force that exists, has
Speaker 1: a counter force pressing against it.
Speaker 2: Maybe it's lazy, that's my excuse. I suspect that it
Speaker 2: has something to do with entroview, though.
Speaker 1: Too optimiz for efficiency, kind of like natural selection.
Speaker 2: It's just something we observe, but we don't know why.
Speaker 2: Do individual processes independently tend to pars the money or
Speaker 2: is there an underlying unified model that polls all behavior
Speaker 2: to a deeper minimization.
Speaker 1: Seems like it would be the only way that it
Speaker 1: could go, because if there was something at a higher energy,
Speaker 1: there was always something that could come lower.
Speaker 4: I was pleased to see I wasn't the only one
Speaker 4: who didn't know the answer, and went with sarcasm.
Speaker 1: I never know what to expect from these responses. I
Speaker 1: always learned so much. Sometimes bill know exactly what I'm
Speaker 1: talking about and get very insightful answers. Other times people
Speaker 1: are confused by the physics word and as is not
Speaker 1: their fault at all, and it seemed to have happened
Speaker 1: in this case. But this is exciting to me because
Speaker 1: it means that not a lot of folks out there
Speaker 1: are familiar with this concept of action being minimized, which
Speaker 1: means we get to teach them all something very very
Speaker 1: cool about the universe.
Speaker 4: Yes, we are helping to make you the most interesting
Speaker 4: person at the party.
Speaker 1: So let's say, Kelly, I'm trying to assess the level
Speaker 1: of sarcasm there, because I am one hundred percent sincerely
Speaker 1: excited about action, and I don't talk about it at
Speaker 1: parties very much, but it is something super duper nerdy
Speaker 1: and cool to discover, like an organizing principle of the universe,
Speaker 1: especially when it's counterintuitive, when it's not the way we
Speaker 1: typically think about stuff. That's like one hundred percent sincerity.
Speaker 1: And I'm assuming you feel the same way I do.
Speaker 3: I do.
Speaker 4: I don't know what kind of parties you're thinking of, Daniel,
Speaker 4: but the parties I go to we talk about things
Speaker 4: like pleasma.
Speaker 1: Okay, all right, Well we're not explaining plasmaka jiggle today
Speaker 1: because I haven't discovered it yet. But we are going
Speaker 1: to talk about action. But let's start by thinking about
Speaker 1: a simple motion of an object, and then we'll talk
Speaker 1: about how we typically understand it, how people probably think
Speaker 1: about its motion, and then we'll switch and think about
Speaker 1: it in another way. So the classic example, of course,
Speaker 1: is a ball flying through the air. You have a ball,
Speaker 1: you're playing catch with your kid or your dog or whatever.
Speaker 1: You throw it and it goes across your yard and
Speaker 1: hits the ground or gets caught by your dog or whatever.
Speaker 1: And from a traditional physics point of view, this isn't
Speaker 1: too complicated. You can understand it by thinking, like you
Speaker 1: throw it with your arms, so it has some initial velocity.
Speaker 1: And we know that things in the universe, if they
Speaker 1: have velocity, they just keep moving unless some force acts
Speaker 1: upon them. And in this case, for example, the force
Speaker 1: is gravity pulling it back down to the Earth. And
Speaker 1: so we can use those various elements to understand the
Speaker 1: motion of the ball. We have velocity, we have acceleration
Speaker 1: that changes its velocity. We can put that together to
Speaker 1: get an equation that describes where the ball is at
Speaker 1: any time, and it comes out to be a parabola. Right,
Speaker 1: It goes up and it comes back down and it
Speaker 1: hits the ground.
Speaker 3: It's also a great song by Tool. Do you think
Speaker 3: everybody hum.
Speaker 1: A few bars of it for us? Kelly?
Speaker 3: No, no, no, no, no. Oh, hey, I'm not gonna
Speaker 3: go anymore.
Speaker 4: So do you think everybody knows what the shape of
Speaker 4: a parabola looks like?
Speaker 1: Oh? It's hard for me to remember a time when
Speaker 1: I didn't know what the shape of a parabolo looks like.
Speaker 1: So I should ask you that question. Kelly, do you
Speaker 1: can you imagine a parabolo?
Speaker 3: Yep, I can, but I also do a fair bit
Speaker 3: of modeling.
Speaker 1: Yeah, okay, so that's a good point. Let's help people
Speaker 1: visualize a parabola.
Speaker 3: It's just a you. You're making it too complicated.
Speaker 1: A parabola is sort of like an upside down you. Right,
Speaker 1: it's a little bit tighter at the top, but basically
Speaker 1: a parabolo is well defined by what happens when you
Speaker 1: throw a ball across your yard. Right, It's going to
Speaker 1: go up, and then it's gonna turn around, it's gonna
Speaker 1: come back to and that's the parabolic shape. It's defined
Speaker 1: by an equation that has like an x squerginit for
Speaker 1: people who like to think about equations, but for visual people,
Speaker 1: it's basically an upside down you. And so that's what
Speaker 1: a brable looks like. Okay, So that's sort of the
Speaker 1: traditional way to think about how things move. You have matter,
Speaker 1: and you have forces. Forces act on matter to provide acceleration.
Speaker 1: A few rounds of calculus and you get your equation
Speaker 1: of motion where the thing is at any time. We're
Speaker 1: good with that.
Speaker 4: So far, we're good, right, And so in this model,
Speaker 4: we're not paying attention to things like friction or wind
Speaker 4: or anything like that.
Speaker 1: That's exactly right, because those things are really hard to
Speaker 1: add using this way. Like wind is a force, but
Speaker 1: it's not constant. Friction is a force, but it depends
Speaker 1: on velocity. So we're going to stick with a simple
Speaker 1: calculation because that's what this approach is good at. Simple calculations,
Speaker 1: what we call conservative forces with constant acceleration. Very easy
Speaker 1: to do those calculations. But there's something interesting about this
Speaker 1: motion if you look at it from another point of view.
Speaker 1: This is going to sound a little bit weird and random,
Speaker 1: but stick with me. So what you do is you
Speaker 1: think about the kinetic energy of this ball. Kinetic energy
Speaker 1: is just the energy of motion, and you usually calculate
Speaker 1: it like one half m v squared vias the velocity.
Speaker 1: So you calculate the kinetic energy of the ball as
Speaker 1: it moves through the air. Cool Now calculate also the
Speaker 1: potential energy of the ball. Potential energy here is just
Speaker 1: from gravity, so it's like mgh just the height of
Speaker 1: the ball. As it goes up it has more potential energy,
Speaker 1: as it goes down has less potential.
Speaker 3: Energy, and m in both of those was mass.
Speaker 1: Yeah, yeah, exactly. And so you calculate these things kinetic
Speaker 1: energy and potential energy. Now do something weird, subtract them.
Speaker 1: Usually we add these things to make total energy. But
Speaker 1: this time, let's subtract them. Let's do kinetic energy minus
Speaker 1: potential energy. So now we're calculating the difference between the
Speaker 1: kinetic energy and the potential energy. You might think, well,
Speaker 1: what does that mean? Intuitively, Like, if you add them,
Speaker 1: it may sense because it's okay, that's total energy. What
Speaker 1: does the difference mean? It means nothing intuitively, It's just
Speaker 1: this weird number we're calculating. Okay, okay. The cool thing
Speaker 1: about this number, The reason we're talking about this number
Speaker 1: is that the path the ball took minimizes that number.
Speaker 1: Like we have the path the ball took. It was
Speaker 1: a parabola. We calculate the kinetic energy minus potential energy.
Speaker 1: That number is smallest for the path that the ball took.
Speaker 1: If you change the path a little bit, you add
Speaker 1: a little divit or middle higher, a little lower, that
Speaker 1: path would have a higher value of kinetic energy minus
Speaker 1: potential energy. So the path that the ball took is
Speaker 1: the one that minimizes this difference between kinetic and potential energy.
Speaker 4: Okay, and so is that just because kinetic energy would
Speaker 4: always be greater whenever you add like a divot, because
Speaker 4: you're making the parabola longer, anytime you're adding a divot
Speaker 4: or something.
Speaker 1: I think you're asking, why is the parabola the path
Speaker 1: that minimizes this difference?
Speaker 2: Right?
Speaker 1: Yeah, and we're gonna explain that. The answer is yes.
Speaker 1: We're gonna explain that in detail in a minute, but
Speaker 1: for now, let's stop talking about kinetic energy. Money is
Speaker 1: potential energy because it's a lot of words, and let's
Speaker 1: just relabel it with a new word, right, so we
Speaker 1: don't have to use so many words. And we're gonna
Speaker 1: call it action. Why we don't call it plasmaca jiggle,
Speaker 1: I don't know, but we're gonna call it action. And
Speaker 1: so this turns out to be a general principle in
Speaker 1: physics that the path of things take you can figure
Speaker 1: it out by finding the path that minimizes the action
Speaker 1: this weird difference between kinetic and potential energy. So we
Speaker 1: started out just like I'm going to do this calculation.
Speaker 1: I'm not gonna tell you why or what it means
Speaker 1: or anything, and now we did it, and we discovered
Speaker 1: something that's actually physically useful. The universe seems to pay
Speaker 1: attention to this. It's not just a number, Daniel calculator.
Speaker 1: I could calculate anything like the number of walnuts times
Speaker 1: the temperature outside right. I can make up whatever quantity
Speaker 1: I want, But that doesn't help me solve a problem.
Speaker 1: It just seem to be important to the universe. This number,
Speaker 1: the action, the difference between kinetic and potential energy is
Speaker 1: all so an arbitrary, random thing that we constructed, but
Speaker 1: it seems to be respected by the universe somehow, because
Speaker 1: the universe, when the ball is flying through the air,
Speaker 1: chooses the path that minimizes this weird number, this thing
Speaker 1: we call action.
Speaker 3: So you can like tell the future if you know.
Speaker 4: So let me it's been a while since I've taken physics,
Speaker 4: and so so I'm imagining you've released the ball, and
Speaker 4: so to do this is it like, you know, you
Speaker 4: stop and you take a picture of the ball at
Speaker 4: every second, and you redo this calculation at every second
Speaker 4: and then you can predict where it's going to be
Speaker 4: the next second by doing this calculation.
Speaker 1: No action, It's exactly the opposite of that, which makes
Speaker 1: it a great question. So the way you described it
Speaker 1: in your mind is the way we typically think about
Speaker 1: the universe, that the past controls the future. We have
Speaker 1: like frame by frame, what happens now affects what's going
Speaker 1: to happen in a moment.
Speaker 2: Right.
Speaker 1: The ball moves this way because it has velocity and
Speaker 1: it has a force pulling on it. That's sort of
Speaker 1: like a computational way of thinking about the universe that
Speaker 1: you calculate it like frame by frame, and that's actually
Speaker 1: called the Newton schema. Newton came up with this idea
Speaker 1: that like the future of the universe is determined by
Speaker 1: the present, and he thought about like universal clocks and
Speaker 1: so many fun digressions we could go on there. And
Speaker 1: that's the way that the typical force story works. You
Speaker 1: think about velocity and forces and you cycle through frame
Speaker 1: by frame. That's not the way the action works. You
Speaker 1: can't use action to predict the future the same way
Speaker 1: because to calculate the path of the ball using action,
Speaker 1: you have to know the initial position and the final
Speaker 1: position already in order to find the path that goes
Speaker 1: from So there's a weird thing here which seems to
Speaker 1: imply maybe that the present depends on the future, you know,
Speaker 1: like where the ball goes now depends on where it lands,
Speaker 1: and so you have to know the future to predict
Speaker 1: the present. Not quite that. We're going to dig into
Speaker 1: it in a minute, but that's actually the fundamental misunderstanding
Speaker 1: at the heart of the movie Arrival.
Speaker 3: WHOA, yeah, I know, all right, stick with us to
Speaker 3: the end.
Speaker 1: Yeah, exactly. So we have this other way of thinking
Speaker 1: about motion where if you know the initial point A
Speaker 1: and the final point B, you can figure out what
Speaker 1: path something took just by calculating this weird thing called
Speaker 1: action and finding the path that minimizes the action. So
Speaker 1: let's work through another example, just to make sure we
Speaker 1: have this in our heads, because it's really important. Let's
Speaker 1: take an even simpler example, a ball with no gravity.
Speaker 1: Right now, we're out in space. Okay, we've ignored Zach
Speaker 1: and Kelly's advice, and you've gone to space and built
Speaker 1: a colony. We've made all sorts of mistakes, but now
Speaker 1: we're out in space and we get to play zero
Speaker 1: G catch with our kids or with our space dog. Right,
Speaker 1: So what happens when you throw a ball in space?
Speaker 3: You die?
Speaker 1: How's it? Going to move you die, Kelly. Doesn't happen immediately.
Speaker 1: I mean, we got lots of radiation and eventually we die,
Speaker 1: but we do we to have one nice afternoon of
Speaker 1: playing catch with our space dog.
Speaker 4: Okay, right, right, So if you're in deep space in
Speaker 4: your space suit, you're gravity's probably negligible. Right, So does
Speaker 4: that mean potential energy is zero?
Speaker 1: Exactly right. So let's think about the motion of a
Speaker 1: ball when there's no potential energy. So the force method
Speaker 1: is really easy here. You throw the ball that has velocity.
Speaker 1: There's no forces, So what's gonna happen. It's just going
Speaker 1: to keep having that velocity. Very intuitive. It's going in
Speaker 1: a certain direction. It keeps going in that direction every
Speaker 1: moment in time. You can predict the future because you
Speaker 1: have its velocity and that tells you exactly where it's
Speaker 1: going to go. Very simple. Okay, Now let's try to
Speaker 1: do that with the action method. So the action method says,
Speaker 1: you know where the ball started, and you know where
Speaker 1: the ball ends up, and you know how much time
Speaker 1: it took to go from A to B. Find the
Speaker 1: path that it took from A to B. And so
Speaker 1: to do this, what you do is consider all the
Speaker 1: possible paths, a straight line, a wiggle, a sinusoid, you know,
Speaker 1: any other sort of crazy path that goes from A
Speaker 1: to B in the same amount of time. Okay, now,
Speaker 1: going from A to B in a specific time, that
Speaker 1: already specifies the average velocity because you know how far
Speaker 1: it's gone and how long it's taken, So you're already
Speaker 1: kind of restricted. So the simplest path, the straight line.
Speaker 1: This one has constant velocity, and so it's going to
Speaker 1: have the smallest action because it has the smallest integrated
Speaker 1: kinetic energy across that path. If you imagine doing something
Speaker 1: else like going super fast first and then slowing down
Speaker 1: at the end, or going super slow for a while
Speaker 1: and then speeding up to get there at the right time,
Speaker 1: all of those things have more deviations in kinetic energy,
Speaker 1: and because kinetic energy has velocity squared in it, it's
Speaker 1: going to end up with the larger kinetic energy integrated
Speaker 1: over the path. So the way to have the smallest
Speaker 1: integrated kinetic energy is to keep your kinetic energy constant.
Speaker 1: That's why straight line with constant velocity is the path
Speaker 1: that minimizes the action. Any deviation in a direction is
Speaker 1: going to require more kinetic energy, which increases your action
Speaker 1: or any chain, the velocity is going to give you
Speaker 1: larger kinetic energy overall. So in the simplest case, action
Speaker 1: also predicts that the ball will go between you and
Speaker 1: your space dog in a straight line.
Speaker 4: Am I being pedantic by thinking like, well, it couldn't
Speaker 4: have sped up halfway because you threw it, And wouldn't
Speaker 4: it just stay the same speed the whole time with
Speaker 4: no friction and no gravity, And so what do we
Speaker 4: gain by thinking about it that way? Because it couldn't
Speaker 4: have done any of those other things?
Speaker 1: You're absolutely right. So you're thinking about this still in
Speaker 1: the Newton force scheme, which makes total sense because it's
Speaker 1: easy to understand why a particle would need a force
Speaker 1: to deviate from the line it's moving on, and so
Speaker 1: you're looking for a force to explain any other kind
Speaker 1: of motion than a straight line. Makes perfect sense. But
Speaker 1: right now we're thinking about this in another way. We're
Speaker 1: not bound to forces as explanations. We're just considering the
Speaker 1: action of various paths, and in this case we don't
Speaker 1: gain anything. In fact, it feels like more complicated to
Speaker 1: do with the action way right, And the action is
Speaker 1: going to make things simpler when we get into Hairer situations.
Speaker 1: But I just want to sort of like line up
Speaker 1: a simple situation so we can get practice thinking about
Speaker 1: the action.
Speaker 4: So you've got us all on the edge of our seats.
Speaker 4: So we're going to take a break, and when we
Speaker 4: get back, you are going to give us a Hairer
Speaker 4: situation where the curse mack amiggle.
Speaker 3: I said, oh, I'm so sorry. We'll get more complicated.
Speaker 4: All right, We're back, and Daniel's going to give us
Speaker 4: a more complicated situation where this concept of action is
Speaker 4: going to help us understand what's going on better.
Speaker 3: Maybe because it's physics.
Speaker 1: It does make it easier to analyze it's really hairy problems.
Speaker 1: It's also the way physicists think about motion, you know,
Speaker 1: when we get to quantum field theory and all that stuff.
Speaker 1: It's fundamentally based on action. And so I really want
Speaker 1: to move people out of the mindset of thinking about
Speaker 1: forces and thinking about action, because like, welcome to the
Speaker 1: cutting edge of physics. This is how we do it,
Speaker 1: all right. So we consider the very simple case you're
Speaker 1: playing catch with your space dog. There's no gravity, things
Speaker 1: moving a straight line, Kelly was bored by that. She's like,
Speaker 1: why do we even do this? Fair point.
Speaker 3: I wasn't bored.
Speaker 1: You were underwhelmed a little.
Speaker 3: You know, probably death was imminent, which is interesting.
Speaker 1: Don't think about the death of my space dog. That's
Speaker 1: not nice.
Speaker 3: Sorry, I do like space dog.
Speaker 1: I'm sure we'll give lots of shielding in our space
Speaker 1: dog spacesuit. Right, Yes, take care of our critters. Yeah,
Speaker 1: because they didn't get to choose whether they go to space.
Speaker 3: Right, No, like I didn't get to choose. Didn't go
Speaker 3: well Forlika.
Speaker 1: No, exactly. All right, so let's get back to other scenarios. Now,
Speaker 1: let's get back to your question about why a ball
Speaker 1: in gravity moves under a parabola. Right, So we're going
Speaker 1: to add gravity back into our situation. Bring our space
Speaker 1: dog back to Earth. Toss a ball to the space
Speaker 1: dog in the backyard. It doesn't move in a straight line.
Speaker 1: It moves in a parabola. The first picture tells us why,
Speaker 1: because you have an acceleration, and acceleration is a second
Speaker 1: derivative of position, and so if you integrate that constant
Speaker 1: acceleration twice, you get an X squared term. You get
Speaker 1: a parabola. It all makes sense. So things move in
Speaker 1: a parabola because there's a constant force. What about the
Speaker 1: action point of view, Why do we move in a parabola, Well,
Speaker 1: we want to minimize this difference between kinetic energy and
Speaker 1: potential energy. Potential energy increases as we go up, right,
Speaker 1: So because we want to minimize action, and action is
Speaker 1: kinetic energy minus potential energy. That means we want to
Speaker 1: have lots of potential energy. So potential energy increases as
Speaker 1: we go up. So we don't want to go up
Speaker 1: fast to get high potential energy. Right, So instead of
Speaker 1: going in a straight line, we go above our target.
Speaker 1: We go higher up in order to get more potential
Speaker 1: energy to minimize our action. But you don't want to
Speaker 1: go too far from the straight line because going too
Speaker 1: far from the straight line requires high kinetic energy. We're
Speaker 1: increasing our speed on the way up and our speed
Speaker 1: on the way down. So the parabola is a perfect
Speaker 1: balance between these things. You get more potential energy without
Speaker 1: getting too much additional kinetic energy. So the parable is
Speaker 1: the path that minimizes the difference between the kinetic energy
Speaker 1: and the potential energy when you have both at play.
Speaker 1: It's this really fascinating harmonic balance between these two very
Speaker 1: different things. And you can think about what the universe
Speaker 1: is doing in two ways. You can think the universe
Speaker 1: is doing the Newton thing like frame by frame, it's thinking,
Speaker 1: the ball is here, I have this force, so I
Speaker 1: have that velocity on it, so it's going to move
Speaker 1: this way. Or you can think about it from the
Speaker 1: action point of view, and you can say, the ball
Speaker 1: started here and went there. What path between those two
Speaker 1: and this amount of time minimizes the difference between kinetic
Speaker 1: and potential energy, and this is the path that does it.
Speaker 1: And it's fascinating because this turns out to be a
Speaker 1: general principle, not just in this one case where you're
Speaker 1: playing ball with your dog, but in every case. The
Speaker 1: least action tells you what the universe does, how things
Speaker 1: get from A to B. And you can start from
Speaker 1: this principle least action, and you can derive F equals MA,
Speaker 1: so you can derive the force equations from it. Like
Speaker 1: Newton just like writ it down. He's like, hey, this works.
Speaker 1: And you might ask, well, where does that come from?
Speaker 1: And the answer is action. Right from action, you can
Speaker 1: derive classical mechanics. Now classical mechanics doesn't then explain like,
Speaker 1: what is action? Why does the universe minimize it? To
Speaker 1: get any insight in that, we're going to have to
Speaker 1: go deeper into action in quantum mechanics and in philosophy.
Speaker 1: But it's fascinating because it seems like underneath all of
Speaker 1: these things, this force picture of the universe, there is
Speaker 1: a deeper principle from which you can derive F equals
Speaker 1: MA WHOA.
Speaker 4: Okay, So one thing I think I'm still stumbling on
Speaker 4: a little bit is that I guess I still feel like, Okay,
Speaker 4: so you throw a ball in the air and you're
Speaker 4: subtracting the potential energy, I still feel like you should
Speaker 4: be getting the least path, not necessarily because you're subtracting
Speaker 4: the potential energy, but because any other path would require
Speaker 4: you to put additional energy into the ball at some.
Speaker 3: Point as it goes through that path.
Speaker 4: And am I just thinking that because I live in
Speaker 4: this world and that's my expectation and I don't realize
Speaker 4: it doesn't have to be my expectation, or am I
Speaker 4: misunderstanding something. No.
Speaker 1: I think you're saying this is the only path it
Speaker 1: can take, because to take any other path something would
Speaker 1: have to do that. Yeah, like you need to go
Speaker 1: and push it or something. And yeah, you're thinking about
Speaker 1: the universe in terms of forces. You have Newton's ideas
Speaker 1: so deeply ingrained in your mind that like a ball
Speaker 1: is going to move it constant velocity unless something changes that, right,
Speaker 1: you have that so deeply ingrained it's obvious to you.
Speaker 1: But that comes from least action. All of Newton's laws
Speaker 1: are derived from the principle of least action. And so
Speaker 1: it turns out that's not the fundamental way the universe works.
Speaker 1: That comes out of insisting that everything minimizes action. And
Speaker 1: it's actually super cool because, as we mentioned earlier, in
Speaker 1: many cases, the force approach is simple and it works,
Speaker 1: and it's very intuitive and connected to our experience because
Speaker 1: this is how our world works, right, Like, we notice
Speaker 1: that you've got to push stuff to get it moving,
Speaker 1: and you've got to push it to turn it and
Speaker 1: all this stuff. We think about the world in terms
Speaker 1: of forces, but sometimes that picture is hairy and it's
Speaker 1: hard to use to do calculations, Like it's easy in
Speaker 1: the examples we talked about, But what if you add wind,
Speaker 1: or what if you add friction or what if, for example,
Speaker 1: you take your ball and you attach a string to it,
Speaker 1: and the string is now tied to a squirrel, and
Speaker 1: the squirrel is on a roller coaster. How are you
Speaker 1: going to do that calculation? Well, you still could in principle, right,
Speaker 1: there are still forces there on the string, and the
Speaker 1: rollercoaster has some applies to force, and the wind is
Speaker 1: a force which now weirdly depends on velocity. And what
Speaker 1: you discover is that it's a mess. Like many things
Speaker 1: in physics, we can only solve a few very simple
Speaker 1: examples because everything else is totally intractable. So the reason
Speaker 1: introductory of physics students usually calculate the path of a
Speaker 1: ball without wind resistance and without friction is because otherwise
Speaker 1: it's a huge rain. And so this force picture is
Speaker 1: good for simple examples, but it becomes totally intractable for
Speaker 1: anything realistic.
Speaker 2: That.
Speaker 1: The amazing thing is the action doesn't The action remains
Speaker 1: fairly simple because you can still just write down the
Speaker 1: kinetic energy and you can write down the potential energy.
Speaker 1: In many of these situations, it's not hard to calculate
Speaker 1: the kinetic energy or the potential energy, and then you
Speaker 1: just find the path that minimizes them. And that's because
Speaker 1: it relies on these concepts of energy, which helps you
Speaker 1: ignore a lot of the complicated details of what happens
Speaker 1: between moment A and moment B. People who have done
Speaker 1: physically problems know, for example, if you start, for example,
Speaker 1: with a roller coaster and it starts from a certain
Speaker 1: height and it goes through all sorts of crazy loop
Speaker 1: to loops, and then you're asked to like calculate the
Speaker 1: velocity of this roller coaster car halfway down the track.
Speaker 1: From a force point of view, you're like, oh, my gosh,
Speaker 1: how am I going to calculate that it's done? All
Speaker 1: these crazy maneuvers have to know the forces and the
Speaker 1: acceleration every moment. It's a nightmare. But from an energy
Speaker 1: calculation point of view, you just have to know, oh,
Speaker 1: it's gone down a certain distance. I know the potential
Speaker 1: energy that gets turned into kinetic energy. Boom, I have
Speaker 1: the answer in one step. This action approach is sort
Speaker 1: of analogous to that because it also relies just on
Speaker 1: these energy quantities which are sort of deeper and more fundamental,
Speaker 1: and don't worry so much about these little details.
Speaker 3: Okay, I like that.
Speaker 1: So when you get to like upper division physics, you
Speaker 1: learn about Lagrangen and Hamiltonian mechanics, from which you can
Speaker 1: derive F equals M. But they start out by calculating
Speaker 1: this difference between kinetic and potential energy, minimizing that and
Speaker 1: use to so many really hairy problems you would never
Speaker 1: imagine trying to calculate with Newton's method that you can
Speaker 1: just pop out in a few lines and get the answer.
Speaker 1: It feels like magic when you first do it. But
Speaker 1: what's happening here is you're accessing a deeper rule of
Speaker 1: the universe.
Speaker 3: Well what is the rule? Because now we're getting into
Speaker 3: the good party tricks.
Speaker 1: This feels like a deeper rule in the universe because
Speaker 1: it works not just for classical mechanics like the cases
Speaker 1: we're talking about, you know, squirrels and strings and wind
Speaker 1: and all sorts of stuff. It also works in every scenario.
Speaker 1: So this action formula that we talked about kinetic energy
Speaker 1: minus potential energy, that's the action for classical mechanics with
Speaker 1: conservative forces. But you can also do this, for example,
Speaker 1: for quantum mechanics, and instead of writing down kinetic energy
Speaker 1: minus potential energy, which require things you don't always know
Speaker 1: about particles, you write down something called the lagrange and density.
Speaker 1: In the case of like quantum field theory, this is
Speaker 1: just the fields that exist and how they interact with
Speaker 1: each other. And so, for example, the standard model of
Speaker 1: particle physics. If you google, like what is the equation
Speaker 1: of the standard model, it shows you this thing that
Speaker 1: starts with L equals and then a bunch of terms.
Speaker 1: That's the lagrangeon of the standard model, and the action
Speaker 1: is the integral of that. And so the way we
Speaker 1: specify what's in the universe, what's out there, all we
Speaker 1: have to do is say what the action is, what
Speaker 1: are the pieces of the action, and how do they interact?
Speaker 1: And everything else falls out of that, Like literally all
Speaker 1: the equations of quantum mechanics and quantum field theory say,
Speaker 1: if you have this action, then all these things happen.
Speaker 1: So the game of particle physics these days, and of
Speaker 1: all physics is to say, well, what is the action
Speaker 1: of the universe. We try lots of different things. We
Speaker 1: try this, we try that, we try the other thing,
Speaker 1: and the ones that turn into rules that align with
Speaker 1: what we see out there in the universe, those are
Speaker 1: the ones we go with. So the standard model of
Speaker 1: particle physics is just a description of the action of
Speaker 1: the universe, not in terms of kinetic energy of a ball,
Speaker 1: but in terms of the fields, their motion, and actually
Speaker 1: in terms of their oscillation, their kinetic energy, and their
Speaker 1: potential energy.
Speaker 4: Okay, so this seems pretty exciting because you know, you
Speaker 4: and I have been recording for over a year now,
Speaker 4: and I don't feel like there have been a lot
Speaker 4: of instances where we've talked about things that play nice
Speaker 4: with both classical mechanics and quantum mechanics. And that could
Speaker 4: be because my memory is.
Speaker 3: Kind of like a sieve, but I don't think so.
Speaker 3: So is this pretty rare?
Speaker 1: This is pretty rare, And it's actually a beautiful way
Speaker 1: to think about the connection between quantum mechanics and classical mechanics,
Speaker 1: and it gives you some insight into like our classical world,
Speaker 1: because when you're calculating the quantum mechanical action, you don't
Speaker 1: just think about an individual path. You think about all
Speaker 1: the various paths perhaps people have heard about, like the
Speaker 1: fine mean path integral approach to quantum mechanics. We imagine
Speaker 1: like an electron goes from here to there. You don't
Speaker 1: just think about one way for it to go from
Speaker 1: here to there. You think about all the well, what's
Speaker 1: happening there is You think about all the possible paths,
Speaker 1: and in classical mechanics, you say, oh, I'm to choose
Speaker 1: the one path that minimizes the action. In quantum mechanics,
Speaker 1: what you do is you take each path, and that
Speaker 1: path has a complex number multiplied by it that depends
Speaker 1: on the action. So you have all these paths and
Speaker 1: each one has this complex number in front of it,
Speaker 1: and the paths near the least action all interfere constructively
Speaker 1: with each other. These complex numbers allow them to contribute together,
Speaker 1: and the paths where the action varies a lot interfere destructively,
Speaker 1: so they cancel out. And so what's happening here is
Speaker 1: that all the paths are contributing, but just like in
Speaker 1: famous quantum mechanical experiments, the ones that are far from
Speaker 1: the least action destructively interfere with each other. They cancel
Speaker 1: themselves out, and so what happens is that you end
Speaker 1: up with this like envelope of paths around the least action.
Speaker 1: And this is so fascinating because that interference depends also
Speaker 1: not just on the action, but on planks constant hbar,
Speaker 1: and as h bar gets bigger, you get more contributions
Speaker 1: from paths near the least action, and as h bar
Speaker 1: gets smaller, you get fewer contributions from paths near the
Speaker 1: least action. So, now here you have a knob that
Speaker 1: you can very smoothly you say, I'm going to crank
Speaker 1: h bar all the way down to zero. What happens
Speaker 1: is that you have only a single path contributing. That's
Speaker 1: classical mechanics. Classical mechanics is quantum mechanics with hbar set
Speaker 1: to zero. If you crank hbar up to some number,
Speaker 1: then you start to get quantum effects where you have
Speaker 1: contributions from things near the least action path. And that's
Speaker 1: the quantum effects that we see. If you cranked up
Speaker 1: hbar beyond what it is in our universe, quantum mechanics
Speaker 1: would be more obvious.
Speaker 2: Right.
Speaker 1: And so this shows you that there's like not just
Speaker 1: a smooth continuum where classical mechanics sits on like one
Speaker 1: edge of it, right, But also that classical least action
Speaker 1: emerges from quantum interference. The reason it seems like we
Speaker 1: live in a classical world is because HBr is so
Speaker 1: small that it looks almost like it's zero from our
Speaker 1: point of view, and you can understand that very clearly
Speaker 1: using this least action approach and thinking about all the
Speaker 1: various paths that the particle would take.
Speaker 4: And so does thinking about things from a least action
Speaker 4: approach make you feel more confident that we're going to
Speaker 4: be able to one day sort of marry these approaches
Speaker 4: a little bit more effectively or not necessarily, because.
Speaker 1: No, it's the most sensible way to think about the
Speaker 1: relationship between quantum mechanics and classical physics. Essentially thinking about
Speaker 1: classical physics as like a zoomed out version of quantum mechanics.
Speaker 1: And we talk a lot about how, you know, classical
Speaker 1: physics emerges from quantum mechanics, and we say, that's kind
Speaker 1: of a mystery because we don't know how to go
Speaker 1: from the laws of quantum mechanics. You know Schroeninger's equation
Speaker 1: for an electron to zoom out to get f equals
Speaker 1: ma for a ball flying through the air, And that's
Speaker 1: true for the force picture, but in the action picture,
Speaker 1: we actually do kind of know how to do that,
Speaker 1: which is amazing. And so there is this connection between
Speaker 1: classical physics and quantum physics, where classical physics is an
Speaker 1: extreme version of it. So that's very beautiful, and unfortunately
Speaker 1: that doesn't solve like the bigger problems in physics, which
Speaker 1: is like how to integrate gravity into quantum mechanics. But amazingly,
Speaker 1: you can also think about gravity from an action point
Speaker 1: of view. It's a very natural way to think about
Speaker 1: general relativity.
Speaker 4: And when we get back from the break, that's exactly
Speaker 4: what we're going to do, all right, So now we're
Speaker 4: going to talk about what least action can tell us
Speaker 4: about gravity.
Speaker 3: Did I say that right?
Speaker 1: You totally?
Speaker 2: Did?
Speaker 1: You sound like a physicist?
Speaker 4: Oh?
Speaker 3: Oh that's great. Now I'm going to get invited to
Speaker 3: all the parties.
Speaker 1: And I meant that, of course, if it wasn't obvious,
Speaker 1: one hundred percent as a compliment, and.
Speaker 3: I took it one hundred percent as a compliment.
Speaker 1: I'm glad there wasn't any doubt, No, never would be
Speaker 1: all right. So we've been talking about least action and
Speaker 1: the way that helps us reimagine classical physics as stuff
Speaker 1: moving from A to B not because of the forces,
Speaker 1: but because it's the path that minimizes the action. And
Speaker 1: then we talked about how you can even use this
Speaker 1: in quantum mechanics, and it provides a nice bridge between
Speaker 1: classical physics and quantum physics. But folks out there are
Speaker 1: of course aware that one of the biggest struggles in
Speaker 1: physics is to unify quantum mechanics with gravity. They're classical
Speaker 1: theory of space time and how things move. And so
Speaker 1: is action something we can use to understand gravity? And
Speaker 1: the answer is yes. In fact, it's quite natural because
Speaker 1: general relativity already has very similar minimal principles.
Speaker 2: Right.
Speaker 1: The principle of least action says you find the path
Speaker 1: that minimizes the action. Well. Already, in general relativity, light,
Speaker 1: for example, follows the path that minimizes its travel time, right,
Speaker 1: And in general things in general relativity follow paths called geodesics.
Speaker 1: Geodesics are the shortest distance from A to B, right,
Speaker 1: And you can calculate the shortest distance by calculating the
Speaker 1: action across that path. Where in this case, what is
Speaker 1: the action. It's the curvature, the curvature along your path.
Speaker 1: So to figure out in general relativity how something will
Speaker 1: go from A to B, you find the path where,
Speaker 1: along with you minimize is not kindemic energy minus potential energy,
Speaker 1: but the action of general relativity, which is just the
Speaker 1: curvature of space. And so you can say, all right,
Speaker 1: my action is the curvature of space, and then you
Speaker 1: say find me the paths that minimize the action, and boom,
Speaker 1: all of general relativity pops out from there. All of
Speaker 1: Einstein's equations just flow from specifying the action to be
Speaker 1: the curvature of space. It's really kind of incredible.
Speaker 3: So I have a question.
Speaker 4: So the curvature of space is influenced by gravity or
Speaker 4: is reflected by gravity.
Speaker 1: Gravity is the motion of things under the influence of
Speaker 1: the curvature.
Speaker 4: Yeah, okay, So the equations that we were talking about
Speaker 4: were kinetic energy minus potential energy and potential energy has
Speaker 4: gravity in the equation. But when we think about general relativity,
Speaker 4: are we not using those equations or like, how does
Speaker 4: it mess things up that the term for gravity is
Speaker 4: in the equation.
Speaker 1: Yeah? Great question. So when we were talking about our
Speaker 1: simple scenario of a ball moving under as a parable,
Speaker 1: we were doing classical physics, but we weren't thinking about
Speaker 1: general relativity. We had a very simple model of objects
Speaker 1: with kinetic energy and potential energy, and we were assuming
Speaker 1: gravity with constants and G was just a number. Now
Speaker 1: we're totally generalizing that and we're going to solve for
Speaker 1: any sort of motion of any object through space and time,
Speaker 1: and the same equations do pop out. But we're doing
Speaker 1: Einsteini and gravity now instead of Newtonian gravity. You know,
Speaker 1: the previous version was like thinking about gravity as a force.
Speaker 1: Now instead we're doing general relativity, and so we're not
Speaker 1: calculating action as kinetic energy and minus potential energy. That's
Speaker 1: the Newtonian way. We're calculating in the Einsteinian way. And
Speaker 1: the incredible thing is that you can just specify the
Speaker 1: action and all of general relativity comes out. This is
Speaker 1: sort of why action is super amazing, because you specify
Speaker 1: it and you have this one set of rules, find
Speaker 1: the path that minimize the action, and that tells you
Speaker 1: all of the physics. All the physics comes out of.
Speaker 3: That tell me more physics that comes out of it.
Speaker 1: Danie, Well, the challenge now to like unify quantum mechanics
Speaker 1: and gravity is to find an action which has both
Speaker 1: gravity and quantum mechanics in it. And we know how
Speaker 1: to define quantum mechanical action, and that gives us all
Speaker 1: quantum field theory. We know how to define general relativity
Speaker 1: action that gives us all of Einstein's equations. We don't
Speaker 1: know how to find a unified action for both of
Speaker 1: those things. So that's sort of the question of quantum
Speaker 1: gravity now expressed in terms of this action principle. What
Speaker 1: is the action that includes both curvature and quantum mechanical fields.
Speaker 1: We don't know that.
Speaker 4: But if we could figure that out, then we would
Speaker 4: know what exactly.
Speaker 1: If we could figure that out, then we would have
Speaker 1: the laws of quantum gravity. Okay, yeah, absolutely, and that
Speaker 1: would be amazing. Yeah, but we can also like zoom
Speaker 1: in on one part of this to give another example,
Speaker 1: like Maxwell's equations. Maxwell's equations are these four equations. They're
Speaker 1: kind of complicated. They have all these differential terms in them,
Speaker 1: you know, changing electric fields costs, magnetic fields and vice versa,
Speaker 1: all this stuff. It was a huge stroke of genius
Speaker 1: when Maxwell unified these, and then Heapicide clarified all of
Speaker 1: them a century or so ago. And now it turns
Speaker 1: out that all of Maxwell's equations pop out if you
Speaker 1: apply this minimal action principle to a vector Fiel. We
Speaker 1: know that the electromagnetic field is a vector field, meaning
Speaker 1: that at every point in space is not just a
Speaker 1: number but like a little arrow. So it has a
Speaker 1: direction and a length. And if you say I have
Speaker 1: a vector field and I'm going to make some simple
Speaker 1: requirements about symmetry, like there's gonna be no preferred frame
Speaker 1: of reference or there's no ether for example, then that
Speaker 1: really constrains the kind of action that you can have.
Speaker 1: And there's basically only one way to write it. And
Speaker 1: from that way of writing it, boom, Maxwell's equations pop out.
Speaker 1: And so you might wonder, like, where do Maxwell's equations
Speaker 1: come from? Well, this tells you if you have a
Speaker 1: vector field that respects some basic symmetries, there's only one
Speaker 1: set of equations that minimize the action of that field.
Speaker 1: Those are Maxwell's equations. And so it tells us something
Speaker 1: maybe deep about the universe, that maybe everything that happens
Speaker 1: in the universe comes because the universe is minimizing action
Speaker 1: and only actions that respect some of these symmetries.
Speaker 4: Okay, so I'm still feeling grumpy at whoever called it action,
Speaker 4: but it feels like this is so fundamentally important that
Speaker 4: this is like Nobel Prize territory, So like, who figured
Speaker 4: out this action thing?
Speaker 1: Yeah, action has been around for a little while. Hamilton
Speaker 1: and Lagrange both came up with this alternative formulation of
Speaker 1: classical mechanics more than one hundred years ago before the
Speaker 1: Nobel Prize even was conceived of, and sort of generalized
Speaker 1: classical mechanics. And then it was Nuther who really gave
Speaker 1: us some deep insight into it because Nuther's theorem is
Speaker 1: this really deep theorem of physics that relates symmetries with
Speaker 1: conservation laws. It says like, well, where does conservation of
Speaker 1: momentum come from? Why does that happen in our universe? Well,
Speaker 1: it happens because of a symmetry. The symmetry is translational symmetry.
Speaker 1: That doesn't matter where you do your experiment. If you
Speaker 1: build a large hadron collider here or around Jupiter or
Speaker 1: in another galaxy, you should always get the same answers.
Speaker 1: Space is the same everywhere. That's where conservation and momentum
Speaker 1: comes from. And check out our whole episode on Nuther's symmetry.
Speaker 1: But there was a crucial detail we glossed over in
Speaker 1: that conversation. Those symmetries that we talk about in Nuther's theorem,
Speaker 1: those are symmetries of the action, and we didn't dig
Speaker 1: into it in that episode because, as you see, action
Speaker 1: is a whole set of baggage to introduce. But it's
Speaker 1: only symmetries of the action that give conservation laws. So
Speaker 1: that means that, like you write down your action, maybe
Speaker 1: it's kinetic energy, mutters potential energy, or it's the curvature
Speaker 1: of space, or its quantum field action. If that action
Speaker 1: is the same here and Jupiter and Alpha Centauri, then
Speaker 1: you get the conservation of momentum. And so it's symmetries
Speaker 1: of this action specifically that Norther showed us give us
Speaker 1: conservation laws. So Nother's theorem is a deep insight not
Speaker 1: just into where conservation laws come from, but why action
Speaker 1: is so fundamentally important.
Speaker 3: It seems like she clearly should have gotten a Nobel.
Speaker 1: She should definitely have. And these prints really guide the
Speaker 1: way that we do particle physics, Like when we devise
Speaker 1: the action of the Standard model, we have to have
Speaker 1: those symmetries because we know those symmetries will give us
Speaker 1: the kinds of conservation laws we see in the universe,
Speaker 1: like we see momentum is conserved, and so we can't
Speaker 1: build actions that don't respect the symmetry that gives us
Speaker 1: conservation of momentum. And it's a bunch more symmetries that
Speaker 1: we know we have to have in our action. So
Speaker 1: when you're devising an action, there's not a lot of
Speaker 1: choices to make, right because you're really restricted by all
Speaker 1: of these symmetries. You can't just add terms willy nilly
Speaker 1: because they would break these symmetries. And so if you
Speaker 1: wanted to start from scratch and devise a new action
Speaker 1: for quantum field theory, there's really only a couple ways
Speaker 1: you can do it. The respect those symmetries, we're super
Speaker 1: duper limited. And so it feels like those symmetries tell
Speaker 1: you what can happen in the universe, right, what's possible,
Speaker 1: and the action tells you what does actually happen. And
Speaker 1: so like all of physics is basically that, right, what
Speaker 1: are the symmetries of the universe, and then what actually
Speaker 1: happens is well, what minimizes the action on those symmetries,
Speaker 1: And so it's a completely different way of thinking about
Speaker 1: the universe instead of like the way you were describing,
Speaker 1: which I think is very intuitive and Newtonian of like
Speaker 1: thinking about the universe frame by frame, what's happening, Let's
Speaker 1: update things in a sort of like computational simulation sort
Speaker 1: of view. Instead, it's thinking about how things go from
Speaker 1: A to B to minimize the action along that path.
Speaker 4: So when you were saying, devise a new action, I'm
Speaker 4: having trouble wrapping my head around what that means because
Speaker 4: when every time you've said action, in my head, I
Speaker 4: have subtracted two different kinds of energy. So what does
Speaker 4: it mean to devise a new action? Is that like
Speaker 4: think of a different path that something could take, or well.
Speaker 1: Everything comes from the action, right, So you want to
Speaker 1: describe the universe, you write down an action, you apply
Speaker 1: this minimal principle. It predicts how things will move, and
Speaker 1: you compare that to what you actually see out there. So,
Speaker 1: in the case of a ball flying through the air,
Speaker 1: if I want to describe that, it works if I
Speaker 1: write down kinetic energy minus potential energy. If I write
Speaker 1: down kinetic energy minus three times potential energy, doesn't work.
Speaker 1: If I do kinetic energy time seven minus two potential energy,
Speaker 1: that doesn't work. It doesn't describe what I'm seeing out
Speaker 1: there in the universe. So if I want to describe
Speaker 1: the universe, I have to find some way to describe
Speaker 1: the action, so that minimizing that action gives me the
Speaker 1: things I see out there in the universe.
Speaker 4: You were using the word action the way people people
Speaker 4: actually use the word action, and the word action the
Speaker 4: way physics people use the word action, and that's what
Speaker 4: was do Okay, I get it now.
Speaker 3: You were using it both ways.
Speaker 1: Oh oops. And so kinetic energy, by the potential energy
Speaker 1: is a good approximate action for that one scenario we
Speaker 1: were talking about throwing a ball in your backyard. The
Speaker 1: action of the universe we don't know, because we have
Speaker 1: an action for quantum field theory and action for general relativity.
Speaker 1: We don't know how to put them together. But the
Speaker 1: goal of physics now is to find what is the
Speaker 1: action of the universe, because once we know that, we
Speaker 1: know what it does. And this is a different way
Speaker 1: of thinking about the universe, and it relies on knowing
Speaker 1: where something was and where something will be and figuring
Speaker 1: out the path between them. And that's a very different
Speaker 1: way of thinking about sort of computationally, frame by frame,
Speaker 1: and it has this sort of feeling this flavor to it.
Speaker 1: As we were talking about earlier, that like the present
Speaker 1: depends on the future. Like if you imagine a photon
Speaker 1: going from here to there, and we know the photon
Speaker 1: follows the path that takes the least amount of time
Speaker 1: from here to there. But when the photon is like
Speaker 1: halfway along the path, we don't know where it's going
Speaker 1: to go yet, Right, it hasn't gotten there yet, So
Speaker 1: how does it decide where it's going to go in
Speaker 1: order to minimize the total path when we haven't figured
Speaker 1: out yet where it is going to go, Right, it
Speaker 1: feels like sort of backwards or it's like depending on
Speaker 1: the future in some way. And this was the vague
Speaker 1: feeling that inspired ken ching short story which inspired the
Speaker 1: film Arrival, the idea that like, maybe aliens come and
Speaker 1: they don't see time and the way we do flowing
Speaker 1: from the past to the future. They experience all of
Speaker 1: time like a book, and they can rifle forwards and backwards.
Speaker 1: And you know, it's inspired by this exact concept, but
Speaker 1: it's a little bit of a I don't know if
Speaker 1: it's a misunderstanding or a misrepresentation, because there is no
Speaker 1: actual retro causality here, you don't have to know the
Speaker 1: whole history of the universe to solve these problems. It
Speaker 1: is true that the path depends on the final destination,
Speaker 1: but you can't change that final destination. It's not like
Speaker 1: you can influence the present using the future. There is
Speaker 1: a dependence on the future outcome, but it's not like
Speaker 1: you can control that. So you can't like change the
Speaker 1: photon's path halfway through. So there is a subtlety there
Speaker 1: which is crucial for the movie Arrival to work as
Speaker 1: a story, But fundamentally it's at odds with the actual
Speaker 1: physics of it.
Speaker 3: I like seeing you be a wet blanket to.
Speaker 1: All right. So we started this whole thing with the
Speaker 1: question why does the universe minimize action? So now we've
Speaker 1: explained what action is and how minimizing action gives us
Speaker 1: all of the physical laws we already discovered in other ways,
Speaker 1: and turns out to be a very general principle. It's
Speaker 1: connected to symmetry and helps us think about quantum mechanics
Speaker 1: and classical mechanics together and maybe tells us that our
Speaker 1: concept of time is a little bit archaic and needs
Speaker 1: to be updated. But what is the answer to the
Speaker 1: question why does the universe minimize action? And the short
Speaker 1: answer is, we don't actually know. It's hard to think
Speaker 1: about action philosophically because it doesn't have a simple intuitive
Speaker 1: analog like forces. They make sense, right, we see forces happen.
Speaker 1: It's easy to think about the universe as fundamentally a
Speaker 1: set of matter and forces acting on that matter, because
Speaker 1: that's sort of the way our minds work.
Speaker 2: Right.
Speaker 1: Whatever action is, it seems to be vitally important to
Speaker 1: the universe, even if it doesn't have a natural intuitive
Speaker 1: analog in our minds. That doesn't mean it's not the
Speaker 1: fundamental principle of the universe. And so philosophers, of course
Speaker 1: have latched onto this and they have raging arguments about
Speaker 1: what action is and what it means. Some suggest that
Speaker 1: what it means that the universe minimizes action is this
Speaker 1: constructive interference principle that like all possible histories do actually exist,
Speaker 1: it's just that most of them cancel each other out,
Speaker 1: and the universe minimizes action because the least action path
Speaker 1: is the only one that survives constructive interference. Between all
Speaker 1: of these paths.
Speaker 3: What happens to the other kellys.
Speaker 1: They cancel themselves out No, yeah, I know there's a
Speaker 1: plus Kelly and a minus Kelly out there that end up.
Speaker 3: In zero, equally valuable Kelly's.
Speaker 1: Well, you know, in the end, the universe minimizes action,
Speaker 1: not because it's lazy or because it prefers simplicity, but
Speaker 1: maybe just because only self supporting things can exist. Things
Speaker 1: that persist and be observed as law governed are things
Speaker 1: that you know, don't interfere with themselves, that reinforce themselves.
Speaker 1: But it's still an open question. You know. Our job
Speaker 1: as scientists and as curious beings in the universe is
Speaker 1: to be open minded about how the universe works, figure
Speaker 1: out those laws, and then just take a step back
Speaker 1: and be like, hmm, what does that mean about the
Speaker 1: universe that it does this instead of that? Why is
Speaker 1: this thing so important to the universe? And that's the
Speaker 1: juicy part, and that's the part we have not deeply understood.
Speaker 4: All right, friends, So put another tick in your tally
Speaker 4: of dKu episodes that end with us saying we don't know.
Speaker 1: So we've done a deep dive into action, which I
Speaker 1: always wanted to do. But even still, there are a
Speaker 1: few places where I was a little bit imprecise to
Speaker 1: simplify things. So for those of you listening very closely,
Speaker 1: and I love all of you, there are some additional
Speaker 1: details I want to mention. First, I said often that
Speaker 1: action is the difference between kinetic and potential energy. Technically,
Speaker 1: that's the lagrong and density, and the action is the
Speaker 1: integral of the difference between the kinetic and the potential energy. Similarly,
Speaker 1: for gr the action is not just the integral of
Speaker 1: the curvature, its volume integral of the Richy scaler, which
Speaker 1: is something that measures the curvature, but it also includes
Speaker 1: the determinant of the metric tensor and a couple other things. Secondly,
Speaker 1: I talked a lot about the principle of least action,
Speaker 1: implying that the action is always minimized, but the actual
Speaker 1: statement is that the action should be stationary, which in
Speaker 1: calculus means its derivatives vanish. That means that it can
Speaker 1: be a minimum, and it often is, but it could
Speaker 1: also be a maximum or even a saddle point. In
Speaker 1: the case of geodesics, for examples, there are several different
Speaker 1: kinds of geodesics. Spacelike geodesics minimize the distance, cool timelike
Speaker 1: geodesics actually maximize the proper time, and then null geodesics
Speaker 1: for light have no proper time. Finally, remember that the
Speaker 1: future does not depend on the past. The path we
Speaker 1: calculate using action between the past and the future depends
Speaker 1: on the boundary conditions including the future and the past ones.
Speaker 1: So knowing where and when the object starts.
Speaker 4: And ends and we look forward to seeing you next time.
Speaker 1: And I hope this has given you another way to
Speaker 1: think about how things happen in the universe and why
Speaker 1: some things happen and other things don't. In the end,
Speaker 1: it all minimizes the action.
Speaker 4: Daniel and Kelly's Extraordinary Universe is produced by iHeartRadio.
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Speaker 1: Extraordinary Universe.
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