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Speaker 1: Physics has set itself quite the task. The job is

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Speaker 1: to explain the whole universe, everything inside of it, and

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Speaker 1: all of its doing and throwing. Usually we think of

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Speaker 1: that in terms of the matter, the stuff, and the

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Speaker 1: forces how that stuff interacts. So when we count our

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Speaker 1: progress towards the big goal of physics, we sometimes think

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Speaker 1: about the number of particles and the number of forces.

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Speaker 1: We reduce that number when we break open matter to

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Speaker 1: see what it's made out of, or when we unify

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Speaker 1: forces like we be merged electricity and magnetism into electromagnetism

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Speaker 1: and then later added the weak force to make the

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Speaker 1: electroweak force sorry magnetism. Eventually, we hope we'll get down

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Speaker 1: to one particle and one force that explains everything that happens.

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Speaker 1: But what if there there is a better way. Maybe

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Speaker 1: forces are intuitive to us, part of the stories we

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Speaker 1: tell about what we see with a simple intuitive analog

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Speaker 1: in our experience. But what if they aren't a natural

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Speaker 1: fit to the real mechanisms of the universe itself? What

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Speaker 1: if forces emerged from something else. Today on the pod,

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Speaker 1: we'll talk about something we've mentioned many times in many contexts.

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Speaker 1: It's time to dive in and talk about the mysterious

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Speaker 1: quantity that has no analog in our intuitive experience, but

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Speaker 1: seems to dominate in the events of the universe, action,

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Speaker 1: and specifically, why the universe seems to minimize it. Welcome

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Speaker 1: to Daniel and Kelly's Extraordinary Minimal Universe.

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Speaker 2: Hello.

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Speaker 3: I'm Kelly Wintersmith.

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Speaker 4: I study parasites and space and it's winter right now,

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Speaker 4: so it is my season of least action.

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Speaker 1: Hi. I'm Daniel. I'm a particle physicist. It's winter here

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Speaker 1: in southern California, though I can hardly tell.

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Speaker 3: So we're.

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Speaker 4: We're talking about potential energy and kinetic energy a little

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Speaker 4: bit today, which reminds me of my intro physics class,

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Speaker 4: which makes me wonder, what is the coolest demonstration you

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Speaker 4: have done for your students as a teacher.

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Speaker 1: Ooh, that's a good question. I think the coolest demonstration

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Speaker 1: I've ever done doesn't actually relate to kinetic or potential energy.

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Speaker 1: I know, there's like those famous ones where you like

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Speaker 1: push a bowling ball away from your nose and then

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Speaker 1: you stand there all cool as it comes back and

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Speaker 1: doesn't crunch you in the face. But I think the

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Speaker 1: most interesting ones are the ones that reveals something about

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Speaker 1: the universe you can't otherwise see. So I once brought

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Speaker 1: in a homemade cloud chamber. This is something you can

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Speaker 1: actually build yourself in your garage with pretty simple ingredients

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Speaker 1: that could show you muons flying through the air. It

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Speaker 1: reveals to you that the world around you is filled

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Speaker 1: with these invisible particles flying at high speeds, and you

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Speaker 1: can build the device using fairly simple ingredients to reveal them.

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Speaker 1: These cloud chambers have like super saturated air, and as

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Speaker 1: the muons fly through, they create these droplets which become visible.

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Speaker 1: You probably have seen them at science museums. I just

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Speaker 1: think that's awesome because it shows you that the world

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Speaker 1: is so much more complex than your senses can reveal.

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Speaker 4: Did we discover muons pretty early on? Because they're so

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Speaker 4: easy to see?

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Speaker 1: We discovered the muon years and years ago using cloud

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Speaker 1: chambers actually, and then you can spot them also using

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Speaker 1: big blocks of emulsion. Emulsion is sort of like a

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Speaker 1: three dimensional bit of photographic plate that you later like

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Speaker 1: slice up and develop as photographs. And we put them

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Speaker 1: on the tops of mountains and we saw a lot

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Speaker 1: of particles shooting through them, and that was the first

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Speaker 1: clue about muons.

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Speaker 4: Yeah, who did we know what they were immediately or

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Speaker 4: did it take a while to work that out?

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Speaker 2: No?

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Speaker 1: Actually, it's sort of a famous surprise because we had

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Speaker 1: the idea of like atomic structure and it was all

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Speaker 1: very nice and neat. We had protons and neutrons and electrons,

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Speaker 1: and then we discovered the muon which wasn't part of

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Speaker 1: the atom. And a famous physicist I Robbie said, who

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Speaker 1: ordered that, like, we don't need this. We're you know,

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Speaker 1: we have a pretty good thing going, like get out

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Speaker 1: to hear universe with your pesky facts.

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Speaker 2: Yeah.

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Speaker 4: No, I've been there running experiments and you're like, no, please,

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Speaker 4: don't do that, universe.

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Speaker 3: But it does it anyway exactly.

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Speaker 1: And you know, the universe is under no obligation to

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Speaker 1: make sense to us, or to do what we expect,

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Speaker 1: or to follow rules that sort of connect with our

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Speaker 1: intuitive way of thinking. Which is why I'm so excited

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Speaker 1: today to finally get to talk about this concept we've

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Speaker 1: been mentioning and referring to for months and months and

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Speaker 1: months now, and we're going to do a deep dive

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Speaker 1: and an explanation of it today. And what is it

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Speaker 1: called called action and the principle of least action, and

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Speaker 1: it's a completely different way to think about motion in

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Speaker 1: the universe and why things fall down, or why things

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Speaker 1: slide the way they do, or even how quantum fields oscillate. Really,

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Speaker 1: it's the most basic principle we've discovered, but it's also

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Speaker 1: kind of counterintuitive, so it takes a little bit of

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Speaker 1: a mental mind shift to think about the universe in

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Speaker 1: terms of action. It's also a terribly terribly named word

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Speaker 1: because it has nothing to do with the word action

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Speaker 1: we use in English.

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Speaker 4: Well, it is a physics concept, so it would have

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Speaker 4: to have a bad name.

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Speaker 1: Why did they do this? You know, they should have

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Speaker 1: just come up with a new name, plasma, cagical or

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Speaker 1: something and use that so that when you hear it,

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Speaker 1: you're like, Okay, this is something new. I have to

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Speaker 1: make a new space in my brain. But if you

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Speaker 1: use an existing word, that has to like share that

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Speaker 1: room in your brain with that other concept which has

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Speaker 1: the same word.

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Speaker 4: Well, I think somebody needs to hold on to plasmacajigle

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Speaker 4: or whatever it was that you said. Thing needs to

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Speaker 4: be named that, and you should be in charge of

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Speaker 4: naming things in physics from here on out.

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Speaker 1: All right, Well, I guess I just need to discover

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Speaker 1: something and then I can name it flasmaca jiggle, and

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Speaker 1: then we'll be all set. You know, I've done the

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Speaker 1: hard part already, and you know, just the pesky bit

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Speaker 1: about actually discovering something in the universe.

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Speaker 3: Yeah, right, yeah, that tiny bit.

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Speaker 4: And so we asked the extraordinaries, why does the universe

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Speaker 4: flazmaca jiggle?

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Speaker 2: No, we didn't. No.

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Speaker 1: I went out there and I asked folks what they

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Speaker 1: knew about action, because this is something we get requests

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Speaker 1: about a lot, and we've mentioned occasionally on the podcast

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Speaker 1: and people ask us, ooh, would you go into more

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Speaker 1: depth about that? And it's something I love doing on

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Speaker 1: the pod, is explaining something on a depth beyond what's

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Speaker 1: typically out there in popular science, but I hope in

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Speaker 1: an actual, approachable way that'll make people really appreciate the

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Speaker 1: way physics is done on the cutting edge. But of course,

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Speaker 1: before we dig into it, I wanted to know what

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Speaker 1: people already knew about this concept, So I asked, folks,

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Speaker 1: why does the universe verse minimize action as usual? If

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Speaker 1: you would like to join this crew of people who

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Speaker 1: respond to these questions without the opportunity to google them.

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Speaker 1: Please write to us questions at Danielankelly dot org. We

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Speaker 1: would love to add your voice in the meantime. Think

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Speaker 1: about it. Why do you think the universe minimizes action?

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Speaker 3: Why does it flasmacajicle.

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Speaker 1: Here's what people have to say. Since I have no

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Speaker 1: idea what this means, I'm forced to fall back on

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Speaker 1: a template answer of.

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Speaker 5: Entropy, because the universe is just bound to follow laws

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Speaker 5: with no shortcuts and no long cuts. So I think

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Speaker 5: that minimizing action is probably another way of saying minimizing

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Speaker 5: divergence from laws.

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Speaker 1: For every action, there's an equal and opposite reaction, So

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Speaker 1: I guess the universe minimizes reactions as well.

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Speaker 4: To safe energy and to minimize possible outcomes.

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Speaker 2: To know, is the universe lazy? Is it just chilled out?

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Speaker 1: It is the world likes to be in its lowest

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Speaker 1: energy state.

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Speaker 2: Because actions speak louder than words, and there's far too

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Speaker 2: much noise pollution.

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Speaker 1: Because anything that happens, or any force that exists, has

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Speaker 1: a counter force pressing against it.

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Speaker 2: Maybe it's lazy, that's my excuse. I suspect that it

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Speaker 2: has something to do with entroview, though.

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Speaker 1: Too optimiz for efficiency, kind of like natural selection.

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Speaker 2: It's just something we observe, but we don't know why.

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Speaker 2: Do individual processes independently tend to pars the money or

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Speaker 2: is there an underlying unified model that polls all behavior

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Speaker 2: to a deeper minimization.

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Speaker 1: Seems like it would be the only way that it

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Speaker 1: could go, because if there was something at a higher energy,

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Speaker 1: there was always something that could come lower.

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Speaker 4: I was pleased to see I wasn't the only one

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Speaker 4: who didn't know the answer, and went with sarcasm.

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Speaker 1: I never know what to expect from these responses. I

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Speaker 1: always learned so much. Sometimes bill know exactly what I'm

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Speaker 1: talking about and get very insightful answers. Other times people

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Speaker 1: are confused by the physics word and as is not

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Speaker 1: their fault at all, and it seemed to have happened

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Speaker 1: in this case. But this is exciting to me because

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Speaker 1: it means that not a lot of folks out there

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Speaker 1: are familiar with this concept of action being minimized, which

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Speaker 1: means we get to teach them all something very very

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Speaker 1: cool about the universe.

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Speaker 4: Yes, we are helping to make you the most interesting

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Speaker 4: person at the party.

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Speaker 1: So let's say, Kelly, I'm trying to assess the level

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Speaker 1: of sarcasm there, because I am one hundred percent sincerely

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Speaker 1: excited about action, and I don't talk about it at

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Speaker 1: parties very much, but it is something super duper nerdy

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Speaker 1: and cool to discover, like an organizing principle of the universe,

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Speaker 1: especially when it's counterintuitive, when it's not the way we

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Speaker 1: typically think about stuff. That's like one hundred percent sincerity.

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Speaker 1: And I'm assuming you feel the same way I do.

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Speaker 3: I do.

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Speaker 4: I don't know what kind of parties you're thinking of, Daniel,

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Speaker 4: but the parties I go to we talk about things

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Speaker 4: like pleasma.

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Speaker 1: Okay, all right, Well we're not explaining plasmaka jiggle today

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Speaker 1: because I haven't discovered it yet. But we are going

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Speaker 1: to talk about action. But let's start by thinking about

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Speaker 1: a simple motion of an object, and then we'll talk

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Speaker 1: about how we typically understand it, how people probably think

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Speaker 1: about its motion, and then we'll switch and think about

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Speaker 1: it in another way. So the classic example, of course,

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Speaker 1: is a ball flying through the air. You have a ball,

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Speaker 1: you're playing catch with your kid or your dog or whatever.

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Speaker 1: You throw it and it goes across your yard and

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Speaker 1: hits the ground or gets caught by your dog or whatever.

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Speaker 1: And from a traditional physics point of view, this isn't

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Speaker 1: too complicated. You can understand it by thinking, like you

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Speaker 1: throw it with your arms, so it has some initial velocity.

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Speaker 1: And we know that things in the universe, if they

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Speaker 1: have velocity, they just keep moving unless some force acts

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Speaker 1: upon them. And in this case, for example, the force

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Speaker 1: is gravity pulling it back down to the Earth. And

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Speaker 1: so we can use those various elements to understand the

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Speaker 1: motion of the ball. We have velocity, we have acceleration

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Speaker 1: that changes its velocity. We can put that together to

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Speaker 1: get an equation that describes where the ball is at

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Speaker 1: any time, and it comes out to be a parabola. Right,

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Speaker 1: It goes up and it comes back down and it

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Speaker 1: hits the ground.

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Speaker 3: It's also a great song by Tool. Do you think

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Speaker 3: everybody hum.

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Speaker 1: A few bars of it for us? Kelly?

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Speaker 3: No, no, no, no, no. Oh, hey, I'm not gonna

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Speaker 3: go anymore.

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Speaker 4: So do you think everybody knows what the shape of

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Speaker 4: a parabola looks like?

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Speaker 1: Oh? It's hard for me to remember a time when

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Speaker 1: I didn't know what the shape of a parabolo looks like.

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Speaker 1: So I should ask you that question. Kelly, do you

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Speaker 1: can you imagine a parabolo?

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Speaker 3: Yep, I can, but I also do a fair bit

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Speaker 3: of modeling.

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Speaker 1: Yeah, okay, so that's a good point. Let's help people

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Speaker 1: visualize a parabola.

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Speaker 3: It's just a you. You're making it too complicated.

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Speaker 1: A parabola is sort of like an upside down you. Right,

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Speaker 1: it's a little bit tighter at the top, but basically

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Speaker 1: a parabolo is well defined by what happens when you

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Speaker 1: throw a ball across your yard. Right, It's going to

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Speaker 1: go up, and then it's gonna turn around, it's gonna

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Speaker 1: come back to and that's the parabolic shape. It's defined

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Speaker 1: by an equation that has like an x squerginit for

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Speaker 1: people who like to think about equations, but for visual people,

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Speaker 1: it's basically an upside down you. And so that's what

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Speaker 1: a brable looks like. Okay, So that's sort of the

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Speaker 1: traditional way to think about how things move. You have matter,

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Speaker 1: and you have forces. Forces act on matter to provide acceleration.

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Speaker 1: A few rounds of calculus and you get your equation

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Speaker 1: of motion where the thing is at any time. We're

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Speaker 1: good with that.

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Speaker 4: So far, we're good, right, And so in this model,

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Speaker 4: we're not paying attention to things like friction or wind

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Speaker 4: or anything like that.

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Speaker 1: That's exactly right, because those things are really hard to

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Speaker 1: add using this way. Like wind is a force, but

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Speaker 1: it's not constant. Friction is a force, but it depends

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Speaker 1: on velocity. So we're going to stick with a simple

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Speaker 1: calculation because that's what this approach is good at. Simple calculations,

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Speaker 1: what we call conservative forces with constant acceleration. Very easy

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Speaker 1: to do those calculations. But there's something interesting about this

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Speaker 1: motion if you look at it from another point of view.

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Speaker 1: This is going to sound a little bit weird and random,

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Speaker 1: but stick with me. So what you do is you

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Speaker 1: think about the kinetic energy of this ball. Kinetic energy

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Speaker 1: is just the energy of motion, and you usually calculate

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Speaker 1: it like one half m v squared vias the velocity.

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Speaker 1: So you calculate the kinetic energy of the ball as

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Speaker 1: it moves through the air. Cool Now calculate also the

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Speaker 1: potential energy of the ball. Potential energy here is just

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Speaker 1: from gravity, so it's like mgh just the height of

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Speaker 1: the ball. As it goes up it has more potential energy,

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Speaker 1: as it goes down has less potential.

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Speaker 3: Energy, and m in both of those was mass.

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Speaker 1: Yeah, yeah, exactly. And so you calculate these things kinetic

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Speaker 1: energy and potential energy. Now do something weird, subtract them.

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Speaker 1: Usually we add these things to make total energy. But

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Speaker 1: this time, let's subtract them. Let's do kinetic energy minus

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Speaker 1: potential energy. So now we're calculating the difference between the

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Speaker 1: kinetic energy and the potential energy. You might think, well,

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Speaker 1: what does that mean? Intuitively, Like, if you add them,

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Speaker 1: it may sense because it's okay, that's total energy. What

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Speaker 1: does the difference mean? It means nothing intuitively, It's just

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Speaker 1: this weird number we're calculating. Okay, okay. The cool thing

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Speaker 1: about this number, The reason we're talking about this number

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Speaker 1: is that the path the ball took minimizes that number.

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Speaker 1: Like we have the path the ball took. It was

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Speaker 1: a parabola. We calculate the kinetic energy minus potential energy.

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Speaker 1: That number is smallest for the path that the ball took.

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Speaker 1: If you change the path a little bit, you add

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Speaker 1: a little divit or middle higher, a little lower, that

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Speaker 1: path would have a higher value of kinetic energy minus

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Speaker 1: potential energy. So the path that the ball took is

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Speaker 1: the one that minimizes this difference between kinetic and potential energy.

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Speaker 4: Okay, and so is that just because kinetic energy would

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Speaker 4: always be greater whenever you add like a divot, because

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Speaker 4: you're making the parabola longer, anytime you're adding a divot

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Speaker 4: or something.

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Speaker 1: I think you're asking, why is the parabola the path

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Speaker 1: that minimizes this difference?

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Speaker 2: Right?

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Speaker 1: Yeah, and we're gonna explain that. The answer is yes.

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Speaker 1: We're gonna explain that in detail in a minute, but

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Speaker 1: for now, let's stop talking about kinetic energy. Money is

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Speaker 1: potential energy because it's a lot of words, and let's

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Speaker 1: just relabel it with a new word, right, so we

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Speaker 1: don't have to use so many words. And we're gonna

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Speaker 1: call it action. Why we don't call it plasmaca jiggle,

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Speaker 1: I don't know, but we're gonna call it action. And

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Speaker 1: so this turns out to be a general principle in

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Speaker 1: physics that the path of things take you can figure

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Speaker 1: it out by finding the path that minimizes the action

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Speaker 1: this weird difference between kinetic and potential energy. So we

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Speaker 1: started out just like I'm going to do this calculation.

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Speaker 1: I'm not gonna tell you why or what it means

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Speaker 1: or anything, and now we did it, and we discovered

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Speaker 1: something that's actually physically useful. The universe seems to pay

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Speaker 1: attention to this. It's not just a number, Daniel calculator.

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Speaker 1: I could calculate anything like the number of walnuts times

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Speaker 1: the temperature outside right. I can make up whatever quantity

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Speaker 1: I want, But that doesn't help me solve a problem.

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Speaker 1: It just seem to be important to the universe. This number,

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Speaker 1: the action, the difference between kinetic and potential energy is

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Speaker 1: all so an arbitrary, random thing that we constructed, but

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Speaker 1: it seems to be respected by the universe somehow, because

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Speaker 1: the universe, when the ball is flying through the air,

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Speaker 1: chooses the path that minimizes this weird number, this thing

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Speaker 1: we call action.

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Speaker 3: So you can like tell the future if you know.

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Speaker 4: So let me it's been a while since I've taken physics,

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Speaker 4: and so so I'm imagining you've released the ball, and

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Speaker 4: so to do this is it like, you know, you

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Speaker 4: stop and you take a picture of the ball at

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Speaker 4: every second, and you redo this calculation at every second

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Speaker 4: and then you can predict where it's going to be

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Speaker 4: the next second by doing this calculation.

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Speaker 1: No action, It's exactly the opposite of that, which makes

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Speaker 1: it a great question. So the way you described it

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Speaker 1: in your mind is the way we typically think about

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Speaker 1: the universe, that the past controls the future. We have

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Speaker 1: like frame by frame, what happens now affects what's going

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Speaker 1: to happen in a moment.

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Speaker 2: Right.

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Speaker 1: The ball moves this way because it has velocity and

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Speaker 1: it has a force pulling on it. That's sort of

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Speaker 1: like a computational way of thinking about the universe that

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Speaker 1: you calculate it like frame by frame, and that's actually

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Speaker 1: called the Newton schema. Newton came up with this idea

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Speaker 1: that like the future of the universe is determined by

347
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Speaker 1: the present, and he thought about like universal clocks and

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Speaker 1: so many fun digressions we could go on there. And

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Speaker 1: that's the way that the typical force story works. You

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Speaker 1: think about velocity and forces and you cycle through frame

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Speaker 1: by frame. That's not the way the action works. You

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Speaker 1: can't use action to predict the future the same way

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Speaker 1: because to calculate the path of the ball using action,

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Speaker 1: you have to know the initial position and the final

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Speaker 1: position already in order to find the path that goes

356
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Speaker 1: from So there's a weird thing here which seems to

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Speaker 1: imply maybe that the present depends on the future, you know,

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Speaker 1: like where the ball goes now depends on where it lands,

359
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Speaker 1: and so you have to know the future to predict

360
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Speaker 1: the present. Not quite that. We're going to dig into

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Speaker 1: it in a minute, but that's actually the fundamental misunderstanding

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Speaker 1: at the heart of the movie Arrival.

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Speaker 3: WHOA, yeah, I know, all right, stick with us to

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Speaker 3: the end.

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Speaker 1: Yeah, exactly. So we have this other way of thinking

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Speaker 1: about motion where if you know the initial point A

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Speaker 1: and the final point B, you can figure out what

368
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Speaker 1: path something took just by calculating this weird thing called

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Speaker 1: action and finding the path that minimizes the action. So

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Speaker 1: let's work through another example, just to make sure we

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Speaker 1: have this in our heads, because it's really important. Let's

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Speaker 1: take an even simpler example, a ball with no gravity.

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Speaker 1: Right now, we're out in space. Okay, we've ignored Zach

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Speaker 1: and Kelly's advice, and you've gone to space and built

375
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Speaker 1: a colony. We've made all sorts of mistakes, but now

376
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Speaker 1: we're out in space and we get to play zero

377
00:18:36,600 --> 00:18:39,680
Speaker 1: G catch with our kids or with our space dog. Right,

378
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Speaker 1: So what happens when you throw a ball in space?

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Speaker 3: You die?

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Speaker 1: How's it? Going to move you die, Kelly. Doesn't happen immediately.

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Speaker 1: I mean, we got lots of radiation and eventually we die,

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Speaker 1: but we do we to have one nice afternoon of

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Speaker 1: playing catch with our space dog.

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Speaker 4: Okay, right, right, So if you're in deep space in

385
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Speaker 4: your space suit, you're gravity's probably negligible. Right, So does

386
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Speaker 4: that mean potential energy is zero?

387
00:19:05,200 --> 00:19:08,040
Speaker 1: Exactly right. So let's think about the motion of a

388
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Speaker 1: ball when there's no potential energy. So the force method

389
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Speaker 1: is really easy here. You throw the ball that has velocity.

390
00:19:14,359 --> 00:19:16,760
Speaker 1: There's no forces, So what's gonna happen. It's just going

391
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Speaker 1: to keep having that velocity. Very intuitive. It's going in

392
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Speaker 1: a certain direction. It keeps going in that direction every

393
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Speaker 1: moment in time. You can predict the future because you

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Speaker 1: have its velocity and that tells you exactly where it's

395
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Speaker 1: going to go. Very simple. Okay, Now let's try to

396
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Speaker 1: do that with the action method. So the action method says,

397
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Speaker 1: you know where the ball started, and you know where

398
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Speaker 1: the ball ends up, and you know how much time

399
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Speaker 1: it took to go from A to B. Find the

400
00:19:40,520 --> 00:19:43,359
Speaker 1: path that it took from A to B. And so

401
00:19:43,480 --> 00:19:45,320
Speaker 1: to do this, what you do is consider all the

402
00:19:45,359 --> 00:19:50,080
Speaker 1: possible paths, a straight line, a wiggle, a sinusoid, you know,

403
00:19:50,240 --> 00:19:53,159
Speaker 1: any other sort of crazy path that goes from A

404
00:19:53,359 --> 00:19:57,359
Speaker 1: to B in the same amount of time. Okay, now,

405
00:19:57,760 --> 00:20:00,159
Speaker 1: going from A to B in a specific time, that

406
00:20:00,200 --> 00:20:03,400
Speaker 1: already specifies the average velocity because you know how far

407
00:20:03,440 --> 00:20:06,880
Speaker 1: it's gone and how long it's taken, So you're already

408
00:20:06,960 --> 00:20:10,400
Speaker 1: kind of restricted. So the simplest path, the straight line.

409
00:20:10,600 --> 00:20:13,680
Speaker 1: This one has constant velocity, and so it's going to

410
00:20:13,760 --> 00:20:17,840
Speaker 1: have the smallest action because it has the smallest integrated

411
00:20:17,920 --> 00:20:22,040
Speaker 1: kinetic energy across that path. If you imagine doing something

412
00:20:22,040 --> 00:20:26,040
Speaker 1: else like going super fast first and then slowing down

413
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Speaker 1: at the end, or going super slow for a while

414
00:20:28,359 --> 00:20:30,840
Speaker 1: and then speeding up to get there at the right time,

415
00:20:31,320 --> 00:20:34,679
Speaker 1: all of those things have more deviations in kinetic energy,

416
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Speaker 1: and because kinetic energy has velocity squared in it, it's

417
00:20:38,400 --> 00:20:41,399
Speaker 1: going to end up with the larger kinetic energy integrated

418
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Speaker 1: over the path. So the way to have the smallest

419
00:20:45,000 --> 00:20:48,680
Speaker 1: integrated kinetic energy is to keep your kinetic energy constant.

420
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Speaker 1: That's why straight line with constant velocity is the path

421
00:20:52,400 --> 00:20:56,080
Speaker 1: that minimizes the action. Any deviation in a direction is

422
00:20:56,160 --> 00:20:58,960
Speaker 1: going to require more kinetic energy, which increases your action

423
00:20:59,440 --> 00:21:01,959
Speaker 1: or any chain, the velocity is going to give you

424
00:21:02,119 --> 00:21:06,040
Speaker 1: larger kinetic energy overall. So in the simplest case, action

425
00:21:06,240 --> 00:21:09,679
Speaker 1: also predicts that the ball will go between you and

426
00:21:09,720 --> 00:21:11,760
Speaker 1: your space dog in a straight line.

427
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Speaker 4: Am I being pedantic by thinking like, well, it couldn't

428
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Speaker 4: have sped up halfway because you threw it, And wouldn't

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Speaker 4: it just stay the same speed the whole time with

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Speaker 4: no friction and no gravity, And so what do we

431
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Speaker 4: gain by thinking about it that way? Because it couldn't

432
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Speaker 4: have done any of those other things?

433
00:21:29,160 --> 00:21:31,959
Speaker 1: You're absolutely right. So you're thinking about this still in

434
00:21:31,960 --> 00:21:35,080
Speaker 1: the Newton force scheme, which makes total sense because it's

435
00:21:35,080 --> 00:21:38,359
Speaker 1: easy to understand why a particle would need a force

436
00:21:38,440 --> 00:21:40,399
Speaker 1: to deviate from the line it's moving on, and so

437
00:21:40,440 --> 00:21:43,200
Speaker 1: you're looking for a force to explain any other kind

438
00:21:43,200 --> 00:21:46,439
Speaker 1: of motion than a straight line. Makes perfect sense. But

439
00:21:46,680 --> 00:21:49,360
Speaker 1: right now we're thinking about this in another way. We're

440
00:21:49,400 --> 00:21:53,320
Speaker 1: not bound to forces as explanations. We're just considering the

441
00:21:53,359 --> 00:21:56,240
Speaker 1: action of various paths, and in this case we don't

442
00:21:56,280 --> 00:21:59,240
Speaker 1: gain anything. In fact, it feels like more complicated to

443
00:21:59,240 --> 00:22:02,040
Speaker 1: do with the action way right, And the action is

444
00:22:02,040 --> 00:22:05,560
Speaker 1: going to make things simpler when we get into Hairer situations.

445
00:22:05,960 --> 00:22:08,040
Speaker 1: But I just want to sort of like line up

446
00:22:08,119 --> 00:22:10,760
Speaker 1: a simple situation so we can get practice thinking about

447
00:22:10,800 --> 00:22:11,200
Speaker 1: the action.

448
00:22:11,520 --> 00:22:13,199
Speaker 4: So you've got us all on the edge of our seats.

449
00:22:13,480 --> 00:22:15,800
Speaker 4: So we're going to take a break, and when we

450
00:22:15,840 --> 00:22:18,120
Speaker 4: get back, you are going to give us a Hairer

451
00:22:18,240 --> 00:22:20,880
Speaker 4: situation where the curse mack amiggle.

452
00:22:21,440 --> 00:22:26,640
Speaker 3: I said, oh, I'm so sorry. We'll get more complicated.

453
00:22:46,200 --> 00:22:48,119
Speaker 4: All right, We're back, and Daniel's going to give us

454
00:22:48,119 --> 00:22:51,480
Speaker 4: a more complicated situation where this concept of action is

455
00:22:51,520 --> 00:22:54,119
Speaker 4: going to help us understand what's going on better.

456
00:22:54,680 --> 00:22:56,840
Speaker 3: Maybe because it's physics.

457
00:22:58,400 --> 00:23:01,120
Speaker 1: It does make it easier to analyze it's really hairy problems.

458
00:23:01,119 --> 00:23:04,320
Speaker 1: It's also the way physicists think about motion, you know,

459
00:23:04,320 --> 00:23:06,320
Speaker 1: when we get to quantum field theory and all that stuff.

460
00:23:06,359 --> 00:23:09,760
Speaker 1: It's fundamentally based on action. And so I really want

461
00:23:09,760 --> 00:23:11,760
Speaker 1: to move people out of the mindset of thinking about

462
00:23:11,760 --> 00:23:14,960
Speaker 1: forces and thinking about action, because like, welcome to the

463
00:23:14,960 --> 00:23:16,840
Speaker 1: cutting edge of physics. This is how we do it,

464
00:23:17,440 --> 00:23:20,280
Speaker 1: all right. So we consider the very simple case you're

465
00:23:20,320 --> 00:23:22,640
Speaker 1: playing catch with your space dog. There's no gravity, things

466
00:23:22,640 --> 00:23:25,280
Speaker 1: moving a straight line, Kelly was bored by that. She's like,

467
00:23:25,320 --> 00:23:27,280
Speaker 1: why do we even do this? Fair point.

468
00:23:27,440 --> 00:23:28,680
Speaker 3: I wasn't bored.

469
00:23:28,800 --> 00:23:30,040
Speaker 1: You were underwhelmed a little.

470
00:23:30,080 --> 00:23:32,280
Speaker 3: You know, probably death was imminent, which is interesting.

471
00:23:34,480 --> 00:23:36,680
Speaker 1: Don't think about the death of my space dog. That's

472
00:23:36,720 --> 00:23:37,280
Speaker 1: not nice.

473
00:23:37,960 --> 00:23:39,280
Speaker 3: Sorry, I do like space dog.

474
00:23:39,440 --> 00:23:41,960
Speaker 1: I'm sure we'll give lots of shielding in our space

475
00:23:42,000 --> 00:23:44,760
Speaker 1: dog spacesuit. Right, Yes, take care of our critters. Yeah,

476
00:23:44,800 --> 00:23:46,720
Speaker 1: because they didn't get to choose whether they go to space.

477
00:23:46,880 --> 00:23:49,359
Speaker 3: Right, No, like I didn't get to choose. Didn't go

478
00:23:49,400 --> 00:23:50,359
Speaker 3: well Forlika.

479
00:23:50,160 --> 00:23:54,040
Speaker 1: No, exactly. All right, so let's get back to other scenarios. Now,

480
00:23:54,119 --> 00:23:57,000
Speaker 1: let's get back to your question about why a ball

481
00:23:57,119 --> 00:24:00,800
Speaker 1: in gravity moves under a parabola. Right, So we're going

482
00:24:00,880 --> 00:24:03,240
Speaker 1: to add gravity back into our situation. Bring our space

483
00:24:03,280 --> 00:24:05,760
Speaker 1: dog back to Earth. Toss a ball to the space

484
00:24:05,800 --> 00:24:08,000
Speaker 1: dog in the backyard. It doesn't move in a straight line.

485
00:24:08,160 --> 00:24:10,800
Speaker 1: It moves in a parabola. The first picture tells us why,

486
00:24:10,840 --> 00:24:13,919
Speaker 1: because you have an acceleration, and acceleration is a second

487
00:24:13,960 --> 00:24:17,000
Speaker 1: derivative of position, and so if you integrate that constant

488
00:24:17,000 --> 00:24:19,400
Speaker 1: acceleration twice, you get an X squared term. You get

489
00:24:19,400 --> 00:24:22,280
Speaker 1: a parabola. It all makes sense. So things move in

490
00:24:22,320 --> 00:24:25,560
Speaker 1: a parabola because there's a constant force. What about the

491
00:24:25,600 --> 00:24:28,640
Speaker 1: action point of view, Why do we move in a parabola, Well,

492
00:24:28,640 --> 00:24:32,000
Speaker 1: we want to minimize this difference between kinetic energy and

493
00:24:32,119 --> 00:24:36,640
Speaker 1: potential energy. Potential energy increases as we go up, right,

494
00:24:36,760 --> 00:24:39,800
Speaker 1: So because we want to minimize action, and action is

495
00:24:39,880 --> 00:24:43,879
Speaker 1: kinetic energy minus potential energy. That means we want to

496
00:24:43,960 --> 00:24:47,800
Speaker 1: have lots of potential energy. So potential energy increases as

497
00:24:47,800 --> 00:24:49,280
Speaker 1: we go up. So we don't want to go up

498
00:24:49,359 --> 00:24:52,800
Speaker 1: fast to get high potential energy. Right, So instead of

499
00:24:52,840 --> 00:24:55,199
Speaker 1: going in a straight line, we go above our target.

500
00:24:55,240 --> 00:24:57,880
Speaker 1: We go higher up in order to get more potential

501
00:24:57,960 --> 00:25:01,000
Speaker 1: energy to minimize our action. But you don't want to

502
00:25:01,040 --> 00:25:04,359
Speaker 1: go too far from the straight line because going too

503
00:25:04,400 --> 00:25:07,040
Speaker 1: far from the straight line requires high kinetic energy. We're

504
00:25:07,080 --> 00:25:09,320
Speaker 1: increasing our speed on the way up and our speed

505
00:25:09,359 --> 00:25:12,400
Speaker 1: on the way down. So the parabola is a perfect

506
00:25:12,440 --> 00:25:16,720
Speaker 1: balance between these things. You get more potential energy without

507
00:25:16,800 --> 00:25:20,800
Speaker 1: getting too much additional kinetic energy. So the parable is

508
00:25:20,840 --> 00:25:24,080
Speaker 1: the path that minimizes the difference between the kinetic energy

509
00:25:24,160 --> 00:25:26,960
Speaker 1: and the potential energy when you have both at play.

510
00:25:27,240 --> 00:25:31,640
Speaker 1: It's this really fascinating harmonic balance between these two very

511
00:25:31,680 --> 00:25:34,719
Speaker 1: different things. And you can think about what the universe

512
00:25:34,800 --> 00:25:36,960
Speaker 1: is doing in two ways. You can think the universe

513
00:25:37,040 --> 00:25:40,280
Speaker 1: is doing the Newton thing like frame by frame, it's thinking,

514
00:25:40,320 --> 00:25:42,439
Speaker 1: the ball is here, I have this force, so I

515
00:25:42,480 --> 00:25:44,200
Speaker 1: have that velocity on it, so it's going to move

516
00:25:44,200 --> 00:25:46,479
Speaker 1: this way. Or you can think about it from the

517
00:25:46,520 --> 00:25:49,000
Speaker 1: action point of view, and you can say, the ball

518
00:25:49,160 --> 00:25:52,480
Speaker 1: started here and went there. What path between those two

519
00:25:52,520 --> 00:25:56,560
Speaker 1: and this amount of time minimizes the difference between kinetic

520
00:25:56,640 --> 00:25:59,399
Speaker 1: and potential energy, and this is the path that does it.

521
00:26:00,000 --> 00:26:02,239
Speaker 1: And it's fascinating because this turns out to be a

522
00:26:02,280 --> 00:26:05,200
Speaker 1: general principle, not just in this one case where you're

523
00:26:05,200 --> 00:26:07,800
Speaker 1: playing ball with your dog, but in every case. The

524
00:26:07,880 --> 00:26:11,359
Speaker 1: least action tells you what the universe does, how things

525
00:26:11,400 --> 00:26:14,080
Speaker 1: get from A to B. And you can start from

526
00:26:14,080 --> 00:26:18,439
Speaker 1: this principle least action, and you can derive F equals MA,

527
00:26:19,080 --> 00:26:22,040
Speaker 1: so you can derive the force equations from it. Like

528
00:26:22,160 --> 00:26:24,560
Speaker 1: Newton just like writ it down. He's like, hey, this works.

529
00:26:24,680 --> 00:26:26,560
Speaker 1: And you might ask, well, where does that come from?

530
00:26:26,920 --> 00:26:30,720
Speaker 1: And the answer is action. Right from action, you can

531
00:26:30,800 --> 00:26:35,679
Speaker 1: derive classical mechanics. Now classical mechanics doesn't then explain like,

532
00:26:35,920 --> 00:26:39,879
Speaker 1: what is action? Why does the universe minimize it? To

533
00:26:39,920 --> 00:26:41,480
Speaker 1: get any insight in that, we're going to have to

534
00:26:41,480 --> 00:26:46,080
Speaker 1: go deeper into action in quantum mechanics and in philosophy.

535
00:26:46,520 --> 00:26:49,520
Speaker 1: But it's fascinating because it seems like underneath all of

536
00:26:49,560 --> 00:26:53,240
Speaker 1: these things, this force picture of the universe, there is

537
00:26:53,280 --> 00:26:56,560
Speaker 1: a deeper principle from which you can derive F equals

538
00:26:56,720 --> 00:26:57,520
Speaker 1: MA WHOA.

539
00:26:58,160 --> 00:27:01,280
Speaker 4: Okay, So one thing I think I'm still stumbling on

540
00:27:01,359 --> 00:27:04,840
Speaker 4: a little bit is that I guess I still feel like, Okay,

541
00:27:04,840 --> 00:27:07,320
Speaker 4: so you throw a ball in the air and you're

542
00:27:07,640 --> 00:27:12,520
Speaker 4: subtracting the potential energy, I still feel like you should

543
00:27:12,560 --> 00:27:16,280
Speaker 4: be getting the least path, not necessarily because you're subtracting

544
00:27:16,320 --> 00:27:19,119
Speaker 4: the potential energy, but because any other path would require

545
00:27:19,160 --> 00:27:23,520
Speaker 4: you to put additional energy into the ball at some.

546
00:27:23,680 --> 00:27:25,800
Speaker 3: Point as it goes through that path.

547
00:27:26,200 --> 00:27:30,000
Speaker 4: And am I just thinking that because I live in

548
00:27:30,040 --> 00:27:32,439
Speaker 4: this world and that's my expectation and I don't realize

549
00:27:32,480 --> 00:27:34,639
Speaker 4: it doesn't have to be my expectation, or am I

550
00:27:34,680 --> 00:27:36,439
Speaker 4: misunderstanding something. No.

551
00:27:36,560 --> 00:27:39,159
Speaker 1: I think you're saying this is the only path it

552
00:27:39,200 --> 00:27:42,440
Speaker 1: can take, because to take any other path something would

553
00:27:42,480 --> 00:27:44,840
Speaker 1: have to do that. Yeah, like you need to go

554
00:27:44,880 --> 00:27:47,920
Speaker 1: and push it or something. And yeah, you're thinking about

555
00:27:47,920 --> 00:27:52,119
Speaker 1: the universe in terms of forces. You have Newton's ideas

556
00:27:52,160 --> 00:27:55,040
Speaker 1: so deeply ingrained in your mind that like a ball

557
00:27:55,080 --> 00:27:58,680
Speaker 1: is going to move it constant velocity unless something changes that, right,

558
00:27:58,760 --> 00:28:00,919
Speaker 1: you have that so deeply ingrained it's obvious to you.

559
00:28:01,440 --> 00:28:04,800
Speaker 1: But that comes from least action. All of Newton's laws

560
00:28:04,840 --> 00:28:08,320
Speaker 1: are derived from the principle of least action. And so

561
00:28:08,359 --> 00:28:11,119
Speaker 1: it turns out that's not the fundamental way the universe works.

562
00:28:11,320 --> 00:28:16,919
Speaker 1: That comes out of insisting that everything minimizes action. And

563
00:28:16,960 --> 00:28:19,959
Speaker 1: it's actually super cool because, as we mentioned earlier, in

564
00:28:20,000 --> 00:28:22,680
Speaker 1: many cases, the force approach is simple and it works,

565
00:28:22,680 --> 00:28:25,320
Speaker 1: and it's very intuitive and connected to our experience because

566
00:28:25,480 --> 00:28:28,479
Speaker 1: this is how our world works, right, Like, we notice

567
00:28:28,520 --> 00:28:30,119
Speaker 1: that you've got to push stuff to get it moving,

568
00:28:30,680 --> 00:28:32,159
Speaker 1: and you've got to push it to turn it and

569
00:28:32,200 --> 00:28:34,280
Speaker 1: all this stuff. We think about the world in terms

570
00:28:34,280 --> 00:28:38,120
Speaker 1: of forces, but sometimes that picture is hairy and it's

571
00:28:38,160 --> 00:28:40,840
Speaker 1: hard to use to do calculations, Like it's easy in

572
00:28:40,880 --> 00:28:44,160
Speaker 1: the examples we talked about, But what if you add wind,

573
00:28:44,320 --> 00:28:47,040
Speaker 1: or what if you add friction or what if, for example,

574
00:28:47,360 --> 00:28:49,800
Speaker 1: you take your ball and you attach a string to it,

575
00:28:50,040 --> 00:28:52,600
Speaker 1: and the string is now tied to a squirrel, and

576
00:28:52,640 --> 00:28:54,920
Speaker 1: the squirrel is on a roller coaster. How are you

577
00:28:55,000 --> 00:28:58,480
Speaker 1: going to do that calculation? Well, you still could in principle, right,

578
00:28:58,560 --> 00:29:01,120
Speaker 1: there are still forces there on the string, and the

579
00:29:01,200 --> 00:29:04,040
Speaker 1: rollercoaster has some applies to force, and the wind is

580
00:29:04,080 --> 00:29:06,880
Speaker 1: a force which now weirdly depends on velocity. And what

581
00:29:06,960 --> 00:29:09,640
Speaker 1: you discover is that it's a mess. Like many things

582
00:29:09,720 --> 00:29:13,040
Speaker 1: in physics, we can only solve a few very simple

583
00:29:13,120 --> 00:29:16,920
Speaker 1: examples because everything else is totally intractable. So the reason

584
00:29:17,400 --> 00:29:20,280
Speaker 1: introductory of physics students usually calculate the path of a

585
00:29:20,320 --> 00:29:24,280
Speaker 1: ball without wind resistance and without friction is because otherwise

586
00:29:24,280 --> 00:29:27,120
Speaker 1: it's a huge rain. And so this force picture is

587
00:29:27,160 --> 00:29:30,880
Speaker 1: good for simple examples, but it becomes totally intractable for

588
00:29:31,040 --> 00:29:32,120
Speaker 1: anything realistic.

589
00:29:32,720 --> 00:29:32,760
Speaker 2: That.

590
00:29:32,880 --> 00:29:38,120
Speaker 1: The amazing thing is the action doesn't The action remains

591
00:29:38,200 --> 00:29:41,120
Speaker 1: fairly simple because you can still just write down the

592
00:29:41,160 --> 00:29:43,760
Speaker 1: kinetic energy and you can write down the potential energy.

593
00:29:43,760 --> 00:29:46,080
Speaker 1: In many of these situations, it's not hard to calculate

594
00:29:46,080 --> 00:29:48,560
Speaker 1: the kinetic energy or the potential energy, and then you

595
00:29:48,640 --> 00:29:51,320
Speaker 1: just find the path that minimizes them. And that's because

596
00:29:51,360 --> 00:29:54,160
Speaker 1: it relies on these concepts of energy, which helps you

597
00:29:54,240 --> 00:29:56,719
Speaker 1: ignore a lot of the complicated details of what happens

598
00:29:56,760 --> 00:29:59,640
Speaker 1: between moment A and moment B. People who have done

599
00:29:59,640 --> 00:30:02,640
Speaker 1: physically problems know, for example, if you start, for example,

600
00:30:02,680 --> 00:30:05,040
Speaker 1: with a roller coaster and it starts from a certain

601
00:30:05,080 --> 00:30:07,640
Speaker 1: height and it goes through all sorts of crazy loop

602
00:30:07,680 --> 00:30:10,080
Speaker 1: to loops, and then you're asked to like calculate the

603
00:30:10,160 --> 00:30:14,080
Speaker 1: velocity of this roller coaster car halfway down the track.

604
00:30:14,480 --> 00:30:16,320
Speaker 1: From a force point of view, you're like, oh, my gosh,

605
00:30:16,320 --> 00:30:17,959
Speaker 1: how am I going to calculate that it's done? All

606
00:30:17,960 --> 00:30:20,120
Speaker 1: these crazy maneuvers have to know the forces and the

607
00:30:20,120 --> 00:30:23,600
Speaker 1: acceleration every moment. It's a nightmare. But from an energy

608
00:30:23,640 --> 00:30:26,000
Speaker 1: calculation point of view, you just have to know, oh,

609
00:30:26,040 --> 00:30:28,800
Speaker 1: it's gone down a certain distance. I know the potential

610
00:30:28,920 --> 00:30:31,800
Speaker 1: energy that gets turned into kinetic energy. Boom, I have

611
00:30:31,880 --> 00:30:34,760
Speaker 1: the answer in one step. This action approach is sort

612
00:30:34,760 --> 00:30:37,080
Speaker 1: of analogous to that because it also relies just on

613
00:30:37,160 --> 00:30:40,720
Speaker 1: these energy quantities which are sort of deeper and more fundamental,

614
00:30:40,800 --> 00:30:43,200
Speaker 1: and don't worry so much about these little details.

615
00:30:43,400 --> 00:30:44,440
Speaker 3: Okay, I like that.

616
00:30:44,560 --> 00:30:46,320
Speaker 1: So when you get to like upper division physics, you

617
00:30:46,400 --> 00:30:49,920
Speaker 1: learn about Lagrangen and Hamiltonian mechanics, from which you can

618
00:30:49,960 --> 00:30:53,400
Speaker 1: derive F equals M. But they start out by calculating

619
00:30:53,440 --> 00:30:57,120
Speaker 1: this difference between kinetic and potential energy, minimizing that and

620
00:30:57,240 --> 00:30:59,760
Speaker 1: use to so many really hairy problems you would never

621
00:31:00,280 --> 00:31:03,360
Speaker 1: imagine trying to calculate with Newton's method that you can

622
00:31:03,440 --> 00:31:05,719
Speaker 1: just pop out in a few lines and get the answer.

623
00:31:06,120 --> 00:31:08,760
Speaker 1: It feels like magic when you first do it. But

624
00:31:08,800 --> 00:31:11,920
Speaker 1: what's happening here is you're accessing a deeper rule of

625
00:31:11,960 --> 00:31:12,680
Speaker 1: the universe.

626
00:31:13,040 --> 00:31:14,760
Speaker 3: Well what is the rule? Because now we're getting into

627
00:31:14,760 --> 00:31:15,760
Speaker 3: the good party tricks.

628
00:31:19,360 --> 00:31:21,760
Speaker 1: This feels like a deeper rule in the universe because

629
00:31:22,080 --> 00:31:25,120
Speaker 1: it works not just for classical mechanics like the cases

630
00:31:25,120 --> 00:31:28,240
Speaker 1: we're talking about, you know, squirrels and strings and wind

631
00:31:28,320 --> 00:31:32,080
Speaker 1: and all sorts of stuff. It also works in every scenario.

632
00:31:32,640 --> 00:31:35,800
Speaker 1: So this action formula that we talked about kinetic energy

633
00:31:35,880 --> 00:31:39,880
Speaker 1: minus potential energy, that's the action for classical mechanics with

634
00:31:40,000 --> 00:31:43,400
Speaker 1: conservative forces. But you can also do this, for example,

635
00:31:43,520 --> 00:31:47,200
Speaker 1: for quantum mechanics, and instead of writing down kinetic energy

636
00:31:47,280 --> 00:31:50,200
Speaker 1: minus potential energy, which require things you don't always know

637
00:31:50,240 --> 00:31:53,920
Speaker 1: about particles, you write down something called the lagrange and density.

638
00:31:54,360 --> 00:31:57,200
Speaker 1: In the case of like quantum field theory, this is

639
00:31:57,440 --> 00:32:00,360
Speaker 1: just the fields that exist and how they interact with

640
00:32:00,400 --> 00:32:03,560
Speaker 1: each other. And so, for example, the standard model of

641
00:32:03,560 --> 00:32:06,320
Speaker 1: particle physics. If you google, like what is the equation

642
00:32:06,400 --> 00:32:08,600
Speaker 1: of the standard model, it shows you this thing that

643
00:32:08,640 --> 00:32:11,360
Speaker 1: starts with L equals and then a bunch of terms.

644
00:32:11,640 --> 00:32:15,080
Speaker 1: That's the lagrangeon of the standard model, and the action

645
00:32:15,240 --> 00:32:18,200
Speaker 1: is the integral of that. And so the way we

646
00:32:18,280 --> 00:32:22,760
Speaker 1: specify what's in the universe, what's out there, all we

647
00:32:22,840 --> 00:32:25,640
Speaker 1: have to do is say what the action is, what

648
00:32:25,680 --> 00:32:28,600
Speaker 1: are the pieces of the action, and how do they interact?

649
00:32:28,640 --> 00:32:31,480
Speaker 1: And everything else falls out of that, Like literally all

650
00:32:31,560 --> 00:32:34,680
Speaker 1: the equations of quantum mechanics and quantum field theory say,

651
00:32:34,720 --> 00:32:37,680
Speaker 1: if you have this action, then all these things happen.

652
00:32:38,120 --> 00:32:40,680
Speaker 1: So the game of particle physics these days, and of

653
00:32:40,720 --> 00:32:43,560
Speaker 1: all physics is to say, well, what is the action

654
00:32:43,760 --> 00:32:46,280
Speaker 1: of the universe. We try lots of different things. We

655
00:32:46,320 --> 00:32:48,200
Speaker 1: try this, we try that, we try the other thing,

656
00:32:48,600 --> 00:32:51,400
Speaker 1: and the ones that turn into rules that align with

657
00:32:51,440 --> 00:32:53,560
Speaker 1: what we see out there in the universe, those are

658
00:32:53,560 --> 00:32:56,240
Speaker 1: the ones we go with. So the standard model of

659
00:32:56,280 --> 00:32:59,240
Speaker 1: particle physics is just a description of the action of

660
00:32:59,280 --> 00:33:02,160
Speaker 1: the universe, not in terms of kinetic energy of a ball,

661
00:33:02,480 --> 00:33:05,600
Speaker 1: but in terms of the fields, their motion, and actually

662
00:33:05,600 --> 00:33:08,680
Speaker 1: in terms of their oscillation, their kinetic energy, and their

663
00:33:08,720 --> 00:33:09,640
Speaker 1: potential energy.

664
00:33:09,960 --> 00:33:12,040
Speaker 4: Okay, so this seems pretty exciting because you know, you

665
00:33:12,040 --> 00:33:13,960
Speaker 4: and I have been recording for over a year now,

666
00:33:14,000 --> 00:33:15,520
Speaker 4: and I don't feel like there have been a lot

667
00:33:15,520 --> 00:33:18,080
Speaker 4: of instances where we've talked about things that play nice

668
00:33:18,120 --> 00:33:22,640
Speaker 4: with both classical mechanics and quantum mechanics. And that could

669
00:33:22,640 --> 00:33:24,080
Speaker 4: be because my memory is.

670
00:33:24,280 --> 00:33:27,520
Speaker 3: Kind of like a sieve, but I don't think so.

671
00:33:27,520 --> 00:33:28,760
Speaker 3: So is this pretty rare?

672
00:33:28,880 --> 00:33:31,040
Speaker 1: This is pretty rare, And it's actually a beautiful way

673
00:33:31,120 --> 00:33:35,719
Speaker 1: to think about the connection between quantum mechanics and classical mechanics,

674
00:33:36,320 --> 00:33:39,840
Speaker 1: and it gives you some insight into like our classical world,

675
00:33:40,520 --> 00:33:44,400
Speaker 1: because when you're calculating the quantum mechanical action, you don't

676
00:33:44,440 --> 00:33:46,960
Speaker 1: just think about an individual path. You think about all

677
00:33:47,000 --> 00:33:50,080
Speaker 1: the various paths perhaps people have heard about, like the

678
00:33:50,160 --> 00:33:53,960
Speaker 1: fine mean path integral approach to quantum mechanics. We imagine

679
00:33:54,000 --> 00:33:56,600
Speaker 1: like an electron goes from here to there. You don't

680
00:33:56,680 --> 00:33:58,600
Speaker 1: just think about one way for it to go from

681
00:33:58,640 --> 00:34:01,400
Speaker 1: here to there. You think about all the well, what's

682
00:34:01,440 --> 00:34:04,200
Speaker 1: happening there is You think about all the possible paths,

683
00:34:04,840 --> 00:34:07,680
Speaker 1: and in classical mechanics, you say, oh, I'm to choose

684
00:34:07,680 --> 00:34:11,600
Speaker 1: the one path that minimizes the action. In quantum mechanics,

685
00:34:11,760 --> 00:34:14,160
Speaker 1: what you do is you take each path, and that

686
00:34:14,239 --> 00:34:17,120
Speaker 1: path has a complex number multiplied by it that depends

687
00:34:17,160 --> 00:34:20,239
Speaker 1: on the action. So you have all these paths and

688
00:34:20,320 --> 00:34:22,400
Speaker 1: each one has this complex number in front of it,

689
00:34:22,840 --> 00:34:26,839
Speaker 1: and the paths near the least action all interfere constructively

690
00:34:26,880 --> 00:34:30,760
Speaker 1: with each other. These complex numbers allow them to contribute together,

691
00:34:31,160 --> 00:34:34,719
Speaker 1: and the paths where the action varies a lot interfere destructively,

692
00:34:35,080 --> 00:34:38,279
Speaker 1: so they cancel out. And so what's happening here is

693
00:34:38,280 --> 00:34:40,799
Speaker 1: that all the paths are contributing, but just like in

694
00:34:41,280 --> 00:34:44,960
Speaker 1: famous quantum mechanical experiments, the ones that are far from

695
00:34:45,000 --> 00:34:48,560
Speaker 1: the least action destructively interfere with each other. They cancel

696
00:34:48,640 --> 00:34:51,600
Speaker 1: themselves out, and so what happens is that you end

697
00:34:51,680 --> 00:34:55,440
Speaker 1: up with this like envelope of paths around the least action.

698
00:34:56,360 --> 00:34:59,719
Speaker 1: And this is so fascinating because that interference depends also

699
00:35:00,120 --> 00:35:03,040
Speaker 1: not just on the action, but on planks constant hbar,

700
00:35:03,760 --> 00:35:06,840
Speaker 1: and as h bar gets bigger, you get more contributions

701
00:35:06,840 --> 00:35:09,440
Speaker 1: from paths near the least action, and as h bar

702
00:35:09,520 --> 00:35:12,880
Speaker 1: gets smaller, you get fewer contributions from paths near the

703
00:35:12,960 --> 00:35:15,840
Speaker 1: least action. So, now here you have a knob that

704
00:35:15,880 --> 00:35:18,160
Speaker 1: you can very smoothly you say, I'm going to crank

705
00:35:18,320 --> 00:35:21,120
Speaker 1: h bar all the way down to zero. What happens

706
00:35:21,360 --> 00:35:24,120
Speaker 1: is that you have only a single path contributing. That's

707
00:35:24,200 --> 00:35:28,719
Speaker 1: classical mechanics. Classical mechanics is quantum mechanics with hbar set

708
00:35:28,760 --> 00:35:31,760
Speaker 1: to zero. If you crank hbar up to some number,

709
00:35:31,880 --> 00:35:33,920
Speaker 1: then you start to get quantum effects where you have

710
00:35:33,960 --> 00:35:38,000
Speaker 1: contributions from things near the least action path. And that's

711
00:35:38,040 --> 00:35:40,400
Speaker 1: the quantum effects that we see. If you cranked up

712
00:35:40,520 --> 00:35:43,240
Speaker 1: hbar beyond what it is in our universe, quantum mechanics

713
00:35:43,280 --> 00:35:44,480
Speaker 1: would be more obvious.

714
00:35:44,840 --> 00:35:45,080
Speaker 2: Right.

715
00:35:45,120 --> 00:35:48,040
Speaker 1: And so this shows you that there's like not just

716
00:35:48,120 --> 00:35:51,279
Speaker 1: a smooth continuum where classical mechanics sits on like one

717
00:35:51,480 --> 00:35:55,279
Speaker 1: edge of it, right, But also that classical least action

718
00:35:55,440 --> 00:35:59,799
Speaker 1: emerges from quantum interference. The reason it seems like we

719
00:36:00,120 --> 00:36:02,799
Speaker 1: live in a classical world is because HBr is so

720
00:36:02,880 --> 00:36:05,799
Speaker 1: small that it looks almost like it's zero from our

721
00:36:05,840 --> 00:36:09,560
Speaker 1: point of view, and you can understand that very clearly

722
00:36:10,000 --> 00:36:12,759
Speaker 1: using this least action approach and thinking about all the

723
00:36:12,840 --> 00:36:14,920
Speaker 1: various paths that the particle would take.

724
00:36:15,480 --> 00:36:18,239
Speaker 4: And so does thinking about things from a least action

725
00:36:18,360 --> 00:36:21,360
Speaker 4: approach make you feel more confident that we're going to

726
00:36:21,360 --> 00:36:25,160
Speaker 4: be able to one day sort of marry these approaches

727
00:36:25,200 --> 00:36:30,200
Speaker 4: a little bit more effectively or not necessarily, because.

728
00:36:30,320 --> 00:36:32,759
Speaker 1: No, it's the most sensible way to think about the

729
00:36:32,800 --> 00:36:37,120
Speaker 1: relationship between quantum mechanics and classical physics. Essentially thinking about

730
00:36:37,120 --> 00:36:40,760
Speaker 1: classical physics as like a zoomed out version of quantum mechanics.

731
00:36:40,760 --> 00:36:43,759
Speaker 1: And we talk a lot about how, you know, classical

732
00:36:43,760 --> 00:36:47,080
Speaker 1: physics emerges from quantum mechanics, and we say, that's kind

733
00:36:47,080 --> 00:36:49,000
Speaker 1: of a mystery because we don't know how to go

734
00:36:49,160 --> 00:36:53,040
Speaker 1: from the laws of quantum mechanics. You know Schroeninger's equation

735
00:36:53,120 --> 00:36:56,120
Speaker 1: for an electron to zoom out to get f equals

736
00:36:56,239 --> 00:36:58,880
Speaker 1: ma for a ball flying through the air, And that's

737
00:36:59,000 --> 00:37:01,760
Speaker 1: true for the force picture, but in the action picture,

738
00:37:01,800 --> 00:37:03,680
Speaker 1: we actually do kind of know how to do that,

739
00:37:03,760 --> 00:37:07,200
Speaker 1: which is amazing. And so there is this connection between

740
00:37:07,560 --> 00:37:11,359
Speaker 1: classical physics and quantum physics, where classical physics is an

741
00:37:11,400 --> 00:37:15,280
Speaker 1: extreme version of it. So that's very beautiful, and unfortunately

742
00:37:15,320 --> 00:37:18,319
Speaker 1: that doesn't solve like the bigger problems in physics, which

743
00:37:18,360 --> 00:37:22,239
Speaker 1: is like how to integrate gravity into quantum mechanics. But amazingly,

744
00:37:22,520 --> 00:37:25,319
Speaker 1: you can also think about gravity from an action point

745
00:37:25,320 --> 00:37:27,480
Speaker 1: of view. It's a very natural way to think about

746
00:37:27,520 --> 00:37:28,560
Speaker 1: general relativity.

747
00:37:28,719 --> 00:37:31,200
Speaker 4: And when we get back from the break, that's exactly

748
00:37:31,200 --> 00:37:52,480
Speaker 4: what we're going to do, all right, So now we're

749
00:37:52,480 --> 00:37:55,839
Speaker 4: going to talk about what least action can tell us

750
00:37:55,880 --> 00:37:57,080
Speaker 4: about gravity.

751
00:37:58,120 --> 00:37:58,960
Speaker 3: Did I say that right?

752
00:37:59,320 --> 00:37:59,840
Speaker 1: You totally?

753
00:38:00,040 --> 00:38:00,160
Speaker 2: Did?

754
00:38:00,239 --> 00:38:01,360
Speaker 1: You sound like a physicist?

755
00:38:01,440 --> 00:38:01,640
Speaker 4: Oh?

756
00:38:01,960 --> 00:38:04,319
Speaker 3: Oh that's great. Now I'm going to get invited to

757
00:38:04,320 --> 00:38:05,360
Speaker 3: all the parties.

758
00:38:07,360 --> 00:38:09,600
Speaker 1: And I meant that, of course, if it wasn't obvious,

759
00:38:09,800 --> 00:38:11,799
Speaker 1: one hundred percent as a compliment, and.

760
00:38:11,800 --> 00:38:14,080
Speaker 3: I took it one hundred percent as a compliment.

761
00:38:14,400 --> 00:38:16,960
Speaker 1: I'm glad there wasn't any doubt, No, never would be

762
00:38:17,040 --> 00:38:20,080
Speaker 1: all right. So we've been talking about least action and

763
00:38:20,400 --> 00:38:24,600
Speaker 1: the way that helps us reimagine classical physics as stuff

764
00:38:24,680 --> 00:38:27,640
Speaker 1: moving from A to B not because of the forces,

765
00:38:27,719 --> 00:38:30,480
Speaker 1: but because it's the path that minimizes the action. And

766
00:38:30,520 --> 00:38:32,399
Speaker 1: then we talked about how you can even use this

767
00:38:32,480 --> 00:38:35,640
Speaker 1: in quantum mechanics, and it provides a nice bridge between

768
00:38:35,680 --> 00:38:39,480
Speaker 1: classical physics and quantum physics. But folks out there are

769
00:38:39,520 --> 00:38:41,960
Speaker 1: of course aware that one of the biggest struggles in

770
00:38:41,960 --> 00:38:46,719
Speaker 1: physics is to unify quantum mechanics with gravity. They're classical

771
00:38:46,800 --> 00:38:50,520
Speaker 1: theory of space time and how things move. And so

772
00:38:50,960 --> 00:38:53,560
Speaker 1: is action something we can use to understand gravity? And

773
00:38:53,600 --> 00:38:57,960
Speaker 1: the answer is yes. In fact, it's quite natural because

774
00:38:58,400 --> 00:39:02,440
Speaker 1: general relativity already has very similar minimal principles.

775
00:39:02,840 --> 00:39:03,000
Speaker 2: Right.

776
00:39:03,040 --> 00:39:05,640
Speaker 1: The principle of least action says you find the path

777
00:39:05,680 --> 00:39:10,920
Speaker 1: that minimizes the action. Well. Already, in general relativity, light,

778
00:39:11,040 --> 00:39:15,879
Speaker 1: for example, follows the path that minimizes its travel time, right,

779
00:39:16,560 --> 00:39:22,120
Speaker 1: And in general things in general relativity follow paths called geodesics.

780
00:39:22,680 --> 00:39:27,279
Speaker 1: Geodesics are the shortest distance from A to B, right,

781
00:39:27,960 --> 00:39:31,799
Speaker 1: And you can calculate the shortest distance by calculating the

782
00:39:31,920 --> 00:39:35,200
Speaker 1: action across that path. Where in this case, what is

783
00:39:35,239 --> 00:39:39,400
Speaker 1: the action. It's the curvature, the curvature along your path.

784
00:39:39,840 --> 00:39:42,759
Speaker 1: So to figure out in general relativity how something will

785
00:39:42,760 --> 00:39:45,360
Speaker 1: go from A to B, you find the path where,

786
00:39:45,600 --> 00:39:49,360
Speaker 1: along with you minimize is not kindemic energy minus potential energy,

787
00:39:49,760 --> 00:39:52,799
Speaker 1: but the action of general relativity, which is just the

788
00:39:52,880 --> 00:39:56,759
Speaker 1: curvature of space. And so you can say, all right,

789
00:39:56,840 --> 00:39:59,279
Speaker 1: my action is the curvature of space, and then you

790
00:39:59,320 --> 00:40:03,000
Speaker 1: say find me the paths that minimize the action, and boom,

791
00:40:03,080 --> 00:40:05,759
Speaker 1: all of general relativity pops out from there. All of

792
00:40:05,760 --> 00:40:09,480
Speaker 1: Einstein's equations just flow from specifying the action to be

793
00:40:09,840 --> 00:40:12,680
Speaker 1: the curvature of space. It's really kind of incredible.

794
00:40:12,719 --> 00:40:13,359
Speaker 3: So I have a question.

795
00:40:13,400 --> 00:40:18,000
Speaker 4: So the curvature of space is influenced by gravity or

796
00:40:18,080 --> 00:40:19,280
Speaker 4: is reflected by gravity.

797
00:40:19,600 --> 00:40:21,759
Speaker 1: Gravity is the motion of things under the influence of

798
00:40:21,800 --> 00:40:22,400
Speaker 1: the curvature.

799
00:40:22,600 --> 00:40:25,000
Speaker 4: Yeah, okay, So the equations that we were talking about

800
00:40:25,040 --> 00:40:29,000
Speaker 4: were kinetic energy minus potential energy and potential energy has

801
00:40:29,080 --> 00:40:33,239
Speaker 4: gravity in the equation. But when we think about general relativity,

802
00:40:33,239 --> 00:40:36,200
Speaker 4: are we not using those equations or like, how does

803
00:40:36,200 --> 00:40:38,560
Speaker 4: it mess things up that the term for gravity is

804
00:40:38,600 --> 00:40:39,320
Speaker 4: in the equation.

805
00:40:39,640 --> 00:40:42,279
Speaker 1: Yeah? Great question. So when we were talking about our

806
00:40:42,320 --> 00:40:45,000
Speaker 1: simple scenario of a ball moving under as a parable,

807
00:40:45,560 --> 00:40:48,160
Speaker 1: we were doing classical physics, but we weren't thinking about

808
00:40:48,160 --> 00:40:51,480
Speaker 1: general relativity. We had a very simple model of objects

809
00:40:51,480 --> 00:40:54,600
Speaker 1: with kinetic energy and potential energy, and we were assuming

810
00:40:54,719 --> 00:40:57,680
Speaker 1: gravity with constants and G was just a number. Now

811
00:40:57,680 --> 00:41:00,799
Speaker 1: we're totally generalizing that and we're going to solve for

812
00:41:00,920 --> 00:41:03,840
Speaker 1: any sort of motion of any object through space and time,

813
00:41:04,360 --> 00:41:06,399
Speaker 1: and the same equations do pop out. But we're doing

814
00:41:06,400 --> 00:41:10,040
Speaker 1: Einsteini and gravity now instead of Newtonian gravity. You know,

815
00:41:10,120 --> 00:41:13,040
Speaker 1: the previous version was like thinking about gravity as a force.

816
00:41:13,480 --> 00:41:16,759
Speaker 1: Now instead we're doing general relativity, and so we're not

817
00:41:16,880 --> 00:41:20,239
Speaker 1: calculating action as kinetic energy and minus potential energy. That's

818
00:41:20,280 --> 00:41:24,319
Speaker 1: the Newtonian way. We're calculating in the Einsteinian way. And

819
00:41:24,440 --> 00:41:26,880
Speaker 1: the incredible thing is that you can just specify the

820
00:41:26,920 --> 00:41:30,880
Speaker 1: action and all of general relativity comes out. This is

821
00:41:30,920 --> 00:41:34,560
Speaker 1: sort of why action is super amazing, because you specify

822
00:41:34,600 --> 00:41:37,120
Speaker 1: it and you have this one set of rules, find

823
00:41:37,120 --> 00:41:39,799
Speaker 1: the path that minimize the action, and that tells you

824
00:41:39,880 --> 00:41:42,200
Speaker 1: all of the physics. All the physics comes out of.

825
00:41:42,120 --> 00:41:43,880
Speaker 3: That tell me more physics that comes out of it.

826
00:41:43,960 --> 00:41:48,000
Speaker 1: Danie, Well, the challenge now to like unify quantum mechanics

827
00:41:48,000 --> 00:41:52,160
Speaker 1: and gravity is to find an action which has both

828
00:41:52,239 --> 00:41:55,160
Speaker 1: gravity and quantum mechanics in it. And we know how

829
00:41:55,200 --> 00:41:57,759
Speaker 1: to define quantum mechanical action, and that gives us all

830
00:41:57,880 --> 00:42:00,960
Speaker 1: quantum field theory. We know how to define general relativity

831
00:42:01,000 --> 00:42:03,680
Speaker 1: action that gives us all of Einstein's equations. We don't

832
00:42:03,680 --> 00:42:06,799
Speaker 1: know how to find a unified action for both of

833
00:42:06,800 --> 00:42:09,440
Speaker 1: those things. So that's sort of the question of quantum

834
00:42:09,520 --> 00:42:13,200
Speaker 1: gravity now expressed in terms of this action principle. What

835
00:42:13,360 --> 00:42:17,080
Speaker 1: is the action that includes both curvature and quantum mechanical fields.

836
00:42:17,200 --> 00:42:18,080
Speaker 1: We don't know that.

837
00:42:18,640 --> 00:42:21,160
Speaker 4: But if we could figure that out, then we would

838
00:42:21,200 --> 00:42:22,880
Speaker 4: know what exactly.

839
00:42:23,080 --> 00:42:24,719
Speaker 1: If we could figure that out, then we would have

840
00:42:24,760 --> 00:42:27,279
Speaker 1: the laws of quantum gravity. Okay, yeah, absolutely, and that

841
00:42:27,280 --> 00:42:29,760
Speaker 1: would be amazing. Yeah, but we can also like zoom

842
00:42:29,800 --> 00:42:33,000
Speaker 1: in on one part of this to give another example,

843
00:42:33,400 --> 00:42:38,040
Speaker 1: like Maxwell's equations. Maxwell's equations are these four equations. They're

844
00:42:38,120 --> 00:42:41,200
Speaker 1: kind of complicated. They have all these differential terms in them,

845
00:42:41,360 --> 00:42:45,080
Speaker 1: you know, changing electric fields costs, magnetic fields and vice versa,

846
00:42:45,120 --> 00:42:47,719
Speaker 1: all this stuff. It was a huge stroke of genius

847
00:42:48,080 --> 00:42:51,040
Speaker 1: when Maxwell unified these, and then Heapicide clarified all of

848
00:42:51,080 --> 00:42:53,799
Speaker 1: them a century or so ago. And now it turns

849
00:42:53,840 --> 00:42:56,360
Speaker 1: out that all of Maxwell's equations pop out if you

850
00:42:56,400 --> 00:43:00,400
Speaker 1: apply this minimal action principle to a vector Fiel. We

851
00:43:00,440 --> 00:43:03,319
Speaker 1: know that the electromagnetic field is a vector field, meaning

852
00:43:03,320 --> 00:43:05,040
Speaker 1: that at every point in space is not just a

853
00:43:05,160 --> 00:43:07,600
Speaker 1: number but like a little arrow. So it has a

854
00:43:07,680 --> 00:43:10,440
Speaker 1: direction and a length. And if you say I have

855
00:43:10,480 --> 00:43:13,480
Speaker 1: a vector field and I'm going to make some simple

856
00:43:13,520 --> 00:43:16,960
Speaker 1: requirements about symmetry, like there's gonna be no preferred frame

857
00:43:17,040 --> 00:43:20,200
Speaker 1: of reference or there's no ether for example, then that

858
00:43:20,280 --> 00:43:23,879
Speaker 1: really constrains the kind of action that you can have.

859
00:43:24,440 --> 00:43:27,440
Speaker 1: And there's basically only one way to write it. And

860
00:43:27,560 --> 00:43:31,520
Speaker 1: from that way of writing it, boom, Maxwell's equations pop out.

861
00:43:31,680 --> 00:43:34,840
Speaker 1: And so you might wonder, like, where do Maxwell's equations

862
00:43:34,840 --> 00:43:37,200
Speaker 1: come from? Well, this tells you if you have a

863
00:43:37,320 --> 00:43:41,319
Speaker 1: vector field that respects some basic symmetries, there's only one

864
00:43:41,360 --> 00:43:44,160
Speaker 1: set of equations that minimize the action of that field.

865
00:43:44,360 --> 00:43:48,239
Speaker 1: Those are Maxwell's equations. And so it tells us something

866
00:43:48,239 --> 00:43:52,040
Speaker 1: maybe deep about the universe, that maybe everything that happens

867
00:43:52,040 --> 00:43:55,920
Speaker 1: in the universe comes because the universe is minimizing action

868
00:43:56,120 --> 00:43:59,439
Speaker 1: and only actions that respect some of these symmetries.

869
00:44:00,280 --> 00:44:02,879
Speaker 4: Okay, so I'm still feeling grumpy at whoever called it action,

870
00:44:03,080 --> 00:44:06,680
Speaker 4: but it feels like this is so fundamentally important that

871
00:44:06,719 --> 00:44:09,520
Speaker 4: this is like Nobel Prize territory, So like, who figured

872
00:44:09,560 --> 00:44:10,399
Speaker 4: out this action thing?

873
00:44:12,360 --> 00:44:15,200
Speaker 1: Yeah, action has been around for a little while. Hamilton

874
00:44:15,400 --> 00:44:19,360
Speaker 1: and Lagrange both came up with this alternative formulation of

875
00:44:19,400 --> 00:44:22,160
Speaker 1: classical mechanics more than one hundred years ago before the

876
00:44:22,200 --> 00:44:26,480
Speaker 1: Nobel Prize even was conceived of, and sort of generalized

877
00:44:26,480 --> 00:44:30,399
Speaker 1: classical mechanics. And then it was Nuther who really gave

878
00:44:30,480 --> 00:44:33,239
Speaker 1: us some deep insight into it because Nuther's theorem is

879
00:44:33,239 --> 00:44:36,640
Speaker 1: this really deep theorem of physics that relates symmetries with

880
00:44:36,760 --> 00:44:40,320
Speaker 1: conservation laws. It says like, well, where does conservation of

881
00:44:40,400 --> 00:44:43,759
Speaker 1: momentum come from? Why does that happen in our universe? Well,

882
00:44:43,760 --> 00:44:48,320
Speaker 1: it happens because of a symmetry. The symmetry is translational symmetry.

883
00:44:48,320 --> 00:44:50,960
Speaker 1: That doesn't matter where you do your experiment. If you

884
00:44:50,960 --> 00:44:54,319
Speaker 1: build a large hadron collider here or around Jupiter or

885
00:44:54,320 --> 00:44:56,680
Speaker 1: in another galaxy, you should always get the same answers.

886
00:44:56,719 --> 00:45:00,200
Speaker 1: Space is the same everywhere. That's where conservation and momentum

887
00:45:00,239 --> 00:45:03,280
Speaker 1: comes from. And check out our whole episode on Nuther's symmetry.

888
00:45:03,520 --> 00:45:06,120
Speaker 1: But there was a crucial detail we glossed over in

889
00:45:06,160 --> 00:45:10,520
Speaker 1: that conversation. Those symmetries that we talk about in Nuther's theorem,

890
00:45:10,600 --> 00:45:13,960
Speaker 1: those are symmetries of the action, and we didn't dig

891
00:45:14,040 --> 00:45:16,400
Speaker 1: into it in that episode because, as you see, action

892
00:45:16,560 --> 00:45:19,480
Speaker 1: is a whole set of baggage to introduce. But it's

893
00:45:19,560 --> 00:45:23,360
Speaker 1: only symmetries of the action that give conservation laws. So

894
00:45:23,400 --> 00:45:25,719
Speaker 1: that means that, like you write down your action, maybe

895
00:45:25,760 --> 00:45:29,200
Speaker 1: it's kinetic energy, mutters potential energy, or it's the curvature

896
00:45:29,200 --> 00:45:32,240
Speaker 1: of space, or its quantum field action. If that action

897
00:45:32,440 --> 00:45:36,279
Speaker 1: is the same here and Jupiter and Alpha Centauri, then

898
00:45:36,360 --> 00:45:40,400
Speaker 1: you get the conservation of momentum. And so it's symmetries

899
00:45:40,520 --> 00:45:44,160
Speaker 1: of this action specifically that Norther showed us give us

900
00:45:44,160 --> 00:45:47,440
Speaker 1: conservation laws. So Nother's theorem is a deep insight not

901
00:45:47,560 --> 00:45:50,560
Speaker 1: just into where conservation laws come from, but why action

902
00:45:50,800 --> 00:45:52,640
Speaker 1: is so fundamentally important.

903
00:45:52,880 --> 00:45:55,200
Speaker 3: It seems like she clearly should have gotten a Nobel.

904
00:45:57,600 --> 00:46:01,799
Speaker 1: She should definitely have. And these prints really guide the

905
00:46:01,840 --> 00:46:05,520
Speaker 1: way that we do particle physics, Like when we devise

906
00:46:05,600 --> 00:46:08,400
Speaker 1: the action of the Standard model, we have to have

907
00:46:08,480 --> 00:46:11,480
Speaker 1: those symmetries because we know those symmetries will give us

908
00:46:11,480 --> 00:46:13,880
Speaker 1: the kinds of conservation laws we see in the universe,

909
00:46:13,920 --> 00:46:17,000
Speaker 1: like we see momentum is conserved, and so we can't

910
00:46:17,040 --> 00:46:20,319
Speaker 1: build actions that don't respect the symmetry that gives us

911
00:46:20,360 --> 00:46:23,600
Speaker 1: conservation of momentum. And it's a bunch more symmetries that

912
00:46:23,640 --> 00:46:26,839
Speaker 1: we know we have to have in our action. So

913
00:46:27,000 --> 00:46:29,160
Speaker 1: when you're devising an action, there's not a lot of

914
00:46:29,239 --> 00:46:32,839
Speaker 1: choices to make, right because you're really restricted by all

915
00:46:32,880 --> 00:46:35,600
Speaker 1: of these symmetries. You can't just add terms willy nilly

916
00:46:35,800 --> 00:46:38,440
Speaker 1: because they would break these symmetries. And so if you

917
00:46:38,520 --> 00:46:41,760
Speaker 1: wanted to start from scratch and devise a new action

918
00:46:42,120 --> 00:46:45,560
Speaker 1: for quantum field theory, there's really only a couple ways

919
00:46:45,560 --> 00:46:48,720
Speaker 1: you can do it. The respect those symmetries, we're super

920
00:46:48,880 --> 00:46:53,959
Speaker 1: duper limited. And so it feels like those symmetries tell

921
00:46:54,000 --> 00:46:57,640
Speaker 1: you what can happen in the universe, right, what's possible,

922
00:46:58,120 --> 00:47:01,480
Speaker 1: and the action tells you what does actually happen. And

923
00:47:01,560 --> 00:47:04,520
Speaker 1: so like all of physics is basically that, right, what

924
00:47:04,640 --> 00:47:08,280
Speaker 1: are the symmetries of the universe, and then what actually

925
00:47:08,280 --> 00:47:12,680
Speaker 1: happens is well, what minimizes the action on those symmetries,

926
00:47:13,080 --> 00:47:15,160
Speaker 1: And so it's a completely different way of thinking about

927
00:47:15,160 --> 00:47:17,760
Speaker 1: the universe instead of like the way you were describing,

928
00:47:17,760 --> 00:47:19,920
Speaker 1: which I think is very intuitive and Newtonian of like

929
00:47:19,960 --> 00:47:23,640
Speaker 1: thinking about the universe frame by frame, what's happening, Let's

930
00:47:23,680 --> 00:47:26,799
Speaker 1: update things in a sort of like computational simulation sort

931
00:47:26,800 --> 00:47:30,040
Speaker 1: of view. Instead, it's thinking about how things go from

932
00:47:30,080 --> 00:47:33,600
Speaker 1: A to B to minimize the action along that path.

933
00:47:34,200 --> 00:47:37,400
Speaker 4: So when you were saying, devise a new action, I'm

934
00:47:37,440 --> 00:47:39,920
Speaker 4: having trouble wrapping my head around what that means because

935
00:47:39,920 --> 00:47:42,120
Speaker 4: when every time you've said action, in my head, I

936
00:47:42,160 --> 00:47:46,080
Speaker 4: have subtracted two different kinds of energy. So what does

937
00:47:46,080 --> 00:47:48,080
Speaker 4: it mean to devise a new action? Is that like

938
00:47:48,120 --> 00:47:51,440
Speaker 4: think of a different path that something could take, or well.

939
00:47:51,280 --> 00:47:53,600
Speaker 1: Everything comes from the action, right, So you want to

940
00:47:53,719 --> 00:47:56,480
Speaker 1: describe the universe, you write down an action, you apply

941
00:47:56,560 --> 00:47:59,759
Speaker 1: this minimal principle. It predicts how things will move, and

942
00:48:00,120 --> 00:48:02,719
Speaker 1: you compare that to what you actually see out there. So,

943
00:48:03,400 --> 00:48:05,160
Speaker 1: in the case of a ball flying through the air,

944
00:48:05,200 --> 00:48:07,480
Speaker 1: if I want to describe that, it works if I

945
00:48:07,480 --> 00:48:10,279
Speaker 1: write down kinetic energy minus potential energy. If I write

946
00:48:10,320 --> 00:48:13,760
Speaker 1: down kinetic energy minus three times potential energy, doesn't work.

947
00:48:13,960 --> 00:48:18,160
Speaker 1: If I do kinetic energy time seven minus two potential energy,

948
00:48:18,200 --> 00:48:20,319
Speaker 1: that doesn't work. It doesn't describe what I'm seeing out

949
00:48:20,360 --> 00:48:23,320
Speaker 1: there in the universe. So if I want to describe

950
00:48:23,320 --> 00:48:25,800
Speaker 1: the universe, I have to find some way to describe

951
00:48:25,800 --> 00:48:29,120
Speaker 1: the action, so that minimizing that action gives me the

952
00:48:29,160 --> 00:48:30,960
Speaker 1: things I see out there in the universe.

953
00:48:31,239 --> 00:48:34,600
Speaker 4: You were using the word action the way people people

954
00:48:34,719 --> 00:48:38,200
Speaker 4: actually use the word action, and the word action the

955
00:48:38,239 --> 00:48:41,840
Speaker 4: way physics people use the word action, and that's what

956
00:48:41,960 --> 00:48:43,120
Speaker 4: was do Okay, I get it now.

957
00:48:43,280 --> 00:48:44,640
Speaker 3: You were using it both ways.

958
00:48:44,920 --> 00:48:48,800
Speaker 1: Oh oops. And so kinetic energy, by the potential energy

959
00:48:49,080 --> 00:48:52,160
Speaker 1: is a good approximate action for that one scenario we

960
00:48:52,200 --> 00:48:55,160
Speaker 1: were talking about throwing a ball in your backyard. The

961
00:48:55,200 --> 00:48:58,080
Speaker 1: action of the universe we don't know, because we have

962
00:48:58,120 --> 00:49:00,960
Speaker 1: an action for quantum field theory and action for general relativity.

963
00:49:01,200 --> 00:49:03,400
Speaker 1: We don't know how to put them together. But the

964
00:49:03,440 --> 00:49:06,120
Speaker 1: goal of physics now is to find what is the

965
00:49:06,160 --> 00:49:08,279
Speaker 1: action of the universe, because once we know that, we

966
00:49:08,360 --> 00:49:11,440
Speaker 1: know what it does. And this is a different way

967
00:49:11,440 --> 00:49:14,680
Speaker 1: of thinking about the universe, and it relies on knowing

968
00:49:14,880 --> 00:49:17,880
Speaker 1: where something was and where something will be and figuring

969
00:49:17,920 --> 00:49:20,840
Speaker 1: out the path between them. And that's a very different

970
00:49:20,840 --> 00:49:23,960
Speaker 1: way of thinking about sort of computationally, frame by frame,

971
00:49:24,560 --> 00:49:27,200
Speaker 1: and it has this sort of feeling this flavor to it.

972
00:49:27,200 --> 00:49:29,480
Speaker 1: As we were talking about earlier, that like the present

973
00:49:29,600 --> 00:49:33,000
Speaker 1: depends on the future. Like if you imagine a photon

974
00:49:33,200 --> 00:49:36,320
Speaker 1: going from here to there, and we know the photon

975
00:49:36,560 --> 00:49:39,680
Speaker 1: follows the path that takes the least amount of time

976
00:49:39,680 --> 00:49:42,239
Speaker 1: from here to there. But when the photon is like

977
00:49:42,280 --> 00:49:45,120
Speaker 1: halfway along the path, we don't know where it's going

978
00:49:45,200 --> 00:49:47,400
Speaker 1: to go yet, Right, it hasn't gotten there yet, So

979
00:49:47,440 --> 00:49:50,120
Speaker 1: how does it decide where it's going to go in

980
00:49:50,200 --> 00:49:52,759
Speaker 1: order to minimize the total path when we haven't figured

981
00:49:52,800 --> 00:49:54,400
Speaker 1: out yet where it is going to go, Right, it

982
00:49:54,400 --> 00:49:57,279
Speaker 1: feels like sort of backwards or it's like depending on

983
00:49:57,360 --> 00:50:00,360
Speaker 1: the future in some way. And this was the vague

984
00:50:00,360 --> 00:50:04,239
Speaker 1: feeling that inspired ken ching short story which inspired the

985
00:50:04,280 --> 00:50:07,759
Speaker 1: film Arrival, the idea that like, maybe aliens come and

986
00:50:08,080 --> 00:50:11,000
Speaker 1: they don't see time and the way we do flowing

987
00:50:11,080 --> 00:50:13,719
Speaker 1: from the past to the future. They experience all of

988
00:50:13,760 --> 00:50:16,400
Speaker 1: time like a book, and they can rifle forwards and backwards.

989
00:50:16,400 --> 00:50:20,719
Speaker 1: And you know, it's inspired by this exact concept, but

990
00:50:21,120 --> 00:50:23,160
Speaker 1: it's a little bit of a I don't know if

991
00:50:23,160 --> 00:50:27,319
Speaker 1: it's a misunderstanding or a misrepresentation, because there is no

992
00:50:27,480 --> 00:50:31,040
Speaker 1: actual retro causality here, you don't have to know the

993
00:50:31,080 --> 00:50:35,040
Speaker 1: whole history of the universe to solve these problems. It

994
00:50:35,160 --> 00:50:39,400
Speaker 1: is true that the path depends on the final destination,

995
00:50:40,160 --> 00:50:42,960
Speaker 1: but you can't change that final destination. It's not like

996
00:50:43,480 --> 00:50:47,520
Speaker 1: you can influence the present using the future. There is

997
00:50:47,560 --> 00:50:50,360
Speaker 1: a dependence on the future outcome, but it's not like

998
00:50:50,480 --> 00:50:53,120
Speaker 1: you can control that. So you can't like change the

999
00:50:53,120 --> 00:50:57,360
Speaker 1: photon's path halfway through. So there is a subtlety there

1000
00:50:57,520 --> 00:51:00,319
Speaker 1: which is crucial for the movie Arrival to work as

1001
00:51:00,320 --> 00:51:03,320
Speaker 1: a story, But fundamentally it's at odds with the actual

1002
00:51:03,360 --> 00:51:04,120
Speaker 1: physics of it.

1003
00:51:04,640 --> 00:51:06,239
Speaker 3: I like seeing you be a wet blanket to.

1004
00:51:08,440 --> 00:51:10,840
Speaker 1: All right. So we started this whole thing with the

1005
00:51:10,960 --> 00:51:15,160
Speaker 1: question why does the universe minimize action? So now we've

1006
00:51:15,200 --> 00:51:18,640
Speaker 1: explained what action is and how minimizing action gives us

1007
00:51:18,680 --> 00:51:21,640
Speaker 1: all of the physical laws we already discovered in other ways,

1008
00:51:21,960 --> 00:51:23,960
Speaker 1: and turns out to be a very general principle. It's

1009
00:51:24,000 --> 00:51:26,600
Speaker 1: connected to symmetry and helps us think about quantum mechanics

1010
00:51:26,640 --> 00:51:29,520
Speaker 1: and classical mechanics together and maybe tells us that our

1011
00:51:29,520 --> 00:51:31,719
Speaker 1: concept of time is a little bit archaic and needs

1012
00:51:31,760 --> 00:51:34,279
Speaker 1: to be updated. But what is the answer to the

1013
00:51:34,360 --> 00:51:38,800
Speaker 1: question why does the universe minimize action? And the short

1014
00:51:38,840 --> 00:51:42,520
Speaker 1: answer is, we don't actually know. It's hard to think

1015
00:51:42,560 --> 00:51:46,840
Speaker 1: about action philosophically because it doesn't have a simple intuitive

1016
00:51:46,840 --> 00:51:50,480
Speaker 1: analog like forces. They make sense, right, we see forces happen.

1017
00:51:50,560 --> 00:51:54,000
Speaker 1: It's easy to think about the universe as fundamentally a

1018
00:51:54,040 --> 00:51:57,160
Speaker 1: set of matter and forces acting on that matter, because

1019
00:51:57,200 --> 00:51:58,799
Speaker 1: that's sort of the way our minds work.

1020
00:51:58,880 --> 00:51:59,120
Speaker 2: Right.

1021
00:51:59,760 --> 00:52:02,480
Speaker 1: Whatever action is, it seems to be vitally important to

1022
00:52:02,560 --> 00:52:05,800
Speaker 1: the universe, even if it doesn't have a natural intuitive

1023
00:52:05,800 --> 00:52:08,520
Speaker 1: analog in our minds. That doesn't mean it's not the

1024
00:52:08,560 --> 00:52:12,600
Speaker 1: fundamental principle of the universe. And so philosophers, of course

1025
00:52:12,600 --> 00:52:15,840
Speaker 1: have latched onto this and they have raging arguments about

1026
00:52:15,840 --> 00:52:19,839
Speaker 1: what action is and what it means. Some suggest that

1027
00:52:19,880 --> 00:52:23,759
Speaker 1: what it means that the universe minimizes action is this

1028
00:52:23,920 --> 00:52:29,640
Speaker 1: constructive interference principle that like all possible histories do actually exist,

1029
00:52:29,880 --> 00:52:32,120
Speaker 1: it's just that most of them cancel each other out,

1030
00:52:32,440 --> 00:52:35,880
Speaker 1: and the universe minimizes action because the least action path

1031
00:52:36,239 --> 00:52:39,879
Speaker 1: is the only one that survives constructive interference. Between all

1032
00:52:39,920 --> 00:52:41,120
Speaker 1: of these paths.

1033
00:52:40,920 --> 00:52:43,680
Speaker 3: What happens to the other kellys.

1034
00:52:43,880 --> 00:52:47,040
Speaker 1: They cancel themselves out No, yeah, I know there's a

1035
00:52:47,040 --> 00:52:49,359
Speaker 1: plus Kelly and a minus Kelly out there that end up.

1036
00:52:49,239 --> 00:52:53,000
Speaker 3: In zero, equally valuable Kelly's.

1037
00:52:55,719 --> 00:52:59,239
Speaker 1: Well, you know, in the end, the universe minimizes action,

1038
00:52:59,400 --> 00:53:03,120
Speaker 1: not because it's lazy or because it prefers simplicity, but

1039
00:53:03,239 --> 00:53:07,600
Speaker 1: maybe just because only self supporting things can exist. Things

1040
00:53:07,600 --> 00:53:11,160
Speaker 1: that persist and be observed as law governed are things

1041
00:53:11,160 --> 00:53:14,719
Speaker 1: that you know, don't interfere with themselves, that reinforce themselves.

1042
00:53:15,120 --> 00:53:17,920
Speaker 1: But it's still an open question. You know. Our job

1043
00:53:18,040 --> 00:53:21,440
Speaker 1: as scientists and as curious beings in the universe is

1044
00:53:21,480 --> 00:53:24,480
Speaker 1: to be open minded about how the universe works, figure

1045
00:53:24,480 --> 00:53:26,359
Speaker 1: out those laws, and then just take a step back

1046
00:53:26,360 --> 00:53:29,000
Speaker 1: and be like, hmm, what does that mean about the

1047
00:53:29,080 --> 00:53:31,840
Speaker 1: universe that it does this instead of that? Why is

1048
00:53:31,880 --> 00:53:34,440
Speaker 1: this thing so important to the universe? And that's the

1049
00:53:34,520 --> 00:53:37,960
Speaker 1: juicy part, and that's the part we have not deeply understood.

1050
00:53:37,640 --> 00:53:40,320
Speaker 4: All right, friends, So put another tick in your tally

1051
00:53:40,520 --> 00:53:44,719
Speaker 4: of dKu episodes that end with us saying we don't know.

1052
00:53:45,880 --> 00:53:48,400
Speaker 1: So we've done a deep dive into action, which I

1053
00:53:48,560 --> 00:53:51,279
Speaker 1: always wanted to do. But even still, there are a

1054
00:53:51,320 --> 00:53:53,960
Speaker 1: few places where I was a little bit imprecise to

1055
00:53:54,000 --> 00:53:57,320
Speaker 1: simplify things. So for those of you listening very closely,

1056
00:53:57,360 --> 00:54:00,400
Speaker 1: and I love all of you, there are some additional

1057
00:54:00,400 --> 00:54:03,480
Speaker 1: details I want to mention. First, I said often that

1058
00:54:03,560 --> 00:54:07,280
Speaker 1: action is the difference between kinetic and potential energy. Technically,

1059
00:54:07,280 --> 00:54:09,759
Speaker 1: that's the lagrong and density, and the action is the

1060
00:54:09,800 --> 00:54:14,400
Speaker 1: integral of the difference between the kinetic and the potential energy. Similarly,

1061
00:54:14,520 --> 00:54:17,719
Speaker 1: for gr the action is not just the integral of

1062
00:54:17,760 --> 00:54:21,600
Speaker 1: the curvature, its volume integral of the Richy scaler, which

1063
00:54:21,640 --> 00:54:24,520
Speaker 1: is something that measures the curvature, but it also includes

1064
00:54:24,760 --> 00:54:28,800
Speaker 1: the determinant of the metric tensor and a couple other things. Secondly,

1065
00:54:29,040 --> 00:54:31,440
Speaker 1: I talked a lot about the principle of least action,

1066
00:54:31,880 --> 00:54:35,320
Speaker 1: implying that the action is always minimized, but the actual

1067
00:54:35,320 --> 00:54:37,840
Speaker 1: statement is that the action should be stationary, which in

1068
00:54:37,880 --> 00:54:41,839
Speaker 1: calculus means its derivatives vanish. That means that it can

1069
00:54:41,920 --> 00:54:43,759
Speaker 1: be a minimum, and it often is, but it could

1070
00:54:43,800 --> 00:54:46,600
Speaker 1: also be a maximum or even a saddle point. In

1071
00:54:46,600 --> 00:54:49,200
Speaker 1: the case of geodesics, for examples, there are several different

1072
00:54:49,280 --> 00:54:55,000
Speaker 1: kinds of geodesics. Spacelike geodesics minimize the distance, cool timelike

1073
00:54:55,080 --> 00:54:59,560
Speaker 1: geodesics actually maximize the proper time, and then null geodesics

1074
00:54:59,560 --> 00:55:03,120
Speaker 1: for light have no proper time. Finally, remember that the

1075
00:55:03,160 --> 00:55:07,239
Speaker 1: future does not depend on the past. The path we

1076
00:55:07,320 --> 00:55:11,600
Speaker 1: calculate using action between the past and the future depends

1077
00:55:11,760 --> 00:55:15,120
Speaker 1: on the boundary conditions including the future and the past ones.

1078
00:55:15,640 --> 00:55:18,760
Speaker 1: So knowing where and when the object starts.

1079
00:55:18,600 --> 00:55:22,200
Speaker 4: And ends and we look forward to seeing you next time.

1080
00:55:22,560 --> 00:55:24,600
Speaker 1: And I hope this has given you another way to

1081
00:55:24,680 --> 00:55:27,120
Speaker 1: think about how things happen in the universe and why

1082
00:55:27,160 --> 00:55:30,520
Speaker 1: some things happen and other things don't. In the end,

1083
00:55:30,760 --> 00:55:32,320
Speaker 1: it all minimizes the action.

1084
00:55:39,400 --> 00:55:42,960
Speaker 4: Daniel and Kelly's Extraordinary Universe is produced by iHeartRadio.

1085
00:55:43,160 --> 00:55:45,800
Speaker 3: We would love to hear from you, We really would.

1086
00:55:45,960 --> 00:55:48,719
Speaker 1: We want to know what questions you have about this

1087
00:55:48,920 --> 00:55:50,560
Speaker 1: Extraordinary Universe.

1088
00:55:50,680 --> 00:55:53,600
Speaker 4: We want to know your thoughts on recent shows, suggestions

1089
00:55:53,640 --> 00:55:54,640
Speaker 4: for future shows.

1090
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Speaker 3: If you contact us, we will get back to you.

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Speaker 1: We really mean it. We answer every message. Email us

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Speaker 1: at Questions at Danielankelly.

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00:56:03,160 --> 00:56:05,240
Speaker 4: Dot org, or you can find us on social media.

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00:56:05,360 --> 00:56:09,160
Speaker 4: We have accounts on x, Instagram, Blue Sky and on

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Speaker 4: all of those platforms.

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Speaker 3: You can find us at D and K Universe.

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Speaker 1: Don't be shy, write to us,