WEBVTT - Why does the Universe minimize action? 0:00:07.800 --> 0:00:11.680 Physics has set itself quite the task. The job is 0:00:11.720 --> 0:00:15.560 to explain the whole universe, everything inside of it, and 0:00:15.880 --> 0:00:19.680 all of its doing and throwing. Usually we think of 0:00:19.720 --> 0:00:22.880 that in terms of the matter, the stuff, and the 0:00:22.880 --> 0:00:27.080 forces how that stuff interacts. So when we count our 0:00:27.160 --> 0:00:31.000 progress towards the big goal of physics, we sometimes think 0:00:31.040 --> 0:00:33.880 about the number of particles and the number of forces. 0:00:34.360 --> 0:00:37.400 We reduce that number when we break open matter to 0:00:37.440 --> 0:00:40.280 see what it's made out of, or when we unify 0:00:40.400 --> 0:00:45.920 forces like we be merged electricity and magnetism into electromagnetism 0:00:46.320 --> 0:00:49.000 and then later added the weak force to make the 0:00:49.200 --> 0:00:54.480 electroweak force sorry magnetism. Eventually, we hope we'll get down 0:00:54.520 --> 0:00:58.520 to one particle and one force that explains everything that happens. 0:00:59.080 --> 0:01:01.880 But what if there there is a better way. Maybe 0:01:02.200 --> 0:01:05.920 forces are intuitive to us, part of the stories we 0:01:06.040 --> 0:01:09.640 tell about what we see with a simple intuitive analog 0:01:09.760 --> 0:01:12.840 in our experience. But what if they aren't a natural 0:01:12.920 --> 0:01:16.600 fit to the real mechanisms of the universe itself? What 0:01:16.720 --> 0:01:21.400 if forces emerged from something else. Today on the pod, 0:01:21.440 --> 0:01:25.440 we'll talk about something we've mentioned many times in many contexts. 0:01:25.959 --> 0:01:28.600 It's time to dive in and talk about the mysterious 0:01:28.720 --> 0:01:32.959 quantity that has no analog in our intuitive experience, but 0:01:33.120 --> 0:01:37.039 seems to dominate in the events of the universe, action, 0:01:37.720 --> 0:01:43.240 and specifically, why the universe seems to minimize it. Welcome 0:01:43.319 --> 0:01:46.840 to Daniel and Kelly's Extraordinary Minimal Universe. 0:02:00.160 --> 0:02:00.560 Hello. 0:02:00.560 --> 0:02:01.560 I'm Kelly Wintersmith. 0:02:01.600 --> 0:02:05.480 I study parasites and space and it's winter right now, 0:02:05.520 --> 0:02:07.360 so it is my season of least action. 0:02:09.760 --> 0:02:13.560 Hi. I'm Daniel. I'm a particle physicist. It's winter here 0:02:13.560 --> 0:02:16.680 in southern California, though I can hardly tell. 0:02:19.200 --> 0:02:19.960 So we're. 0:02:21.720 --> 0:02:25.280 We're talking about potential energy and kinetic energy a little 0:02:25.280 --> 0:02:29.080 bit today, which reminds me of my intro physics class, 0:02:29.440 --> 0:02:33.560 which makes me wonder, what is the coolest demonstration you 0:02:33.639 --> 0:02:35.480 have done for your students as a teacher. 0:02:37.919 --> 0:02:41.160 Ooh, that's a good question. I think the coolest demonstration 0:02:41.320 --> 0:02:44.320 I've ever done doesn't actually relate to kinetic or potential energy. 0:02:44.360 --> 0:02:46.680 I know, there's like those famous ones where you like 0:02:46.880 --> 0:02:48.960 push a bowling ball away from your nose and then 0:02:49.000 --> 0:02:51.880 you stand there all cool as it comes back and 0:02:51.960 --> 0:02:54.440 doesn't crunch you in the face. But I think the 0:02:54.480 --> 0:02:57.119 most interesting ones are the ones that reveals something about 0:02:57.120 --> 0:02:59.960 the universe you can't otherwise see. So I once brought 0:03:00.080 --> 0:03:03.240 in a homemade cloud chamber. This is something you can 0:03:03.280 --> 0:03:07.040 actually build yourself in your garage with pretty simple ingredients 0:03:07.240 --> 0:03:10.600 that could show you muons flying through the air. It 0:03:10.639 --> 0:03:13.280 reveals to you that the world around you is filled 0:03:13.360 --> 0:03:16.760 with these invisible particles flying at high speeds, and you 0:03:16.800 --> 0:03:20.840 can build the device using fairly simple ingredients to reveal them. 0:03:21.639 --> 0:03:24.800 These cloud chambers have like super saturated air, and as 0:03:24.840 --> 0:03:28.400 the muons fly through, they create these droplets which become visible. 0:03:28.600 --> 0:03:31.079 You probably have seen them at science museums. I just 0:03:31.120 --> 0:03:33.080 think that's awesome because it shows you that the world 0:03:33.120 --> 0:03:36.440 is so much more complex than your senses can reveal. 0:03:36.680 --> 0:03:39.320 Did we discover muons pretty early on? Because they're so 0:03:39.360 --> 0:03:40.160 easy to see? 0:03:40.280 --> 0:03:43.520 We discovered the muon years and years ago using cloud 0:03:43.600 --> 0:03:46.880 chambers actually, and then you can spot them also using 0:03:46.920 --> 0:03:50.720 big blocks of emulsion. Emulsion is sort of like a 0:03:50.760 --> 0:03:54.880 three dimensional bit of photographic plate that you later like 0:03:54.960 --> 0:03:58.000 slice up and develop as photographs. And we put them 0:03:58.040 --> 0:03:59.920 on the tops of mountains and we saw a lot 0:04:00.280 --> 0:04:02.880 of particles shooting through them, and that was the first 0:04:02.920 --> 0:04:04.000 clue about muons. 0:04:04.080 --> 0:04:06.280 Yeah, who did we know what they were immediately or 0:04:06.280 --> 0:04:07.520 did it take a while to work that out? 0:04:07.720 --> 0:04:07.800 No? 0:04:07.880 --> 0:04:10.680 Actually, it's sort of a famous surprise because we had 0:04:10.680 --> 0:04:12.920 the idea of like atomic structure and it was all 0:04:13.000 --> 0:04:15.880 very nice and neat. We had protons and neutrons and electrons, 0:04:16.240 --> 0:04:18.800 and then we discovered the muon which wasn't part of 0:04:18.839 --> 0:04:22.360 the atom. And a famous physicist I Robbie said, who 0:04:22.480 --> 0:04:25.440 ordered that, like, we don't need this. We're you know, 0:04:25.440 --> 0:04:27.640 we have a pretty good thing going, like get out 0:04:27.680 --> 0:04:30.000 to hear universe with your pesky facts. 0:04:31.000 --> 0:04:31.200 Yeah. 0:04:31.279 --> 0:04:34.119 No, I've been there running experiments and you're like, no, please, 0:04:34.120 --> 0:04:35.160 don't do that, universe. 0:04:35.200 --> 0:04:36.800 But it does it anyway exactly. 0:04:36.839 --> 0:04:39.400 And you know, the universe is under no obligation to 0:04:39.600 --> 0:04:42.560 make sense to us, or to do what we expect, 0:04:42.960 --> 0:04:45.240 or to follow rules that sort of connect with our 0:04:45.360 --> 0:04:48.640 intuitive way of thinking. Which is why I'm so excited 0:04:48.640 --> 0:04:51.880 today to finally get to talk about this concept we've 0:04:51.880 --> 0:04:55.080 been mentioning and referring to for months and months and 0:04:55.120 --> 0:04:57.120 months now, and we're going to do a deep dive 0:04:57.240 --> 0:04:59.440 and an explanation of it today. And what is it 0:04:59.480 --> 0:05:04.080 called called action and the principle of least action, and 0:05:04.120 --> 0:05:06.919 it's a completely different way to think about motion in 0:05:06.960 --> 0:05:10.000 the universe and why things fall down, or why things 0:05:10.000 --> 0:05:14.080 slide the way they do, or even how quantum fields oscillate. Really, 0:05:14.120 --> 0:05:17.400 it's the most basic principle we've discovered, but it's also 0:05:17.600 --> 0:05:20.640 kind of counterintuitive, so it takes a little bit of 0:05:20.640 --> 0:05:23.400 a mental mind shift to think about the universe in 0:05:23.520 --> 0:05:27.760 terms of action. It's also a terribly terribly named word 0:05:28.080 --> 0:05:30.320 because it has nothing to do with the word action 0:05:30.520 --> 0:05:31.640 we use in English. 0:05:32.000 --> 0:05:34.280 Well, it is a physics concept, so it would have 0:05:34.320 --> 0:05:35.240 to have a bad name. 0:05:35.800 --> 0:05:37.640 Why did they do this? You know, they should have 0:05:37.800 --> 0:05:40.640 just come up with a new name, plasma, cagical or 0:05:40.640 --> 0:05:43.240 something and use that so that when you hear it, 0:05:43.240 --> 0:05:45.919 you're like, Okay, this is something new. I have to 0:05:45.920 --> 0:05:48.160 make a new space in my brain. But if you 0:05:48.240 --> 0:05:50.640 use an existing word, that has to like share that 0:05:50.760 --> 0:05:53.480 room in your brain with that other concept which has 0:05:53.520 --> 0:05:54.280 the same word. 0:05:54.720 --> 0:05:57.720 Well, I think somebody needs to hold on to plasmacajigle 0:05:58.279 --> 0:06:00.560 or whatever it was that you said. Thing needs to 0:06:00.600 --> 0:06:02.640 be named that, and you should be in charge of 0:06:02.720 --> 0:06:04.279 naming things in physics from here on out. 0:06:04.320 --> 0:06:06.400 All right, Well, I guess I just need to discover 0:06:06.520 --> 0:06:09.560 something and then I can name it flasmaca jiggle, and 0:06:09.600 --> 0:06:11.200 then we'll be all set. You know, I've done the 0:06:11.200 --> 0:06:14.240 hard part already, and you know, just the pesky bit 0:06:14.240 --> 0:06:16.200 about actually discovering something in the universe. 0:06:16.400 --> 0:06:18.040 Yeah, right, yeah, that tiny bit. 0:06:18.160 --> 0:06:21.880 And so we asked the extraordinaries, why does the universe 0:06:22.200 --> 0:06:23.279 flazmaca jiggle? 0:06:23.880 --> 0:06:28.640 No, we didn't. No. 0:06:28.760 --> 0:06:30.560 I went out there and I asked folks what they 0:06:30.640 --> 0:06:33.560 knew about action, because this is something we get requests 0:06:33.600 --> 0:06:37.040 about a lot, and we've mentioned occasionally on the podcast 0:06:37.040 --> 0:06:38.800 and people ask us, ooh, would you go into more 0:06:38.839 --> 0:06:41.280 depth about that? And it's something I love doing on 0:06:41.279 --> 0:06:44.200 the pod, is explaining something on a depth beyond what's 0:06:44.279 --> 0:06:47.080 typically out there in popular science, but I hope in 0:06:47.120 --> 0:06:50.240 an actual, approachable way that'll make people really appreciate the 0:06:50.279 --> 0:06:53.440 way physics is done on the cutting edge. But of course, 0:06:53.480 --> 0:06:55.400 before we dig into it, I wanted to know what 0:06:55.480 --> 0:06:58.960 people already knew about this concept, So I asked, folks, 0:06:59.080 --> 0:07:02.800 why does the universe verse minimize action as usual? If 0:07:02.800 --> 0:07:04.440 you would like to join this crew of people who 0:07:04.520 --> 0:07:07.279 respond to these questions without the opportunity to google them. 0:07:07.640 --> 0:07:11.160 Please write to us questions at Danielankelly dot org. We 0:07:11.200 --> 0:07:14.280 would love to add your voice in the meantime. Think 0:07:14.320 --> 0:07:17.800 about it. Why do you think the universe minimizes action? 0:07:18.280 --> 0:07:20.560 Why does it flasmacajicle. 0:07:22.040 --> 0:07:24.640 Here's what people have to say. Since I have no 0:07:24.720 --> 0:07:26.720 idea what this means, I'm forced to fall back on 0:07:26.800 --> 0:07:27.960 a template answer of. 0:07:28.680 --> 0:07:32.160 Entropy, because the universe is just bound to follow laws 0:07:32.760 --> 0:07:35.960 with no shortcuts and no long cuts. So I think 0:07:36.000 --> 0:07:40.520 that minimizing action is probably another way of saying minimizing 0:07:40.680 --> 0:07:42.080 divergence from laws. 0:07:42.320 --> 0:07:47.000 For every action, there's an equal and opposite reaction, So 0:07:47.040 --> 0:07:51.160 I guess the universe minimizes reactions as well. 0:07:51.280 --> 0:07:56.720 To safe energy and to minimize possible outcomes. 0:07:57.040 --> 0:07:59.480 To know, is the universe lazy? Is it just chilled out? 0:08:00.080 --> 0:08:02.680 It is the world likes to be in its lowest 0:08:02.800 --> 0:08:03.760 energy state. 0:08:03.880 --> 0:08:07.400 Because actions speak louder than words, and there's far too 0:08:07.480 --> 0:08:08.840 much noise pollution. 0:08:08.840 --> 0:08:12.480 Because anything that happens, or any force that exists, has 0:08:12.640 --> 0:08:16.320 a counter force pressing against it. 0:08:16.360 --> 0:08:19.200 Maybe it's lazy, that's my excuse. I suspect that it 0:08:19.280 --> 0:08:21.040 has something to do with entroview, though. 0:08:21.120 --> 0:08:24.080 Too optimiz for efficiency, kind of like natural selection. 0:08:24.440 --> 0:08:28.400 It's just something we observe, but we don't know why. 0:08:29.040 --> 0:08:33.880 Do individual processes independently tend to pars the money or 0:08:33.960 --> 0:08:37.480 is there an underlying unified model that polls all behavior 0:08:37.600 --> 0:08:40.280 to a deeper minimization. 0:08:40.160 --> 0:08:42.720 Seems like it would be the only way that it 0:08:42.720 --> 0:08:45.760 could go, because if there was something at a higher energy, 0:08:46.040 --> 0:08:48.440 there was always something that could come lower. 0:08:48.920 --> 0:08:50.880 I was pleased to see I wasn't the only one 0:08:50.920 --> 0:08:55.520 who didn't know the answer, and went with sarcasm. 0:08:55.600 --> 0:08:57.839 I never know what to expect from these responses. I 0:08:57.840 --> 0:09:01.280 always learned so much. Sometimes bill know exactly what I'm 0:09:01.280 --> 0:09:04.319 talking about and get very insightful answers. Other times people 0:09:04.360 --> 0:09:07.840 are confused by the physics word and as is not 0:09:07.920 --> 0:09:10.600 their fault at all, and it seemed to have happened 0:09:10.640 --> 0:09:12.880 in this case. But this is exciting to me because 0:09:12.920 --> 0:09:14.679 it means that not a lot of folks out there 0:09:14.679 --> 0:09:18.400 are familiar with this concept of action being minimized, which 0:09:18.440 --> 0:09:20.560 means we get to teach them all something very very 0:09:20.600 --> 0:09:21.760 cool about the universe. 0:09:21.920 --> 0:09:24.360 Yes, we are helping to make you the most interesting 0:09:24.400 --> 0:09:25.520 person at the party. 0:09:26.160 --> 0:09:30.959 So let's say, Kelly, I'm trying to assess the level 0:09:31.000 --> 0:09:36.160 of sarcasm there, because I am one hundred percent sincerely 0:09:36.320 --> 0:09:39.000 excited about action, and I don't talk about it at 0:09:39.000 --> 0:09:41.720 parties very much, but it is something super duper nerdy 0:09:41.800 --> 0:09:45.200 and cool to discover, like an organizing principle of the universe, 0:09:45.280 --> 0:09:48.360 especially when it's counterintuitive, when it's not the way we 0:09:48.440 --> 0:09:52.079 typically think about stuff. That's like one hundred percent sincerity. 0:09:52.240 --> 0:09:54.199 And I'm assuming you feel the same way I do. 0:09:54.320 --> 0:09:54.520 I do. 0:09:54.640 --> 0:09:56.720 I don't know what kind of parties you're thinking of, Daniel, 0:09:56.720 --> 0:09:59.360 but the parties I go to we talk about things 0:09:59.400 --> 0:09:59.920 like pleasma. 0:10:01.120 --> 0:10:05.079 Okay, all right, Well we're not explaining plasmaka jiggle today 0:10:05.120 --> 0:10:07.040 because I haven't discovered it yet. But we are going 0:10:07.080 --> 0:10:10.280 to talk about action. But let's start by thinking about 0:10:10.320 --> 0:10:13.080 a simple motion of an object, and then we'll talk 0:10:13.080 --> 0:10:15.920 about how we typically understand it, how people probably think 0:10:15.960 --> 0:10:18.520 about its motion, and then we'll switch and think about 0:10:18.520 --> 0:10:21.920 it in another way. So the classic example, of course, 0:10:22.080 --> 0:10:24.680 is a ball flying through the air. You have a ball, 0:10:24.720 --> 0:10:27.360 you're playing catch with your kid or your dog or whatever. 0:10:27.480 --> 0:10:30.040 You throw it and it goes across your yard and 0:10:30.160 --> 0:10:32.640 hits the ground or gets caught by your dog or whatever. 0:10:33.120 --> 0:10:36.240 And from a traditional physics point of view, this isn't 0:10:36.240 --> 0:10:39.000 too complicated. You can understand it by thinking, like you 0:10:39.080 --> 0:10:41.559 throw it with your arms, so it has some initial velocity. 0:10:42.120 --> 0:10:44.160 And we know that things in the universe, if they 0:10:44.200 --> 0:10:47.319 have velocity, they just keep moving unless some force acts 0:10:47.360 --> 0:10:50.000 upon them. And in this case, for example, the force 0:10:50.080 --> 0:10:53.360 is gravity pulling it back down to the Earth. And 0:10:53.440 --> 0:10:56.360 so we can use those various elements to understand the 0:10:56.360 --> 0:10:59.680 motion of the ball. We have velocity, we have acceleration 0:10:59.800 --> 0:11:03.200 that changes its velocity. We can put that together to 0:11:03.200 --> 0:11:06.280 get an equation that describes where the ball is at 0:11:06.320 --> 0:11:08.959 any time, and it comes out to be a parabola. Right, 0:11:09.000 --> 0:11:10.960 It goes up and it comes back down and it 0:11:11.040 --> 0:11:11.760 hits the ground. 0:11:12.000 --> 0:11:15.920 It's also a great song by Tool. Do you think 0:11:15.960 --> 0:11:16.960 everybody hum. 0:11:16.840 --> 0:11:18.920 A few bars of it for us? Kelly? 0:11:20.040 --> 0:11:22.800 No, no, no, no, no. Oh, hey, I'm not gonna 0:11:22.840 --> 0:11:23.319 go anymore. 0:11:23.360 --> 0:11:26.199 So do you think everybody knows what the shape of 0:11:26.200 --> 0:11:27.240 a parabola looks like? 0:11:27.520 --> 0:11:30.560 Oh? It's hard for me to remember a time when 0:11:30.559 --> 0:11:32.560 I didn't know what the shape of a parabolo looks like. 0:11:32.600 --> 0:11:34.720 So I should ask you that question. Kelly, do you 0:11:34.760 --> 0:11:36.040 can you imagine a parabolo? 0:11:36.520 --> 0:11:39.160 Yep, I can, but I also do a fair bit 0:11:39.200 --> 0:11:39.679 of modeling. 0:11:39.920 --> 0:11:42.600 Yeah, okay, so that's a good point. Let's help people 0:11:42.920 --> 0:11:44.479 visualize a parabola. 0:11:45.200 --> 0:11:47.840 It's just a you. You're making it too complicated. 0:11:47.960 --> 0:11:50.560 A parabola is sort of like an upside down you. Right, 0:11:50.760 --> 0:11:53.760 it's a little bit tighter at the top, but basically 0:11:53.800 --> 0:11:55.840 a parabolo is well defined by what happens when you 0:11:55.880 --> 0:11:57.839 throw a ball across your yard. Right, It's going to 0:11:57.920 --> 0:11:59.640 go up, and then it's gonna turn around, it's gonna 0:11:59.640 --> 0:12:03.320 come back to and that's the parabolic shape. It's defined 0:12:03.360 --> 0:12:05.599 by an equation that has like an x squerginit for 0:12:05.640 --> 0:12:08.280 people who like to think about equations, but for visual people, 0:12:08.360 --> 0:12:11.200 it's basically an upside down you. And so that's what 0:12:11.240 --> 0:12:13.400 a brable looks like. Okay, So that's sort of the 0:12:13.440 --> 0:12:17.640 traditional way to think about how things move. You have matter, 0:12:17.800 --> 0:12:21.199 and you have forces. Forces act on matter to provide acceleration. 0:12:21.679 --> 0:12:24.160 A few rounds of calculus and you get your equation 0:12:24.280 --> 0:12:27.000 of motion where the thing is at any time. We're 0:12:27.040 --> 0:12:27.440 good with that. 0:12:27.480 --> 0:12:29.480 So far, we're good, right, And so in this model, 0:12:29.520 --> 0:12:33.400 we're not paying attention to things like friction or wind 0:12:33.600 --> 0:12:34.680 or anything like that. 0:12:34.679 --> 0:12:37.400 That's exactly right, because those things are really hard to 0:12:37.440 --> 0:12:40.560 add using this way. Like wind is a force, but 0:12:40.640 --> 0:12:44.079 it's not constant. Friction is a force, but it depends 0:12:44.120 --> 0:12:46.720 on velocity. So we're going to stick with a simple 0:12:46.720 --> 0:12:50.599 calculation because that's what this approach is good at. Simple calculations, 0:12:50.679 --> 0:12:54.840 what we call conservative forces with constant acceleration. Very easy 0:12:54.880 --> 0:12:58.560 to do those calculations. But there's something interesting about this 0:12:58.640 --> 0:13:00.800 motion if you look at it from another point of view. 0:13:01.240 --> 0:13:03.720 This is going to sound a little bit weird and random, 0:13:03.800 --> 0:13:06.520 but stick with me. So what you do is you 0:13:06.559 --> 0:13:09.560 think about the kinetic energy of this ball. Kinetic energy 0:13:09.600 --> 0:13:12.200 is just the energy of motion, and you usually calculate 0:13:12.240 --> 0:13:15.640 it like one half m v squared vias the velocity. 0:13:15.960 --> 0:13:18.240 So you calculate the kinetic energy of the ball as 0:13:18.240 --> 0:13:22.120 it moves through the air. Cool Now calculate also the 0:13:22.120 --> 0:13:25.160 potential energy of the ball. Potential energy here is just 0:13:25.160 --> 0:13:28.440 from gravity, so it's like mgh just the height of 0:13:28.480 --> 0:13:31.400 the ball. As it goes up it has more potential energy, 0:13:31.520 --> 0:13:33.520 as it goes down has less potential. 0:13:33.240 --> 0:13:35.319 Energy, and m in both of those was mass. 0:13:35.400 --> 0:13:39.520 Yeah, yeah, exactly. And so you calculate these things kinetic 0:13:39.640 --> 0:13:43.400 energy and potential energy. Now do something weird, subtract them. 0:13:43.600 --> 0:13:46.000 Usually we add these things to make total energy. But 0:13:46.040 --> 0:13:49.400 this time, let's subtract them. Let's do kinetic energy minus 0:13:49.440 --> 0:13:52.679 potential energy. So now we're calculating the difference between the 0:13:52.760 --> 0:13:55.960 kinetic energy and the potential energy. You might think, well, 0:13:56.040 --> 0:13:59.360 what does that mean? Intuitively, Like, if you add them, 0:13:59.679 --> 0:14:01.960 it may sense because it's okay, that's total energy. What 0:14:01.960 --> 0:14:05.840 does the difference mean? It means nothing intuitively, It's just 0:14:05.920 --> 0:14:09.360 this weird number we're calculating. Okay, okay. The cool thing 0:14:09.360 --> 0:14:11.840 about this number, The reason we're talking about this number 0:14:12.320 --> 0:14:16.120 is that the path the ball took minimizes that number. 0:14:16.640 --> 0:14:18.040 Like we have the path the ball took. It was 0:14:18.080 --> 0:14:21.280 a parabola. We calculate the kinetic energy minus potential energy. 0:14:21.560 --> 0:14:24.560 That number is smallest for the path that the ball took. 0:14:25.080 --> 0:14:27.000 If you change the path a little bit, you add 0:14:27.040 --> 0:14:30.240 a little divit or middle higher, a little lower, that 0:14:30.280 --> 0:14:34.080 path would have a higher value of kinetic energy minus 0:14:34.120 --> 0:14:37.440 potential energy. So the path that the ball took is 0:14:37.440 --> 0:14:42.000 the one that minimizes this difference between kinetic and potential energy. 0:14:42.280 --> 0:14:45.880 Okay, and so is that just because kinetic energy would 0:14:45.880 --> 0:14:48.720 always be greater whenever you add like a divot, because 0:14:48.760 --> 0:14:52.760 you're making the parabola longer, anytime you're adding a divot 0:14:52.840 --> 0:14:53.200 or something. 0:14:53.640 --> 0:14:56.520 I think you're asking, why is the parabola the path 0:14:56.560 --> 0:14:58.240 that minimizes this difference? 0:14:58.520 --> 0:14:58.720 Right? 0:14:58.880 --> 0:15:01.120 Yeah, and we're gonna explain that. The answer is yes. 0:15:01.120 --> 0:15:03.360 We're gonna explain that in detail in a minute, but 0:15:03.360 --> 0:15:05.480 for now, let's stop talking about kinetic energy. Money is 0:15:05.520 --> 0:15:07.440 potential energy because it's a lot of words, and let's 0:15:07.480 --> 0:15:09.960 just relabel it with a new word, right, so we 0:15:09.960 --> 0:15:11.840 don't have to use so many words. And we're gonna 0:15:11.840 --> 0:15:14.800 call it action. Why we don't call it plasmaca jiggle, 0:15:14.880 --> 0:15:17.760 I don't know, but we're gonna call it action. And 0:15:17.880 --> 0:15:20.880 so this turns out to be a general principle in 0:15:20.960 --> 0:15:23.640 physics that the path of things take you can figure 0:15:23.640 --> 0:15:26.680 it out by finding the path that minimizes the action 0:15:26.960 --> 0:15:30.400 this weird difference between kinetic and potential energy. So we 0:15:30.440 --> 0:15:32.760 started out just like I'm going to do this calculation. 0:15:32.800 --> 0:15:34.880 I'm not gonna tell you why or what it means 0:15:34.960 --> 0:15:37.560 or anything, and now we did it, and we discovered 0:15:37.560 --> 0:15:41.520 something that's actually physically useful. The universe seems to pay 0:15:41.560 --> 0:15:44.520 attention to this. It's not just a number, Daniel calculator. 0:15:44.560 --> 0:15:47.720 I could calculate anything like the number of walnuts times 0:15:47.720 --> 0:15:50.560 the temperature outside right. I can make up whatever quantity 0:15:50.600 --> 0:15:53.120 I want, But that doesn't help me solve a problem. 0:15:53.160 --> 0:15:56.120 It just seem to be important to the universe. This number, 0:15:56.440 --> 0:15:59.760 the action, the difference between kinetic and potential energy is 0:15:59.760 --> 0:16:02.960 all so an arbitrary, random thing that we constructed, but 0:16:03.160 --> 0:16:06.360 it seems to be respected by the universe somehow, because 0:16:06.400 --> 0:16:08.480 the universe, when the ball is flying through the air, 0:16:08.880 --> 0:16:12.320 chooses the path that minimizes this weird number, this thing 0:16:12.360 --> 0:16:13.040 we call action. 0:16:13.360 --> 0:16:15.440 So you can like tell the future if you know. 0:16:17.040 --> 0:16:20.120 So let me it's been a while since I've taken physics, 0:16:20.440 --> 0:16:23.560 and so so I'm imagining you've released the ball, and 0:16:23.600 --> 0:16:26.920 so to do this is it like, you know, you 0:16:26.960 --> 0:16:29.040 stop and you take a picture of the ball at 0:16:29.040 --> 0:16:32.920 every second, and you redo this calculation at every second 0:16:33.000 --> 0:16:34.560 and then you can predict where it's going to be 0:16:34.640 --> 0:16:37.120 the next second by doing this calculation. 0:16:37.760 --> 0:16:41.160 No action, It's exactly the opposite of that, which makes 0:16:41.160 --> 0:16:44.200 it a great question. So the way you described it 0:16:44.240 --> 0:16:46.560 in your mind is the way we typically think about 0:16:46.560 --> 0:16:49.640 the universe, that the past controls the future. We have 0:16:49.720 --> 0:16:52.600 like frame by frame, what happens now affects what's going 0:16:52.640 --> 0:16:53.600 to happen in a moment. 0:16:54.120 --> 0:16:54.280 Right. 0:16:54.320 --> 0:16:56.760 The ball moves this way because it has velocity and 0:16:56.800 --> 0:16:59.200 it has a force pulling on it. That's sort of 0:16:59.240 --> 0:17:02.560 like a computational way of thinking about the universe that 0:17:02.600 --> 0:17:05.040 you calculate it like frame by frame, and that's actually 0:17:05.080 --> 0:17:07.399 called the Newton schema. Newton came up with this idea 0:17:07.440 --> 0:17:09.720 that like the future of the universe is determined by 0:17:09.760 --> 0:17:12.080 the present, and he thought about like universal clocks and 0:17:12.480 --> 0:17:15.160 so many fun digressions we could go on there. And 0:17:15.280 --> 0:17:18.520 that's the way that the typical force story works. You 0:17:18.600 --> 0:17:21.399 think about velocity and forces and you cycle through frame 0:17:21.440 --> 0:17:25.560 by frame. That's not the way the action works. You 0:17:25.600 --> 0:17:28.080 can't use action to predict the future the same way 0:17:28.200 --> 0:17:32.160 because to calculate the path of the ball using action, 0:17:32.560 --> 0:17:35.199 you have to know the initial position and the final 0:17:35.240 --> 0:17:38.400 position already in order to find the path that goes 0:17:38.400 --> 0:17:40.879 from So there's a weird thing here which seems to 0:17:40.920 --> 0:17:44.399 imply maybe that the present depends on the future, you know, 0:17:44.480 --> 0:17:48.160 like where the ball goes now depends on where it lands, 0:17:48.560 --> 0:17:50.200 and so you have to know the future to predict 0:17:50.240 --> 0:17:52.440 the present. Not quite that. We're going to dig into 0:17:52.440 --> 0:17:56.439 it in a minute, but that's actually the fundamental misunderstanding 0:17:56.720 --> 0:17:58.480 at the heart of the movie Arrival. 0:17:58.920 --> 0:18:01.600 WHOA, yeah, I know, all right, stick with us to 0:18:01.640 --> 0:18:02.000 the end. 0:18:02.200 --> 0:18:05.480 Yeah, exactly. So we have this other way of thinking 0:18:05.520 --> 0:18:08.480 about motion where if you know the initial point A 0:18:08.720 --> 0:18:10.960 and the final point B, you can figure out what 0:18:11.119 --> 0:18:14.040 path something took just by calculating this weird thing called 0:18:14.080 --> 0:18:17.800 action and finding the path that minimizes the action. So 0:18:17.960 --> 0:18:20.359 let's work through another example, just to make sure we 0:18:20.440 --> 0:18:23.000 have this in our heads, because it's really important. Let's 0:18:23.040 --> 0:18:26.360 take an even simpler example, a ball with no gravity. 0:18:26.480 --> 0:18:29.440 Right now, we're out in space. Okay, we've ignored Zach 0:18:29.480 --> 0:18:31.639 and Kelly's advice, and you've gone to space and built 0:18:31.640 --> 0:18:34.360 a colony. We've made all sorts of mistakes, but now 0:18:34.359 --> 0:18:36.440 we're out in space and we get to play zero 0:18:36.600 --> 0:18:39.680 G catch with our kids or with our space dog. Right, 0:18:40.000 --> 0:18:42.479 So what happens when you throw a ball in space? 0:18:42.760 --> 0:18:43.160 You die? 0:18:43.200 --> 0:18:47.400 How's it? Going to move you die, Kelly. Doesn't happen immediately. 0:18:47.560 --> 0:18:50.800 I mean, we got lots of radiation and eventually we die, 0:18:50.920 --> 0:18:53.720 but we do we to have one nice afternoon of 0:18:53.840 --> 0:18:55.400 playing catch with our space dog. 0:18:55.440 --> 0:18:58.159 Okay, right, right, So if you're in deep space in 0:18:58.200 --> 0:19:02.360 your space suit, you're gravity's probably negligible. Right, So does 0:19:02.400 --> 0:19:04.760 that mean potential energy is zero? 0:19:05.200 --> 0:19:08.040 Exactly right. So let's think about the motion of a 0:19:08.080 --> 0:19:11.119 ball when there's no potential energy. So the force method 0:19:11.160 --> 0:19:14.200 is really easy here. You throw the ball that has velocity. 0:19:14.359 --> 0:19:16.760 There's no forces, So what's gonna happen. It's just going 0:19:16.840 --> 0:19:19.960 to keep having that velocity. Very intuitive. It's going in 0:19:20.000 --> 0:19:22.680 a certain direction. It keeps going in that direction every 0:19:22.720 --> 0:19:24.720 moment in time. You can predict the future because you 0:19:24.720 --> 0:19:27.560 have its velocity and that tells you exactly where it's 0:19:27.560 --> 0:19:30.800 going to go. Very simple. Okay, Now let's try to 0:19:30.800 --> 0:19:33.760 do that with the action method. So the action method says, 0:19:33.840 --> 0:19:35.880 you know where the ball started, and you know where 0:19:35.880 --> 0:19:38.160 the ball ends up, and you know how much time 0:19:38.200 --> 0:19:40.479 it took to go from A to B. Find the 0:19:40.520 --> 0:19:43.359 path that it took from A to B. And so 0:19:43.480 --> 0:19:45.320