Why does the Universe minimize action?

24:43Eczema is unpredictable but you can flare less with Epglyss a once monthly treatment for moderate to severe eczema After an initial four month or longer dosing phase about four in ten people taking Epglyss achieved itch relief and clear or almost clear skin at 16 weeks. And most of those people maintain skin that's still more clear at one year with monthly dosing. Hebglis, Librikizumab, LBKZ, a 250 milligram per two milliliter injection, is a prescription medicine used to treat adults and children 12 years of age and older who weigh at least 88 pounds or 40 kilograms with moderate to severe eczema.

25:14Also called atopic dermatitis that is not well controlled with prescription therapies used on the skin or topicals or who cannot use topical therapies. Hebglis can be used with or without topical corticosteroids. Don't use if you're allergic to Hebglis. Allergic reactions can occur that can be severe. Eye Tell your doctor if you have new or worsening eye problems. You should not receive a live vaccine when treated with Epglyss. Before starting Epglyss, tell your doctor if you have a parasitic infection. Ask your doctor about Epglyss and visit epglyss.lily.com or call 1-800-LILY-RX or 1-800-545-5979.

25:43Every business has an ambition. PayPal Open is the platform designed to help you grow into yours. With access to business loans so you can expand and hundreds of millions of PayPal customers worldwide. Your customers can pay all the ways they want today with PayPal, Venmo, Pay Later, and all major cards so you can focus on the future. When you need a partner trusted by millions, there's one platform for all business. PayPal Open. Grow today at PayPalOpen.com. Loan subject to approval in available locations. Hey everyone, it's Cal Penn. I'm the host of Earsay, the Audible and iHeart Audiobook Club.

26:21This week on the podcast, I am sitting down with Ray Porter, the narrator of Andy Weir's audiobook Project Hail Mary. Massive sci-fi adventure about survival and science and what happens when you wake up alone very far from earth. I really had to make a decision because I caught myself getting that frog in my throat and starting to get teary as I'm narrating some of these sections. And it's like, okay, yo, yo, yo, is this indulgent? And I really thought about it. I was like, no, at this point, it would kind of be betraying the trust the author and the listener have in telling this story if I don't go through it.

26:58But there's places in this book that deeply emotionally affected me. And I left it on the mic. That's great. Because it served the story. People will say like, oh, my God, I cried at the end. It's like, yeah, dude, me too. Listen to Earsay, the Audible and iHeart Audiobook Club on the iHeartRadio app or wherever you get your podcasts. This is Jacob Goldstein from What's Your Problem? Business software is expensive. And when you buy software from lots of different companies, it's not only expensive, it gets confusing, slow to use, hard to integrate. Odoo solves that because all Odoo software is connected on a single affordable platform.

27:37Save money without missing out on the features you need. Odoo has no hidden costs and no limit on features or data. Odoo has over 60 apps available for any needs your business might have, all at no additional charge. Everything from websites to sales to inventory to accounting, all linked and talking to each other. Check out Odoo at O-D-O-O dot com. That's O-D-O-O dot com.

28:13All right, we're back. And Daniel's going to give us a more complicated situation where this concept of action is going to help us understand what's going on better. Maybe. Because it's physics. It does make it easier to analyze really hairy problems. It's also the way physicists think about motion. You know, when we get to quantum field theory and all that stuff, it's fundamentally based on action. And so I really want to move people out of the mindset of thinking about forces and thinking about action. because like, welcome to the cutting edge of physics. This is how we do it. All right. So we consider the very simple case.

28:47You're playing catch with your space dog. There's no gravity. Things move in a straight line. Kelly was bored by that. She's like, why do we even do this? Fair point. I wasn't bored. You were underwhelmed a little. You know, probably death was imminent, which is interesting. Don't think about the death of my space dog. That's not nice. Oh, I'm sorry. I do like space dogs. I'm sure we'll give lots of shielding in our space dog spacesuit, right? Yes, take care of our critters. Because they didn't get to choose whether to go to space, right? No, Leica didn't get to choose. Didn't go well for Leica.

29:17No, exactly. All right, so let's get back to other scenarios. Now let's get back to your question about why a ball in gravity moves under a parabola, right? So we're going to add gravity back into our situation, bring our space dog back to Earth, toss a ball to the space dog in the backyard. It doesn't move in a straight line. It moves in a parabola. The force picture tells us why, because you have an acceleration. Acceleration is a second derivative of position. And so if you integrate that constant acceleration twice, you get an x squared term, you get a parabola, and it all makes sense. So things move in a parabola because there's a constant force.

29:52What about the action point of view? Why do we move in a parabola? Well, we want to minimize this difference between kinetic energy and potential energy. Potential energy increases as we go up, right? So because we want to minimize action, and action is kinetic energy minus potential energy, that means we want to have lots of potential energy. So potential energy increases as we go up. So we don't want to go up fast to get high potential energy, right? So instead of going in a straight line, we go above our target. We go higher up in order to get more potential energy to minimize our action. But you don't want to go too far from the straight line because going too far from the straight line requires high kinetic energy.

30:34We're increasing our speed on the way up and our speed on the way down. So the parabola is a perfect balance between these things. You get more potential energy without getting too much additional kinetic energy. So the parabola is the path that minimizes the difference between the kinetic energy and the potential energy when you have both at play. It's this really fascinating harmonic balance between these two very different things. And you can think about what the universe is doing in two ways. You can think the universe is doing the Newton thing, like frame by frame. It's thinking the ball is here.

31:08I have this force, so I have that velocity on it, so it's going to move this way. Or you can think about it from the action point of view. And you can say the ball started here and went there. What path between those two in this amount of time minimizes the difference between kinetic and potential energy, and this is the path that does it. And it's fascinating because this turns out to be a general principle, not just in this one case where you're playing ball with your dog, but in every case, the least action tells you what the universe does, how things get from A to B. And you can start from this principle, least action, and you can derive F equals MA.

31:46So you can derive the force equations from it. Newton just wrote it down. He's like, hey, this works. And you might ask, well, where does that come from? And the answer is action, right? From action, you can derive classical mechanics. Now, classical mechanics doesn't then explain what is action. Why does the universe minimize it? To get any insight on that, we're going to have to go deeper into action in quantum mechanics and in philosophy. But it's fascinating because it seems like underneath all of these things, this force picture of the universe, there is a deeper principle from which you can derive F equals MA.

32:24Whoa. Okay, so one thing I think I'm still stumbling on a little bit is that I guess I still feel like, okay, so you throw a ball in the air and you're subtracting the potential energy. I still feel like you should be getting the least path, not necessarily because you're subtracting the potential energy, but because any other path would require you to put additional energy into the ball at some point as it goes through that path. And am I just thinking that because I live in this world and that's my expectation and I don't realize it doesn't have to be my expectation? Or am I misunderstanding something?

33:03No, I think you're saying this is the only path it can take because to take any other path, something would have to do that. You'd need to go and push it or something. And yeah, you're thinking about the universe in terms of forces. You have Newton's ideas so deeply ingrained in your mind that a ball is going to move at constant velocity unless something changes that. You have that so deeply ingrained that it's obvious to you. But that comes from least action. All of Newton's laws are derived from the principle of least action. And so it turns out that's not the fundamental way the universe works that comes out of insisting that everything minimizes action.

33:44And it's actually super cool because as we mentioned earlier, in many cases, the force approach is simple and it works and it's very intuitive and connected to our experience because this is how our world works, right? Like we notice that you got to push stuff to get it moving and you got to push it to turn it and all this stuff. We think about the world in terms of forces, But sometimes that picture is hairy and it's hard to use to do calculations. Like it's easy in the examples we talked about, but what if you add wind or what if you add friction? Or what if, for example, you take your ball and you attach a string to it and the string is now tied to a squirrel and the squirrel is on a roller coaster?

34:21How are you going to do that calculation? Well, you still could in principle, right? There are still forces there, this tension on the string and the roller coaster applies a force. and the wind as a force, which now weirdly depends on velocity. And what you discover is that it's a mess. Like many things in physics, we can only solve a few very simple examples because everything else is totally intractable. So the reason introductory physics students usually calculate the path of a ball without wind resistance and without friction is because otherwise it's a huge pain. And so this force picture is good for simple examples, but it becomes totally intractable for anything realistic.

34:59Now, the amazing thing is the action doesn't. The action remains fairly simple because you can still just write down the kinetic energy and you can write down the potential energy. In many of these situations, it's not hard to calculate the kinetic energy or the potential energy, and then you just find the path that minimizes them. And that's because it relies on these concepts of energy, which helps you ignore a lot of the complicated details of what happens between moment A and moment B. People who have done physics problems know, for example, if you start, for example, with a roller coaster and it starts from a certain height and it goes through all sorts of crazy loop-de-loops and then you're asked to calculate the velocity of this roller coaster car halfway down the track, from a force point of view, you're like, oh my gosh, how am I going to calculate that?

35:45It's done all these crazy maneuvers. I have to know the forces and the acceleration every moment. It's a nightmare. But from an energy calculation point of you. You just have to know, oh, it's gone down a certain distance. I know the potential energy that gets turned into kinetic energy. Boom, I have the answer in one step. This action approach is sort of analogous to that because it also relies just on these energy quantities, which are sort of deeper and more fundamental and don't worry so much about these little details. Okay, all right, I like that. So when you get to like upper division physics, you learn about Lagrangian and Hamiltonian mechanics from which you can derive F equals ma, but they start out by calculating this difference between kinetic and potential energy, minimizing that.

36:24And there's so many really hairy problems you would never even imagine trying to calculate with Newton's method that you can just pop out in a few lines and get the answer. It feels like magic when you first do it. But what's happening here is you're accessing a deeper rule of the universe. Well, what is the rule? Because now we're getting into the good party tricks.

36:46this feels like a deeper rule in the universe because it works not just for classical mechanics like the cases we're talking about you know squirrels and strings and wind and all sorts of stuff it also works in every scenario so this action formula that we talked about kinetic energy minus potential energy that's the action for classical mechanics with conservative forces But you can also do this, for example, for quantum mechanics. And instead of writing down kinetic energy minus potential energy, which require things you don't always know about particles, you write down something called the Lagrangian density.

37:21In the case of like quantum field theory, this is just the fields that exist and how they interact with each other. And so, for example, the standard model of particle physics, if you Google like what is the equation of the standard model, it shows you this thing that starts with L equals and then a bunch of terms. That's the Lagrangian of the standard model, and the action is the integral of that. And so the way we specify what's in the universe, what's out there, all we have to do is say what the action is. What are the pieces of the action and how do they interact? And everything else falls out of that.

37:58Literally all the equations of quantum mechanics and quantum field theory, say if you have this action, then all these things happen. So the game of particle physics these days and of all physics is to say, well, what is the action of the universe? We try lots of different things. We try this, we try that, we try the other thing. And the ones that turn into rules that align with what we see out there in the universe, those are the ones we go with. So the standard model of particle physics is just a description of the action of the universe, not in terms of kinetic energy of a ball, but in terms of the fields, their motion and actually in terms of their oscillation, their kinetic energy and their potential energy.

38:37Okay, so this seems pretty exciting because, you know, you and I have been recording for over a year now, and I don't feel like there have been a lot of instances where we've talked about things that play nice with both classical mechanics and quantum mechanics. And that could be because my memory is kind of like a sieve, but I don't think so. So is this pretty rare? This is pretty rare, and it's actually a beautiful way to think about the connection between quantum mechanics and classical mechanics. And it gives you some insight into like our classical world. Because when you're calculating the quantum mechanical action, you don't just think about an individual path.

39:13You think about all the various paths. Perhaps people have heard about like the Feynman path integral approach to quantum mechanics. We imagine like an electron goes from here to there. You don't just think about one way for it to go from here to there. you think about all the possible ways. Well, what's happening there is you think about all the possible paths. And in classical mechanics, you say, okay, I'm going to choose the one path that minimizes the action. In quantum mechanics, what you do is you take each path and that path has a complex number multiplied by it that depends on the action.

39:46So you have all these paths and each one has this complex number in front of it. And the paths near the least action all interfere constructively with each other. These complex numbers allow them to contribute together. And the paths where the action varies a lot interfere destructively, so they cancel out. And so what's happening here is that all the paths are contributing, but just like in famous quantum mechanical experiments, the ones that are far from the least action destructively interfere with each other. They cancel themselves out. And so what happens is that you end up with this like envelope of paths around the least action.

40:23And this is sort of fascinating because that interference depends also not just on the action, but on Planck's constant h-bar. And as h-bar gets bigger, you get more contributions from paths near the least action. And as h-bar gets smaller, you get fewer contributions from paths near the least action. So now here you have a knob that you can very smoothly. You say, I'm going to crank h-bar all the way down to zero. What happens is that you have only a single path contributing. That's classical mechanics. Classical mechanics is quantum mechanics with h-bar set to zero. If you crank h-bar up to some number, then you start to get quantum effects where you have contributions from things near the least action path.

41:04And that's the quantum effects that we see. If you cranked up h-bar beyond what it is in our universe, quantum mechanics would be more obvious, right? And so this shows you that there's like not just a smooth continuum where classical mechanics sits on like one edge of it, right? But also that classical least action emerges from quantum interference. The reason it seems like we live in a classical world is because H bar is so small that it looks almost like it's zero from our point of view. And you can understand that very clearly using this least action approach and thinking about all the various paths that the particle would take.

41:42And so does thinking about things from a least action approach make you feel more confident that we're going to be able to one day sort of marry these approaches a little bit more effectively? Or not necessarily? No, it's the most sensible way to think about the relationship between quantum mechanics and classical physics. Essentially thinking about classical physics as like a zoomed out version of quantum mechanics. And we talk a lot about how, you know, classical physics emerges from quantum mechanics. And we say that's kind of a mystery because we don't know how to go from the laws of quantum mechanics, you know, Schrodinger's equation for an electron, to zoom out to get F equals ma for a ball flying through the air.

42:25And that's true for the force picture. But in the action picture, we actually do kind of know how to do that, which is amazing. And so there is this connection between classical physics and quantum physics, where classical physics is an extreme version of it. So that's very beautiful. And unfortunately, that doesn't solve like the bigger problems in physics, which is like how to integrate gravity into quantum mechanics. But amazingly, you can also think about gravity from an action point of view. It's a very natural way to think about general relativity. And when we get back from the break, that's exactly what we're going to do.

43:08Eczema is unpredictable, but you can flare less with Epglyss, a once-monthly treatment for moderate to severe eczema. After an initial four-month or longer dosing phase, about 4 in 10 people taking Epglyss achieved itch relief and clear or almost-clear skin at 16 weeks. And most of those people maintain skin that's still more clear at one year with monthly dosing. EBCLIS, Librikizumab, LBKZ, a 250 milligram per two milliliter injection is a prescription medicine used to treat adults and children 12 years of age and older who weigh at least 88 pounds or 40 kilograms with moderate to severe eczema.

43:39Also called atopic dermatitis that is not well controlled with prescription therapies used on the skin or topicals or who cannot use topical therapies. EBCLIS can be used with or without topical corticosteroids. Don't use if you're allergic to EBCLIS. Allergic reactions can occur that can be severe. Eye problems can occur. Tell your doctor if you have new or worsening eye problems. You should not receive a live vaccine when treated with EpGliss. Before starting EpGliss, tell your doctor if you have a parasitic infection. Ask your doctor about EpGliss and visit epgliss.lily.com or call 1-800-LILY-RX or 1-800-545-5979.

44:08Every business has an ambition. PayPal Open is the platform designed to help you grow into yours with access to business loans so you can expand and hundreds of millions of PayPal customers worldwide. Your customers can pay all the ways they want today with PayPal, Venmo, Pay Later, and all major cards so you can focus on the future. When you need a partner trusted by millions, there's one platform for all business. PayPal Open. Grow today at paypalopen.com. Loan subject to approval in available locations. Hey everyone, it's Cal Penn. I'm the host of Earsay, the Audible and iHeart Audiobook Club.

44:46This week on the podcast, I'm sitting down with Ray Porter, the narrator of Andy Weir's audiobook project, Hail Mary. massive sci-fi adventure about survival and science and what happens when you wake up alone very far from Earth. I really had to make a decision because I caught myself getting that frog in my throat and starting to get teary as I'm narrating some of these sections. And it's like, okay, yo, yo, yo, is this indulgent? And I really thought about it. I was like, no, at this point, it would kind of be betraying the trust the author and the listener have in telling this story if I don't go through it.

45:23But there's places in this book that deeply emotionally affected me. And I left it on the mic. That's great. Because it served the story. People will say like, oh, my God, I cried at the end. It's like, yeah, dude, me too. Listen to Earsay, the Audible and iHeart Audiobook Club, on the iHeartRadio app or wherever you get your podcasts. This is Jacob Goldstein from What's Your Problem? Business software is expensive. And when you buy software from lots of different companies, it's not only expensive, it gets confusing, slow to use, hard to integrate. Odoo solves that because all Odoo software is connected on a single affordable platform.

46:02Save money without missing out on the features you need. Odoo has no hidden costs and no limit on features or data. Odoo has over 60 apps available for any needs your business might have, all at no additional charge. Everything from websites to sales to inventory to accounting, all linked and talking to each other. Check out Odoo at O-D-O-O dot com. That's O-D-O-O dot com.

46:38All right, so now we're going to talk about what least action can tell us about gravity. Did I say that right? You totally did. You sound like a physicist. Oh, that's great. Now I'm going to get invited to all the parties. And I meant that, of course, if it wasn't obvious, 100 % as a compliment. And I took it 100 % as a compliment. I'm glad there wasn't any doubt. No, never would be. All right. So we've been talking about least action and the way that it helps us reimagine classical physics as stuff moving from A to B, not because of the forces, but because it's the path that minimizes the action.

47:16And then we talked about how you can even use this in quantum mechanics, and it provides a nice bridge between classical physics and quantum physics. But folks out there are, of course, aware that one of the biggest struggles in physics is to unify quantum mechanics with gravity, their classical theory of space-time and how things move. And so is action something we can use to understand gravity? And the answer is yes. In fact, it's quite natural because general relativity already has very similar minimal principles, right? The principle of least action says you find the path that minimizes the action.

47:54Well, already in general relativity, light, for example, follows the path that minimizes its travel time, right? And in general, things in general relativity follow paths called geodesics. geodesics are the shortest distance from A to B, right? And you can calculate the shortest distance by calculating the action across that path, where in this case, what is the action? It's the curvature, the curvature along your path. So to figure out in general relativity how something will go from A to B, you find the path where along which you minimize is not cadetic energy minus potential energy, but the action of general relativity, which is just the curvature of space.

48:41And so you can say, all right, my action is the curvature of space. And then you say, find me the paths that minimize the action and boom, all of general relativity pops out from there. All of Einstein's equations just flow from specifying the action to be the curvature of space. It's really kind of incredible. So I have a question. So the curvature of space is influenced by gravity or is reflected by gravity. Gravity is the motion of things under the influence of the curvature. Yeah. Okay. So the equations that we were talking about were kinetic energy minus potential energy and potential energy has gravity in the equation.

49:17But when we think about general relativity, are we not using those equations? Or like, how does it mess things up that the term for gravity is in the equation? Yeah, great question. So when we were talking about our simple scenario of a ball moving under as a parabola, We were doing classical physics, but we weren't thinking about general relativity. We had a very simple model of objects with kinetic energy and potential energy. And we were assuming gravity was constants and g was just a number. Now we're totally generalizing that. And we're going to solve for any sort of motion of any object through space and time.

49:50And the same equations do pop out, but we're doing Einsteinian gravity now instead of Newtonian gravity. The previous version was thinking about gravity as a force. Now instead, we're doing general relativity. And so we're not calculating action as kinetic energy minus potential energy. That's the Newtonian way. We're calculating in the Einsteinian way. And the incredible thing is that you can just specify the action and all of general relativity comes out. This is sort of why action is super amazing because you specify it and you have this one set of rules. Find the paths that minimize the action and that tells you all of the physics.

50:27All of the physics comes out of that. Tell me more physics that comes out of it, Daniel. Well, the challenge now to unify quantum mechanics and gravity is to find an action which has both gravity and quantum mechanics in it. And we know how to define quantum mechanical action, and that gives us all quantum field theory. We know how to define general relativity action, and that gives us all Einstein's equations. We don't know how to find a unified action for both of those things. So that's sort of the question of quantum gravity now expressed in terms of this action principle. What is the action that includes both curvature and quantum mechanical fields?

51:03We don't know that. But if we could figure that out, then we would know what exactly? If we could figure that out, then we would have the laws of quantum gravity. Okay. Yeah, absolutely. And that would be amazing. Yeah. But we can also like zoom in on one part of this to give another example, like Maxwell's equations. Maxwell's equations are these four equations. They're kind of complicated. They have all these differential terms in them, you know, changing electric fields, cost magnetic fields, and vice versa, all this stuff. It was a huge stroke of genius when Maxwell unified these and then Heaviside clarified all of them a century or so ago.

51:39Now, it turns out that all of Maxwell's equations pop out if you apply this minimal action principle to a vector field. We know that the electromagnetic field is a vector field, meaning that every point in space is not just a number, but like a little arrow. So it has a direction and a length. And if you say, I have a vector field, and I'm going to make some simple requirements about symmetry, like there's going to be no preferred frame of reference, or there's no ether, for example, then that really constrains the kind of action that you can have. And there's basically only one way to write it.

52:13And from that way of writing it, boom, Maxwell's equations pop out. And so you might wonder like, well, where do Maxwell's equations come from? Well, this tells you if you have a vector field that respects some basic symmetries, there's only one set of equations that minimize the action of that field. Those are Maxwell's equations. And so it tells us something maybe deep about the universe, that maybe everything that happens in the universe comes because the universe is minimizing action and only actions that respect some of these symmetries. Huh. Okay. So I'm still feeling grumpy at whoever called it action, but it feels like this is so fundamentally important that this is like Nobel Prize territory.

52:55So like who figured out this action thing? Yeah. Action has been around for a little while. Hamilton and Lagrange both came up with this alternative formulation of classical mechanics more than 100 years ago before the Nobel Prize even was conceived of and sort of generalized classical mechanics. And then it was Neuther who really gave us some deep insight into it because Neuther's theorem is this really deep theorem of physics that relates symmetries with conservation laws. It says like, well, where does conservation of momentum come from? Why does that happen in our universe? Well, it happens because of a symmetry.

53:32The symmetry is translational symmetry. That doesn't matter where you do your experiment. If you build a large hadron collider here or around Jupiter or in another galaxy, you should always get the same answers. Space is the same everywhere. That's where conservation and momentum comes from. And check out our whole episode on Neurther's symmetry. But there was a crucial detail we glossed over in that conversation. Those symmetries that we talk about in Neurther's theorem, those are symmetries of the action. And we didn't dig into it in that episode because, as you see, action is a whole set of baggage to introduce.

54:05But it's only symmetries of the action that give conservation laws. So that means that you write down your action, maybe it's kinetic energy minus potential energy, or it's the curvature of space, or it's quantum field action. If that action is the same here and Jupiter and Alpha Centauri, then you get conservation of momentum. And so it's symmetries of this action specifically that Noether showed us give us conservation laws. So Noether's theorem is a deep insight not just into where conservation laws come from, but why action is so fundamentally important. Seems like she clearly should have gotten a Nobel.

54:43She should definitely have. And these principles really guide the way that we do particle physics. When we devise the action of the standard model, we have to have those symmetries because we know those symmetries will give us the kinds of conservation laws we see in the universe. We see momentum is conserved, and so we can't build actions that don't respect the symmetry that gives us conservation of momentum. And it's a bunch more symmetries that we know we have to have in our action. So when you're devising an action, there's not a lot of choices to make because you're really restricted by all of these symmetries.

55:20You can't just add terms willy-nilly because they would break these symmetries. And so if you wanted to start from scratch and devise a new action for quantum field theory, there's really only a couple ways you can do it that respect those symmetries. We're super duper limited. And so it feels like those symmetries tell you what can happen in the universe, right? What's possible. And the action tells you what does actually happen. And so like all of physics is basically that, right? What are the symmetries of the universe? And then what actually happens is, well, what minimizes the action on those symmetries?

55:59And so it's a completely different way of thinking about the universe instead of like the way you were describing, which I think is very intuitive and Newtonian of like thinking about the universe frame by frame, what's happening, let's update things in a sort of like computational simulation sort of view. Instead, it's thinking about how things go from A to B to minimize the action along that path. So when you were saying devise a new action, I'm having trouble wrapping my head around what that means. Because every time you've said action, in my head I have subtracted two different kinds of energy.

56:32So what does it mean to devise a new action? Is that like think of a different path that something could take? Well, everything comes from the action, right? So you want to describe the universe. You write down an action. you apply this minimal principle, it predicts how things will move. And then you compare that to what you actually see out there. So in the case of a ball flying through the air, if I want to describe that, it works if I write down kinetic energy minus potential energy. If I write down kinetic energy minus three times potential energy, it doesn't work. If I do kinetic energy times seven minus two potential energy, that doesn't work.

57:05It doesn't describe what I'm seeing out there in the universe. So if I want to describe the universe, I have to find some way to describe the action so that minimizing that action gives me the things I see out there in the universe. You were using the word action the way people people actually use the word action and the word action the way physics people use the word action. And that's what was, okay, I get it now. You were using it both ways. Oh, oops. And so kinetic energy by potential energy is a good approximate action for that one scenario we were talking about, throwing a ball in your backyard.

57:41The action of the universe, we don't know because we have an action for quantum field theory, an action for general relativity. We don't know how to put them together. But the goal of physics now is to find what is the action of the universe? Because once we know that, we know what it does. And this is a different way of thinking about the universe. And it relies on knowing where something was and where something will be and figuring out the path between them. And that's a very different way of thinking about sort of computationally frame by frame. And it has this sort of feeling, this flavor to it, as we were talking about earlier, that the present depends on the future.

58:17Like if you imagine a photon going from here to there, and we know the photon follows the path that takes the least amount of time from here to there. But when the photon is like halfway along the path, we don't know where it's going to go yet, right? It hasn't gotten there yet. So how does it decide where it's going to go in order to minimize the total path when we haven't figured out yet where it is going to go, right? It feels like sort of backwards or it's like depending on the future in some way. And this was the vague feeling that inspired Ken Chi-ing's short story, which inspired the film Arrival.

58:52The idea that maybe aliens come and they don't see time in the way we do flowing from the past to the future. They experience all of time like a book and they can rifle forwards and backwards. And it's inspired by this exact concept. But it's a little bit of a, I don't know if it's a misunderstanding or a misrepresentation, because there is no actual retro causality here. You don't have to know the whole history of the universe to solve these problems. It is true that the path depends on the final destination, but you can't change that final destination. It's not like you can influence the present using the future.

59:33There is a dependence on the future outcome, but it's not like you can control that. So you can't change the photon's path halfway through. So there is a subtlety there, which is crucial for the movie Arrival to work as a story, but fundamentally it's at odds with the actual physics of it. I like seeing you be a wet blanket too. All right. So we started this whole thing with the question, why does the universe minimize action? So now we've explained what action is and how minimizing action gives us all of the physical laws we already discovered in other ways and turns out to be a very general principle is connected to symmetry and helps us think about quantum mechanics and classical mechanics together and maybe tells us that our concept of time is a little bit archaic and needs to be updated.

1:00:19But what is the answer to the question, why does the universe minimize action? And the short answer is, we don't actually know. it's hard to think about action philosophically because it doesn't have a simple intuitive analog. Like forces, they make sense, right? We see forces happen. It's easy to think about the universe as fundamentally a set of matter and forces acting on that matter because that's sort of the way our minds work, right? But whatever action is, it seems to be vitally important to the universe. Even if it doesn't have a natural intuitive analog in our minds, that doesn't mean it's not the fundamental principle of the universe.

1:00:57And so philosophers, of course, have latched onto this and they have raging arguments about what action is and what it means. Some suggest that what it means that the universe minimizes action is this constructive interference principle that like all possible histories do actually exist. It's just that most of them cancel each other out. And the universe minimizes action because the least action path is the only one that survives constructive interference between all of these paths. What happens to the other Kellys? They cancel themselves out. No. Yeah, I know. There's a plus Kelly and a minus Kelly out there that end up at zero.

1:01:36What? Yeah. But they're equally valuable Kellys. Well, in the end, the universe minimizes action not because it's lazy or because it prefers simplicity, but maybe just because only self-supporting things can exist, things that persist and be observed as law-governed are things that don't interfere with themselves, that reinforce themselves. But it's still an open question. Our job as scientists and as curious beings in the universe is to be open-minded about how the universe works, figure out those laws, and then just take a step back and be like, hmm, what does that mean about the universe that it does this instead of that?

1:02:18Why is this thing so important to the universe? And that's the juicy part. And that's the part we have not deeply understood. All right, friends, so put another tick in your tally of DKU episodes that end with us saying we don't know. So we've done a deep dive into action, which I always wanted to do. But even still, there are a few places where I was a little bit imprecise to simplify things. So for those of you listening very closely, and I love all of you, there are some additional details I want to mention. First, I said often that action is the difference between kinetic and potential energy.

1:02:53Technically, that's the Lagrangian density, and the action is the integral of the difference between the kinetic and the potential energy. Similarly, for GR, the action is not just the integral of the curvature, it's a volume integral of the Ricci scalar, which is something that measures the curvature, but it also includes the determinant of the metric tensor, and a couple other things. Secondly, I talked a lot about the principle of least action, implying that the action is always minimized. But the actual statement is that the action should be stationary, which in calculus means its derivatives vanish.

1:03:27That means that it can be a minimum, and it often is, but it could also be a maximum or even a saddle point. In the case of geodesics, for example, there are several different kinds of geodesics. Space-like geodesics minimize the distance, cool. Time-like geodesics actually maximize the proper time. And then null geodesics for light have no proper time. Finally, remember that the future does not depend on the past. The path we calculate using action between the past and the future depends on the boundary conditions, including the future and the past ones. So knowing where and when the object starts and ends.

1:04:06And we look forward to seeing you next time. And I hope this has given you another way to think about how things happen in the universe and why some things happen and other things don't. In the end, it all minimizes the action.

1:04:25Daniel and Kelly's Extraordinary Universe is produced by iHeartRadio. We would love to hear from you. We really would. We want to know what questions you have about this extraordinary universe. We want to know your thoughts on recent shows, suggestions for future shows. If you contact us, we will get back to you. We really mean it. We answer every message. Email us at questions at danielandkelly.org. Or you can find us on social media. We have accounts on X, Instagram, Blue Sky, and on all of those platforms, you can find us at D &K Universe. Don't be shy. Write to us. Running a business shouldn't feel like surviving a software group project.

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