What is negative temperature?

00:00:08
Speaker 1: Hey, Jorge, do you have any concerns about raising your kids in southern California? I don't. It's pretty great out here, although I do feel like they miss out on some things they do. What's missing in southern California? Well, definitely not plastic surgery, we got that covered for sure. But you know, there are experiences kids growing up here that they don't get that other kids do. Yeah, like what you know, like experiencing winter, snowfall. I mean, I guess I miss winter, but I wouldn't say I'm missing winter. Would you say, you know, misshoveling snow, putting on multiple layers of clothes, multiple layers of clothes. What does that even mean? Man? If you're like layers of clothes, what does that even mean? I'm recording this naked. You don't think kids should know about winter? No, I'm definitely anti winter. That's when I'm teaching my kids about winter avoided at all costs. But what if they don't? What if they end up living there and then are you going to go visit them? Depends how cute grandkids are. I guess that's pretty coold. Daniela, Hi, I'm or handmade cartoonists and the co author of Frequently Asked Questions about the Universe. Hi, I'm Daniel. I'm a physics professor at u C Irvine and a high energy physicist, and I definitely prefer high energy air molecules. You don't like low energy air? No? I like it hot outside. You know, when I moved to California, I discovered that sunshine makes me happy. Do you think maybe that's your upbringing? You grew up in New Mexico, right, and then you went to school in Texas. I did. I'm a desert person, but you know, New Mexico was pretty cold. Los Almos is seven thousand feet in elevation, and so we got a lot of snow. I remember one year we got fifty five inches overnight. I was not a happy camp Well, so you'm are of a desert person or a dessert person? Dessert in the desert, and do you like your desserts hot or cold? I like them both. I'm not picky. But anyways, welcome to our podcast, Daniel and Jorge Explained the Universe, a production of My Heart Radio in which we are hot on the mysteries of the universe and we think that everything about it is pretty cool. We want to understand how the universe works, what the rules are that govern how it operates, and whether or not we can understand them. We think one of the most fundamental questions about being alive, about being human, is why are things the way that they are? And what else could happen in this universe? That's right. We don't give a cold shoulder to the big questions out there because it is a wonderful universe full of amazing things, and sometimes we wish we could freeze it all so we can study it a little bit better. That's right. These are hot topics for us to understand, and as we look out around us in the universe, we want to understand why some things are the way they are, Why some things are hot, why somethings are cold, Why hot things tend to heat up cold things, Why cold things tend to cool down hot things. Yeah, because we want people to warm up to the extremes of the universe and all of the amazing things that can happen and many different temperatures out there. The universe has a pretty wide range from super hot explosive supernovas and hearts of neutron stars really vast voids of empty space exactly. And one of the best ways to understand how the universe works, to make it reveal it is underlying truth, the rules that governed it, is to look at the extremes to find out what is the most of something that can happen. How bright can things get, how fast can this spen, how empty can space be, how dense can matter be? So on this podcast, we'd like to explore those extremes because we think those are the places that the universe is cornered, is forced to tell us something about how the rules work. These are the edge cases, the ones where we hope the truth will reveal itself. Yeah, we have a whole series of episodes where talk about extreme things in the universe, the coldest, the brightest, the biggest. Daniel have we done the most delicious thing in the universe yet? That's just been a side research project of mine for a long time. You're just gathering data more and more every year. Yeah, you know, I'm not trying to mind my personal experience for podcast episodes, but that's a good idea. Or maybe the most delicious thing in the universe is the universe. It's a pretty tasty place. Well, the universe is the only thing in the universe, right, so it's both the most delicious and the most disgusting thing to eat in the universe. Also the most filling, I guess. But we have done a whole series of episodes on extremes and we encourage you to go back through the archive and check them out. But we did do those sort of the hottest and coldest things in the universe. Those are two episodes you can download, right, Yeah, that's right. And we recently organized a curated list of all of our episodes on our website. Listeners have been asking for us to sort the episodes by topic, and so now we have them grouped by cosmology or particle physics, or science fiction or extreme universe. So go to our website Daniel and Jorge dot com and look at the list of episodes by topic. Yeah, so it's kind of like a menu. So if you're feeling like, hey, you know, I could use a little cosmology today, or I could use a little you know, fundamental particles with my meal, you can go and help yourself. That's right, Order up a side dish of black holes. So we have talked about temperature a lot in this podcast, But recently you've got in a few questions about a new and interesting topic that's kind of floating out there, right exactly, Folks are interested in the extremes of temperature, all the way down to absolute zero, or all the way up to absolute hot, the hottest that things can get in the universe before temperature doesn't even make any sense. But over the last year so I've gotten a few emails asking me to talk about something that sounds like it makes no sense at all, something that has been bouncing around on the internet and inspire the curiosity of several listeners whether or not it's possible to go even below absolute zero. So today on the podcast, we'll be asking the question, what is negative temperature? Negative temperature? What now, Daniel, is this temperature that is not an optimist or what always looks on the dark side of things? Yeah, this is grumpy temperature exactly, whatever makes you feel bad. It's not how positivemperature. Yeah, this is a weird concept. I guess, well, I guess people are familiar with negative temperature, right, Like in some places it gets so cold it's like minus fifteen degrees, right, yeah, And like negative forty is where celsius and fahrenheit meat so on some scales, negative temperature is a pretty common experience. But I think people are probably thinking about Kelvin. You mean this physical concept is more about absolute temperature and whether or not it can be negative. Yeah. The Kelvin scale goes from zero, which is supposed to be this scenario where nothing is moving and everything is basically frozen up to very high values when things are wriggling around. So from that perspective, you know, like, what does it mean to have negative of temperature? Can you move less than not moving at all? Right? That is pretty weird. But is that maybe just the scaler thing, like we use the wrong scale. But no, because it's absolute temperature, right, there are like hard limits or at least I thought there were hard limits to absolute temperature or the Kelvin scale right zero to infinity kind of zero to the plank temperature. Actually, there is this maximum temperature beyond which we think that gravity will take over in quantum gravity effects will be important And we don't even know what temperature means there. Wait, what it's called absolute hot? Absolute hot or absolutely hot? Absolute hot is absolutely hot? For sure? It sounds like a new vodka brand, but it touches on these interesting questions of like what is temperature anyway? You know, as human as, we have experiences in the world, and then we try to build models, physical ideas that describe those things. And then we have to find a way to like mathematically express some things that we experience temperature or something that's like very tuitive to us. But in our physical models we need like equations and numbers to describe these things. And sometimes that's easy to do, like velocity or location, and sometimes it's a little bit fuzzy, and so we're gonna get into like what does temperature really mean anyway? Man? Yeah, So we have this temperature in the absolute temperature within the Kelvin scale, and so for example, like what is room temperature in kelvin zero and celsius corresponds to two hundred and seventy three in kelvin, So comfortable temperature in celsius is like twenty five, which would be like two hundred nineties something in kelvin. Okay, so room temperature is two hundred ninety eight, let's say in kelvin, and then freezing is two d seventy three, And I guess what temperature does water boil, so it would be three three, three seventy three or a hundred celsius. Okay. So then as you start to cool things and make things colder, the kelvin goes down and down and down and down. And I think we talked about what is the coldest thing? We've gotten something here on Earth? Right, Yeah, we have on the coldest thing in the universe and the coldest thing on Earth. And physicists regularly do experiments with super duper cold objects, things that like the micro kelvin temperature just about what we thought was the absolute minimum temperature, which is actually a tiny little bit above absolute zero, that's right. We talked about how the maybe the coldest thing in the universe is something you're on Earth that scientists have been able to cool down to almost zero kelvin zero point zero zero zero zero zero zero one kelvin. And so the question is can you actually go below? Right? Is there such a thing as negative absolute temperature exactly? That is the question today? Or is it even possible? I guess? And what are physicists thinking? So as usually were wondering how many people out there had thought about this question or wondered whether temperature can go negative? And so Daniel went out there into the internet or your campus. These are Internet answers and thanks again everybody who volunteers to answer these weird email the questions. If you'd like to receive some strange questions for future podcast as episodes in your inbox, please don't be shy or right to us two questions at Daniel and Jorge dot com. That's right, and you can be as positive or as negative as you want in your answers. But think about it for a second, right now, do you think absolute temperature can be negative? Here's what people had to say. This is a loaded question. Um, but if my bank account can have a negative balance, so too can a cemometer unless it's measuring in kelvin. He never goes Belusira. Well, because you're asking this, I'm going to assume that that's what the topic is. But right, persons think would be you can't you can't have a negative temperature because I'm thinking like kelvin, right, I mean, obviously you can have like a negative celsius or something, but like you can't have like a negative like kelvin amount of temperature. So no, I don't think you can. I think it zero Kelvin the molecules actually stopped moving. Not molecules, I mean particles actually stopped moving as far as I know, probably wrong, but that's my understanding. Well, on the Celsius and Fahrenheit scales, you can have a nick it of value for your temperature, but on the Kelvin or ranking scales, with positive temperature being amount of energy and zero absolute zero being um no heat energy. In that case, for a negative temperature, you would have to have this um. You'd be like a black hole of energy, or just the potential to absorb energy from somewhere else. But maybe you don't actually exist and you're just something mathematicians use. Like I my first impression would be no, I don't think you can, since if your particles are studic, then your temperature would be absolute zero. I don't I don't know. Maybe unless the particles are moving back in time some way, then you could have negative temperature. I really don't know. I'm making this up as I go, Daniel, I think you forgot about you how you moved in California, and you forgot that you can go negative during the year. I do not believe it's possible to have a negative temperature. There is a reason why absolute zero is called. Absolute temperature is the sum of the kinetic energy of the particles of the objects being measured. And I don't believe something can have negative motion unless there is some oddity and the fact that measuring motion requires the existence of a reference point, and with a boundless, infinite universe, where is that absolute reference point? But otherwise there is no possibility for negative temperature. I'm going to go with no. And also it depends on what context we're talking about this in. For example, if you're dead, I think your temperature can be negative because you'd be frozen in a refrigerator or something. But as a living human being, having a negative temperature I think would be impossible because we are made up of water and that water would freeze if it was a negative temperature, meaning we wouldn't be able to be alive. Um, blood would not be able to move, our heart couldn't beat, and things like that. Mmm. Okay, a lot of negative responses, not a lot of positive yeses. No, not a lot of believers in negative temperature, but some good creative answers you think they should have been more positive, like yes, maybe it can. I believe in your universe. You're beautiful. I think that they should have had more faith in physicists to break the rules and think outside the bounds of what is normally possible. It should have been more temperature positive that it can be negative exactly because you know, the history of physics is littered with examples of doing things that we thought were once impossible, of discovering the universe works in a way different from the way that we had imagined, of breaking the rules that we once thought were iron clad. Are you saying physicists just basically do things and they're like, you have some kind of chip on your shoulder, Hey, Daniel, I dare you to understand the universe. I think it's exciting to imagine what's impossible might be possible, to think about it. You know, that's the job of science fiction authors to think, could we get to a nearby star faster than the speed of light? How might that be possible. It's also the job of physicists to think, like, what are the actual rules of the universe? Which ones can be broken, which ones can be bent, which ones seem like rules but only in certain circumstances, and actually aren't fundamentally rules at all, although I guess you have to be careful, right, Like you don't want to dare a physicist to find a way to blow up the world or create a black hole in the center of the of our planet. Yeah, I think we've tried that already. Actually, I see you were there and that what. I guess you gave up? You I hope, well, I hope or failed. No, we are still trying to create black holes. It's a large hager on collider. In fact, we recently turned the collider back on a few weeks ago. Oh man, you're not gonna give up, are you? You know, just after we turned on the collider, the government of the UK collapsed and Boris Johnson was forced to resign as Prime minister. Really, do you think there's a correlation there. There's definitely a correlation. I don't know about causation. We'll have to turn the thing on and off a few times and see what other governments fall. I think there are other things going on besides you switching on the collider, just you know, a few things here and on on our world stage. I don't know. I don't keep up with politics, man, So I see you just flip on the switch. All right, Well, this is a fascinating question. Can absolutely temperature go negative? Can it be minus something degrees absolute? And so Daniel, that is a weird phrase, negative temperature. What does it mean? It all comes down to what we mean by temperature. And normally when we talk about temperature, we're talking about how hot something feels. You know, you touch something it feels hot, you touch something it feels cold. You have a sense for whether it's hot or cold outside. That's about like the energy flow between you and some other object. But we also have a concept for like what's going on inside, like micro physical picture of why some things are hot and some things are cold. What's going on inside something that's hot that makes it different from something that's cold. And this eco physical picture mostly is about like how much the atoms inside are moving, Like if they're zooming around a lot and jiggling a lot, if they have a lot of energy, then the thing they make up feels hot. If they're mostly not moving, they're not jiggling or whizzing around, then the thing they make up feels cold. Right, And we have ways to measure that, right, like we have devices that called thermometer, as you probably know that. Can I tell you a little bit about that kind of internal moving around of things. Yeah, And what's interesting is that thermometer is measure things that are related to temperature. None of them actually directly measure temperature itself. Wait, what a thermometer does not meter metter temperature? I know it's called a thermometer, but it doesn't actually meter thermo. I mean, take, for example, the classic bulb thermometer. What is it. It's a little pot of liquid with a tube above it. And what it's really measuring is the volume of the liquid because there's a relationship. As the liquid gets hotter, its volume increases and so it climbs up that cylinder and so you're not directly measuring temperature. You're measuring the volume, which is you think related to the temperature. Right. It's like those glass tubes with the little red line. What's actually happening is that when you stick it into like let's say, boiling water, it heats up the little red liquid and it expands. And then the more it expands, I guess, the hotter the water was. But you're saying it's not actually measuring the temperature of the water. No, it's measuring the volume of that little red liquid inside the thermometer, which of course is related to temperature, but it's indirect, right. There are other ways that are also indirect that you can measure temperature, like the thermostat in your house, the one that decides whether or not to turn on the air conditioning, that doesn't have a little ball of liquid in it. It has something called a bimetallic strip. It has two kinds of metal bonded together, and the two kinds of metal have different properties. One of them expands faster when the heat up than the other one. So if the metallic strip heats up, then it tends to bend in one direction because half of it is expanding faster than the other one, and then like closes some circuit and decides to turn on your air conditioning. So that's measuring the bending of this piece of metal, which again is related to the temperature, but it's one step indirect, right. Well, I mean, maybe it depends on what you mean by measure, but it does sort of measure the temperature of the metallic strip, right, which is I guess related to the temperature of the air around it. Yeah, I mean it's measuring the bending of the metallic strip, which is related to the temperature. Right, Like, how would you actually measure the temperature directly? You'd have to go, like measure the velocity of those particles themselves inside the object, how much they're wiggling, and that would tell you the temperature. Instead, you're measuring something which is determined by that property. So, I mean, I'm not criticizing thermometers. I'm not saying the whole thing is a hoax. Right, it's not a scam. Are you anti thermometer? I'm grow thermometer. You're saying it's all a big pharma conspiracy. No, But if we're going to think carefully about what temperature means, and let's think about what our devices are actually measuring, what they're really probing, and not just what numbers they're reading out, maybe we should have a disclaimer. You know, you should trust your thermometer. If it says you have a hundred and six degray fever, maybe you should call a doctor. Yeah, I'm not a thermometer denier or anything like that. You're a temperature denier. No, I'm not like that guy who says birds aren't real. All right, Well, that that so what you're saying. Usually we measure things like the effects of temperature and not maybe what we define temperature to be exactly. Yeah, that's right, But we do have a model again for what temperature is. We imagine that what's going on inside that liquid or inside the metal is that they're made of atoms, and those atoms wiggle and move or they fly around or they flow around, and the degree of that motion is we usually what we talk about for temperature, but this is a model of temperature. We call this the kinetic model of temperature. Is this idea that something is hot when the atoms inside of it have more kinetic energy, and something is cold when the atoms inside of it have less kinetic energy. And it's not just motion, like, it's not just velocity. You can also have spinning and vibrating and all this kind of stuff, And so it's related to this idea of kinetic energy, right, how fast things are moving. So from that perspective, you might imagine like if temperature is related to kinetic energy, or kinetic energy is either zero or more than zero, so how could you possibly have negative temperature? Right? It seems like that should tell you that temperature is zero or above zero, right, because you're saying it's sort of a measure of the I guess the average kinetic energy of of something, And I guess if it's air, you're measuring the kinetic energy of the air particles flying around. Those have kinetic energy. But if it's like a block of wood or a block of metal, then I guess the atoms aren't moving around, but they're still vibrating and bumping against each other. Right, And so you if you kind of were to measure all of those particles and take the average velocity and I guess squared it and all that, then you would get the temperature. Yeah, And there's some mathematics you can look up about exactly how tempered sure is defined based on the number of degrees of freedom, the number of ways you can move or wiggle and all this kind of stuff. But that's the basic idea for your classic definition of temperature. Right, average energy, and in fact, kinetic energy you calculated by squaring the velocity of something, right, which means that it should always be positive. Yeah, kinetic energy is always positive, right, unless I guess you have imaginary energy. Unless I imaginary velocity like I imagined I went to the post office today, but I didn't because he had negative energy because I didn't eat enough dessert in the desert to fuel my trip. There you go, easy solution. All right, Well, let's get into what exactly is temperature, whether that definition of temperature as kinect energy makes sense, and whether or not it's possible for it to be negative. But first, let's take a quick break or I we're asking a pretty trippy question, which is can you have negative absolute temperature? Which is sort of an oxymoron, right, negative absolute because absolute usually means it can only be positive. Mm. Yeah, it's a pretty psycho kind of idea negative temperature, and it really gets at the heart of this question, like what is temperature anyway? You know, which we talked about several times on the podcast, because it's kind of a slippery idea. Yeah, and I know you sort of hate talking about it, right, you know you're not a fan of thermodynamics. Wait, is it because you're a thermodenier? Is it? It's all making sense now, it's because it's complicated, and thermodynamics involves like thousands and thousands or millions or billions of particles. I like thinking about individual particles bouncing off each other, really reducing the universe down to the simplest little bits and their rules. It's hard to think about swarms, you know, Right, does that mean you're antidemocracy, Daniel, I don't pay attention to politics, right the official line. Oh, that's right, we forgot form. We established that earlier. Yeah, it kind of gets into the question of what is temperature anyway, Like is it really the kinetic energy of the particles inside of it? And what does that even mean? It is really interesting question and we talked about it several times. Even in this idea of temperature as like the kinetic energy of particles, you can ask weird questions like what's the kinetic energy of one particle? Can a single particle have kinetic energy? Well, a single particle can, right, You're wondering if it can have temperature? Yes, can a single particle have temperature because it can have kinetic energy. And that sort of shows you something about the limits of this idea of temperature as kinetic energy, because we mean more by temperature than just like how much energy is in something. We also mean something about how heat flows. Right, we have this intuitive experience that we want to somehow describe as if you put like a block of ice in your coffee, then the ice will melt, right because the heat will flow from the coffee to the ice cube. So temperature is also about how how heat flows. He tends to flow from hot things too cold things, So when we define temperature, we also want this idea of heat flow. But I guess you're saying there's some sort of tension between our intuitive understanding of temperature and maybe the official physics definition of it, because I guess you know, we talked about the hottest things in the universe, and one of the hottest things in the universe is is kind of empty space, right, or at least mostly empty space, because it's mostly empty, there's not much in it, but there are particles in it that are moving really fast, and so it does technically have a high temperature empty space. But if you were there, you would freeze, And so that I think that's what you're saying, is that, like, well, that's kind of kind of intuitive. How can I freeze if it's one of the hottest things in the universe, And so it kind of makes your brain pop a little bit. Yeah, out in the middle of empty space. There are very fast moving particles, but not very many of them. So if you went into empty space, those particles would give you energy, but you'd be losing energy more quickly than you beginning energy because you'd be readiating it out into spaces. You would freeze. That's counterintuitive. There's another idea here, though, which is the idea of equilibrium. We talk about temperature in terms of many particles rather than a single particle, because temperature really is about like an object in equilibrium, it's like settled. It's a statement about many many things. It's an emergent property, not the property of an individual object. The way, for example, like um the cost of something, the value of something is an emergent property of the market. You can say I'm gonna make some piece of art and I'm gonna claim it's worth a billion dollars. Well, if you can only sell it for seventy four dollars, then what is its value. It's value really is seventy four dollars. So the value of your art is really determined sort of by like the market price for what is willing to bear. In the same way, temperature isn't really the property of a particle. It's like the property of a system of objects. It's an average emergent quantity. Well, are you saying that that's one way to measure temperature, because right before you said that you can calculate it as the average kinetic energy of the particles inside of something. Yeah, but you can't define a temperature for a single particle. Even for this kinetic theory of temperature, you can't define temperature for a single particle. It has to do more with equilibrium sets of particles. But what if I have empty space and there's only one particle in it, within the kinetic energy of that particle basically define the temperature of that empty space. Well, in the same way that like if you are the only person in the world and you create some art and you say it's worth a billion dollars, you're defining the value of that. You can't really sell it for a billion dollars. Is nobody else in that universe. So in that same way, like a single particle doesn't really have a temperature. I guess I'm not sure what you're saying that our definition of particle temperature doesn't make sense. Is that what you're saying or that it breaks down. Yeah, it breaks down. It breaks down intuitively or an actual like math. I guess it breaks down intuitively, not an actual math. I mean an individual particle can hit an object and deposit its energy, right, that can happen. There's no problem there. We can calculate how that happens. But that doesn't mean that we can talk about the temperature of this object. Temperature, in the end is a macroscopic quantities, not a microscopic quantity. It emerges the way like consciousness does. Like can you say that an individual neuron in your brain is conscious? No, but somehow they come together to make your brain self aware. Not a process we understand, but individual neurons we don't think are self aware in the same way, like a particle doesn't have a temperature, and so it's a little bit slippery because temperature is is like intuitive thing we want to describe and not something hard and fixed about individual particles. Oh okay, So I think what you're saying is that our intuitive sense of what temperature is and the official physics definition of what temperature is kind of matches up or makes sense. If you have a lot of particles in something or something is dense. But in some of these extreme cases, like if you're down to one particle in empty space, then our intuitive definition and the official definition sort of like start to diverge or don't start to match well together. Yeah, that's right. And to make it even more confusing, we have more than one official definition of temperature. Like we have one definition of temperature, which is what we talked about earlier, related to the average kinetic energy of the particles, But we have another completely separate definition of temperature. Wait, what we have a second definition of temperature? We do. We have a thermodynamic definition of temperature. So one earlier we call that the kinetic theory of temperature relates to the motion of the particles. Now we have another one thermodynamic definition, which is about how heat flows. This one comes from the observation that heat flows from hot things too cold things, and so this one tries to build a definition of temperature that says if two things are at the same temperature, no heat flows between them. And if one thing is a higher temperature and the other one has a lower temperature, he will flow from the higher temperature thing to the lower temperature thing. So trust to build a theory of temperature that matches that experience. And I see you're saying, like it's a different way to basically think about temperature, Like temperature is not. Maybe the kinetic energy of the particles is just kind of like a relative property or relative quantity, Like you know, something has more temperature than something else. If the heat flows from the first thing to the second thing. That's gonna saying, I guess zero would be if heat can't flow from this thing to anything, then it must be at zero. That's kind of what you're saying, like, let's measure zero to be that exactly, And so then you can come up with a new mathematical expression or how to measure this other idea of temperature, thermodynamic temperature in the same way that for the kinetic theory. You can say, oh, it's about the motion of the particles, and then you can go and write the math and say, here's the kinetic energy and vibrational energy, and I can actually calculate and constructed. In that same way, you can write down mathematical expressions for thermodynamic temperature, and they relate to entropy into energy and they help you understand like why heat flows from hot things to cold things. So it gives you a really interesting thermodynamic insight into like why these things happen. But is that really sort of different in the kinetic I guess view of things, because I imagine if you have something where all the particles are moving a lot that would be hot, and something that's not moving a lot that would be cold, and you put it together, the moving things would you know, bump up against the other things. And that's why that's what kind of what heat flow is. It's like the energy of one thing going to the other. Most of the time, these two definitions agree about what temperature is and also how energy flows from hot things too cold things. So in many scenarios you could use either one. But as we'll see, thermodynamic temperature has some weird behaviors in strange systems at extremes that might allow the existence of negative temperatures. So I guess if you go keep going and keep defining temperature in terms of heat flow, then that's when you might get into trouble. Yeah, into trouble, or into this weird territory where temperature can have non zero negative values and like what does that mean? And in the end, it reflects something about you know, what temperature means? What question are you asking about the universe when you calculate this number. So then you're saying this different definition of temperature is the thermodynamic version. Uh, and it's related to entropy. What does that mean? So thermodynamic temperature tries to give us a sense for like why things flow from one thing to the other. You know why when you with that ice cube in your cup of coffee and you come back in an hour, everything is about an even temperature, right, why do things like to even out? And the answer is entropy. The second law of thermodynamics says that entropy always increases. And people sometimes think about entropy is like the amount of disorganization in the universe, the messiness in the universe, and that you know that works in some certain circumstances. But that more accurate description of entropy is like how many ways can you arrange something? How many different configurations of an object and you have like in the different microscopic particles that match, you know, the things that you're measuring about it. And a basic concept in thermodynamics is that every configuration is equally likely, and so if you have some state, some condition that has lots of possible ways to achieve it, many possible internal configurations. You just more likely to end up in that state. Say, for example, you have a bunch of coins and you throw them all on the floor, right, how many ways are there to get all heads up? There's only one way. How many ways are there to get all heads down? There's only one way. There's lots of ways to get fifty heads up and fifty heads down. So if you throw a bunch of coins on the floor, you're much more likely to end up in that state. Those states have higher entropy, So the universe tend towards these arrangements with there's lots of ways, lots of configurations to get the same value. So that's what entropy is, right, I guess in terms of that, that coffee cup and the ice cube, it's almost like you're saying, like, if I take some water and I take some coffee, and I imagine water and coffee in a cup, it's much more likely for it to be all mixed up together in the in the tepid temperature, right, then it would be likely for all the water to be congregated in one place, locked together into an ice cube and then all of the coffee to be hot surrounding that blog. That's kind of what you're saying. And I think you're saying that the melted ice cube, tepid coffee, watery coffee is more likely to happen, and therefore it's a state of higher entropy. Exactly if you let the energy flow from the hot coffee into the ice cube, then opens up more configurations, right, You can arrange that in many, many more ways. Now, that's why energy flows from hot things too cold things, because when it does so, it increases the entropy. It opens up the number of ways you can arrange the little internal bits, right, But that's not why it does it right. I think what you're saying is that's how thermodynamic says it. Why does it right? Like, if you were to look at it from a totally different perspective, you would see the molecules of the eyes and the coffee interacting and bumping against against each other, and that's why you would say that the heat, the energy goes from one place to the other. But if you were to put on your thermoid dynamic glasses, you would kind of ignore all those interactions. And just say, oh, yeah, of course it's because of the entropy that it's going up exactly. Yeah. So it's another way to explain it. It's like a completely different approach, a different set of ideas, and most of the time they predict the same thing. And so in this thermodynamic context where you're thinking about the energy flow and the entropy, then it's this relationship between energy and entropy that tells us what temperature is. If two things have this same temperature, then we don't want any energy to flow between them. So what we want is if two things have the same relationship between energy and entropy, then we shouldn't have any more energy flow. Like for example, if moving some energy from the ice cube to the coffee cup doesn't increase the entropy anymore, then energy won't flow. So the definition of temperature for thermodynamics doesn't have to do with the kinetic energy objects. It has to do with the derivative of energy with respect to entropy. How the energy and entropy are related to each other. I feel like you're saying that maybe temperature is relative if you look at it from a thermodynamic point of view. And so let's get dig into this connection between energy, heat and temperature and entropy. But first, let's take another quick break. All right, we are getting hot and heavy here talking about possibly negative temperature. Can you have negative absolute temperature? And it may be possible depends on how you define temperature. I guess most people know that, right, Like, if you define temperature in terms of fahrenheit, then yeah, you can have negative temperature or itself as you think, yeah, you can have negative temperature, but you're saying this is something more fundamental, like maybe, um, the universe can allow negative absolute temperature. Yeah, and it goes to the heart of this question, or like what do we mean by temperature anyway? And you know, we define these things to describe our experience and then we explore their extreme to say where does this break down? Does this really make sense? This is something that's universal or only something that's useful in certain contexts. So we came up with this idea of thermodynamic temperature that basically tells you how energy flows around to maximize entropy. The two things have the same temperature, then we don't expect energy to flow between them. And you know, you can have two things that are very different. One thing could have a lot more capacity for different configurations than the other one, and whether energy flows from one object to another depend on like are you going to increase the entropy by moving that energy along? And so it is this relationship between energy and entropy that is the thermodynamic definition of temperature. Technically, it's the derivative of energy with respect to entropy. So do you increase the energy as entropy increases? That's the temperature I see, And I guess maybe my question is why would you do that? Why would you define it this way? Is it because it matches usually with our other definition of temperature, or like why would you call this temperature? Also, it's a totally different approach, and it's the macroscopic approach, and it has some advantages. You know. The microscopic one is weirdly time invariant. The laws of physics governing how things bounce against each other, those look the same forward and backwards, and so it's hard to go from like a microscopic picture of atoms as like little balls, to an understanding of how a state evolves forward in time with entropy. It's complicated to go from one to the other. This is a picture of thermodynamics that deals directly with macroscopic quantities. It says, look, these are the things we can measure, the entropy, the energy, these are things we're interested in. Not all of science has to be reductionists. There are other ways to gain understanding and explanation than just to tear things apart into their tiny bits. Sometimes you do that and you don't get any understanding. Like when you look at the brain, psychology is valuable even if neuroscience can't yet explain it. Right right, Well, let's dig into this a little bit because I am a little bit confused. So you're saying, the thermodynamic definition of temperature is the derivative of say it again, energy flow divided by entropy. Yeah, it's the derivative of energy with respect to entropy. So energies E and entropy is S. So temperature in this sense is d E D S. Apologize for introducing math to the body. Yeah, what are you doing to me here? Okay? So it's uh, it's kind of like saying how energy changes if you change entropy exactly, because the key idea again is that entropy is always going to be maximized, and so what array angagement of the stuff? What arrangement of the energy is going to give you the most entropy, And so to know whether something is going to flow from one object to another, you have to know, like how much energy does some entropy cost? If I want to increase the entropy over here, how much energy does it cost me? If I'm gonna gain more entropy by moving the energy over than I lose where the energy came from, then let's do it. So you have to understand, like how much entropy do you get per energy? And that's basically what temperature is, right, But then what are you trying to measure the temperature of like one thing or two things? You know what I mean? Like if I told you what's the thermodynamic temperature of an ice cube, how would you calculate it? Well, I would measure how quickly it gains new possible configurations as I increase its energy as you put it in coffee. I can measure the energy of the atoms in the ice cube or in some other way. Yeah, I guess the question is just like if I give you an ice cube, how would you measure the thermodynamic temperature of it? I would measure how it's entropy changes as I change its energy, right, So the temperature there is the relate ationship between the energy and the entropy. So you change one and you measure the other. Right, But how would you measure its entropy? Well, you know, you can measure entropy by measuring temperature and energy, because it's a relationship between the three. And that's the thing I always hated about thermodynamics is that you feel like you're just going in circles. Sometimes. Well, it's good, we're spending an hour here discussing something you hate. I'm sure people are following along, right right along. All right, Well, let's maybe take a step. But I think what you're saying is that temperature is kind of this weird thing, and if you look at it from a thermodynamic point of view, you can look at it in terms of how it changes with respect to entropy. Like if it something has a lot of temperature, something is hot in the thermodynamic sense, that means what it takes a lot of entropy, or it doesn't take a lot of entropy. Something is hot in a thermodynamic sense, it means that it costs a lot of energy to change its entropy. And so if you want to take some of that energy away, it doesn't reduce its entropy very very much. So if you have a really hot link it surrounding your ice cube, you can take some of that energy out of the liquid and put it into the ice cube, and you're not going to lose a whole lot of entropy from the liquid. Right, high temperature means high D E D s, so you can take energy away without losing a whole lot of entropy. And because the ice cube is cold, right, has low D E D s and as you add energy to it, you get a lot more entropy. So you lose a little bit of entropy from the hot liquid and you gain a lot of entropy into the cold ice cube for the same amount of energy. I see. It's almost like the cost of entropy for something exactly. It's like exchange rates. Yeah, it's like how much bang for your buck does energy give you in in the entropy of something Like if something an ice cube which is cold, you get a lot of entropy just by you know, breathing on it with your warm breath, but a cold cup of coffee you need a lot of energy to reduce its entropy. Yes, So now we have Jorges economic theory of temperature. Yes, my My coffee theory is you can buy entropy cheap from a hot liquid, and you can sell it at a high price in your cold ice cube exactly. Okay, So that's the thermo dynamic definition, and it matches up with the regular definition because I guess if something is zero kelvin, entropy is cheap for something like that, right, Like I just got to put in a little bit of energy and I get a whole bunch of entropy. But if something is like a million degrees kelvin, you know it's gonna take me a lot of energy to increase the entropy or something that's already super entropic. And it's also about the relationship. Like this makes a lot of sense for most things because for most things, as you add energy, you get more entropy. As you add energy to a liquid, you free the particles and then they become gas and they can move in new ways and find new arrangements, and as you cool things down, they get less entropy. So if entropy is always increasing with energy, then this makes perfect sense. And that's what it does for the ideal gas. And you're like kinetic theory of temperature and they line up as you say, you mean like you always get something for your money, exactly. But condensed matter physicists can imagine in some kinds of weird materials where this isn't true, some kind of weird materials whereas you add more energy, you actually get fewer micro states. Do you have decreasing entropy, So as the thing has more and more energy, there might be fewer ways to arrange it, and that would lead to negative temperature. M All right, now we're getting to the question of the episode, which is you're saying that if you define temperature in the thermoidyanatic way, um, there are things potentially or theoretically I guess that could have negative temperature because when you put energy into them, they actually sort of get neater, right or colder exactly, they get neater, they have fewer ways to arrange themselves. And here's an example. Imagine a bunch of particles in a line, and these particles are fixed on the line. They can't move at all. The only thing they can do is be spin up or spin down. Put these particles in a magnetic field, so that like spin up has more energy than spin down for example, meaning more energy meaning like it that just want to spin down, Yeah exactly. Costs more energy to spin up than to spin down, like trying to stand up a stick. Yeah exactly. So now imagine all these particles spin down right minimum energy, there'd be no entropy because there's only one way to arrange all of these things. It's just like getting all heads when you flip a bunch of coins, or getting all tails. Right, there's only one way to arrange them, so they're all spin down, so there's zero entropy. It's minimum entropy, like the block of ice. Right, everything is like neatly ordered in a state that um it wants to be in exactly. Now, as you add energy, some atoms start to flip right, and you quickly add entropy. There's lots of ways to arrange it. Now, if you say, well, I have enough energy to flip one atom, well, there's a bunch of different ways to do that. You can flip any of the atoms. If you want to flip five atoms, you have enough energy to flip five atoms, right, then there's lots and lots of ways, and so as you add energy, the entropy increases. Totally normal so far, but what happens once you pass the halfway point, once more than half of the atoms are flipped up, and as you keep adding energy, you're reducing the number of ways you can arrange the system until all the way up to the maximum energy, when everything is flipped up, there's only one way to arrange the system at the maximum energy. So in the second half there after you pass the halfway point, as you're adding energy, you're losing entropy, so you have the opposite relationship between energy and entropy. WHOA, Okay, So it's kind of like the coins that like you're saying right, like, if all the coins are heads up, that's minimum entropy. Yeah, that's zero entropy, and half of them heads up heads down is maximum entropy. But then if you go all the way I even keep going, and somehow you're able to flip all of the coins tails up, then that's also zero entropy. Yeah exactly. And so you have maximum energy and zero entropy. And this is a really weird system and not something we actually see in nature, but in principle. Because you are adding energy but reducing entropy, that's technically negative temperature. So everything above the halfway point there has negative temperature. It has d E D S is a negative value. I see in this weird situation, after all the coins are heads and tails up, you're saying, it actually starts to have a negative temperature again because the entropy is going down again as I put more energy into it, exactly, And so the system would prefer less energy would flow towards a higher entropy situation, which is more of a mix, right, Like you try to buy more entropy with your energy, but you actually lose entropy. That's what it means to be cold in this definition of temperature. And this gets really weird. Like let's say you have two of these things. Now you have two of these lines of atoms, and you put them in touch so they can share energy. Right, where is the energy going to go? Say one of them has a higher value of temperature than the other one. Well, in this case, something with negative temperature actually has more energy then the thing with positive temperature, right, because they get to negative temperature you have to go above the halfway point, so half of them are flipped up. So in this case, the heat actually flows from the higher energy negative temperature system to the positive temperature system, which sounds kind of bonkers and backwards well, yeah, yeah, it does sound bankers. But I feel like you're trying to maybe trying to fudge some of these definitions, right, because like these things, these coins only have this weird property because you kind of introducing this bias with the magnet. Right, it's not actually heat or energy, right, it's sort of something different that's going from one to the other. It is energy, right. It takes energy to be like misaligned with the magnet, for example, and so it really is energy. The question really is like what does this mean by temperature? We introduce this definition of thermodynamic temperature so that we could describe the kind of things we see in the world, right, heat flowing from high temperature objects to low temperature objects. And this is just an example of this definition pushed to the extreme where it really doesn't make any sense anymore. The same way we push the definition of kinetic temperature to the extreme by asking what is the temperature of one particle? In this case, while you can get technically negative temperature, it really shows the breakdown of this idea of thermodynamic temperature more than like actually being negative in any meaningful way. M I see you're saying it like if I define temperature as the cost of entropy per bank per bug for energy. Um, that doesn't work if you have a situation where it actually like if you put in more energy, it actually lose this entropy exactly. Yeah, it just doesn't really work. And you can see that because it predicts that things flow from negative temperature to positive temperature. What's the point of temperature then? If it doesn't even align with our ideas and our experience? All right, Well, I mean it's sort of like kind of I feel like it's almost kind of like going to celsius or fahrenheit, right, you're sort of changing the scale of things maybe, and so then therefore you can have negative temperatures if you define things this way. Yeah, it's true. You could always define temperatures to be negative as well. I think this one is interesting because it shows you, not like that the universe breaks the rules or anything, but it shows you that these ideas that we invent to try to describe our experience, they have limits, and those limits aren't physical limits, they're like conceptual limits. Like this idea doesn't really work in that circumstance. The whole concept of temperature doesn't really make sense for this weird invented system right, Like it's like, maybe we have a way of describing and calling things in the universe and calculating things, but maybe that's not really how the universe works. Like, maybe the universe has its own way of doing things that are beyond what we're able to describe, kind of or define. Is that what you're saying. Yeah, it's like the way you can talk about feelings for a person, but can you talk about feelings for like a rock or a river. You know, it's an idea but doesn't really make sense in the same way that like temperature makes sense in certain contexts or certain behaviors emerge and have relationships, but not in all context You can't ask what is the temperature of every arbitrary system that you event doesn't always make sense? I see, But what if I an imaginary friend, Rob, can I still assign thermodynamic happiness to it? Depends how much it's willing to spend to get more entropy? Yeah, be flippid and it lands heads up? But what does that mean? It means it's time for dessert, all right? So then, um, that's kind of where this idea of negative temperature is. I think what you're saying is that some physicists, if they go by this definition, are allowed to call things as having negative temperature. Right, So maybe, like most people were saying, no, that's impossible, you can have negative temperature, you would say, well, it depends on who you talk to and what you mean by temperature. Yeah, exactly, and whether you think it even makes sense to apply temperature to these crazy, bonkers, weird situations that will never arise in our universe. So does that mean I can be a thermoid dynamic temperature denier but still a regular temperature positivist. You can be whatever you want, man. So thanks to everybody who wrote in to ask us to talk about that tricky concept. I hope that was useful. We hope you enjoy that and maybe made you think about what it actually means for something to be hot and cold. Like, maybe what we experience in our everyday lives is just what we experience in our everyday lives. Maybe it doesn't always apply to everything in the universe. Thanks for joining us, see you next time. Thanks for listening, and remember that. Daniel and Jorge Explain the Universe is a production of I Heart Radio For More podcast from my heart Radio, visit the i heart Radio app, Apple podcasts, or wherever you listen to your favorite shows. Yeah.