Speaker 1: There are so many topics in physics that are hard
Speaker 1: to grapple with to deeply understand, and it's not helped
Speaker 1: by the fact that often physicists have given these things
Speaker 1: confusing names. Electrons, for example, have quantum spin, but they're
Speaker 1: not actually spinning. Moments of inertia have nothing to do
Speaker 1: with moments of time. Work and power have very different
Speaker 1: meanings in physics and in English. But sometimes even when
Speaker 1: physicists invent a brand new word to convey a new idea,
Speaker 1: it's still slippery to grasp. So today in the pod,
Speaker 1: we're going to try to grab hold of one of
Speaker 1: the trickiest concepts in physics, one that's often tossed about
Speaker 1: and attached to a simple explanation, but whose subtle power
Speaker 1: isn't usually clearly explained. Today in the pod, we are
Speaker 1: tackling entropy. What is it? Does it explain why our
Speaker 1: teenager's rooms are so messy, or why coffee spills out
Speaker 1: of cups but not back into them. Does it tell
Speaker 1: us about the fate of the universe or the nature
Speaker 1: of time? Is it about order and chaos? Why did
Speaker 1: physicists even devise this concept? Welcome to Daniel and Kelly's
Speaker 1: Extraordinarily Disorderly Universe.
Speaker 2: Hello. My name is Kelly Wiener Smith, and I often
Speaker 2: make jokes about entropy increasing in my home, and today
Speaker 2: I'm gonna find out if that joke is scientifically accurate
Speaker 2: or not. Hi.
Speaker 1: I'm Daniel. I'm a particle a physicists, and I think
Speaker 1: that there's always one person in the marriage who's more
Speaker 1: orderly and one person is more chaotic.
Speaker 2: Yeah, it's pretty easy to identify who's who in my marriage.
Speaker 2: Are you the more orderly or the more chaotic in
Speaker 2: your marriage? Katrina seems pretty orderly, but so do you.
Speaker 1: I don't want to slander my wife on air, especially
Speaker 1: if she's not here to defend herself, so I'll say
Speaker 1: that in some categories, I'm more orderly, and in some categories,
Speaker 1: she's more on top of stuff, and that's why we're
Speaker 1: such a good team.
Speaker 2: Ah, I'm going to slander my husband. He's the chaotic
Speaker 2: force in our family, he absolutely is. But he's also,
Speaker 2: you know, a lot of the creative force. So it
Speaker 2: works out.
Speaker 1: Yeah, exactly. Well. The yin and yang is what makes
Speaker 1: it exciting, isn't it.
Speaker 2: It keeps things fresh, that's for sure. So I was
Speaker 2: thinking about the topic for today, and when I think
Speaker 2: about entropy, the first thing that comes to mind is
Speaker 2: jazz music. And when I googled entropy and jazz, actually
Speaker 2: a lot of things came up. People have like studied
Speaker 2: jazz music through the lens of entropy. Do you like
Speaker 2: jazz music? What do you think?
Speaker 1: Wow, that's fascinating. I never connected entropy and jazz music.
Speaker 1: There's some jazz music I like, but I like things
Speaker 1: that are a little bit more melodic. So just like
Speaker 1: a wandering sprinkle of nodes doesn't do it for me.
Speaker 1: I need a little bit of rhythm and some beat
Speaker 1: to it and whatever. So I'm more of a blues
Speaker 1: guy than jazz, how about you.
Speaker 2: It depends on my mood. There are some moods that
Speaker 2: I'm in where jazz is exactly what I want and
Speaker 2: it's exactly what I need to listen to while I'm writing.
Speaker 2: And then there's other moods where it does make me
Speaker 2: feel kind of frustrated and overwhelmed. So, but you know,
Speaker 2: I feel that way for a lot of different kinds
Speaker 2: of music. I've got like very particular kinds of music
Speaker 2: for different kinds of moods.
Speaker 1: I appreciate the jazz nerds though, because they help me
Speaker 1: understand how almost any human endeavor there are so many
Speaker 1: layers to it, you know, like people who appreciate wine
Speaker 1: and they can tell the difference between like a five
Speaker 1: hundred dollars bottle of wine and a five thousand dollars
Speaker 1: bottle of wine, whereas like I can't tell the difference
Speaker 1: between ten dollars and twenty dollars bottles of wine, Or
Speaker 1: like how many levels of skale there are two chess,
Speaker 1: you know, where like a level twenty person will be
Speaker 1: the level eighteen person will be the level seventeen person. Consistently.
Speaker 1: I feel that same way about jazz, because people talk
Speaker 1: about it and they're like, Wow, this guy is a
Speaker 1: genius and so amazing in this way and that way,
Speaker 1: and I'm just like at the beginning of a journey
Speaker 1: of appreciating that. But I love when human culture goes
Speaker 1: really deep on something and people could appreciate the fine
Speaker 1: nuances of it.
Speaker 2: Yeah, you know, if I had endless time and money,
Speaker 2: I would love to just like jump into different cultures
Speaker 2: and just sort of like appreciate and absorb, you know,
Speaker 2: the various features that are exciting to them and just
Speaker 2: sort of enjoy their culture for a little while. And
Speaker 2: I very briefly jumped into jazz as I've had different
Speaker 2: friends who do jazz things and it's a very cool culture.
Speaker 2: But I am still at the early phases of like
Speaker 2: what is good? I don't know. I just know that
Speaker 2: this makes me smile.
Speaker 1: Well, something I do have very strong opinions about because
Speaker 1: I spent a lot of time perfecting my tastes about
Speaker 1: it is pizza making. I'm an at home pizza maker,
Speaker 1: and I have like strong opinions about like, you know,
Speaker 1: the stretchiness of the dough and the puffiness of the
Speaker 1: crust and the darkness of the sauce and whatever, because
Speaker 1: I've made a lot of pizzas in my house, so
Speaker 1: I know like exactly what I like in a pizza.
Speaker 1: What have you nerded out on? What are you like
Speaker 1: a level twenty expert in?
Speaker 2: Hmm? Well, so first I'll say that my husband also
Speaker 2: nerds out on pizza, which is making me wonder if
Speaker 2: we sh make pizza when you're here to visit or
Speaker 2: if we shouldn't. Uh oh, Zach and I will have
Speaker 2: a discussion about that. What am I a level twenty
Speaker 2: nerd on. I don't know. I guess I'm sort of
Speaker 2: a generalist. I like lots of things. I mean, I'm
Speaker 2: really into the moths in our area, and I spent
Speaker 2: two years learning about Russian and Russian culture and like
Speaker 2: the language. But I don't know if I'm like a
Speaker 2: level twenty on either one.
Speaker 1: Of those things. Well, I can tell you moths not
Speaker 1: very good on pizza. I mean they're delicious, but really
Speaker 1: not a popular topic.
Speaker 2: No, I totally believe that. But I've pulled us far
Speaker 2: from our topic. Today. We're talking about entropy, and you know,
Speaker 2: I think first we should find out what our audience
Speaker 2: thinks entropy means.
Speaker 1: That's right, let's try to beat back the chaos and
Speaker 1: stay on topic today, Kelly good luck. So I went
Speaker 1: out there and I asked folks what they thought entropy was,
Speaker 1: because I was curious what connections people had made in
Speaker 1: their minds. Maybe they'll also connect it to jazz or
Speaker 1: blues or pizza making or moth loving. Let's hear what
Speaker 1: folks had to say. The tendency of a closed system
Speaker 1: to kind of go from order to disorder unless you
Speaker 1: add energy to go from order to disorder only I
Speaker 1: had my head around it.
Speaker 2: Entropy is a measure of the remaining free energy in
Speaker 2: a specific.
Speaker 1: Volume homogene as milk toast, a description of the state
Speaker 1: of a system in terms of its energy. The more
Speaker 1: different configurations the system can have and be in the
Speaker 1: same state, the higher the entropy it has. Matter being
Speaker 1: either organized or being in a chaotic state, the degree
Speaker 1: of disorder and a physical system.
Speaker 2: The amount of energy in a system that can't.
Speaker 1: Be recovered, describes the level of organization.
Speaker 2: As time progresses, entropy progresses.
Speaker 1: I think it's the tendency of energy to spread out
Speaker 1: slow crawl towards simplicity that the universe imposes on everything. Disorder,
Speaker 1: aos the absence of order. Things degrade over time. It
Speaker 1: feels weird because that seems made up what disorder is
Speaker 1: and what order is. Or if there are more configurations,
Speaker 1: the entropy is higher number of micro states of the system,
Speaker 1: which can result in the current macro state.
Speaker 2: Things want to move from a higher embodied energy state
Speaker 2: to a lower one. Well, no pizza in those answers,
Speaker 2: but actually a lot of variety in the answers there.
Speaker 1: Yeah, I think we really capture something here that there's
Speaker 1: a general sense that entropy goes up and that it
Speaker 1: has to do something with order and disorder, but also
Speaker 1: that there are multiple concepts of entropy. Right, this sensitive
Speaker 1: energy and entropy and a sense of organization related to entropy.
Speaker 1: And so I think that captures like the big chaotic
Speaker 1: confusion that is most people's understanding of what entropy actually is.
Speaker 2: I do think this idea has escaped into like the
Speaker 2: general consciousness, and maybe it has disconnected from its physics
Speaker 2: definitions in that process.
Speaker 1: Yeah, I think you see a lot of tech bros
Speaker 1: on social media using enterpa if they know what it means.
Speaker 2: I mean, it's nowhere near as bad as the word quantum.
Speaker 2: But let's clear things up today exactly.
Speaker 1: It's getting there, though.
Speaker 2: It's getting there, all right. So tell me about the
Speaker 2: first time the word entropy was used.
Speaker 1: Yeah, entropy is a fun topic because it's not an
Speaker 1: ancient topic. Right. People have been talking about motion and
Speaker 1: velocity and energy and time since people have been like
Speaker 1: smoking whatever and sitting in caves and looking up at
Speaker 1: the night sky and wondering how the universe.
Speaker 2: Works, the things that bring us all together.
Speaker 1: Yeah, so you can go back and look at the
Speaker 1: Sumerians thinking about the path of the planets and the
Speaker 1: length of the year, and you know, the structure of
Speaker 1: the Solar system and stuff like that. But entropy is
Speaker 1: a recent concept. It's less than two hundred years old.
Speaker 1: It's a word that was invented fairly recently as people
Speaker 1: were puzzling over engines and wheels and energy.
Speaker 2: Oh so was the idea that, like, it's hard to
Speaker 2: keep an engine working because entropy sort of overtime makes
Speaker 2: the system less reliable or tell me more about this history.
Speaker 1: Yes, so it's the early eighteen hundreds and there's the
Speaker 1: Carnea cycle and so this French physicist Carno actually a
Speaker 1: father's son team we're thinking about engines and heat and
Speaker 1: there was sort of a mystery at the time, like
Speaker 1: what is heat? Anyway, people had the sense that the
Speaker 1: universe had a microscopic explanation that could help you understand
Speaker 1: the macroscopic view, like you know, this is around the
Speaker 1: time when we're about to get Dalton and thinking about
Speaker 1: the existence of atoms. So that idea is out there
Speaker 1: that like maybe this microscopic stuff, you know, and also
Speaker 1: biologically right, like the germ theory is coming out around
Speaker 1: this time, you know, within decades at least, so people
Speaker 1: were wondering, like, what is heat? Is heat like a particle,
Speaker 1: is it a substance? Does it flow from one thing
Speaker 1: to the other. Remember early ideas of like electric charge,
Speaker 1: where like there were two of them and they were
Speaker 1: a liquid and they flowed. So this is sort of
Speaker 1: like an idea that was out there. People were wondering,
Speaker 1: how do engines work? What is energy? What is heat?
Speaker 1: How are they all related? And in eighteen twenty four
Speaker 1: Carnot put his finger on this idea that differences in
Speaker 1: heat can be used to do useful stuff like if
Speaker 1: you have something that's hot and something that's cold, energy
Speaker 1: will flow from the hot thing to the cold thing,
Speaker 1: and you can use that to do stuff sort of
Speaker 1: like the way water flows from uphill to downhill, and
Speaker 1: if you capture that flow, you put like a water
Speaker 1: wheel there. You can use that to do stuff like
Speaker 1: grind your wheat into flour. Right, very useful. But if
Speaker 1: the water is all flat, you can't use it to
Speaker 1: do anything. And so heat differences can be used to
Speaker 1: produce work. That's Carno's big insight in the early eighteen.
Speaker 2: Hundreds, did we have the steam engine at this point.
Speaker 1: Yet, yeah, steam engines existed at this point, and that's
Speaker 1: a great example of how you use heat. Right, you
Speaker 1: heat the steam, it rises, it turns your turbine. You
Speaker 1: can use that to do work or these days to
Speaker 1: make electricity. Right, and so Carne understood that engines can
Speaker 1: do this, engines can turn heat differences into work. But
Speaker 1: he describes sort of a perfect engine one where you
Speaker 1: can turn heat differences into work, and then you could
Speaker 1: use that work to create heat differences, so back and
Speaker 1: forth and back and forth and sort of perfectly without
Speaker 1: any loss. But he also had this idea that, well,
Speaker 1: sometimes you have imperfect engines, that something is lost, creeps
Speaker 1: out of your cycle. This is an imperfect engine. Eventually
Speaker 1: it'll wind down, you'll turn a heat difference into work,
Speaker 1: and then you'll turn that work into a heat difference.
Speaker 1: But you get a little bit less, sort of like
Speaker 1: the way if you drop a ball. In principle, the
Speaker 1: potential energy the ball turns into kinetic energy and then
Speaker 1: it bounces back up and it regains all of that
Speaker 1: potential energy. But in practice there's a little bit of
Speaker 1: friction and there's losses in the system, and the ball
Speaker 1: doesn't bounce forever, right, in the same way. He understood
Speaker 1: that this happened, but he didn't describe it mathematically. It
Speaker 1: wasn't for a few more decades that people sort of
Speaker 1: described this with equations and sort of more mathematical concepts.
Speaker 2: Okay, but even today, we don't have a perfect engine, right,
Speaker 2: all of our engines are imperfect.
Speaker 1: All of our engines are imperfect. Exactly. And it was
Speaker 1: Claussius who sounds like he's it would be an ancient
Speaker 1: Greek guy he does, I know, yeah, exactly. I imagine
Speaker 1: him in a robe, even though he probably just wore
Speaker 1: a suit and had a top hat. But Classius defined
Speaker 1: it mathematically, and he thought of it as the stuff
Speaker 1: that's flowing, like entropy is leaving the system, it's moving
Speaker 1: through It's like a physical thing. And he connected it
Speaker 1: to temperature. And so his contribution was essentially invent this
Speaker 1: concept of entropy to help us understand why some engines
Speaker 1: are imperfect. And he thought of it as a thing
Speaker 1: which flows to the system, like a real physical thing,
Speaker 1: not just like hey, here's a number, we're calculating it.
Speaker 1: We define it like you could invent anything, right, you
Speaker 1: could invent the jigiblions and define it as like the
Speaker 1: number of apples in the universe minus the number of
Speaker 1: ice cream cones. And that doesn't necessarily have to mean anything, right,
Speaker 1: But sometimes you invent a number and it means something
Speaker 1: in the universe. It like describes someone which actually exists
Speaker 1: or is important. And so he connected entropy not just
Speaker 1: to heat, but also to temperature. Right. Temperature also something
Speaker 1: people were trying to understand. And so we're going to
Speaker 1: get into the mathematics of what that all means and
Speaker 1: how it works a little later on. But Colossius's other
Speaker 1: big contribution was the word. He created the word entropy.
Speaker 1: Before this, we had heat and we had temperature. But
Speaker 1: Colossius created the word entropy to think about energy flow.
Speaker 2: And so at this point he's thinking about the movements
Speaker 2: of heat or the movement of energy. But like so
Speaker 2: when I think of entropy, I usually think of like
Speaker 2: stuff getting lost. Was the idea of stuff getting lost
Speaker 2: or getting disordered part of this idea or is he
Speaker 2: just tracking the flow of things not disordered?
Speaker 1: Disorder comes later with Boltzmann. We'll get to there in
Speaker 1: a minute. But he's thinking about the energy flow and
Speaker 1: where does it go, and he's using that to understand
Speaker 1: why engines will wind down, right for sure, because entropy
Speaker 1: is one of the reasons energy doesn't flow completely perfectly.
Speaker 1: But I also love the story of how he came
Speaker 1: up with the word. So entropy is like a word
Speaker 1: he invented. He took the letters E N from energy
Speaker 1: because it's related to energy, and then he took the
Speaker 1: word trophy from the Greek word for change. So he's like, oh,
Speaker 1: this is cool entropy. And you know, he was cognizant
Speaker 1: of the fact that this is something he was inventing,
Speaker 1: and it was kind of a recent idea. So that's
Speaker 1: why he reached all the way back to Greek, because
Speaker 1: he wanted it to connect it with like ancient languages
Speaker 1: and ancient thoughts, and he said, quote, I prefer going
Speaker 1: to the ancient languages for the names of important scientific quantities,
Speaker 1: so that they may mean the same thing in all
Speaker 1: living tongues. I think he was hoping that, like, if
Speaker 1: he uses a Greek root, then even like Romanians and
Speaker 1: Bulgarians and English speakers and everybody is going to have
Speaker 1: some understanding intuitively of what this concept means.
Speaker 2: Now I am imagining him saying that in a toga.
Speaker 1: He's carving it into marble.
Speaker 2: Right, and has history judged this to have been a
Speaker 2: good decision.
Speaker 1: I don't know. I mean, listen to the listeners, Like,
Speaker 1: entropy is very confusing. I don't think anybody has the
Speaker 1: same idea of what entropy is. And there's famous physicists
Speaker 1: a few decades ago, Leon Cooper, who won the Nobel
Speaker 1: Prize for superconductivity. So like a dude knows his stuff
Speaker 1: and he says the COLOSSI has quote succeeded in coining
Speaker 1: a word that means the same thing to everybody. Nothing.
Speaker 1: I don't know. If I invent something so pervasive that
Speaker 1: people are griping about it, then like, hey, you know
Speaker 1: I've done something. All publicity is good publicity, right, We'll.
Speaker 2: Never be sure about that, but okay.
Speaker 1: And so at this point we have sort of these
Speaker 1: macroscopic handles on it. We're describing temperature and energy and
Speaker 1: entropy as things we can measure about the stuff we experience, right,
Speaker 1: A macroscopic that means like stuff in our world the
Speaker 1: human scale, you know, like you can take a thermometer
Speaker 1: and you can put it in your water. You can
Speaker 1: measure the temperatures, the number you can measure about like
Speaker 1: large amounts of physical things. But people again wanted to
Speaker 1: understand these things microscopically, like what happens down below? If
Speaker 1: you're understanding the particles, what is this all mean? And
Speaker 1: on the show we do that a lot, and people
Speaker 1: are often writing in to ask me, like, well, what's
Speaker 1: really happening at the particle level during hawking radiation or
Speaker 1: when light bounces off a mirror or something like, what's
Speaker 1: really going on? As if like the reductionist explanation reveals
Speaker 1: something truer, And you know, we'll talk about that in
Speaker 1: a minute, but I want people to understand that there
Speaker 1: are many layers of the universe of reality. None of
Speaker 1: them are more true than the other. We have this
Speaker 1: sense that like, as you go deeper, maybe you're approaching
Speaker 1: some fundamental layer of explanation, but every layer is useful.
Speaker 1: You know, the macroscopic view, the human level view of
Speaker 1: the universe is just as valid and just as useful,
Speaker 1: even if there is another layer underneath. Because the amazing
Speaker 1: thing is that you can write equations that work to
Speaker 1: describe the macroscopic without understanding the microscopic. The universe gives
Speaker 1: us that that access to many different layers of reality.
Speaker 2: So if every layer is useful, what I'm hearing you
Speaker 2: say is that it's okay that I skip chemistry. I
Speaker 2: can focus on the other useful layers. We tell me
Speaker 2: just as much.
Speaker 1: I'm saying, and unfortunately you can quote me on this.
Speaker 1: Chemistry has its uses. There are places where there are
Speaker 1: problems you can't solve using biology or we're using physics.
Speaker 1: You need that intermediate step where you're like, you're thinking
Speaker 1: about the stoichiometry and whatever. So you're like, yes, chemist's
Speaker 1: out there. I appreciate you. It's not that chemistry is terrible,
Speaker 1: it's just that I can't do it.
Speaker 2: Same same Yep, No, I appreciate you too, all right.
Speaker 1: So then late eighteen hundreds we have Boltzmann. He's one
Speaker 1: of the guys that founded statistical mechanics and thinking about
Speaker 1: things in terms of the particles. You really want to understand,
Speaker 1: like what is temperature in terms of the particles, Like
Speaker 1: if I have something hot and something cold, what's going
Speaker 1: on microscopically? And he made this huge contribution connecting temperature
Speaker 1: to microscopic motion and specifically defining entropy in terms of
Speaker 1: what's going on microscopically. This is a huge leap forward
Speaker 1: and really one of the only places in physics or
Speaker 1: maybe even in science where we have a mathematical bridge
Speaker 1: between two different layers of reality, where you can take
Speaker 1: the microscopic understanding of like particles whizzing around and use
Speaker 1: it to derive the macroscopic rules right different levels of reality.
Speaker 1: Is like when you have different kinds of laws, Like
Speaker 1: particles have different behavior than liquid flowing, but we know
Speaker 1: liquids are made of particles, and so liquids are this
Speaker 1: thing that emerge from particles, and usually we don't know
Speaker 1: how to derive it. We can like find the laws
Speaker 1: for liquids and find the laws for particles, but we
Speaker 1: don't know how to connect them, right, Like you can't
Speaker 1: derive fluid mechanics from the standard model. But here he
Speaker 1: developed an understanding of what's going on for particles and
Speaker 1: he built the mathematical bridge, like you can derive the
Speaker 1: ideal gas law from Boltzmann's description of what's happening with
Speaker 1: these particles. It's amazing. It's like the only place I've
Speaker 1: ever seen this kind of connection where like, not only
Speaker 1: do you have a reductionist ability to see the lower level.
Speaker 1: But also there's like a mathematical bridge that shows you
Speaker 1: why it works. It's kind of incredible.
Speaker 2: Why is that so rare?
Speaker 1: Because the universe is complicated, you know, like to go
Speaker 1: from micros gopic to macroscopic, you have to describe a
Speaker 1: lot of stuff, and usually they're two hurdles chaos and approximations.
Speaker 1: Chaos because like, sometimes the tiny little details matter, you know,
Speaker 1: like butterfly flaps its wings in China, hurricane goes a
Speaker 1: different direction, like, so you can't ignore those little details,
Speaker 1: which means you have to keep track of lots and
Speaker 1: lots and lots of little details, like remember how many
Speaker 1: atoms there are in a drop of water, right, like
Speaker 1: Avagajo's number is a big, big number. Calculating all those
Speaker 1: details is essentially impossible, so you end up making approximations.
Speaker 1: And sometimes those approximations work, like Boltzmann's big contribution was
Speaker 1: finding ways to calculate these averages that work mostly, but
Speaker 1: sometimes they don't, and maybe we just don't have the
Speaker 1: right kind of math. So in principles should be possible,
Speaker 1: but the approximations we make along the way and the
Speaker 1: sensitivity to the little details make it really, really hard.
Speaker 1: That's why we need chemistry.
Speaker 2: All right, Well, on that note, let's take a break
Speaker 2: so that we can sort of absorb the fact that
Speaker 2: we need chemistry and in terms with that, and when
Speaker 2: we get back we'll talk about the different actual definitions
Speaker 2: of entropy. All Right, we're back. We've all come to
Speaker 2: terms with the fact that we need chemistry in our life.
Speaker 2: And I have a confession to make. I actually minored
Speaker 2: in chemistry and my birthday is October twenty third, which
Speaker 2: is ten twenty three Avagadro's number ten to the twenty third.
Speaker 2: So when I was in college, all of my parties
Speaker 2: were chemistry themed parties. We would play like periodic table games.
Speaker 2: I know this confession time.
Speaker 1: Haring this on me. Now we've been working together for
Speaker 1: so long.
Speaker 2: I felt like I had to tell you I can't
Speaker 2: live this lie anymore.
Speaker 1: Daniel, was this burning a hole in your psyche all
Speaker 1: these times?
Speaker 2: But I cannot tell you how large my bill was
Speaker 2: at the glassware depot because I they broke so much
Speaker 2: glass in my chemistry journey. I decided there's no way
Speaker 2: I can make a living out of this. I can
Speaker 2: maybe just become bankrupt. But anyway, Okay, let's get back
Speaker 2: to entropy. We've talked about how you can study heat
Speaker 2: to do work and how that heat sort of moves around.
Speaker 2: Tell me about the relationship between those phenomena with entropy.
Speaker 1: Yeah, So what we end up with is a description
Speaker 1: of entropy from several different perspectives. We have like Carno
Speaker 1: and Classius. Their description of entropy is like something the
Speaker 1: same level is like temperature and energy a macroscopic quantity, right,
Speaker 1: a thermodynamic quantity that relates to like temperature and energy flow.
Speaker 1: And then we have Boltzman. He describes entropy statistically in
Speaker 1: terms of like the little particles and how you average
Speaker 1: those up and how that emerges from those tiny details.
Speaker 1: Later on, a guy named Shannon creates an idea of
Speaker 1: information entropy, which is probably what people were talking about
Speaker 1: when they connect jazz to entropy. So we have three
Speaker 1: different definition of entropy, and they're actually more. There's like
Speaker 1: five different definitions of entropy and they're all related. And
Speaker 1: we'll talk about the statistical and the thermodynamic definitions of
Speaker 1: entropy today, but they're connected. They're not the same thing,
Speaker 1: but they are similar and you might think, like, what
Speaker 1: are you talking about. How can you have different definitions
Speaker 1: of the same thing, Right, Well, we already have that,
Speaker 1: Like for temperature temperature, we have a statistical view of temperature.
Speaker 1: We may have a thermodynamic view of temperature. These things
Speaker 1: are a little bit fuzzy, and just like we have
Speaker 1: different levels of understanding of the universe, some of which
Speaker 1: are useful sometimes and not others. Like particle physics great
Speaker 1: when you're at the LEDC, not so useful when you're
Speaker 1: pouring liquid into beakers. Right, they're useful in some cases
Speaker 1: and not useful in others. Because we don't have a
Speaker 1: complete understanding of the universe. We have these approximate, limited
Speaker 1: views into the universe, and you've got to pick which
Speaker 1: toolkit you use. So that's why we end up with
Speaker 1: several different definitions of entropy. But you know they are connected,
Speaker 1: and today we're going to show you some of those connections.
Speaker 2: Biologist, I'm thinking about the definition of species of the
Speaker 2: word species, right, same sort of situation. We'll have a
Speaker 2: whole episode on that at some point.
Speaker 1: Please. That sounds fascinating.
Speaker 2: Yeah, we could drink and discuss this for like weeks
Speaker 2: on end If we have enough biologists together that and
Speaker 2: somehow we'll start talking about boop.
Speaker 1: But anyway, also, and then I get to have fake
Speaker 1: outrage and how ridiculous you guys are.
Speaker 2: That's fair, that's fair taste in my own medicine. All right,
Speaker 2: let's start with the statistical definition.
Speaker 1: Okay, So statistical definition is a good entry point because
Speaker 1: I think it connects to a lot of people's intuitive
Speaker 1: description of entropy as related to chaos or disorder or something.
Speaker 1: And you often hear people say entropy is a measure
Speaker 1: of disorder in the universe. But that's missing a lot
Speaker 1: of really important nuance that I really want people to
Speaker 1: grab hold of. Entropy does have to do with order,
Speaker 1: but specifically, it's a relative quantity. It's not an absolute
Speaker 1: thing where you're like, you measure the disorder and you
Speaker 1: get a number. It has to do with how much
Speaker 1: information you have about two relative levels of the universe,
Speaker 1: and it requires you to define those two levels. So
Speaker 1: we have like a macroscopic view, things you can observe
Speaker 1: like temperature or energy or density or something that you
Speaker 1: can measure sort of at the human level, and then
Speaker 1: micro states things that you can't observe arrangements of the
Speaker 1: particles or something inobservable that would give you that same
Speaker 1: macro state. So you have to pick these two levels, right,
Speaker 1: macro and micro in order to even define entropy. Entropy
Speaker 1: has to do with how many different micro states you
Speaker 1: can have that are consistent with the same macro state
Speaker 1: that you measure.
Speaker 2: I would love an example.
Speaker 1: All right, So let's do an example. Let's say, for example,
Speaker 1: you have ten coins and you flip them. They're either
Speaker 1: heads or tails. Okay, and let's say that macroscopically, because
Speaker 1: you have limited information about the universe, all you can
Speaker 1: know is how many heads there are. You can't tell
Speaker 1: which coin is heads and which coin is tails. You
Speaker 1: can just know how many heads there are, So maybe
Speaker 1: this five, maybe this ten. Macroscopically, you always have limited information,
Speaker 1: like when you measure the temperature of your coffee. You're
Speaker 1: not measuring the speed of every individual particle. You have
Speaker 1: some big overall average quantity, right, So that's your macroscopic information,
Speaker 1: and then we'll define the microscopic is like, actually, which
Speaker 1: coins are heads? Right? So you know microscopically, like maybe
Speaker 1: it's the first five or heads and the second fiber
Speaker 1: tails or whatever. Okay, so we've defined a macro state
Speaker 1: and a micro state. An entropy is a measure of
Speaker 1: how many micro states you can have for a given
Speaker 1: macro state. So say, for example, my macro state, which
Speaker 1: is just how many heads there are? I flip all
Speaker 1: the coins and I tell you there are zero heads. Well,
Speaker 1: how many micro states are there they can give you
Speaker 1: zero heads? How many arrangements of those coins can give
Speaker 1: you zero heads one? They all yeah, exactly. So that's
Speaker 1: a very small number of micro states. What if I
Speaker 1: do it again, and this time I can tell you, well,
Speaker 1: the macro state is that one of the coin has heads.
Speaker 1: How many microstate are there that can give you one
Speaker 1: coin having heads? Ten exactly? Ten? Choose one for the
Speaker 1: mathematicians out there. Now, if I say, okay, we do
Speaker 1: it again, and this time we got five heads, how
Speaker 1: many micro states are there?
Speaker 2: I'm gonna give you the middle finger because I can't
Speaker 2: calculate that on air.
Speaker 1: It's a big number, right, It's like ten times nine
Speaker 1: times eight whatever. It's a big number. So the point
Speaker 1: is each macro state has a different number of micro states.
Speaker 1: Some of them have only one arrangement of the coins
Speaker 1: that will give you the same macro state, that's low entropy.
Speaker 1: If you have few micro states that are consistent with
Speaker 1: that macro state, it's low entropy. If you have a
Speaker 1: lot of micro states that are consistent with your macro state,
Speaker 1: like if your macro state is five heads, then there's
Speaker 1: lots of different arrangements of that, that's high entropy. Okay,
Speaker 1: So the key here it's not just disorder like how
Speaker 1: scrambled are the heads and tails. It's relative lack of
Speaker 1: knowledge between the micro state and the macro state.
Speaker 2: Okay, I get that.
Speaker 1: If you hold onto that in your head, it actually
Speaker 1: makes it very easy to understand why entropy tends to
Speaker 1: increase in the universe. You just need one more piece
Speaker 1: of information. If you assume that all the micro states
Speaker 1: are equally likely, like any particular arrangement is equally likely,
Speaker 1: And that's true in this example of the coins, because
Speaker 1: like you know, every coin toss is independent. You're just
Speaker 1: as likely to get all heads as all tails or
Speaker 1: any other particular arrangement like heads tails, heads tails heads tails,
Speaker 1: fine specifying them exactly, every micro state is equally likely.
Speaker 1: What does that mean? Well, if you just slip all
Speaker 1: the coins, you're more likely to get a macro state
Speaker 1: that has high entropy, because the macro states that have
Speaker 1: low entropy by definitions are the ones with few micro states,
Speaker 1: Like it's hard to get all heads or hard to
Speaker 1: get all tails. There's lots and lots of ways to
Speaker 1: get five heads and fives tails. So if you keep
Speaker 1: flipping coins right, then on average, you're going to get
Speaker 1: higher entropy than lower entropy. And so the universe does
Speaker 1: this not with coin but with quantum states. If each
Speaker 1: quantum state of the universe is equally likely, then the
Speaker 1: universe tends towards higher entropy because as you keep flipping coins,
Speaker 1: you're more likely to get microscopic configurations that give you
Speaker 1: higher entropy, just because there are more of them.
Speaker 2: So so far, I haven't heard anything that would suggest
Speaker 2: that that makes the universe more disordered or anything like that.
Speaker 2: And is that right?
Speaker 1: So here we get a little slippery because we have
Speaker 1: a nice crisp mathematical definition of micro states and macro
Speaker 1: states and numbers, and entropy is mathematically the log of
Speaker 1: the number of micro states. So what do we mean
Speaker 1: by disorder? Disorder is like one of these intuitive words
Speaker 1: that we use that we don't have a crisp definition
Speaker 1: of but we can try to connect it, you know.
Speaker 1: So for example, if I told you all the coins
Speaker 1: are the same, you'd be like, oh, that's nice and ordered.
Speaker 1: If I told you, oh, it's a scrambled headstaales tails
Speaker 1: has whatever, that would seem more disordered, right, And so
Speaker 1: in that sense it connects with that intuitive definition. But
Speaker 1: I think there are other examples that are maybe more intuitive.
Speaker 2: When I hear disorder, my connotation of disorder is that
Speaker 2: it's something bad is happening, or like we're moving towards
Speaker 2: a state of more badness. But what we're really saying
Speaker 2: is that as entropy increases at like each individual point
Speaker 2: of interest, it's just harder to predict what's happening at
Speaker 2: each of those spots.
Speaker 1: Yeah, I don't think you need to connect disorder with badness,
Speaker 1: you know, to think that maybe the universe is just
Speaker 1: getting jazzier as time goes on.
Speaker 2: That sounds good, That sounds good depending on my mood.
Speaker 1: You know, we're getting rid of the melody, we're kicking
Speaker 1: out inchin ideas about keys and whatever, and we're just
Speaker 1: wandering up and down the scale without a plan. The
Speaker 1: universe is just getting jazzier.
Speaker 2: Is it less planned or is it just you don't
Speaker 2: have as good a handle at the microscale of what's
Speaker 2: going on, Like, does that necessarily result in something less planned?
Speaker 2: I guess you would say that zero heads is a
Speaker 2: more planny state to be in than five heads. Is
Speaker 2: that what we're saying.
Speaker 1: I have a little bit of trouble with the intuitive
Speaker 1: concept of disorder again, because it's not very well defined.
Speaker 1: I think it's maybe easier to think about it in
Speaker 1: terms of where stuff is physically rather than heads and tails.
Speaker 1: So let's take another example that's maybe more intuitive. So
Speaker 1: let's say, for example, you have one hundred particles in
Speaker 1: a box, and instead of just knowing like the average
Speaker 1: energy of those particles, your macroscopic measurement can tell you
Speaker 1: the energy distribution, So you can tell the difference between
Speaker 1: like all the energies in one particle or the energy
Speaker 1: is shared, okay, And so if all the energy is
Speaker 1: in just one of those hundred particles, one of them
Speaker 1: is like going crazy whizzing around. The other ones are
Speaker 1: just sitting there. How many microstates are there that are
Speaker 1: consistent with that? Well, one hundred, because there's one hundred
Speaker 1: particles and you can't tell which particle is which, but
Speaker 1: there's one hundred ways you could give all the energy
Speaker 1: to just one particle. On the other hand, and if
Speaker 1: you share the energy, right, if you're in a macro
Speaker 1: state where the energy is smoothly shared between them, now
Speaker 1: you have a lot of different particles that have energy,
Speaker 1: so there's like one hundred times ninety nine times ninety
Speaker 1: eight whatever. There's lots of different ways to arrange those
Speaker 1: particles so that they share the energy. So you know
Speaker 1: that seems more disordered because now you have more particles
Speaker 1: whizzing around than rather than just one particle, and you
Speaker 1: can make sort of similar arguments about physical locations of particles.
Speaker 1: If your macro state is to measure the distribution of
Speaker 1: the particles, right, then having all the particles in one
Speaker 1: corner of the box gives you very few ways to
Speaker 1: arrange the particles, whereas having the particles all the way
Speaker 1: through the box, there's lots of different ways to arrange
Speaker 1: those particles. And so the reason that happens is that
Speaker 1: those have higher entropy, or another way to say that
Speaker 1: is that there are just more ways for that to
Speaker 1: happen in the universe. So if all the micro states
Speaker 1: are equally likely, the ones with more entropy are more likely.
Speaker 1: And in that sense, entropy is connected to disorder because
Speaker 1: it tends to share energy, spread energy out and also
Speaker 1: spread particles out, so it tends to make things smooth
Speaker 1: and even rather than like clumped and tight together.
Speaker 2: All right, now, I'm with you. That definition landed better
Speaker 2: for me, I think or that example.
Speaker 1: All right, cool, yeah, but it's important to understand that
Speaker 1: the statistical definition of entropy really requires you to define
Speaker 1: these two levels, and so there is no absolute sense
Speaker 1: of entropy. Like you and I could look at the
Speaker 1: same system and have different numbers for entropy. If you
Speaker 1: have a different macro state, if you can observe more
Speaker 1: fine grain details than I can, we have different macro states.
Speaker 1: If we're thinking about different micro states, we have different entropies.
Speaker 1: Entropy is a relative thing like velocity, right, So it's
Speaker 1: not some fundamental thing in the universe from a statistical
Speaker 1: point of view. It's this relative thing. But it's also
Speaker 1: connected to energy and temperature and this thermodynamic sense of
Speaker 1: entropy that CLAUSI is invented.
Speaker 2: So could we go through this example again, but think
Speaker 2: about how bolts then identified the macro and the micro states.
Speaker 1: Yeah, absolutely, let's do that, and then let's think about
Speaker 1: how that gives us a handle on energy. And it's
Speaker 1: going to take us to understanding why energy flows and
Speaker 1: the macroscopic sense of energy. And so let's back up
Speaker 1: a thing about bolt men. Before we talk about entry,
Speaker 1: Let's just talk about temperature, because temperature is this other
Speaker 1: thing where we have like a definition of it microscopically
Speaker 1: and macroscopically. Temperature macroscopically is like, well, you put a
Speaker 1: thermometer in something, right, or you touch something you can
Speaker 1: feel it's hot or it's cold. But we also amazingly
Speaker 1: have this microscopic sense of temperature. Microscopically, we think about
Speaker 1: just particles in their velocities. Like it gets more complicated,
Speaker 1: you're talking about solids and liquids and whatever in different
Speaker 1: like vibrational states. But just imagine a box of particles
Speaker 1: and it's a simple gas and the particles are whizzing around.
Speaker 1: What happens when something is hot is those particles have
Speaker 1: higher speeds, and when something is cold, those particles have
Speaker 1: lower speeds. And I think a lot of people already
Speaker 1: have a sense of this, But what maybe you don't
Speaker 1: appreciate is that this really is a mapping between the
Speaker 1: microscopic and the macroscopic. You're like, hot equals high speed particles,
Speaker 1: cold equals low speed particles. That's amazing, it's incredible that
Speaker 1: we have this connection. Right, And those are two different
Speaker 1: definitions of temperature definition, one statistical microscopic sense of like
Speaker 1: particles moving, the other macroscopic thermodynamic definition of temperature where
Speaker 1: you're like, it's hot, it's cold, right, I feel hot
Speaker 1: and therefore heat is flowing from me. Right, This is incredible,
Speaker 1: And this is what Boltzman did. He connected these two
Speaker 1: senses of temperature microscopically and macroscopically.
Speaker 2: So just to nail the point home, high temperature is
Speaker 2: more entropy, is that right, because they're moving around and
Speaker 2: more disordered.
Speaker 1: Oh, no, great question. And entropy is a slightly more
Speaker 1: subtle connection to temperature. When energy flows to erase a
Speaker 1: temperature difference, like when something goes from hot to cold,
Speaker 1: entropy is the stuff that's being transported. And sort of
Speaker 1: the same way that like if you imagine an electric
Speaker 1: circuit and you have a voltage difference, what happens when
Speaker 1: you have a voltage difference, you have flow of current, right,
Speaker 1: you have charges flowing from one to the other to
Speaker 1: balance that out. Charges the stuff that's transported. When energy
Speaker 1: flows to erase a temperature difference. You can think of it,
Speaker 1: entropy is like the charge of that system. It's the
Speaker 1: stuff that's being transported. And so there's this connection between
Speaker 1: energy and heat and temperature and entropy. That's a little
Speaker 1: bit subtle, but I think it's important to understand. So
Speaker 1: we're familiar with the idea that energy flows, right, things
Speaker 1: flow from hot to cold. Why does that happen? Right?
Speaker 1: Why do things flow from hot to cold? The answer
Speaker 1: is that when things flow from hot to cold, the
Speaker 1: number of microstates tends to increase. Right, Just like the
Speaker 1: example we talked about in a minute ago with the particles,
Speaker 1: If you have one really really hot particle in ninety
Speaker 1: nine cold ones that has less entropy than sharing the
Speaker 1: energy among the particles, there's more ways to arrange it.
Speaker 1: If you can give it to all the part articles,
Speaker 1: then just give it to one. They're more micro states.
Speaker 1: So what happens when you have a temperature difference is
Speaker 1: even opportunity to increase the entropy. So energy moves to
Speaker 1: maximize the micro states, not because like, oh, the universe
Speaker 1: likes energy to be spread out or something like that.
Speaker 1: It's because all the micro states are equally likely and
Speaker 1: energy flows in a way that increases the number of
Speaker 1: micro states, right. Maximizing entropy is what causes energy to flow,
Speaker 1: or another way to say it is like energy flowing
Speaker 1: is increasing the entropy, right, and energy stops flowing when
Speaker 1: it no longer will increase the microstates. If you have
Speaker 1: like two systems next to each other, A and B,
Speaker 1: energy will flow from one to the other if it
Speaker 1: increases the number of microstates. Right. So, now as energy
Speaker 1: is flowing from A to B, A is losing energy,
Speaker 1: It's going to have fewer micro states. You're losing microstates,
Speaker 1: but B is gaining them. And this will happen as
Speaker 1: long as the gain and B is greater than the law.
Speaker 1: So as soon as that equalizes, as soon as moving
Speaker 1: energy from one system to another will not increase the
Speaker 1: total number of micro states, energy stops flowing, and that's
Speaker 1: what we define to be temperature. Temperature is this relationship
Speaker 1: between energy and entropy in a material. If the temperatures
Speaker 1: are equal, there's no gain in energy flowing. It does
Speaker 1: increase the energy. So that's the definition of temperature thermodynamically.
Speaker 1: If the temperatures are equal, no energy flow. And mathematically
Speaker 1: we define temperature to be this ratio of a change
Speaker 1: in energy to a change in entropy. Chemist out there
Speaker 1: probably know it's DEDs. So you don't have to have
Speaker 1: an equal energy between systems. What you need is equal temperature,
Speaker 1: which means that any energy that moves will make an
Speaker 1: equal change in the entropy. And so when the temperature
Speaker 1: is equal between the two objects, no heat will flow
Speaker 1: because dedes is the same. That's the definition of temperature thermodynamically. Right,
Speaker 1: we have the microscopic definition of temperature. It's like particles
Speaker 1: whizzing around. It's their speed. Now we have this weird
Speaker 1: thermodynamic definition of temperature as the ratio of energy to entropy.
Speaker 1: It turns out you can derive one from the other. Right,
Speaker 1: you can start with the mathematics of kinetic energy of
Speaker 1: particles and derive this definition. That's what Boltimant did. It's
Speaker 1: incredible mathematical bridge of temperature from one to the other
Speaker 1: and also helps us understand entropy from one to the other.
Speaker 1: And so that's sort of the thermodynamic sense of entropy,
Speaker 1: and I think it's amazing because it tells us why
Speaker 1: energy flows. Energy flows to increase the number of microstates,
Speaker 1: and it will stop flowing when the number of microstates
Speaker 1: will not be increased.
Speaker 2: Okay, I exactly kept up with that explanation. So my
Speaker 2: brain has no questions yet. So let's take a break
Speaker 2: and when we get back, we'll see what Kelly's brain
Speaker 2: has to offer. And we're back. So now we have
Speaker 2: two different definitions of entropy. Let's talk about some applications
Speaker 2: of this knowledge.
Speaker 1: Yeah, entropy has a lot of really deep consequences, and
Speaker 1: it touches so many topics and physics, from time to life,
Speaker 1: to black holes, to the Big Bang to the future
Speaker 1: of the universe. It's really incredibly pervasive. One reason is
Speaker 1: that it's so simple. It just tells us about how
Speaker 1: systems evolve. They evolve from less likely to more likely
Speaker 1: and what does that mean the consequences And one of
Speaker 1: the deepest connections with entropy is what we heard the
Speaker 1: listeners say that somehow entropy is responsible for why time
Speaker 1: moves forwards. And I remember hearing this for the first
Speaker 1: time thinking, what, that's crazy, that would explain such a
Speaker 1: deep mystery, right, Like, we have these three directions of
Speaker 1: space and one of time, and we know space and
Speaker 1: time are related and connected by relativity, but time is different.
Speaker 1: You can always revisit a location in space, but you
Speaker 1: can't revisit a location in time. And you can move
Speaker 1: positive and negative in the X axis, but only positive
Speaker 1: in the time axis. And why forwards are not backwards?
Speaker 1: And like what does this all mean? So there's some
Speaker 1: deep mysteries here about what time is.
Speaker 2: The idea here that if entropy is increasing, you're never
Speaker 2: going to get all the particles back in that same configuration,
Speaker 2: and that's why you can't go back in time. Oh no,
Speaker 2: you're laughing.
Speaker 1: I love that. I think that is sort of a
Speaker 1: summary of how physicists put it. The argument is a
Speaker 1: little bit more elaborated. It's that when we look at
Speaker 1: the laws of physics, so many of them are reversible.
Speaker 1: They don't seem to prefer one direction. You know, for example,
Speaker 1: in a vacuum, if you bounce a ball, it hits
Speaker 1: the floor, comes back up, It'll come back up to
Speaker 1: the same height, and so that path is reversible. Right.
Speaker 1: If you play a video of that happening in a
Speaker 1: vacuum with this new end energy loss, then you can't
Speaker 1: tell if the video is being played backwards or forwards.
Speaker 1: The same laws of physics supply and describe it perfectly,
Speaker 1: same with particles, almost completely. And so people were wondering
Speaker 1: for a long time, like, well, if the laws of
Speaker 1: physics don't care if time goes forwards or backwards, they
Speaker 1: work both ways, why does time go forwards? And so
Speaker 1: entropy seems to be one of the places where physics
Speaker 1: has a preference for one direction or the other, right,
Speaker 1: like it likes the micro states to increase, so energy
Speaker 1: increases with time. And then there's this leap people make.
Speaker 1: They say, oh, energy and time increase together, therefore that's
Speaker 1: why time moves forwards. And I'm not sure I follow
Speaker 1: that leap of logic, Like I will accept that entropy
Speaker 1: and time are connected. Entropy increases as time goes up.
Speaker 1: But that same law could tell you, like, well, the
Speaker 1: universe could still run backwards. It just wouldn't be symmetric.
Speaker 1: It would just mean that if the universe ran backwards,
Speaker 1: entropy would decrease. That law predicts that also, it predicts
Speaker 1: that if time ran backwards, Andy, will, why don't we
Speaker 1: live in that universe. I don't know it's consistent with
Speaker 1: the second law of physics, right as long as time
Speaker 1: runs backwards. So I don't believe that the second law
Speaker 1: physics tells you why time runs forwards. It connects time
Speaker 1: and entropy, but it doesn't tell you why time goes
Speaker 1: forward or backwards. There could be folks out there living
Speaker 1: in another universe where time runs backwards and entropy is decreasing,
Speaker 1: and they're claiming that entropy is the reason time runs backwards.
Speaker 1: Of course they don't call it backwards. There's definitely some
Speaker 1: interesting hints there, but I don't believe that it conclusively
Speaker 1: shows us why time goes forwards.
Speaker 2: So maybe I've missed this, but I think that's the
Speaker 2: first time we've used the phrase second law.
Speaker 1: The second law is just a statement that entropy increases
Speaker 1: as time goes on. Okay, delta S is greater than zero, right,
Speaker 1: S is the symbol for entropy, and so it just
Speaker 1: says the entropy increases as time marches on.
Speaker 2: All right, So if I can hijack the conversation for
Speaker 2: a second, oh please do so. You know, as someone
Speaker 2: who spends a lot of time with evolutionary biologists. I've
Speaker 2: been to a couple creationism evolution debates and they get spicy.
Speaker 1: That really bends the meaning of a word debate.
Speaker 2: Also, I felt like I learned a lot by thinking
Speaker 2: through the arguments. But anyway, so a common point that
Speaker 2: is brought up during these discussions is that the second
Speaker 2: law says that things should be getting more disordered with time.
Speaker 2: So how do you have evolution creating more complex organisms
Speaker 2: over time? And what is the answer that you would
Speaker 2: give them? The answer I heard, if this is helpful,
Speaker 2: is it has to do something with the second law
Speaker 2: being about if you're in a closed system. But the
Speaker 2: Earth isn't a closed system because energy is coming in
Speaker 2: from the sun, and so if you're not in a
Speaker 2: closed system, none of that holds, Is that right?
Speaker 1: Yeah, I'm thinking about it for a minute first, because
Speaker 1: I'm wondering what it is meant here by complexity, you know,
Speaker 1: like and whether it even is connected to entropy, statistically
Speaker 1: order disorder, micro states, macro states, or if it's just
Speaker 1: this sort of like intuitive this seems similar to that,
Speaker 1: So let's use one word in place of the other.
Speaker 1: I'm not even really sure that complexity is connected to entropy.
Speaker 1: At all. But it's definitely true that life and entropy
Speaker 1: have a close connection because living things tend to decrease
Speaker 1: their local entropy. My body is a system that decreases
Speaker 1: its entropy. You might wonder, like, well, if entropy is
Speaker 1: supposed to always increase, how does that happen. Well, as
Speaker 1: you say, I'm not isolated, right, I have a huge
Speaker 1: environment around me, and so I exchange energy with the
Speaker 1: environment and do all sorts of complicated stuff to locally
Speaker 1: make my entropy go down. Overall, I'm increasing the entropy
Speaker 1: of the environment I'm interacting with more than my entropy
Speaker 1: is decreasing, So overall second law is fine. The point
Speaker 1: of the second law is you can't pick out a
Speaker 1: one part of a system and say the entropy always
Speaker 1: has to increase for every sub part of the system.
Speaker 1: It's just the whole system where entropy has to increase.
Speaker 1: The same way, like you can't apply conservation of energy
Speaker 1: to just half of a system and say, oh, the
Speaker 1: energy is flowing out of this and so energy is
Speaker 1: not conserved. Like energy is conserved for the whole system.
Speaker 1: Entropy increases for the whole system. So actually, this is
Speaker 1: one way that some physicists think we should define life.
Speaker 1: It's like systems that decrease their local entropy at the
Speaker 1: expense of the environment. Because you know, biologists spend hours arguing, like,
Speaker 1: what is life anyway in the system that can reproduce
Speaker 1: is it's something that passes on genetic information? Whatever is
Speaker 1: all these definitions of life? And this is sort of
Speaker 1: a physics based definition of life. It's something that decreases
Speaker 1: its local entropy. Doesn't violate the second law of thermodynamics
Speaker 1: to decrease your local entropy at all. And I don't
Speaker 1: know how to think about evolution in terms of complexity.
Speaker 1: Like I guess evolution has produced systems that tend to
Speaker 1: decrease their local entropy more and more as time goes on.
Speaker 1: But to me, that's not a violation of the second
Speaker 1: law of thermodynamics at all, or really says anything about
Speaker 1: micro versus macro states.
Speaker 2: Interesting, That's not an answer I heard it any of
Speaker 2: the debates that I attended. I was raised We don't
Speaker 2: need too much of Kelly history here. And I was
Speaker 2: raised Catholic in a family where and I know Catholicism
Speaker 2: is okay with evolution, But I was raised in a
Speaker 2: family where the young Earth hypothesis that Earth is only
Speaker 2: six thousand years old was held pretty tightly, and so
Speaker 2: I went to a lot of these debates to try
Speaker 2: to figure out how I felt about it on my own,
Speaker 2: and the answer I always heard from the evolutionary billogist
Speaker 2: was well, we're not a closed system or whatever. So anyway,
Speaker 2: that was really interesting. W what a virus be alive
Speaker 2: according to the physicist definition of life?
Speaker 1: That's a good question, I think it would be. I
Speaker 1: once had a conversation with Sarah AMRII Walker, and she
Speaker 1: wrote a fascinating book last year about this whole question.
Speaker 1: So I should ask her that, but I think so.
Speaker 1: But let me ask you, what was it that convinced
Speaker 1: you that the Earth is not young, that it's billions
Speaker 1: of years old and not thousands of years old, assuming,
Speaker 1: of course, that you got there. I did.
Speaker 2: I did it was? I mean, I took enough classes
Speaker 2: where I learned about the various ways we date rocks
Speaker 2: and about the fossil record and how complete it was,
Speaker 2: and just sort of engaged more with what we actually
Speaker 2: know in the science, and it became pretty clear to
Speaker 2: me that the data was pointing to an Earth much
Speaker 2: much much much, much, much much older than six thousand
Speaker 2: years old.
Speaker 1: Yeah. Wow, fascinating. So thinking about deep time and the
Speaker 1: history of the universe in the future of the universe.
Speaker 1: Entropy is also connected to these ideas of like the
Speaker 1: Big Bang and the future of the universe and black holes.
Speaker 1: And there's a lot of confusion out there about what
Speaker 1: entropy tells us about these things. I think partially because
Speaker 1: people are thinking about entropy from a temperature point of
Speaker 1: view or a gravitational point of view, which are actually
Speaker 1: a little bit different, and people are thinking about no
Speaker 1: entropy meaning no temperature. So I thought'd be useful to
Speaker 1: go through these a little bit and help untangle some
Speaker 1: of the confusion.
Speaker 2: Go for it.
Speaker 1: So let's start the very beginning with the Big Bang. Right.
Speaker 1: If the universe is increasing in entropy all the time,
Speaker 1: then as you go back in time, the universe is
Speaker 1: decreasing in entropy, and that means that entropy gets lower
Speaker 1: and lower and lower, which means, you know, if you
Speaker 1: go back to the very first moments that we can
Speaker 1: think about what we call the Big Bang, when the
Speaker 1: universe was very hot and very dense, then that must
Speaker 1: have been very low entropy, right, because entropy is increasing,
Speaker 1: so entry must have been very, very low. But it's
Speaker 1: hard to get your head around. Like I'm imagining a hot,
Speaker 1: dense gas and it's pretty smooth, right, it's not very clumpy.
Speaker 1: That doesn't seem to me like a very low entropy situation.
Speaker 1: In fact, it seems like I'm disorganized and everything's flying around.
Speaker 1: How is that low entropy? This is confusing to people,
Speaker 1: But the key thing to understand is the dominant force
Speaker 1: there is gravity. So instead of thinking about entropy from
Speaker 1: a point of view of like the temperature of the particles,
Speaker 1: think about the arrangements of the particles and what's a
Speaker 1: more likely arrangement.
Speaker 2: So gravity is pulling everything to one spot, whereas without
Speaker 2: that it would have been all over the place and
Speaker 2: much more disordered and spread out. Is that the idea.
Speaker 2: I'm going to stop trying to finish your sentences because
Speaker 2: it reveals a little I'm understanding. But I think I'm
Speaker 2: getting this.
Speaker 1: A gravitational point of view, Being really spread out is
Speaker 1: very low entropy, and being clumped together is higher entropy. Right,
Speaker 1: Because gravity is not the same as heat, gravity tends
Speaker 1: to clump things together instead of spread things out, and
Speaker 1: so from a gravity point of view, being very spread
Speaker 1: out is rare. Like if you have a bunch of
Speaker 1: matter and you let it sit there, like, it's very
Speaker 1: rare for it to be perfectly spread out like for
Speaker 1: that to happen, everything would have to be in perfect balance,
Speaker 1: like a universe that's completely smooth, where there's no perturbations.
Speaker 1: That's what be required for gravity to not be able
Speaker 1: to clump things together. So gravity likes to clump things together.
Speaker 1: Clumping things together increases their entropy. From a gravitational point
Speaker 1: of view, Remember we set entropy is relative. It's not
Speaker 1: like there's a certain number for the universe or certain
Speaker 1: number even for a system. It depends on the arrangements
Speaker 1: and what you'd define as the macro and the micro states.
Speaker 1: And so from a gravitational point of view, an initial
Speaker 1: state where everything is very spread out is quite unlikely.
Speaker 1: And actually one of the deep mysteries of the universe
Speaker 1: is why did the universe begin in such a low
Speaker 1: entropy state. If we're going from a low entropy to
Speaker 1: high entropy and it turns out there's actually going to
Speaker 1: be a maximum entropy of the universe, then the sort
Speaker 1: of the time it takes to get to the maximum entropy,
Speaker 1: which we call the heat death, which we'll talk about
Speaker 1: in a minute, defines a sort of the interesting period
Speaker 1: of the universe. Once we get to the heat death,
Speaker 1: the universe isn't really very interesting anymore. So how low
Speaker 1: the entropy is when we begin sort of defines how
Speaker 1: long we can do interesting stuff right, and we're sort
Speaker 1: of lucky the universe begin with very very low entropy,
Speaker 1: Like if it started with very very high entropy, not
Speaker 1: much would happen. I just sort of continue that way.
Speaker 1: And so one of the mysteries of entropy actually is
Speaker 1: like why it started with such low entropy. And as
Speaker 1: gravity continues to do its work, it makes black holes, right,
Speaker 1: it can clump these things together, and black holes actually
Speaker 1: have the maximum entropy, Like there's no way to arrange
Speaker 1: a mass with higher entropy than a black hole. It's
Speaker 1: like the maximum entropy arrangement of a system. And the
Speaker 1: fact that black holes have an entropy is really fascinating,
Speaker 1: and it was one of the ways that Hawking and
Speaker 1: his collaborators figured out that black holes must glow a
Speaker 1: little bit, because having entropy means you can define temperature
Speaker 1: for black holes, and if you can find temperature for
Speaker 1: black holes, then you can think about them glowing like
Speaker 1: everything else in the universe that has temperature. So you
Speaker 1: can derive Hawking radiation thermodynamically, saying like, well, if it
Speaker 1: has entropy, it's got to have some temperature and then
Speaker 1: it should glow in the universe. And you can think
Speaker 1: about the temperature of a black hole. And actually, really
Speaker 1: really massive black holes have lower temperature, which is why
Speaker 1: they glow less than small black holes that have higher
Speaker 1: temperature than they glow brighter. And a lot of people
Speaker 1: think that Hawking derived his idea of Hawking radiation from
Speaker 1: like thinking about the little particles near the edge of
Speaker 1: the black hole. But that's not true. Actually, it's not
Speaker 1: where the derivation comes from. It comes from thermodynamics, because
Speaker 1: we don't understand the gravity for little particles, like there
Speaker 1: is no way to think through that little example microscopically
Speaker 1: of what happens to the particles. We only have a
Speaker 1: macroscopic understanding of Hawking radiation because, as we've said many
Speaker 1: times on the show, we don't understand quantum gravity.
Speaker 2: I'm trying to decide if I can rescue my comparison
Speaker 2: about my house being a mess with entropy. Could I
Speaker 2: say my house is like a black hole because that's
Speaker 2: where the maximum entropy is, or I really need to
Speaker 2: let this comparison go. I think this is where disordered
Speaker 2: has a negative connotation to me, and I think that
Speaker 2: maybe that's been holding me back this whole time.
Speaker 1: I'm not going to comment because I feel like that's
Speaker 1: going to put me in the middle of your marriage.
Speaker 2: Okay, let's move on there.
Speaker 1: And I want Zach to like me, so all right.
Speaker 2: Let's move on to heat death.
Speaker 1: Yeah, so what's going to happen at the end of
Speaker 1: the universe. Well, you know, gravity clumps things together into
Speaker 1: black holes eventually, but those black holes also glow, right,
Speaker 1: and so you get the universe increasing its entropy, you
Speaker 1: get black holes, and those black holes glow out photons.
Speaker 1: And so the final end point of the universe is
Speaker 1: those black holes evaporate into photons and the universe just
Speaker 1: filled with this hawking radiation, sometimes photons, sometimes other particles,
Speaker 1: and that's the state of maximum entropy. So how do
Speaker 1: we understand the entropy in this whole story? It's low
Speaker 1: when the universe begins with matter mostly spread out, and
Speaker 1: then grows as the universe gathers together things into massive
Speaker 1: objects like black holes, and then keeps growing as the
Speaker 1: universe converts those black holes back into a bath of
Speaker 1: matter and radiation from black hole evaporation. How does that
Speaker 1: make sense in terms of our definition of entropy and
Speaker 1: microstates and all that. Yeah, the answer is it really
Speaker 1: doesn't because we don't have micro states for gravity. That
Speaker 1: would require understanding how gravity works for particles, and we
Speaker 1: just don't, not until somebody cracks quantum gravity. So this
Speaker 1: concept of black hole entropy is not statistical. It's thermodynamic,
Speaker 1: as we mentioned a minute ago. It's derived from arguments
Speaker 1: about temperature and about energy. We know that a black
Speaker 1: hole entropy grows with its surface area, and that lines
Speaker 1: up with our understanding that entropy grows because gravity will
Speaker 1: gather stuff together to make black holes larger. But then
Speaker 1: how does it make sense for entropy to keep growing
Speaker 1: as though a black holes evaporate away to something that
Speaker 1: resembles the early universe Again, But it turns out the
Speaker 1: heat death bath of radiation is not the same as
Speaker 1: the early universe conditions. We think that the quantum information
Speaker 1: is still there. The whole history of the universe is encoded,
Speaker 1: and so the particles that evaporated from the black holes
Speaker 1: are all entangled together in a complicated way. People are
Speaker 1: still figuring out that holds that information. So the answer
Speaker 1: is we still aren't sure about a lot of this
Speaker 1: black hole information, and entropy is a very active area
Speaker 1: of research. And that's the best explanation I can give.
Speaker 2: You, Daniel, that was a perfect explanation.
Speaker 1: And so we end up with this situation where energy
Speaker 1: is sort of surprisingly spread out again, but it's not cold.
Speaker 1: People confuse the heat death of the universe and think, oh,
Speaker 1: nothing is moving. They think of it like death freezing.
Speaker 1: But it's not absolute zero. It just means there's no
Speaker 1: way to get anything done the way like Carnot was saying,
Speaker 1: that you need energy differences to get stuff done. Like
Speaker 1: you run your temperature, you need hot and coals. The
Speaker 1: energy can flow from hot to cold. You need water
Speaker 1: to flow downhill so you can capture it with your
Speaker 1: water wheel. If everything is flat and smooth, then there's
Speaker 1: no way to do anything useful, right, And so that's
Speaker 1: what the heat death is. Not when everything is frozen,
Speaker 1: not when particles can't move, but when there's no way
Speaker 1: to do anything useful in the universe. And so that's
Speaker 1: why you can't have like life or anything else interesting
Speaker 1: because everything's maximumly spread out. You can't take advantage of
Speaker 1: any energy differences because there aren't any anymore.
Speaker 2: We know what temperature the heat death will be if
Speaker 2: it's not absolute zero.
Speaker 1: Yeah, it's a great question. It depends on how long
Speaker 1: it takes, because as the universe expands, it cools, and
Speaker 1: we don't know actually how quickly the universe will be
Speaker 1: expanding in the future. It's accelerating, but you know, the
Speaker 1: mechanism for that acceleration is dark energy, which is not understood.
Speaker 1: So unfortunately I can't give you a number for that today.
Speaker 2: Well. One of the things I love about our conversations
Speaker 2: is that so often halfway through a lesson, which is
Speaker 2: what some of these end up feeling like. I feel
Speaker 2: like I enter the conversation thinking Okay, I know what
Speaker 2: we're talking about, and I leave thinking, wow, that was
Speaker 2: a lot different than what I thought the answer was
Speaker 2: going to be. And so I always leave and think
Speaker 2: about the conversation like much longer into the day. It
Speaker 2: sticks with me for a while, and so thank you
Speaker 2: for helping me realize that I shouldn't be making entropy
Speaker 2: jokes about my house, and now I'll start thinking about
Speaker 2: jokes about how no work can get into I'm gonna
Speaker 2: start working on that.
Speaker 1: Yeah, or you know, use jazz instead. Hey, Zach, can
Speaker 1: you jazz up the kitchen a little bit? Or the
Speaker 1: kitchen has gotten a little too jazzy.
Speaker 2: A little too jazzy, I think is the problem with
Speaker 2: the kitchen. It needs more melody.
Speaker 1: I love thinking about these topics, and especially helping people
Speaker 1: understand how they really work, because so often the real
Speaker 1: understanding of it is more fascinating and more interesting. We're
Speaker 1: not throwing a wet blanket on people's idea of entropy.
Speaker 1: We're showing them how exciting, how jazzy it actually is.
Speaker 2: Yes, and I'm trying to make myself feel a little
Speaker 2: bit better about the multiple times in this conversation where
Speaker 2: I got the answer exactly opposite correct, And I guess
Speaker 2: I'm hoping that this is a place where people can
Speaker 2: come with their incorrect, preconceived notions Oh yeah, and not
Speaker 2: feel self conscious about having it wrong. Absolutely, because if
Speaker 2: Kelly can be wrong so often and can continue to
Speaker 2: move through her life with any degree of confidence, then
Speaker 2: you should also feel welcome to ask us anything, So
Speaker 2: reach out.
Speaker 1: Yeah, and if one of our explanations didn't make sense
Speaker 1: to you, please do reach out. It's not just Kelly
Speaker 1: you gets to ask questions, and not just me. You
Speaker 1: get to ask Kelly biology questions. We want to hear
Speaker 1: your questions. Please do write to us two questions at
Speaker 1: Daniel and Kelly dot org. We'll ride back to you.
Speaker 2: We respond to everybody, looking forward to hearing from you.
Speaker 1: All right, until then, everybody keep it chassy.
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