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Entropy and Life
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0:00
Life needs order. This isn’t just what exhausted parents say, it’s a property of nature. Life requires structure. The human body for example isn’t just a bag of mixed atoms – the atoms are ordered, they’re in very specific places. Like, organs and stuff. Look, what do I know, I’m a physicist, not a physician. Physics doesn’t tell you much about life, but it tells you that entropy cannot decrease. And as entropy increases, order gets destroyed.
0:30
This is why things break, why we age, and why the universe will eventually become a big, disordered bag of mixed particles. At some point, life in the universe will become impossible. That’s kind of depressing. But is it right? What does physics really tell us about entropy increase? What is entropy to begin with? And how will everything end? That’s what we’ll talk about today.
0:59
Imagine you’re driving through the rain. Drops fall onto your window making little splashes. The street gets wet, you drive through puddles and realize that the wiper on your car really needs replacement. It sounds normal enough. But why do we never see water collect on the street to form drops which then fly into the sky and make clouds? Why do parts on your car break on their own but never repair themselves on their own?
1:26
Physicists call it the “arrow of time” and it’s the reason why we get older but never younger. Its origin has remained somewhat of a mystery. That’s because according to the equations that we use to describe nature, it’s totally possible for people to get younger, or for water drops to flow up into the sky. The equations we have found work both forward and backward in time. We say they are “time reversible”. We can totally write down an equation
1:56
that makes water fly into the sky. In reality though, this doesn’t happen. So, what gives? The reason is that to explain what goes on in nature you don’t just need an equation that tells you how things change. You also need what’s called an initial state. You need to know what changes. This initial state is the entire configuration of the system at any one moment in time, for example the positions and momenta of all particles. You take this initial state,
2:26
and then you calculate what it does. Physics basically comes down to the unforgettable TikTok “I had an initial state and guess what happened next.” The thing is now that there are a lot of initial states that will make water drop down from the sky. But very few that will make it flow back up. To get this done, you’d have to very precisely arrange all the molecules in the ground to spit the water back
2:50
out and the molecules in the air to create just the right drift for the drops to fly back up. It’s so incredibly unlikely it never happens. Physicists quantify this probability with entropy. Entropy is a measure for how likely a system is to be in a certain configuration. Suppose you have a box and there’s air inside. The air is made of molecules that move around. It’s very unlikely that they all sit on the right side of the box. If that was so, the entropy would be small. It’s very
3:22
likely that they are almost evenly distributed in the box. The entropy in this case would be large. So what’s going to happen if you put air in only one side of a box? Well, it’s going to spread out. Because that’s the likely thing to happen. And once the air is in a likely state, it’s most likely to stay there. This means the distribution is going to remain approximately even. And luckily so because it’d be inconvenient if you entered a room and all the air went into a corner.
3:51
We call such approximately even distribution an “equilibrium”. It’s not that the air molecules stopped moving when they’re in equilibrium, they’re still zipping around. But on the average the distribution stays the same for a very long time. Physicists talk about entropy not just to confuse people on YouTube, but because it has practical purposes. If you have a system with small entropy you can do “work” with it. In physics “work” means
4:20
useful energy. You can do something with it. For example, when the air is on one side of the box, you can put a divider in the middle and the air pressure will move it. You could convert this motion to electric energy and then do something else with it. Charge your phone, power a light, drill a hole into the wall and ruin your neighbour’s podcast recording. Every time you create structure, you do it by drawing on a reservoir of low entropy.
4:48
When a system has reached equilibrium and the average remains the same, there’s still energy in it, because the molecules are still moving around, but it’s not useful energy. You can’t do work with it anymore. Physicists call this useless energy “heat”. Formally, entropy measures the number of microstates per macrostate. A microstate is the exact definition of the state of the system. For the molecules in the box
5:16
that could be the position and momenta of each of the particles. A macrostate, on the other hand, is a state that we, as macroscopic objects, are interested in. For our box, that could be how many molecules are on the left and how many are on the right side of the box. A macrostate is an average over many microstates. If you want to know the entropy you then ask how many possible ways there are for the air molecules
5:44
to zip around so that there are approximately the same number on each side. Answer is, there are a lot of those, so that’s likely and the entropy is large. If they’re all on one side, there are far fewer ways to get this done, so that’s unlikely and the entropy is small. Technically the entropy is the logarithm of the number of microstates, multiplied by a constant called Boltzmann’s constant. If you remember one thing about
6:12
the logarithm it’s probably that the logarithm of 1 is zero. This means the entropy is zero if and only if there is exactly one microstate for your macrostate. Ok, so why does entropy increase? Entropy increases because that’s the likely thing to happen. And that removes part of the mystery about the arrow of time. Because it explains why we observe some things and not others, even though the laws of nature work both forward
6:42
and backward in time. Because one way is more likely than the other. An egg that falls to the ground, breaks. It doesn’t jump up and unbreak. Alright, we sorted it out. But this brings up another question. If low entropy states, like eggs, are unlikely, why do we have them to begin with? Why isn’t the universe in equilibrium already when that’s most likely? We don’t know. We do know that the universe must have started in a state of low entropy,
7:14
a very unlikely state, but we have no idea why. It’s often called the “Past Hypothesis”, a term introduced by the philosopher David Alberts. It just posits that this is what it was, but doesn’t explain why. The entropy of our universe has been increasing ever since the big bang because that’s what’s likely to happen. But this is the total entropy. In some parts of the universe, entropy can, and does remain small, for a very long time,
7:42
because it doesn’t have to be evenly distributed. Indeed, we can shovel around entropy ourselves. If you have a reservoir of low entropy, you can use that to lower the entropy elsewhere. And luckily we have a big low entropy reservoir nearby though it’s more commonly called the sun. The sun started out at low entropy. As it fuses atomic nuclei, its entropy increases. Again, because that’s the likely thing to happen. As the entropy of the sun increases,
8:13
it sends energy with low entropy to us in form of sunlight. We can use that to create electricity and lower the entropy of something else. We can use it to run a fridge and keep the eggs cool. Or power a light and find out what’s under the couch. Or maybe better not. It's a similar story with fossil fuels. They’re low in entropy. If we burn them, we increase the entropy of those fuels, or their remains, and we can use that to
8:42
decrease the entropy of something else. For example, we can manufacture goods and products. These are all low entropy objects with specific structures that we have created. But eventually this will stop working because we will run out of low entropy reservoirs. Our sun will run out of fuel. Earth’s core will go cold. Other stars will run out of fuel. And eventually, 10 to the 100 years or so from now, the universe will come into thermal equilibrium,
9:11
entropy will be as large as it can get, and nothing will happen, on the average. Physicists call this “heat death”. The word is somewhat misleading because it doesn’t mean it’ll be hot. To the contrary it’ll be very cold and very dark. “Heat” refers to the useless energy that I mentioned previously. It’d better be called “high entropy death”. What does entropy have to do with order?
9:37
This has always confused me. I now think the brief answer is “nothing”. Because “order” doesn’t have a well-defined meaning. For example, imagine you are pouring milk into tea. At the beginning they are neatly separated, ordered, you could say. At the end they are evenly mixed. I would also call this ordered. But in physics this even distribution doesn’t count as order. This is why I don’t find this referral to order useful, because what looks
10:00
ordered to us is due to human perception and expectation, rather than a property of nature. This reference to order causes a lot of confusion. For example, as we saw earlier, the entropy in the early universe must have been small. Back then, matter was very evenly distributed with small fluctuations in the density which then grew to galaxies. At the end of the universe, matter will again be evenly distributed with small fluctuations in density. Both cases seem
10:25
equally ordered, if you wish. So how can it be that the one has low entropy and the other high? It’s because in the early universe the density of the matter is high, and this means the gravitational force is strong. And the gravitational force is attractive, so it wants to draw the stuff together. An even distribution of matter when gravity is strong is incredibly unlikely. It’s unstable. It wants to clump. This even distribution therefore had low entropy. At
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the end of the universe, however, matter will be very thinly distributed, and gravity will be weak, so it doesn’t want to clump again. This is a very likely situation. So the entropy is high. And what’s with information. Ah, yes, the relation between entropy and information is subtle. It comes from the definition of entropy as the number of microstates per macrostate. Remember that to calculate the entropy you average over microstates.
11:25
This means you throw away information. In a macrostate, there’s something you don’t know. So high entropy means low information and low entropy means high information. All that I told you so far is pretty standard textbook stuff and if you picked a random physicist on the street and asked them if they agree, you should let them go because they have better things to do. Now I want to tell you why I don’t think heat death is how life will end.
11:54
Remember that entropy counts the number of microstates per macrostate. But what is a macrostate? A macrostate is a state that we as humans are interested in. It’s something we choose to calculate a quantity that is useful for our purposes. It’s an average description that we’re interested in, maybe because we want to understand how efficiently a fridge will work, or how much power an engine will have. Those are good reasons, but a macrostate has
12:24
no fundamental significance, and it makes no sense to use it to talk about the fate of the universe. See, a system is always only in one microstate. That is true for the molecules in the box and also for the entire universe. They are in one particular configuration, one particular state. The probability of this microstate is 1, and that of all other states zero. And as the state changes in time, this will remain so. The entropy of this one microstate per
12:54
microstate is always zero and stays zero. The second law of thermodynamics doesn’t say that entropy increases. It says it doesn’t decrease. But it can full well remain constant. The reason we get more complicated probabilities and the reason we say entropy increases is because we lack information about some systems. If we put air molecules in the corner of a box, we don’t know where they’re going, but at least we know where they are. If we now let the air
13:25
spread into the entire box, it’s still the same microstate. It’s still a microstate that one minute ago was in the corner of the box. But we can’t tell. We used to have information about the state. We no longer have. That’s why entropy increases. Because we lose access to information. But there are always macrostates that will turn a high entropy system into a low entropy system. For the molecules in the box for example you could put in a divider like this. It’s just
13:55
that this would require information that we cannot easily access. We can access it, but for that we’d need another low entropy reservoir, so nothing would be gained. The relevant point is now that our notion of entropy is based on the physical properties of macroscopic devices that we humans have easy access to. It isn’t a fundamental property of nature. I believe that as the universe gets older and entropy increases according to us,
14:26
new complex systems will emerge that rely on different macrostates, macrostates that we ourselves could never use. And for those complex systems, call them living beings, the entropy will be small again. So life will go on, but in a form very different from us. And what about quantum mechanics, I hear you ask. Quantum mechanics doesn’t change anything about this. In quantum mechanics, the universe is still in exactly one microstate. It’s just that now it’s one big wave-function.
15:00
I sometimes hear people say that the Heisenberg Uncertainty principle implies there are quantities that you cannot measure at the same time, for example position and momentum. But this is a misunderstanding. You can full well measure both. It’s just that if you can predict the outcome of one of those measurements very well, you can say very little about the outcome of the other measurement. I talked about this in more detail in an earlier video.
15:28
So if, in 10 to the 100 years, you arrive at the end of the universe and they’ve put up a sign saying sorry we’re closed, tell them Sabine sent you. This was the most optimistic and uplifting video I’ve ever done and can ever do. It can only go downhills from here. Big questions like this got me interested in physics. The fascinating thing about them is that you don’t need all that much maths to understand them. It’s differential equations
15:56
and probabilities, and that’s basically it. If you want to know more about the maths behind what I talked about today I recommend you try Brilliant.org who have been sponsoring this video. Brilliant offers courses on a large variety of topics in science and mathematics. They have excellent courses on differential equations, as well as on the fundamentals of statistics, and knowledge and uncertainty. Like all their courses, they come with interactive
16:23
visualizations and follow-up questions, so you can check your understanding right away. Brilliant is a fresh and new approach to learning. I wish it’d been around when I was a student because I’ve found it highly effective to understand and also to remember material. I even have my own course on Brilliant now, that’s an introduction to quantum mechanics. It starts from the very basics and doesn’t require you to
16:49
bring background knowledge. My course covers topics such as interference, superpositions and entanglement, the uncertainty principle, and Bell’s theorem. And afterwards, maybe you want to continue learning more about quantum computing or special relativity. If you're interested in trying Brilliant out, use our link Brilliant.org/Sabine and sign up for free. You'll get to try out everything Brilliant has to offer for 30 days, and the
17:18
first 200 subscribers using this link will get 20 percent off the annual premium subscription. Thanks for watching, see you next week.
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