The Most Misunderstood Concept in Physics

- This is a video about one of the

most

important, yet least understood,

concept

s in all of

physics

. It governs everything from molecular collisions to massive storms. From the beginning of the universe through all its evolution, until its inevitable end. In fact, it can determine the direction of time and even be the reason life exists. To see the confusion around this topic, you just need to ask a simple question. What does the Earth get from the sun? - What does the earth get from the sun? - Well, are they rays of light? - What do we get from the sun? - Heat. - Warmth. - Warmth, light. - Vitamin D, we obtain it from... - We obtain vitamin D from ultraviolet rays. - Well, a lot of energy. - What does the earth get from this, energy? - Yes, energy. - Energy. - He got over it.

Every day, the Earth receives a certain amount of energy from the sun. And so how much energy does the Earth radiate into space relative to the amount it receives from the Sun? - Probably not so much, I, you know, I don't think it's just radiating backwards. - I would say less. - Less. - Less. - I say less. - I guess around 70%? - It's a fraction. - I would say 20%. - Because... - Because we used some of that. - We use part of the energy. - Mm-hmm. - We consume a lot, right? - But the thing about energy is that it never goes away.

You can't really use it. - It would have to break even, right? The same amount, yes. - You know, cause and effect. It would be the same in some ways, right? - For

most

of Earth's history, there should be exactly the same amount of energy coming from the Sun as the Earth radiates into space. - Wow. - Because if we didn't do that, then the earth would get much hotter, that would be a problem. - That would be a big problem. - So, if that's the case... - Yes. - So what do we really get from the sun? - Good question. - Hmm. - It gives us a nice tan. - It gives us a nice tan, I love it.

We are getting something special from the sun. - I don't know, what do we get without energy? - But nobody talks about that. To answer that, we have to go back to a discovery made two centuries ago. In the winter of 1813, France was being invaded by the armies of Austria, Prussia, and Russia. The son of one of Napoleon's generals was Sadi Carnot, a 17-year-old student. On December 29 he writes a letter to Napoleon asking him to join the fight. Napoleon, worried about the battle, never responds. but Carnot fulfills his wish a few months later, when Paris is attacked.

The students defend a castle just east of the city, but there is no match for the advancing armies, and Paris falls after only a day of fighting. Forced to retreat, Carnot is devastated. Seven years later, he goes to visit his father, who fled to Prussia after the fall of Napoleon. His father was not only a general, but also a physicist. He wrote an essay on how energy is transferred more efficiently in mechanical systems. When his son comes to visit, they talk at length about the great advance of the time: steam engines. Steam engines were already used to power ships, extract minerals and dig ports.

And it was clear that the future industrial and military power of nations depended on having the best steam engines. But French designs were falling behind those of other countries such as Britain. So, Sadi Carnot took it upon herself to find out why. At that time, even the best steam engines only converted about 3% of thermal energy into useful mechanical work. If he could improve that, he could give France a huge advantage and restore her place in the world. So he spends the next three years studying heat engines, and one of his key ideas has to do with how an ideal heat engine would work, one without friction and without losses to the environment.

Does it look like this. Take two really large metal bars, one hot and one cold. The engine consists of a chamber filled with air, where heat can only enter or exit through the bottom. Inside the chamber is a piston that is connected to a flywheel. The air starts at a temperature just below that of the hot bar. First, the hot rod is contacted with the chamber. The air inside expands with the heat flowing into it to maintain its temperature. This pushes the piston up, turning the flywheel. The hot rod is then removed, but the air in the chamber continues to expand, except now without heat coming in, the temperature decreases.

Ideally, until it reaches cold bar temperature. The cold rod comes into contact with the chamber and the flywheel pushes the piston down. And as the air is compressed, heat is transferred to the cold bar. The cold bar is removed. The flywheel compresses the gas by further increasing its temperature until it is just below that of the hot rod. The hot rod is then reconnected and the cycle is repeated. Through this process, the heat from the hot rod is converted into flywheel energy. And what is interesting to note about Carnot's ideal machine is that it is completely reversible.

If you ran the engine in reverse, first the air expands lowering the temperature, then the chamber comes into contact with the cold bar, the air expands further, extracting heat from the cold bar. The air is then compressed, increasing its temperature. The chamber is placed on top of the hot bar and the energy of the flywheel is used to return heat to the hot bar. No matter how many cycles were executed in the forward direction, the same number could be executed in reverse and, in the end, everything would return to its original state without the need for additional energy input.

So when running an ideal engine, nothing really changes. You can always undo what you did. What then is the efficiency of this motor? Since it is completely reversible, you might expect the efficiency to be 100%, but that is not the case. In each cycle, the power of the flywheel increases by the amount of heat flowing into the chamber from the hot rod, minus the heat leaving the chamber through the cold rod. So to calculate the efficiency, we divide this energy by the heat input of the hot rod. Now the heat entering the hot side is equal to the work done by the gas on the piston, and this will always be greater than the work done by the piston on the gas on the cold side, which is equal to the heat leaving.

And this is because on the hot side, the hot gas exerts greater pressure on the piston than that same gas when it is cold. To increase engine efficiency, you can increase the hot side temperature, decrease the cold side temperature, or both. Lord Kelvin discovers Carnot's ideal heat engine and realizes that it could form the basis of an absolute temperature scale. Imagine that the gas is allowed to expand by an extreme amount, so much so that it cools to the point where all particles in the gas stop moving. Then they would put no pressure on the piston and no work would be needed to compress it on the cold side, so no heat would be lost.

This is the idea of ​​absolute zero and would allow a 100% efficient engine. Using this absolute temperature scale, the Kelvin scale, we can replace the amount of heat entering and leaving with the temperature of the hot and cold side respectively, because they are directly proportional. So we can express efficiency like this, which we can rewrite like this. What we have learned is that the efficiency of an ideal heat engine does not depend on the materials or design of the engine, but fundamentally on the temperatures of the hot and cold sides. To achieve 100% efficiency, you would need infinite temperature on the hot side or absolute zero on the cold side, both of which are impossible in practice.

Therefore, even without friction and losses to the environment, it is impossible to make a heat engine 100% efficient. And that is because to return the piston to its original position, it is necessary to discharge heat into the cold rod. So not all the energy remains in the flywheel. Now, in Carnot's time, high-pressure steam engines could only reach temperatures of up to 160 degrees Celsius. So its theoretical maximum efficiency was 32%, but its actual efficiency was more like 3%. This is because real motors experience friction, dissipate heat to the environment, and do not transfer heat at constant temperatures. So for the same amount of heat coming in, less energy ends up at the flywheel.

The rest spreads along the walls of the cylinder, the flywheel shaft, and radiates to the outside. When energy is diffused like this, it is impossible to recover it. So this process is irreversible. The total amount of energy did not change, but it became less usable. Energy is more usable when it is concentrated and less usable when it is dispersed. Decades later, German physicist Rudolf Clausius studies the Carnot engine and finds a way to measure how dispersed the energy is. He calls this quantity entropy. When all the energy is concentrated in the hot rod, the entropy is low, but as the energy spreads to the surroundings, the entropy of the chamber walls and shaft will increase.

This means that the same amount of energy is present, but in this more dispersed form, it is less available to do work. In 1865, Clausius thus summarized the first two laws of thermodynamics. First, the energy of the universe is constant. And second, the entropy of the universe tends to a maximum. In other words, energy is distributed over time. The second law is fundamental for many phenomena in the world. That is why hot things cool down and cold things heat up, why gas expands to fill a container, why you can't have a perpetual motion machine, because the amount of usable energy in a closed system is always constant. decreasing.

The most common way to describe entropy is as disorder, which makes sense because it is associated with things becoming more mixed, random, and less ordered. But I think the best way to think of entropy is as the tendency of energy to expand. So why is energy distributed over time? I mean, most laws of

physics

work exactly the same way forward or backward in time. So how does this clear time dependence arise? Well, let's consider two small metal bars, one hot and one cold. For this simple model, we will consider only eight atoms per rod. Each atom vibrates according to the number of energy packets it has.

The more packages, the more it vibrates. So let's start with seven energy packs on the left bar and three on the right. The number of energy packets in each bar is what we will call state. First, let's consider just the left bar. It has seven energy packets, which can move freely around the network. This happens non-stop. Energy packets jump randomly from one atom to another giving different energy configurations, but the total energy remains the same all the time. Now, let's return the cold bar with just three packets and put it together. Power packs can now jump between both bars creating different configurations.

Each unique configuration is equally likely. So what happens if we take a snapshot in an instant and see where all the energy packs are? So stop, look at this. There are now nine power packs on the left bar and only one on the right bar. Thus, the heat has gone from cold to hot. Shouldn't that be impossible because it decreases entropy? Well, this is where Ludwig Boltzmann made an important idea. Heat flowing from cold to hot is not impossible, it is simply improbable. There are 91,520 configurations with nine power packs on the left bar, but 627,264 with five power packs on each bar.

That is, the energy is more than six times more likely to be distributed evenly between the bars. But if you add up all the possibilities, you'll find that there's still a 10.5% chance that the left bar will end up with more energy packs than it started with. So why don't we see this happening around us? Well, watch what happens as we increase the number of atoms to 80 per bar and the energy packets to 100, with 70 on the left bar and 30 on the right. There is now only a 0.05% chance that the left solid will end up hotter than it started.

And this trend continues as we continue to expand the system. In everyday solids there are about 100 trillion trillion atoms and even more energy packets. Therefore, heat flowing from cold to hot is so unlikely that it never happens. Think of it like a Rubik's Cube. Right now it's completely fixed, but I'll close my eyes and do some random turns. If I keep doing this, it will be further and further away from being resolved. But how can I be sure I'm really messing up this cube? Well, because there's only one way to solve it, a few ways to almost solve it, and quintillion ways to make it almost completely random.

Without thought or effort, each spin moves the Rubik's Cube from a highly improbable state (that of being solved) to a more probable state: a total disaster. So if the natural tendency of energy is to spread out and make things more complicated, then how is it possible?have something like air conditioning where the cold inside of a house gets colder and the outside gets hotter? The energy goes from cold to hot, decreasing the entropy of the house. Well, this decrease in entropy is only possible by increasing the entropy by a larger amount elsewhere. In this case, in a power plant, concentrated chemical energy and carbon are released, heating the power plant in its surroundings, propagating the electrical generators to the turbine, heating the cables to the house and producing waste heat. in the fans and compressor.

Any decrease in entropy that is achieved in the house is more than offset by the increase in entropy necessary for that to happen. But if the total entropy constantly increases and anything we do only accelerates that increase, then how is any structure left on Earth? How are the hot parts separated from the cold parts? How does life exist? Well, if the Earth were a closed system, the energy would be completely dispersed, that is, all life would cease, everything would decay and mix, and eventually reach the same temperature. But fortunately the Earth is not a closed system because we have the sun.

What the sun really gives us is a constant flow of low entropy concentrating accumulated energy. The energy we get from the sun is more useful than the energy we give back. It is more compact, it is more grouped. Plants capture this energy and use it to grow and create sugars. Animals then eat plants and use that energy to maintain their bodies and move. Larger animals get their energy by eating smaller animals and so on. And with each step of the way, the energy becomes more distributed. - Okay, interesting. - Yes. - Oh wow, I didn't know that. - There you go.

Ultimately, all the energy that reaches Earth from the sun is converted into thermal energy and then radiated back into space. But in reality it is the same amount. I know this is... - You know this is... - I'm a PhD in physics. - Oh, okay, but anyway, then... - I trust you. The increase in entropy can be seen in the relative number of photons arriving and leaving the Earth. For every photon received from the sun, 20 photons are emitted, and everything that happens on earth, plants growing, trees falling, herds stampeding, hurricanes and tornadoes, people eating, sleeping and breathing.

All of this happens in the process of converting fewer higher-energy photons into 20 times more lower-energy photons. Without a concentrated energy source and a way to dispose of scattered energy, life on Earth would not be possible. It has even been suggested that life itself may be a consequence of the second law of thermodynamics. If the universe is trending toward maximum entropy, then life offers a way to accelerate that natural trend, because life is spectacularly good at converting low entropy into high entropy. For example, the surface layer of seawater produces between 30 and 680% more entropy when cyanobacteria and other organic matter are present than when they are not.

Jeremy England goes one step further. He has proposed that if there is a constant flow of accumulated energy, this could favor structures that dissipate that energy. And over time, this results in better and better energy sinks, which eventually results in life. Or in his own words: "You start with a random group of atoms, and if you shine a light on it for long enough, you shouldn't be surprised if you get a plant." So life on Earth survives thanks to the Sun's low entropy, but then where did the Sun get its low entropy from? The answer is the universe.

If we know that the total entropy of the universe increases with time, then yesterday the entropy was lower and the day before even lower, and so on, until the Big Bang. So right after the Big Bang, that was when the entropy was lowest. This is known as the past hypothesis. It does not explain why entropy was low, only that it must have been so for the universe to develop as it has. But the early universe was hot, dense and almost completely uniform. That is, everything was mixed and the temperature was basically the same everywhere, varying by at most 0.001%.

So what does this low entropy look like? Well, what we have left out is gravity. Gravity tends to clump matter together. So, taking gravity into account, having all matter distributed in this way would be an extremely unlikely state, and that is why it has low entropy. Over time, as the universe expanded and cooled, matter began to clump together into denser regions. And in doing so, enormous amounts of potential energy were converted into kinetic energy. And this energy could also be used in the same way that water flowing downhill can drive a turbine. But when the pieces of matter started colliding with each other, some of their kinetic energy was converted into heat.

So the amount of useful energy decreased. In this way, entropy increases. Over time, the useful energy was used. As they did so, stars, planets, galaxies, and life formed, increasing entropy all the time. The universe began with about 10 to 88 Boltzmann constants of entropy. Today, all stars in the observable universe have about 9.5 times 10 to 80. The interstellar and intergalactic medium combined have almost 10 times as much, but still only a fraction of the early universe. The neutrinos and photons of the cosmic microwave background contain much more. In 1972, Jacob Bekenstein proposed another source of entropy: black holes. He suggested that the entropy of a black hole should be proportional to its surface area.

So, as a black hole grows, its entropy increases. Famous physicists thought the idea was silly, and rightly so. According to classical thermodynamics, if black holes have entropy, then they should also have temperature. But if they have temperatures, they should emit radiation and ultimately not be black. The person who set out to prove Bekenstein wrong was Stephen Hawking. But to his surprise, his results showed that black holes emit radiation, now known as Hawking radiation, and have a temperature. The black hole at the center of the Milky Way has a temperature of about one hundred billionth of a Kelvin and emits radiation that is too weak to detect.

Still pretty black. But Hawking confirmed that black holes have entropy and Bekenstein was right. Hawking was able to refine Bekenstein's proposal and determine how much entropy they have. The supermassive black hole at the center of the Milky Way has between 10 and 91 Boltzmann entropy constants. This is 1,000 times more than the early observable universe and 10 times more than all other particles combined. And that's just a black hole. All black holes together represent 3 times 10 to the 104 Boltzmann constants of entropy. So almost all the entropy of the universe is contained in black holes. That means the early universe only had about 0.000000000000003% of the entropy it has now.

So, entropy was low, and everything that happens in the universe, such as the formation of planetary systems, the merger of galaxies, the collision of asteroids, the death of stars, and the flowering of life, all of that can happen because the Entropy of the universe was low and has been increasing. , and everything happens in one direction. We never see an asteroid crash or a planetary system mix with the cloud of dust and gas that formed it. There is a clear difference between going to the past and going to the future, and that difference comes from entropy. The fact that we are moving from improbable states to more probable states is the reason there is an arrow of time.

This is expected to continue until eventually the energy is distributed so completely that nothing interesting will happen again. This is the heat death of the universe. In the distant future, more than 10 to 100 years from now, after the last black hole has evaporated, the universe will be in its most likely state. Now, even on a large scale, you would not be able to distinguish between time moving forward or backward, and the arrow of time itself would disappear. So it seems that entropy is a terrible thing that inevitably leads us towards the most boring outcome imaginable. But just because maximum entropy has low complexity doesn't mean that low entropy has maximum complexity.

Actually, it's more like this tea and milk. I mean, holding it like that isn't very interesting. But when I pour the milk, the two start to mix and these beautiful patterns emerge. They emerge in an instant and before you know it, they are featureless again. Both low and high entropy are low complexity. It is in the middle where complex structures appear and thrive. And since that's where we are, let's take advantage of the low entropy we have while we can. With the right tools, we can understand almost anything, from a cup of tea going cold to the evolution of the entire universe.

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