Some people say there's no progress in physics. I'd never say such a thing, of course, because there's just been a major breakthrough on a 125year-old problem. David Hilbert's famous sixth problem. This breakthrough unites three of the most important theories in physics. And it also shows how irreversible behavior emerges from time reversible laws. That's a big deal. Even though that breakthrough came from mathematicians, not from physicists. Physicists were busy redefining the kilogram again or whatever it is that we do now. But let's have a look. Before we talk about mathematicians who revolutionize physics, a big thank you to all my supporters, especially those in Patreon tiers 4 and higher. This channel would not be possible without your help. And you can help me too either on Patreon or by joining this channel right here on YouTube. Now about Hilbert's problems. In the year 1900, the mathematician David Hilbert presented a list of 23 unsolved problems which he thought should guide mathematical research in the 20th century. Some have been solved, some remain open, and some are so vaguely formulated that we're still arguing about what it would even mean to solve them. But one of the most ambitious ones is number six. Hilbert asked for an axiomatic foundation of physics. In other words, he wanted physicists to stop making things up and instead derive the equations they use from well-defined assumptions. If that could be done, it would solve one of the biggest puzzles of our existence. That is why time passes in only one direction. Because on the level of atoms, forward in time works the same way as backward in time. Yet, this is clearly not the case in our everyday life. So, how does that happen? Yes, you've been told it's to do with entropy increase, and that's probably correct, but it's never been proved for the laws of physics that actually describe atoms. And that was Hilbert's point. Stop making up plausible explanations. Derive them. Hilbert mentioned that a good place to start with this sixth problem would be to understand how the equations of fluid dynamics arise from the motion of atoms. Fluids after all are made of particles and in principle we could just track every single molecule. But there are way too many of them. Instead, physicists use three different theories depending on the scale they look at. At the microscopic level, particles follow basically Newton's laws and bounce off each other. At the intermediate level or messoscopic level, we don't care about each particle, just the statistical average. That's described by what's called the Boltzman equation. And at the macroscopic level, we have equations for the flow of air and water, the Oiler and Navia Stokes equations. Each of these descriptions works in its own regime and we expect that the higher levels can be derived from the lower ones. But Hilbert asked, well, where's the derivation? That's what the authors of the new paper did. It's a fairly long technical paper. Hasn't been peer-reviewed, and I admit that I don't understand the details, but it plausibly looks like they actually solve the problem. They show that if you take a large number of tiny hard spheres or bouncing around in a box and let them follow Newton's laws, then as you zoom out, you first get the Bosman equation and then you get the equations of fluid dynamics. This was previously done approximately for short times. But the difficulty that they overcame was to extend the short time result to longer times. For this, they developed a clever way of tracking and classifying all possible collision histories and then evaluating their probabilities. In some sense, it's a straightforward calculation devils in the details. I actually find this a very impressive result. Why does this matter? For one thing, it justifies the equations that we use every day in engineering, weather prediction, and aerodynamics. We now know they aren't just good guesses. They follow from the underlying laws. But maybe more interestingly, this shows in detail how irreversible behavior can emerge from reversible laws and why time has a direction for us. It's like the first step to answering Isac Asimov's last question. How can we decrease entropy? that I think is the ultimate question that any living being in this universe will eventually ask that and when did my joints begin making this sound? But as impressive as this breakthrough is, it doesn't entirely solve Hilbert's sixth problem. That it also include quantum mechanics, relativity, turbulence, uh the question of how to get cheese to stick to the pizza when you cut it. So, no, the problem hasn't been solved, but a piece just clicked into place. On the meter, this gets a zero out of 10. Even if it's wrong, it's serious and deeply offensive to the physicists who take great pride in making things up that sound reasonable problems. I'm sure you have a few, but problem solving is a skill that you can train just like any other. I found that a simple and effective way to do this is with Brilliant. All courses on Brilliant have interactive visualizations and come with follow-up questions. What you see here is from their newly updated maths courses, no matter how abstract the topic seems. Brilliant courses have intuitive visualizations that really click into my brain. And Brilliant covers a large variety of topics in science, computer science, and maths from general scientific thinking to dedicated courses, just what I'm interested in. And they're adding new courses each month. Sounds good. I hope it does. You can try Brilliant yourself for free if you use my link, brilliant.org/sabina or scan the QR code. That way, you'll get to try out everything Brilliant has to offer for a full 30 days, and you'll get 20% off the annual premium subscription. So, go and give it a try. I'm sure you won't regret it. Thanks for watching. See you tomorrow.