 So what I looked at, first of all, was how Schrodinger derived the Schrodinger equation. And like, what he actually did was to start from the Hamilton-Jakobi equation, have you seen that? Yeah, yeah. Where you basically, you have this function that's called Hamilton's principal function S. And it's kind of like a potential for the momentum in the sense that in the Hamilton-Jakobi theory, you think of, instead of thinking about where the particle, thinking of a single particle and a single trajectory, you think about all possible trajectories. And like, thinking of them all at once, the momentum becomes like a vector field instead of just a vector. And it's a vector field whose integral curves are the trajectories, the possible trajectories. So it's more like a vector calculus approach to classical mechanics, which is interesting because it already looks like a field theory or something. And then the thing is, so it's already, it already, like if you're going to develop a theory of particle physics and you're alive in the 1920s, this is the obvious place to start because you don't know the initial condition. So you don't know which trajectory the particle's on. So you have to think about all possible trajectories at once and then come up with some kind of probabilistic theory based on that. So initially you say, okay, let's start with Hamilton-Jakobi theory and then a probabilistic version of that, which is entirely, initially entirely classical. And then you just like, so you could just, and another nice thing about Hamilton-Jakobi theory and just, which is just a logical consequence of like conservation of matter or at least in non-relativistic theories is that the trajectory satisfy the conservation equation that is then never created or destroyed. So like d rho by dt plus grad of rho v equals, rho is the density of trajectory. A continuity equation. Right, continuity equation. So where rho is the density of trajectories in space and if you think about it, that's exactly the rho that you want to use as like the probability of finding the particle because you find it where the trajectories are more dense. Exactly. So if you normalize rho, it basically becomes a probability density function. Yeah. You already like the Hamilton-Jakobi equation and the continuity equation can basically be seen as like what are going to become the real and imaginary parts of the Schrodinger equation. Oh, okay, so it's a real and imaginary. But it's not quite there yet because this is classical. So the leap is that for some random reason Schrodinger makes the Hamilton's principle function, which is like this potential for the momentum, i.e. like p is grad s, whatever you call it. He makes s complex and the imaginary part, the adds to it. So he keeps the real part the same, but he adds an imaginary part to it, which is log, natural log of the probability density function, log rho, or it's actually minus i h bar over 2 log rho. And you can show that the reason why he does that is because it means that the average momentum, because it's now probabilistic theory, so if you integrate the momentum over all space times by rho, it's not changed because rho times grad log rho, when you take the derivative of a log, it pulls out a 1 over rho, which hits the rho at the front and gives you a total derivative. So basically he just picked it because it just doesn't mess with the classical values. It's the only thing. It's pretty much the most obvious thing you can pick that doesn't mess with the classical values. I don't think he knew why he was doing it. Interesting. And I don't think anyone knows why he's doing it. But if you think about this log rho thing, as a variable, its average value is the integral over all space of rho log rho, which is just the entropy of the system. So basically it's related to, I think that you could actually derive the Schrodinger equation from first principles, not from first principles, but as a natural extension of combining classical mechanics, statistics, and information theory, and that's basically what I'm trying to do.