Sean Carroll

How long does it take to solve the traveling salesman problem? But when it comes to physically moving things in the world, things that have many parts like a human body, okay, the complexity of the human body is not simply encapsulated by the distribution of its parts through space.

We talk about the processes that go on in the human body, the creation of ATP and the traveling of white blood cells that Jim Allison talked about through the body to fight diseases and things like that. So it should be the least surprising thing in the world that there are different ways to quantify what we call complexity.

We talk about the processes that go on in the human body, the creation of ATP and the traveling of white blood cells that Jim Allison talked about through the body to fight diseases and things like that. So it should be the least surprising thing in the world that there are different ways to quantify what we call complexity.

And the word complicated is generally not a technical term that people use in this context. So when I say that complexity and complicated are different, what I really just mean is that we have an informal notion when things are complicated. we have several different formal notions of when things are complex.

And the word complicated is generally not a technical term that people use in this context. So when I say that complexity and complicated are different, what I really just mean is that we have an informal notion when things are complicated. we have several different formal notions of when things are complex.

And if you really want to be careful, you should tell me what version of complexity you're referring to when you say something is complex. Matthew Fritz says, is the Dirac equation just a special case of the Schrodinger equation? I remember learning that the Dirac equation is the first successful relativistic treatment of quantum mechanics.

And if you really want to be careful, you should tell me what version of complexity you're referring to when you say something is complex. Matthew Fritz says, is the Dirac equation just a special case of the Schrodinger equation? I remember learning that the Dirac equation is the first successful relativistic treatment of quantum mechanics.

But you generally talk about the Schrodinger equation as being the equation of quantum mechanics. Yes, that is completely true. I am completely right about this one, even though there's sort of a lingering set of places where you could hear the wrong answer about this. So the story is, of course, in fact, people don't usually tell the story. The story is that Schrodinger knew about relativity.

But you generally talk about the Schrodinger equation as being the equation of quantum mechanics. Yes, that is completely true. I am completely right about this one, even though there's sort of a lingering set of places where you could hear the wrong answer about this. So the story is, of course, in fact, people don't usually tell the story. The story is that Schrodinger knew about relativity.

When he wrote down his equation, the Schrodinger equation, he wrote down a non-relativistic equation. But he knew about relativity perfectly well. He first tried to write down a relativistic equation. And he came up with, I'm pretty sure he came up with basically what we now call the Klein-Gordon equation. which is a relativistic wave equation.

When he wrote down his equation, the Schrodinger equation, he wrote down a non-relativistic equation. But he knew about relativity perfectly well. He first tried to write down a relativistic equation. And he came up with, I'm pretty sure he came up with basically what we now call the Klein-Gordon equation. which is a relativistic wave equation.

It just doesn't fit the data if you try to solve it for electron energy levels, etc. So he eventually found his non-relativistic equation. And what happened was Klein and Gordon tried to find a relativistic equation. So did Dirac. They were aiming at different things. Dirac was aiming at the electron, which has spin. It is now what we call a fermion.

It just doesn't fit the data if you try to solve it for electron energy levels, etc. So he eventually found his non-relativistic equation. And what happened was Klein and Gordon tried to find a relativistic equation. So did Dirac. They were aiming at different things. Dirac was aiming at the electron, which has spin. It is now what we call a fermion.

Klein and Gordon, their equation turns out to describe scalar fields, scalar particles, which were not known to actually exist at the time, but theorists could talk about them. But they're both perfectly relativistic. Neither one of them is a generalization or replacement for the Schrodinger equation. They're very useful in physics, but for a completely different purpose.

Klein and Gordon, their equation turns out to describe scalar fields, scalar particles, which were not known to actually exist at the time, but theorists could talk about them. But they're both perfectly relativistic. Neither one of them is a generalization or replacement for the Schrodinger equation. They're very useful in physics, but for a completely different purpose.

The Dirac equation and the Klein-Gordon equation are both classical equations of motion for fields. The Klein-Gordon equation is the classical equation of motion for a spinless field. The Dirac equation is the classical equation of motion for a spin-1 field that has electric charge.

The Dirac equation and the Klein-Gordon equation are both classical equations of motion for fields. The Klein-Gordon equation is the classical equation of motion for a spinless field. The Dirac equation is the classical equation of motion for a spin-1 field that has electric charge.

Okay, so it includes both the electron, spin up and spin down, and the positron, spin up and spin down, the particle and its antiparticle. So Dirac thought that he was generalizing the Schrodinger equation, but it turns out that that's not what he was doing, okay? So the correct interpretation, and people sort of hang on to that mistake.

Okay, so it includes both the electron, spin up and spin down, and the positron, spin up and spin down, the particle and its antiparticle. So Dirac thought that he was generalizing the Schrodinger equation, but it turns out that that's not what he was doing, okay? So the correct interpretation, and people sort of hang on to that mistake.

It sounds good when you say, well, there was Schrodinger, and he had the non-relativistic thing, and then Dirac came along and he made it relativistic. The relativistic thing is quantum field theory. That's what the relativistic thing is. But even in quantum field theory, you start with the classical field, And Dirac and Klein and Gordon gave us equations for those classical fields.