Sean Carroll

Because space is the arena in which interactions are local, just like we talked about in quantum field theory, in the particle physics way of talking, or in the

Kinetic theory way of talking, atoms bump into each other when they are at the same point in space, not when they're moving at the same speed or something like that.

So there is a way of coarse-graining the particle or atomic description by taking averages over region of space, and that way is one of an infinite number.

of ways that I could possibly coarse-grain, but it's certainly the useful one.

And the reason why it's useful is the answers that I get out of doing that coarse-graining, out of saying, OK, I'm going to take a little tiny box with some particles in it, some atoms, and I'm going to define macroscopic coarse-grain variables like pressure and density and temperature.

Those variables that I get are sufficient to give me a self-contained autonomous emergent theory.

I can talk about fluid mechanics or atmospheric or weather for that matter, right?

Atmospheric science without knowing about atoms.

Most meteorologists don't need to know about atoms to do their job.

It would be weird if you needed to know about atoms or the standard model of particle physics.

This is Philip Anderson's More is Different.

I can talk about the emergent level without knowing about the lower level beneath it.

They're both interesting.

They're both connected.

They need to be compatible with each other.

But I don't need to know about one to talk about the other.

That doesn't mean that the relationship between them is arbitrary.

Fluid mechanics is a coarse-grained version of statistical mechanics or atomic physics or whatever you want to call it.

But that coarse-graining is not arbitrary.

It's a very, very specific way of,