Sean Carroll

Or at a slightly deeper level, when we talk about quantum field theory, literal regions of space have different vibrating fields in them, and they are local.

Their dynamics are local in the sense that they only talk to their nearest neighbors, okay?

So both of those definitions of space are intimately related, as I said, but what matters is that they're there.

And they're certainly there from the start in the usual way of talking about physics.

Again, the usual thing that we would teach you is we start with that.

then we just say okay how do we put this into quantum mechanical context and our current project is going backwards how do you start from a big vector in an abstract hilbert space with no subdivision into regions of space or objects or anything like that how do you find them so the question is how do you subdivide hilbert space so that subsystems represent useful things in their own right there's some sort of tangible physical meaning to this subsystem of hilbert space

And that sounds a little weak, right?

A little fuzzy, a little unclear.

Like, is that just back to some Copenhagen level, you know it when you see it kind of thing?

If there's an infinite number of ways to divide up Hilbert space, how do we know when we get the right one?

How do you know that your right one is the same as my right one, right?

But in fact, I think it's not nearly as weak or as subjective as it sounds.

This is a very common feature of emergence, right?

Forget about quantum mechanics for a second, okay?

Think about classical statistical physics, which is to say statistical mechanics leading and emerging into thermodynamics or fluid mechanics.

I use this example all the time, so you all know it.

If I have a bunch of atoms in the room around me, in the air, atoms and molecules, I can coarse-grain them to get things like temperature and density and pressure and so forth.

I get a fluid mechanical description of the air in the room.

But that's not given as an obvious thing to do.

When I do that emergence, I can define things like temperature and density and pressure by making a little average over small regions of space.