Sean Carroll

It can have influences that travel slower than the speed of light, but not faster than the speed of light.

And the way that shows up in the laws of physics is if I do that poking of the electromagnetic field, that interacts directly with values that the field has right next door.

its nearest neighbors, as we say.

Go back to this picture where I've subdivided all of space around me into little cubes.

The cube, any one cube, only touches and interacts with the cubes that are next to it.

It doesn't immediately and directly influence what's going on very, very far away, at least as far as the unmeasured quantum dynamics is concerned.

So as much as quantum measurement seems to involve some kind of non-locality,

quantum field theory, when it's not being measured, seems to be very, very local.

And we can think of that as an implication of a certain way of dividing up Hilbert space, of carving Hilbert space at its joints.

Namely, we carve up Hilbert space into the combination of

The Hilbert space happening at this little cube in front of me, and the Hilbert space happening at that little cube in front of me, and all the cubes around me in space.

All of the little lattice subdivisions of space go into Hilbert space.

And so that is a particular way of dividing up Hilbert space.

Dividing it up so that it looks like space, so that it looks local, okay?

So I just gave you two ways in which space was important.

One is sort of a very high level way when we just talk about the division into objects, cats and boxes and observers and things like that.

We divide up Hilbert space.

A cat has its factor of Hilbert space.

An observer has its factor of Hilbert space.

A box has its factor and so forth.