Sean Carroll

So you need the idea of space to talk about the idea of fields.

And in fact, quantum mechanically, if you want to talk about the Hilbert space for a field theory, what you can do, and there's more technicalities here that we're glossing over.

Sorry about that, physicists listening to this.

If I divide space into little regions, right?

Like I take the room that I'm in right now and I subdivide it into little cubes one millimeter across on every side.

So a huge number of little cubes locating different parts of the room that I'm in.

every one of those little cubes of space has uh fields that can vibrate in it and i can express the wave function of the field in the room as a whole as the combination the tensor product of all of the different things that the fields are doing in every box and of course you can be entangled with each other as as much as you want because it's quantum mechanics

And the reason why I'm going through all those details is because in that sort of division of what the field is into values of the field at different locations in space, the crucially, crucially important thing about quantum field theory is that the field's interactions are local.

in space and also local in time.

And this is a little bit, this is something where the philosophers of quantum mechanics and their working physicists talk past each other a lot because to the philosophers, remember John Bell proved that there is some kind of nonlocality in quantum measurement.

The working physicists often think that quantum measurement is trivial, and what they care about, what they're doing all their—spending all their time calculating, doing Feynman diagrams and things, is the pre-measurement dynamics of the system.

So when you have the electromagnetic field interacting with electrons and quarks and so forth, the way that a typical particle physicist says, you know, they pour all of their effort

into calculating the wave function and the quantum state evolving.

And then they say, okay, at the end, we observe it, the wave function collapses and that's easy.

Okay?

So to working particle physicists,

What they care about is the unmeasured or unitary dynamics of the system, and that, as far as we know, is strictly local in physics.

That's just a way of saying that if I poke, let's say, the electromagnetic field at one point, it doesn't instantly change throughout the whole universe.

Einstein taught us that's not even a meaningful statement.

Instead, it changes within the influence of its future, in what we call its future light cone.