Sean Carroll

It could equally well be a function of momentum.

You don't even have to mention position.

It's implicit, and you can transform the wave function and pull it out, but it's not necessary necessarily.

OK, like that's a deep fact.

Position is not necessary to talk about the wave function of the universe.

Hmm.

So what is necessary?

What is fundamental?

Where is the wave function living?

And here's where there's a slightly confusing discourse that you might bump into about the difference between wave functions and fields, right?

A field is something that lives in space.

It is a function of space.

By space, I mean good old three-dimensional space where we all live.

At every point in space, there's a value for the electric field.

It's a little vector, a little arrow pointing somewhere.

At every point in space, there's a value of the magnetic field, of the gravitational field, of the Higgs field, of what have you.

Wave functions aren't like that, in part just because of entanglement, right?

If I have two particles with positions x1 and x2, the wave function is a function of what we call the configuration space of the two-particle system.

It's x1 and x2, and if x1 is really three different variables, x1, y1, z1, and likewise x2 is really x2, y2, z2,

That configuration space for two particles is a six-dimensional space.