Sean Carroll

And in quantum mechanics, just good old ordinary quantum mechanics of a single particle, the only kinds of states that you can get, the only kind of wave function you can get with a definite velocity or momentum

is spread out all over space.

It is a plane wave that is not localized to any position whatsoever.

This is a reflection of the uncertainty principle.

If you know the momentum exactly, you know the position not at all, right?

So any localized quantum wave function necessarily involves parts of it moving at different velocities.

And there is a rigorous version of that statement, which is to say I can take the quantum wave function as a function of position

I can transform it into a quantum wave function as a function of momentum, that is to say as a superposition of different states with definite momentum.

And then what I would find is that it's not perfectly localized in momentum.

There's different momenta and they move different speeds and that's the answer to the question.

So in a very real sense, wave functions spread out because different parts of the wave function are moving at different velocities.

Okay.

The version of the answer that says no, it is not true, is you shouldn't really reify, that is to say, take too literally the idea that the wave function is literally a combination of particles at different positions, okay?

It is spread out over position.

It's literally a superposition of different possible measurement outcomes for the particle.

But if you're an Everettian, like I am, or if you're any other person who is realist about the wave function, then when the particle is not being observed, it doesn't have a position.

It's not that it has many positions.

It's not even that there are many particles with slightly different positions and it's a combination of all of them.

What the particle has is a wave function.

And the wave function represents different places you could see the particle were you to measure it.