Sean Carroll

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.

But when you're not measuring it, it's not that there are particles with different positions or different speeds.

So when you ask the question, literally phrased, do the different positions move through space at identical speeds?

No, because there are not quote unquote different positions for the particle, right?

If you visualize it in your head, I have something that looks like, you know, a bell curve, okay?

A distribution with a peak that tails off to right and left, and that's my wave function.

And what I said earlier is that the wave function spreads out over time.

But that spreading out, certainly you could casually attach words to it like different parts moving at different velocities.

But it's not that I can point to a specific position x and saying, what is the velocity of this position?

There is no direct assignment of velocities to positions in that wave function.

There's only the wave function as a whole.

So in order not to get confused further down the road in thinking about quantum mechanics, I think it's worth trying to just be persnickety and get it exactly right, which is the way that you'll get some real insight on what the wave function is actually doing.