Sean Carroll

You have to disbelieve in reality until you actually measure something, which is even arguably a heavier lift.

But it's a different kind of heavy lift, philosophically speaking.

Okay, so that's the minimal introduction to Everettian quantum mechanics, but that's not where I want to dwell here.

I want to talk about sort of good old textbook quantum mechanics because I've been saying something over and over again, and maybe it's been bugging you or maybe it hasn't, but it's certainly something you should think about.

Okay.

I said that the wave function of, let's say, go back to a single electron, don't worry about entanglement or observers or anything like that.

Again, textbook, simple, undergraduate, first semester, quantum mechanics.

I said that the wave function assigns a number, a complex number as it happens, to every possible measurement outcome.

But then what I spoke of was measuring the position of the electron.

That's not the only thing that I could measure.

For example, even if I forget about the fact that electrons have spin, I could measure the velocity or the momentum equivalently of the electron.

So naively, or at least taking my words overly literally, you might think, okay, so the wave function is a superposition of every possible measurement outcome, so that would include both positions and momenta of the electrons, okay?

That's not right.

I think actually if you carefully parse the words I've said so far, it's compatible with that, but I didn't make it explicit, so let's make it explicit right now.

If you give me, as it turns out, as Schrodinger himself, you know, noted, if you give me the wave function as a function of just position, which makes sense if you were thinking about it incorrectly as a field, this is why people get mixed up right from the start.

So you think of psi of x, okay, the wave function as a function of the possible positions you could see the electron in, then you're done.

You don't separately give me psi of x and p, x being the letter we use to denote positions and p being the letter we use to denote momenta.

You don't need to do that.

You can actually calculate the probability of getting a momentum measurement outcome from psi of x, from just you give me the wave function as a function of position measurement outcomes.

you can figure out what the probability is of different momentum measurements.