Sean Carroll

So people talk about expressing the wave function in position space or expressing the wave function in momentum space, okay?

It's the same wave function, the same information about the state of the system, just expressed using different variables.

And just as a little flag here, all this discussion about how I can express the wave function in either position or momentum is not a minor technicality.

This is going to be the essence of everything we're talking about in the rest of this podcast, so pay attention to it.

Classically, if I have a particle, I can tell you the momentum and you know nothing about the position and vice versa.

Quantum mechanically, if I give you the wave function as a function of momentum, I know everything about the wave function as a function of position and vice versa.

It's very, very different.

And this is part of why quantum mechanics is hard and why it's hard to accept because position and momentum in this realist view of the wave function are not what exists.

What exists is the wave function.

Position and momentum are just sort of projections of what really exists onto different possible axes.

There are different possible outcomes of asking different questions of the wave function and getting different possible answers, okay?

So this is driving you in the direction, and I hope that you take this direction seriously, of saying that position and momentum aren't all that fundamental.

at the end of the day, right?

There's something called the wave function.

We had to invent it to explain the data.

And we invented it in a world where in our heads position was very fundamental, right?

Like things are located in position.

And the very existence of a quantum mechanical wave function says, well, okay, things aren't quite located in position.

They have wave functions as a function of position.

But then there's this extra thing that says, well, actually the wave function isn't necessarily a function of position.