Sean Carroll

That's already weird.

But there's an extra weirdness is that even if you have a huge number of particles, Avogadro's number of particles or whatever, you can still do momentum space.

You can still cast the wave function as a function of Avogadro's number of momentum components rather than position components.

And in fact, as you might begin to suspect—

there's an infinite number of combinations of position and momenta that work equally well as coordinates on some giant dimensional space where the wave function lives, okay?

So that's already, it's sort of a demotion of our notions of the fundamentality of space and velocity and things like that.

In fact, what it's pointing at, and this is, so I'm going to finally say out loud what we've been hinting at here is,

is that what you call position and what you call momentum are choices of what questions to ask, okay?

When you have the wave function, you say, what is the probability of observing it in some position?

You're making a choice.

You're choosing to ask some question to do a certain kind of observation.

that it's going to give you a certain kind of answer.

You can also do different questions.

You can make different choices.

I'm going to ask, what about the momentum of this particle?

Or I'm going to ask about, what is 1 over the square root of the position plus the momentum?

You're allowed to do that if you want to do that.

You're allowed to ask all sorts of questions, and you will get different answers.

And the underlying physics doesn't change, OK?

So this is a very, very familiar circumstance in physics where you have a way of describing something, but it's the thing that matters, not your description of it, okay?