Sean Carroll

The answer is, if you have two electrons, then they can be entangled.

What that means is, remember that first electron that I said we're going to treat like a little wave, but we know it's not exactly right.

Here's another way of thinking about it that actually is much closer to reality.

The electron's wave function is a combination, the technical word we use is a superposition, of every possible measurement outcome.

So when you have this picture of an electron in an orbital and it's sort of shaped like lobes or balloons or whatever, what that's trying to tell you is, that's what the wave function is, but you're not going to see the wave function when you look at it.

you're going to see is a dot and if you take that function that you plotted in the pretty picture and you take it square you just take the absolute value squared of this function that's the probability that you will see the measurement outcome to be the electron is located at that position

So really that function that you call the wave function of the electron is a superposition of every possible answer to the question, where will the electron be were I to look at it?

Even if you don't look at it,

The wave function still has that status.

So what is the difference?

So in one way of thinking about it, you think of a wave located in space.

That's the way we usually picture these things.

That's what we are used to growing up in physics with things like the electric field and the gravitational field.

We have the notion of a field.

A field is something that has a value at every location in space.

When you think of the wave function of an electron, boy, it sure looks like a field, doesn't it?

There's a little picture of how big it is in the pictures of the orbitals of atoms, and you can use that to calculate the probability of different measurement outcomes.

The description of the electron's wave function as either a field in space,

or a superposition of different possible measurement outcomes, the second one just sounds sort of unnecessarily fussy, like maybe it's true, right?

Okay, but what are we learning by doing that?