Sean Carroll

And what we're saying here is instead of psi of electron 1 and psi for electron 2, there's only one psi.

There's only one wave function.

It's the wave function of the universe, ultimately.

And it's a function of the position of electron one and the position of electron two.

Okay?

So that's very different, radically different than classical mechanics where you would just have whatever particle one is doing and whatever particle two is doing.

quantum mechanics is telling you that this superposition of both electrons at once is the state of the universe.

And the reason why, or the state of the two-electron system anyway, the reason why that implies entanglement is because there might be relationships between the probability of seeing one electron in one location and another electron in another location.

Like, let's actually make our lives easy and switch to an electron and a proton.

So they're two obviously different particles, okay?

Maybe the wave function of your two-particle system could be the electron is probably here or there.

There's like two locations, two boxes it could be in.

It could be in box A or box B. And the proton could be in box A or box B, okay?

But they're absolutely not in the same box.

So there is some wave function, some part of the superposition is electron is in box A, proton is in box B. There's also some part of the wave function that says proton is in box A, electron is in box B. But there's no part of the wave function that says the electron and proton are both in box A or both in box B.

Totally new.

That's entanglement.

Nothing like this happens in classical mechanics.

But if you think of the wave function as a superposition of every possible measurement outcome...

it kind of makes sense, right?