Sean Carroll

They had a version of the theory that worked pretty well.

Now, it becomes a little more complicated when you go from one electron to two electrons.

You might not think it's that complicated.

Isaac Newton went from the gravitational field of one planet to the gravitational field of two planets, right, without that much difficulty.

At least in the world of Newton or Einstein or Maxwell or any of the giants of pre-quantum physics, there's no special difficulty in going from a theory explaining one object to a theory explaining two objects.

You just now have two things happening.

You have one electron doing its thing.

It has a wave, a wave function.

And you have the other electron.

It should have its own wave function.

It turns out that's just not how it works, and we can go into justifications for this, but we have other fish to fry, so I'm just going to tell you the answer.

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.