Sean Carroll explains quantum entanglement as a single wave function for two particles where measuring one updates what you know about the other, with no classical equivalent. He then describes it in terms of quantum fields: empty space contains vibrating fields that are entangled locally, with nearby modes more strongly entangled than distant ones.
Can you say what is entanglement? It seems one of the most fundamental ideas of quantum mechanics.
Well, let's temporarily buy into the textbook interpretation of quantum mechanics. And what that says is that this wave function, so it's very small outside the atom, very big in the atom. Basically, the wave function, you take it and you square it. You square the number. That gives you the probability of observing the system at that location. So if you say that for two electrons, there's only one wave function, and that wave function gives you the probability of observing both electrons at once, doing something. Okay, so maybe the electron can be here or here, here or here, and the other electron can also be there. But we have a wave function set up where we don't know where either electron is going to be seen, but we know they'll both be seen in the same place. Okay, so we don't know exactly what we're going to see for either electron, but there's entanglement between the two of them. There's. There's a sort of conditional statement. If we see one in one location, then we know the other one's going to be doing a certain thing. So that's a feature of quantum mechanics that is nowhere to be found in classical mechanics. In classical mechanics, there's no way I can say, well, I don't know where either one of these particles is. But if I know. If I find out where this one is, then I know where the other one is. That just never happens. They're truly separate.
And in general, it feels like if you think of a wave function, like, as a dance floor, it seems like entanglement is strongest between things that are dancing together closest. So there's a closeness that's important.
Well, that's another step. We have to be careful here, because in principle, if you're talking about the entanglement of two electrons, for example, they can be totally entangled or totally unentangled no matter where they are in the universe. There's no relationship between the amount of entanglement and the distance between two electrons. But we now know that, you know, the reality of our best way of understanding the world is through quantum fields, not through particles. So even the electron, not just gravity and electromagnetism, but even the electron and the quarks and so forth, are really vibrations in quantum fields. So even empty space is full of vibrating quantum fields. And those quantum fields in empty space are. Are entangled with each other in exactly the way you just said. If they're nearby, if you have, like, two vibrating quantum fields that are nearby, then they will be highly entangled. If they're far away, they will not be entangled.
So what do quantum fields in a vacuum look like? Empty space. Just so.
Like empty space. It's as empty as it can be.
But they're still a field. It's just.
Yeah, it.
What is? Nothing.
Just like right here, this location in space, there's a gravitational field which I can detect by dropping something.
Yes.
I don't see it, but there it is.
