Physicists just won the Nobel prize for proving that this is true. I’ve read the articles and don’t get it.
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Imagine a magic apple tree. Every year, the apple tree grows exactly two apples, always exactly one green and one red, and flings them each a mile away in opposite directions one to Bob’s house and one to Alice’s house. Which person gets which color of apple is decided randomly.
You’re Alice. You hear the apple fall in your yard. What color is it?
If this is a classical magic apple tree (“classical” meaning “non-quantum”), obviously, you don’t know. But in actual fact it *is* either red or green; it’s just that *you*, Alice, don’t know.
But if this is a quantum magic apple tree, it’s a little different. The apple’s color is *actually* neither red nor green but a superposition of both. It’s not that you personally don’t know which one; it’s that it *actually* is this funny in-between non-color until you go into your yard and look at it. Once you look at it, only then does it become (say) green.
That’s the core of the idea, and the TLDR stops there. But it’s kind of weird, isn’t it? How could you tell the difference between a quantum and a classical magic apple tree?
That’s where Bell’s Inequality comes in (that’s the mathematical/theoretical statement; two of the Nobel Prize winners this year worked on showing the results *experimentally*). It involves entanglement so let’s cover that first. Entanglement just means that if you know the state of one apple, you know (or at least know *better*) what the state of another apple is.
So in this case, Alice and Bob’s apples are *entangled* because Alice initially doesn’t know Bob’s apple’s color, but once she sees her own apple is green, she now immediately knows that Bob’s is red.
The exact math of Bell’s Inequality is a bit complicated to explain here (and doesn’t quite work intuitively for this analogy of apple colors; you’d need to run this on a different set of properties). But the key idea is that Alice and Bob don’t go into the yard and look at the *color* of the apple, but randomly look at some sort of related properties, and then compare what they get with each other. The results for classical magic apple trees would follow Bell’s Inequality, but for quantum magic apple trees they wouldn’t.
By the way, I didn’t touch on the term “local” but we have to add that term as a qualifier because there’s a loophole to Bell’s Inequality where the apples can send each other faster-than-light messages to coordinate their measurement results in the Bell’s Inequality experiments. If we allow for that, we don’t preclude the possibility of a defined (“real”) state that includes inter-apple communication. In fact, that’s the usual interpretation of what’s happening, that entangled apples/particles *instantly* know about the state of their partners – though not without controversy. But it’s worth noting that, if this is indeed how it works, this inter-apple communication cannot be hijacked by humans or anything other than the apples themselves to actually send faster-than-light messages to each other; only the apples themselves would be able to use these messages, and only to coordinate for measurements.
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