Here, from <http://www.scottaaronson.com/blog/?p=2464>:
> A few weeks ago, Hensen et al., of the Delft University of Technology > and Barcelona, Spain, put out a paper reporting the first experiment > that violates the Bell inequality in a way that closes off the two > main loopholes simultaneously: the locality and detection loopholes. > Well, at least with ~96% confidence. This is big news, not only > because of the result itself, but because of the advances in > experimental technique needed to achieve it. Last Friday, two > renowned experimentalists—Chris Monroe of U. of Maryland and Jungsang > Kim of Duke—visited MIT, and in addition to talking about their own > exciting ion-trap work, they did a huge amount to help me understand > the new Bell test experiment. So OK, let me try to explain this. > > While some people like to make it more complicated, the Bell > inequality is the following statement. Alice and Bob are cooperating > with each other to win a certain game (the “CHSH game“) with the > highest possible probability. They can agree on a strategy and share > information and particles in advance, but then they can’t communicate > once the game starts. Alice gets a uniform random bit x, and Bob gets > a uniform random bit y (independent of x). Their goal is to output > bits, a and b respectively, such that a XOR b = x AND y: in other > words, such that a and b are different if and only if x and y are > both 1. The Bell inequality says that, in any universe that satisfies > the property of local realism, no matter which strategy they use, > Alice and Bob can win the game at most 75% of the time (for example, > by always outputting a=b=0). > > What does local realism mean? It means that, after she receives her > input x, any experiment Alice can perform in her lab has a definite > result that might depend on x, on the state of her lab, and on > whatever information she pre-shared with Bob, but at any rate, not on > Bob’s input y. If you like: a=a(x,w) is a function of x and of the > information w available before the game started, but is not a > function of y. Likewise, b=b(y,w) is a function of y and w, but not > of x. Perhaps the best way to explain local realism is that it’s the > thing you believe in, if you believe all the physicists babbling > about “quantum entanglement” just missed something completely > obvious. Clearly, at the moment two “entangled” particles are > created, but before they separate, one of them flips a tiny coin and > then says to the other, “listen, if anyone asks, I’ll be spinning up > and you’ll be spinning down.” Then the naïve, doofus physicists > measure one particle, find it spinning down, and wonder how the other > particle instantly “knows” to be spinning up—oooh, spooky! > mysterious! Anyway, if that’s how you think it has to work, then you > believe in local realism, and you must predict that Alice and Bob can > win the CHSH game with probability at most 3/4. > > What Bell observed in 1964 is that, even though quantum mechanics > doesn’t let Alice send a signal to Bob (or vice versa) faster than > the speed of light, it still makes a prediction about the CHSH game > that conflicts with local realism. (And thus, quantum mechanics > exhibits what one might not have realized beforehand was even a > logical possibility: it doesn’t allow communication faster than > light, but simulating the predictions of quantum mechanics in a > classical universe would require faster-than-light communication.) In > particular, if Alice and Bob share entangled qubits, say > $$\frac{\left| 00 \right\rangle + \left| 11 > \right\rangle}{\sqrt{2}},$$ then there’s a simple protocol that lets > them violate the Bell inequality, winning the CHSH game ~85% of the > time (with probability (1+1/√2)/2 > 3/4). Starting in the 1970s, > people did experiments that vindicated the prediction of quantum > mechanics, and falsified local realism—or so the story goes. Discussion in <https://news.ycombinator.com/item?id=10269297> OK, so local realism is dead. But what is it? An excerpt from above: > Perhaps the best way to explain local realism is that it’s the thing > you believe in, if you believe all the physicists babbling about > “quantum entanglement” just missed something completely obvious. And here's the tl;dr: > (And thus, quantum mechanics exhibits what one might not have > realized beforehand was even a logical possibility: it doesn’t allow > communication faster than light, but simulating the predictions > of quantum mechanics in a classical universe would require > faster-than-light communication.) Another chunk: > The violation of the Bell inequality has a schizophrenic status in > physics. To many of the physicists I know, Nature’s violating the > Bell inequality is so trivial and obvious that it’s barely even > worth doing the experiment: if people had just understood and > believed Bohr and Heisenberg back in 1925, there would’ve been no > need for this whole tiresome discussion. Me, I like the many worlds interpretation. But it's just an interpretation. What matters is the math.