"In the same paper, Bell also discussed two rather unwelcome properties of hidden-variables theories. The first was contextuality. This tells us that, except in trivial cases, any hidden-variable theory must be such that the result of measuring a particular observable will depend on which other observable) are measured simultaneously. The second was nonlocality. All me hidden-variable models that Bell examined, including Bohms, had the unpleasant feature that the behaviour of a particular particle depended on the properties of all others, however far away they were. In the EPR case, the measurement result obtained on one particle would depend on what measurement is performed on the second. As Bell said, this was the resolution of the EPR problem that Einstein would have liked least, and it is in this sense that it may be said that Bell proved Einstein wrong."
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. The first such result was introduced by John Stewart Bell in 1964, building upon the Einstein–Podolsky–Rosen paradox, which had called attention to the p
"The purpose of the first part is to convince the reader that the formalism leading to Bells inequalities is very general and reasonable. What is surprising is that such a reasonable formalism conflicts with quantum mechanics. In fact, situations exhibiting a conflict are very rare, and quantum optics is the domain where the most significant tests of this conflict have been carried out"
"Thats all. Thats the difficulty. Thats why quantum mechanics cant seem to be imitable by a local classical computer. Ive entertained myself always by squeezing the difficulty of quantum mechanics into a smaller and smaller place, so as to get more and more worried about this particular item. It seems to be almost ridiculous that you can squeeze it to a numerical question that one thing is bigger than another. But there you are—it is bigger than any logical argument can produce, if you have this kind of logic."
"I’ve had experts in quantum field theory – people who’ve spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them, or other simple conceptual things like Grover’s algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem."
"Bell’s theorem is the most profound discovery of science."
"The experimental verification of violations of Bell’s inequality for randomly set measurements at space-like separation is the most astonishing result in the history of physics. Theoretical physics has yet to come to terms with what these results mean for our fundamental account of the world. Experimentalists, from Freedman and Clauser and Aspect forward, deserve their share of the credit for producing the necessary experimental conditions and for steadily closing the experimental loopholes available to the persistent skeptic. But the great achievement was Bell’s. It was he who understood the profound significance of these phenomena, the prediction of which can be derived easily even by a freshman physics student. Unfortunately, many physicists have not properly appreciated what Bell proved: they take the target of his theorem— what the theorem rules out as impossible—to be much narrower and more parochial than it is. Early on, Bell’s result was often reported as ruling out determinism, or hidden variables. Nowadays, it is sometimes reported as ruling out, or at least calling in question, realism. But these are all mistakes. What Bell’s theorem, together with the experimental results, proves to be impossible (subject to a few caveats we will attend to) is not determinism or hidden variables or realism but locality, in a perfectly clear sense. What Bell proved, and what theoretical physics has not yet properly absorbed, is that the physical world itself is non-local."
"Theres an interesting scientific principle that a wrong answer can be much more stimulating to the field than just sort of finding the answer thats in the back of the book. A wrong result gets people excited. Worried. Obviously, you dont really want that to be happening—its OK for a theorist to come up with a speculative new theory that gets shot down, but experimentalists are supposed to be very careful and their error limits are supposed to be realistic. Unfortunately, with this experiment, whenever youre looking for a stronger correlation, any kind of systematic error you can imagine typically weakens it and moves it toward the hidden-variable range. It was a hard experiment. In those days, at any rate, with the kind of equipment I had, and … well, what can I say? I screwed up."