Bell's theorem

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Bell's theorem is a no-go theorem famous for drawing an important line in the sand between quantum mechanics (QM) and the world as we know it classically.


  • The purpose of the first part is to convince the reader that the formalism leading to Bell's 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
    • Alain Aspect, "Bell's Theorem: The Naive View of an Experimentalist", in Quantum [Un]speakables (2002) edited by Reinhold A. Bertlmann and Anton Zeilinger
  • One of these articles, written by N. David Mermin, gave me a tremendous shock. Mermin described the results of experiments that had been carried out as recently as 198210 test something called Bell's theorem using two-photon 'cascade' emission from excited calcium atoms. Put simply, Bell's theorem says that my idea of naive realism is in conflict with the predictions of quantum theory in a way that can be tested in the laboratory in special experiments on pairs of quantum particles. These experiments had been done: quantum theory had been proved right and naive realism wrong! There in a montage was a pictorial history of the debate about reality and the experiments that had been done to test it (reproduced opposite). This work struck me as desperately important to my understanding of physical reality, something that as a scientist I felt I ought to know about. This discovery also made me feel rather embarrassed. Here I was, proud of my scientific qualifications and with almost 10 years' experience in chemical physics research at various prestigious institutions around the world, and I had been going around with a conception of physical reality that was completely wrong! Why hadn't somebody told me about this before?
    • Jim Baggott, The Meaning of Quantum Theory (1992), Preface
  • Bell’s theorem is the most profound discovery of science.
    • Henry P. Stapp, "Bell's Theorem and World Process", Nuovo Cimento, Vol. 29B, No. 2, p. 270 (1975).
  • The gist of Bell's theorem is this: no local model of reality can explain the results of a particular experiment.
    • Nick Herbert Quantum Reality - Beyond The New Physics Chapter 11, The Einstein-Podolsky-Rosen Paradox, p. 199
  • Bell himself managed to devise such a proof which rejects all models of reality possessing the property of "locality". This proof has since become known as Bells theorem. It asserts that no local model of reality can underlie the quantum facts. Bell's theorem says that reality must be non-local.
    • Nick Herbert Quantum Reality - Beyond The New Physics Chapter 12, Bell's Interconnectedness Theorem, p. 212
  • Physicists continue to debate whether Bell's theorem is airtight or not. However, the real question is not whether Bell can prove beyond doubt that reality is non-local, but whether the world is in fact non-local.
    • Nick Herbert Quantum Reality - Beyond The New Physics Chapter 13, The Future Of Quantum Reality, p. 238
  • There's an interesting scientific principle that a wrong answer can be much more stimulating to the field than just sort of finding the answer that's in the back of the book. A wrong result gets people excited. Worried. Obviously, you don't really want that to be happening—it's 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 you're 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.
    • Michael Horne (physicist), , as quoted by Louisa Gilder, in The Age of Entanglement, Vintage Books, 2008, p. 286: Quote regarding his wrong experimental results that implied that quantum mechanics yielded the wrong prediction regarding Bell's theorem.
  • 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 Bohm's, 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.
    • Andrew Whitaker, "John Bell and the most profound discovery of science", Physics World (December 1998)

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External links[edit]

Wikipedia has an article about:
  • Bell's Theorem by Abner Shimony (2004) in the Stanford Encyclopedia of Philosophy.