Einstein–Podolsky–Rosen paradox (EPR paradox) is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen (EPR), with which they argued that the description of physical reality provided by quantum mechanics was incomplete.
In a 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing them. Resolutions of the paradox have important implications for the interpretation of quantum mechanics.
https://en.wikipedia.org/wiki/Bell%27s_theorem
As Bell wrote later, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."[5]
To date, Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems do, in fact, behave.[6][7]
While the significance of Bell's theorem is not in doubt, its full implications for the interpretation of quantum mechanics remain unresolved.
In QM, predictions are formulated in terms of probabilities — for example, the probability that an electron will be detected in a particular place, or the probability that its spin is up or down. The idea persisted, however, that the electron in fact has a definite position and spin, and that QM's weakness is its inability to predict those values precisely. The possibility existed that some unknown theory, such as a hidden variables theory, might be able to predict those quantities exactly, while at the same time also being in complete agreement with the probabilities predicted by QM. If such a hidden variables theory exists, then because the hidden variables are not described by QM the latter would be an incomplete theory.
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