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The famous 1964 paper of John Stewart Bell, in which "Bell's inequality" is established, begins by assuming two things. (The paper can be found here: https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf) One of them is "locality", which means (non-mathematically) that distant objects cannot affect one another instantaneously. Mathematically, Bell ...


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Probability is the connection between the mathematical apparatus of quantum mechanics and experimental observation, data in the real world (it's what gives quantum mechanics the status of a scientific theory). A more appropriate question (for the philosophy section ) is related to the multitude of interpretations of quantum mechanics, but there is not ...


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Probabilities in quantum mechanics always respect the calculus of probabilities by definition. The square amplitudes of a set of orthogonal states, which are the quantities used to compute probabilities in quantum mechanics, don't always respect the calculus of probability, see: https://arxiv.org/abs/math/9911150


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