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The term "hidden variable theory" is used in the interpretation of quantum mechanics. It refers to all types of the theory that attempt to account for the probabilistic features of quantum mechanics by the mechanism of underlying inaccessible variables. A local hidden variable theory has the added requirement of being consistent with local realism, requiring that distant events be independent, ruling out ''instantaneous'' (i.e. faster-than-light) interactions between separate events. The mathematical implications of a local hidden variable theory in regard to the phenomenon of quantum entanglement were explored by physicist John S Bell. Bell's 1964 paper (see Bell's theorem) showed that local hidden variables cannot reproduce the quantum measurement correlations that quantum mechanics predicts. The theory of quantum entanglement predicts that separated particles can briefly share common properties and respond to certain types of measurement as if they were a single particle. In particular, a measurement on one particle in one place can alter the probability distribution for the outcomes of a measurement on the other particle at a different location. If a measurement setting in one location instantaneously modifies the probability distribution that applies at a distant location, then local hidden variables are ruled out. For an expanded description, see Bell's theorem. A series of experiments, called Bell test experiments, have provided partial experimental confirmation of the entanglement phenomenon, but local hidden variable theory can still explain the probabilistic nature of quantum measurement due to loopholes in experimental Bell tests. ==Local hidden variables and the Bell tests== Bell's theorem starts with the implication of the principle of local realism: That separated measurement processes are independent. Based on this premise, the probability of a coincidence between separated measurements of particles with correlated (e.g. identical or opposite) orientation properties can be written: :: (1) where is the probability of detection of particle with hidden variable by detector , set in direction , and similarly is the probability at detector , set in direction , for particle , sharing the same value of . The source is assumed to produce particles in the state with probability . Using (1), various ''Bell inequalities'' can be derived, these inequalities provide limits on the possible behaviour of local hidden variable models. When John Bell originally derived his inequality, it was in relation to pairs of entangled spin-1/2 particles, every one of those emitted being detected. Bell showed that when detectors are rotated with respect to each other, local realist models must yield a correlation curve that is bounded by a straight line between maxima (detectors aligned), whereas the quantum correlation curve is a cosine relationship. The first Bell test experiments were not performed with spin 1/2 particles, and were performed with photons which have spin 1. A classical local hidden variable prediction for photons, based on Maxwell's equations, yields a cosine curve but of reduced amplitude such that the curve still lies within the straight-line limits specified in the original Bell inequality. Note that while a great variety of realist models could be proposed, they cannot be arbitrary because they must still yield results consistent with classical experiments, as in the example with photons, where the model must still yield Malus' Law. Bell's theorem assumes that measurement settings are completely independent, and not in principle determined by the universe at large. If this assumption were to be incorrect, as proposed in superdeterminism, conclusions drawn from Bell's theorem may be invalidated. The theorem also relies on very efficient and space-like separated measurements, not yet satisfied simultaneously experimentally. Such arguments are generally called ''loophole theories.'' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「local hidden variable theory」の詳細全文を読む スポンサード リンク
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