Shortly after John S. Bell's proof of his celebrated theorem (► Bell's Theorem) in 1964 [6] experiments started [13] that tried to check whether nature actually was as counterintuitive as the theorem implied. At the same time it became clear that it would be very difficult to carry out an experiment that tested Bell's original version of the inequality, because it had been derived using very stringent assumptions.
The first difficulty was with Bell's assumption of perfect correlations. That is, if the measurement functions of the hidden variable model are A(a, λ) and B(b, λ), where λ denotes the hidden variable, a and b the analyzer directions, Bell had assumed that they obey A(a, λ) = −B(a, λ). This assumption, however, is difficult to justify, because no real experiment will ever live up to it.
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Weihs, G. (2009). Loopholes in Experiments. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_109
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