I fell upon another discord between realism and quantum mechanics while studying Bell's theorem :(adsbygoogle = window.adsbygoogle || []).push({});

If we consider measurement of 2 spin 1/2 particles, with operators A, A', B and B' which are set respectively at 0, 45, 90 and 135 degrees (like in Bell experiment), we have [tex] A=\left(\begin{array}{cc} 1 & 0\\0 & -1\end{array}\right)[/tex], and so on, and call the products

[tex]C_1=A\otimes B,C_2=A\otimes B', C_3=A'\otimes B, C_4=A'\otimes B'[/tex]

then local realism implies [tex] C_4=C_1 C_2 C_3[/tex]

whereas quantum mechanics predicts [tex]C_4=-C_1 C_2 C_3[/tex]

However I thought about this difference :

it's not because the operator has a minus sign in quantum mechanics that the result also has a minus sign, since QM gives only the probabilities, so that in fact QM could give the same result as local realism but not all the time.

Hence this does not prove that QM is not explainable in term of local realism ?

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# Another proof that local realism does not work

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