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    • 3.4: Bell's Theorem
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/03%3A_Quantum_Entanglement/3.04%3A_Bell's_Theorem
      In 1964, John S. Bell published a bombshell paper showing that the predictions of quantum theory are inherently inconsistent with hidden variable theories. The amazing thing about this result, known a...In 1964, John S. Bell published a bombshell paper showing that the predictions of quantum theory are inherently inconsistent with hidden variable theories. The amazing thing about this result, known as Bell’s theorem, is that it requires no knowledge about the details of the hidden variable theory, just that it is deterministic and local. Here, we present a simplified version of Bell’s theorem due to Mermin (1981).
    • 15.3: Hidden Variables - Bell’s Inequality and Aspect’s experiment
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/15%3A_The_Quantum_Mechanics_Nobody_Rreally_Understands/15.03%3A_Hidden_Variables_-_Bells_Inequality_and_Aspects_experiment
      \[P_{HV} (\theta , \phi ) = \frac{1}{2\pi} \oint \left( \cos^2 (\theta − \chi ) − \sin^2 (\theta − \chi ) \right) \left( \cos^2 (\phi − \chi ) − \sin^2 (\phi − \chi ) \right) d\chi = \frac{1}{2} \cos ...\[P_{HV} (\theta , \phi ) = \frac{1}{2\pi} \oint \left( \cos^2 (\theta − \chi ) − \sin^2 (\theta − \chi ) \right) \left( \cos^2 (\phi − \chi ) − \sin^2 (\phi − \chi ) \right) d\chi = \frac{1}{2} \cos 2(\theta − \phi ) \nonumber\] \[P_{QM} (\theta , \phi ) = \frac{1}{2\pi} \oint \left( \cos^2 (\theta − \chi ) − \sin^2 (\theta − \chi ) \right) \left( \cos^2 (\theta − \phi ) − \sin^2 (\theta − \phi ) \right) d\chi = \cos 2(\theta − \phi ) \nonumber\]

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