A proof of Bells inequality Difficulty 34

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This is a companion video to • (Non-)Locality, the Einstein-Podolsky... in which I discussed the relation between Bell's inequality and locality. In this video, I give a full proof of Bell's inequality in a very general setting, starting only from the assumption of locality. • Difficulty level: 3/4 (orange). Prerequisites: probability distributions, conditional probabilities, expectations, integrals. • See • (Non-)Locality, the Einstein-Podolsky... for an introductory video on Bell's inequality and locality. • This video was filmed at the Department of Mathematics, Rutgers University in Piscataway, NJ, on November 19, 2022. • Very special thanks go to Sasha Pohle for helping me produce this video, as well as to Sheldon Goldstein and Michael Kiessling for their useful feedback and comments. • Photo credits: • J. Bell: CERN • 00:00 Introduction • 02:11 Bell's theorem • 04:22 Setup • 07:42 Locality • 09:34 Back to Setup • 11:21 Back to Locality • 12:40 Statement of the theorem • 14:53 Proof • 22:04 Discussion • 24:53 Conclusion

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