The Original Bell Theorem without Calculus

Bell’s theorem is a topic of perennial fascination. Publishers and the general public have a steady appetite for approachable books about its implications. The scholarly literature includes many analogies to Bell’s theorem and simple derivations of Bell inequalities, and some of these simplified discussions are the basis of interactive web pages. Less well known is that the original Bell theorem is virtually unaffected when the calculus is taken away. Indeed, the only use of integrals in Bell’s derivation is to compute averages. We can simply replace integrals with the word “average.” The resulting proof of Bell’s theorem is just as easy to understand, and just as shocking, as the analogies designed to ease comprehension.