A card game for Bell's theorem and its loopholes

Abstract

In 1964 John Stewart Bell made an observation about the behavior of particles separated by macroscopic distances that had puzzled physicists for at least 29 years, when Einstein, Podolsky and Rosen put forth the famous EPR paradox. Bell made certain assumptions leading to an inequality that entangled particles are routinely observed to violate in what are now called Bell test experiments. As an alternative to showing students a "proof" of Bell's inequality, we introduce a card game that is impossible to win. The solitaire version is so simple it can be used to introduce binomial statistics without mentioning physics or Bell's theorem. Things get interesting in the partners' version of the game because Alice and Bob can win, but only if they cheat. We have identified three cheats, and each corresponds to a Bell's theorem "loophole". This gives the instructor an excuse to discuss detector error, causality, and why there is a maximum speed at which information can travel.