File:Bell's theorem entanglement in a long tube.svg

English: Bell's theorem experiments involve advanced quantum systems that model the production of photons or particles with spin. To alleviate this, one can imagine two free particles that do not interact, but are confined to occupy a narrow tube (with an infinite potential preventing a non-zero amplitude unless r<R.) We combine four wave functions, two for each particle. The coordinates of Alice (unprimed) and Bob (primed) of (x,y,x',y'), or equivalently (r,θ,r',θ'). The wavefunctions vary with angle as sinθ or cosθ (two orthogonal functions). This is designed to supplement the Card game for Bell's theorem and its loophole.