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A counterexample to Bell's theorem is presented which uses a pair of photonsinstead of spin-1/2 particles used in our previous counterexamples. A locallycausal protocol is provided for Alice and Bob, which allows them to simulateobserving photon polarizations at various angles, and record their results asA=+/-1 in S^3 and B=+/-1 in S^3, respectively. When these results are compared,the correlations are seen to be exactly those predicted by quantum mechanics;namely cos 2(alpha - beta), where alpha and beta are the angles of polarizers.The key ingredient in our counterexample is the topology of 3-sphere, whichremains closed under multiplication, thus preserving the locality condition ofBell.

Failure of Bell's Theorem and the Local Causality of the Entangled Photons