A counterexample to Bell's theorem is presented which uses a pair of photons
instead of spin-1/2 particles used in our previous counterexamples. A locally
causal protocol is provided for Alice and Bob, which allows them to simulate
observing photon polarizations at various angles, and record their results as
A=+/-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, which
remains closed under multiplication, thus preserving the locality condition of
Bell.Comment: 4 pages; Further elaborations may be found in arXiv:0904.4259,
arXiv:quant-ph/0703179, arXiv:0707.1333, arXiv:0806.3078, and
arXiv:quant-ph/070324
