Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. This well known fact was brought forth by Einstein, Podolsky, and Rosen in 1935. Today it is widely believed that any hopes of restoring local causality within a realistic theory have been undermined by Bell's theorem and its supporting experiments. By contrast, we provide a strictly local, deterministic, and realistic explanation for the correlations observed in two such supporting experiments performed at Orsay and Innsbruck. (...) To this end, a pair of local variables is constructed to simulate detections of photon polarizations at various angles, chosen freely by Alice and Bob. These generate purely random outcomes: A = +/-1 and B = +/-1. When these outcomes are compared, however, the correlation between them turn out to be exactly equal to -cos2, with the corresponding CHSH inequality violated for the polarization angles alpha, alpha', beta, and beta' in precisely the manner predicted by quantum mechanics. The key ingredient in our explanation is the topology of 3-sphere, which remains closed under multiplication, thus preserving the locality condition of Bell. (shrink)

The discipline of parallelization in the manifold of all possible measurement results is shown to be responsible for the existence of all quantum correlations, with the upper bound on their strength stemming from the maximum of possible torsion within all norm-composing parallelizable manifolds. A profound interplay is thus uncovered between the existence and strength of quantum correlations and the parallelizability of the spheres S^0, S^1, S^3, and S^7 necessitated by the four real division algebras. In particular, parallelization within a unit (...) 3-sphere is shown to be responsible for the existence of EPR and Hardy type correlations, whereas that within a unit 7-sphere is shown to be responsible for the existence of all GHZ type correlations. Moreover, parallelizability in general is shown to be equivalent to the completeness criterion of EPR, in addition to necessitating the locality condition of Bell. It is therefore shown to predetermine both the local outcomes as well as the quantum correlations among the remote outcomes, dictated by the infinite factorizability of points within the spheres S^3 and S^7. The twin illusions of quantum entanglement and non-locality are thus shown to stem from the topologically incomplete accountings of the measurement results. (shrink)

An elementary topological error in Bell's representation of the EPR elements of reality is identified. Once recognized, it leads to a topologically correct local-realistic framework that provides exact, deterministic, and local underpinning of at least the Bell, GHZ-3, GHZ-4, and Hardy states. The correlations exhibited by these states are shown to be exactly the classical correlations among the points of a 3 or 7-sphere, both of which are closed under multiplication, and hence preserve the locality condition of Bell. The alleged (...) non-localities of these states are thus shown to result from misidentified topologies of the EPR elements of reality. When topologies are correctly identified, local-realistic completion of any arbitrary entangled state is always guaranteed in our framework. This vindicates EPR, and entails that quantum entanglement is best understood as an illusion. (shrink)

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. (shrink)

In a recent arXiv preprint Richard Gill has criticized an experimental proposal published in a journal of theoretical physics which describes how to detect a macroscopic signature of fermionic sign changes. Here I point out that his worries stem from his own elementary algebraic and conceptual mistakes, and present several event-by-event numerical simulations which expose the vacuity of his claims by explicit computations.