2011/01/10 by Joy Christian, Christian, Joy · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1101.1958
openalex publication_date 2011/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S0, S1, S3, and S7 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 S3 and S7. The twin illusions of quantum entanglement and non-locality are thus shown to stem from the topologically incomplete accountings of the measurement results.