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Journal of Advanced Physics

Violation of the Bell Inequalities by Weyl Conformal Quantum Geometrodynamics A Re-Interpretation of Quantum Nonlocality

F. De Martini, Enrico Santamato

Published Jun 3, 2015• 4 citations
Publisher
DOI
10.1166/jap.2015.1195

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Since the 1935 proposal by Einstein Podolsky and Rosen the riddle of nonlocality, today demonstrated by innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a non relativistic approach based on the Weyl's conformal differential geometry applied to the Hamilton-Jacobi solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the nonlocality rests on the entanglement of the spin internal variables, playing the role of "hidden variables". At the end, the violation of the Bell inequalities is demonstrated without recourse to the common nonlocality paradigm. A discussion over the role of the "% \textit{internal space"} of any entangled dynamical system involves deep conceptual issues, such the \textit{indeterminism} of quantum mechanics and explores the in principle limitations to any exact dynamical theory when truly "hidden variables" are present. Because of the underlying geometrical foundations linking necessarily gravitation and quantum mechanics, the theory presented in this work may be considered to belong to the unifying "quantum gravity" scenario.

arXiv:1203.0033•Feb 29, 2012•6 citations
The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyl's differential geometry are presented. The theory applied to the case of the relativistic single quantum spin 1/2 leads a novel and unconventional derivation of Dirac's equation. The further extension of the theory to the case of two spins 1/2 in EPR entangled state and to the related violation of Bell's inequalities leads, by an exact albeit non relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.
Since the 1935 proposal by Einstein, Podolsky and Rosen the riddle of nonlocality, today demonstrated by the violation of Bell's inequalities within innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a nonrelativistic approach based on conformal differential geometry applied to the solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the quantum nonlocality may be understood on the basis of a conformal quantum geometrodynamics acting necessarily on the full "configuration space" of the entangled particles. At the end, the violation of the Bell inequalities is demonstrated without making recourse to the common nonlocality paradigm.
Since the 1935 proposal by Einstein Podolsky and Rosen the riddle of nonlocality, today demonstrated by innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a non relativistic approach based on the Weyl's conformal differential geometry applied to the Hamilton-Jacobi solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the nonlocality rests on the entanglement of the spin internal variables, playing the role of "hidden variables". At the end, the violation of the Bell inequalities is demonstrated without recourse to the common nonlocality paradigm. A discussion over the role of the "% \textit{internal space"} of any entangled dynamical system involves deep conceptual issues, such the \textit{indeterminism} of quantum mechanics and explores the in principle limitations to any exact dynamical theory when truly "hidden variables" are present. Because of the underlying geometrical foundations linking necessarily gravitation and quantum mechanics, the theory presented in this work may be considered to belong to the unifying "quantum gravity" scenario.