Bell's theorem as a signature of nonlocality: a classical counterexample

Details Bell's theorem as a signature of nonlocality: a classical counterexample Bell's theorem as a signature of nonlocality: a classical counterexample

2007-09-13

arxiv.org/abs/0709.2114v3

Phys. Rev. A 77 062110, 2008 (with the title: Relevance of Bell's theorem as a signature of nonlocality: Case of classical ang

Physics

Quantum Physics

Extended manuscript. Significant changes

Scientific paper

10.1103/PhysRevA.77.062110

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.

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