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Physical Review A

Reply to “Comment on ‘Relevance of Bell’s theorem as a signature of nonlocality: Case of classical angular momentum distributions’ ”

A. Matzkin

Published Apr 10, 2009• 0 citations
Publisher

Abstract

In this Reply, we show that the main argument of the criticism given in the preceding Comment is inconsistent with the assumption lying at the basis of the model introduced in the original paper [A. Matzkin, Phys. Rev. A 77, 062110 (2008)]. We further clarify some issues concerning the interplay between noncommuting measurements and conservation laws in order to reply to the additional criticism contained in the comment.

DOI
10.1103/physreva.79.046102

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Comment on “Relevance of Bell’s theorem as a signature of nonlocality: Case of classical angular momentum distributions”

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A missing paragraph from the original work [A. Redondo, Phys. Rev. A 39, 4366 (1989] that is being commented upon [preceding paper, Cioslowski and Levy, Phys. Rev. A 40, 6727 (1989)] is included. The relationship between this work and a theorem by Lieb [E. Lieb, Phys. Rev. Lett. 46, 457 (1981); 47, 69 (1981)] is also noted.

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In this Reply, we show that the main argument of the criticism given in the preceding Comment is inconsistent with the assumption lying at the basis of the model introduced in the original paper [A. Matzkin, Phys. Rev. A 77, 062110 (2008)]. We further clarify some issues concerning the interplay between noncommuting measurements and conservation laws in order to reply to the additional criticism contained in the comment.
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 the 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, in particular noncommutativity of single-particle measurements. We discuss to what extent a violation of these assumptions is a faithful marker of nonlocality.
In Phys. Rev. A 101, 022117 (2020), it was argued that Bell inequalities are based on classical not quantum physics, and, hence, their violation in experiments provides no support for the claimed existence of peculiar nonlocal and superluminal influences in the real (quantum) world. This Reply to Lambare's Comment, Phys. Rev. A 104, 066201 (2021), on that paper seeks to clarify some issues related to the correct use of Hilbert space quantum mechanics for identifying the microscopic causes of later macroscopic measurement outcomes, a matter not properly addressed by Bell, who used classical hidden variables in place of the Hilbert subspaces (equivalently, their projectors) employed by von Neumann in Mathematical Foundations of Quantum Mechanics.