Zig-zag dynamics in a Stern-Gerlach spin measurement

• URL: http://arxiv.org/abs/2311.13406v2
• Date: Sat, 24 Feb 2024 18:18:19 GMT
• Title: Zig-zag dynamics in a Stern-Gerlach spin measurement
• Authors: Simon Krekels, Christian Maes, Kasper Meerts, Ward Struyve
• Abstract summary: We visualize the trajectories following the Bohmian zig-zag dynamics. The corresponding trajectories exhibit a zig-zagging, as the result of the coupling between left- and right-handed electron states. Results clarify the different meanings of spin'' as a property of the wave function and as a random variable in the SternGerlach setup.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The one-century-old Stern-Gerlach setup is paradigmatic for a quantum measurement. We visualize the electron trajectories following the Bohmian zig-zag dynamics. This dynamics was developed in order to deal with the fundamentally massless nature of particles (with mass emerging from the Brout-Englert-Higgs mechanism). The corresponding trajectories exhibit a stochastic zig-zagging, as the result of the coupling between left- and right-handed chiral Weyl states. This zig-zagging persists in the nonrelativistic limit, which will be considered here, and which is described by the Pauli equation for a nonuniform external magnetic field. Our results clarify the different meanings of ``spin'' as a property of the wave function and as a random variable in the Stern-Gerlach setup, and they illustrate the notion of effective collapse. We also examine the case of an EPR-pair. By letting one of the entangled particles pass through a Stern-Gerlach device, the nonlocal influence (action-at-a-distance) on the other particle is manifest in its trajectory, e.g. by initiating its zig-zagging.

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