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arXiv · 2311.13406

Zig-zag dynamics in a Stern-Gerlach spin measurement

Simon Krekels·Christian Maes·Kasper Meerts·Ward Struyve
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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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Simon Krekels, Christian Maes, Kasper Meerts, Ward Struyve. 2024-02-24. Zig-zag dynamics in a Stern-Gerlach spin measurement. https://doi.org/10.1098/rspa.2023.0861

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