Zig-zag dynamics in a Stern-Gerlach spin measurement
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| author | Krekels, Simon Maes, Christian Meerts, Kasper Struyve, Ward |
| author_facet | Krekels, Simon Maes, Christian Meerts, Kasper Struyve, Ward |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13406 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Zig-zag dynamics in a Stern-Gerlach spin measurement Krekels, Simon Maes, Christian Meerts, Kasper Struyve, Ward Quantum Physics Statistical Mechanics 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. |
| title | Zig-zag dynamics in a Stern-Gerlach spin measurement |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2311.13406 |