Zig-zag dynamics in a Stern-Gerlach spin measurement

TL;DR

This paper visualizes Bohmian zig-zag trajectories in a Stern-Gerlach experiment, clarifying the nature of spin and demonstrating nonlocal effects in entangled particles within a nonrelativistic framework.

Contribution

It introduces a Bohmian zig-zag dynamics approach to analyze spin measurement and nonlocality in the nonrelativistic limit of the Stern-Gerlach setup.

Findings

Trajectories exhibit stochastic zig-zagging due to chiral coupling.

Results clarify the distinction between wave function properties and measurement outcomes.

Nonlocal influence affects entangled particles' trajectories through the measurement process.

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.