Zig-zag dynamics in a Stern–Gerlach spin measurement

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Simon Krekels, Christian Maes, Kasper Meerts, Ward Struyve
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引用次数: 0

Abstract

The 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 non-relativistic limit, which will be considered here, and which is described by the Pauli equation for a non-uniform 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 non-local influence (action-at-a-distance) on the other particle is manifest in its trajectory, e.g. by initiating its zig-zagging.

斯特恩-格拉赫自旋测量中的之字形动力学
拥有百年历史的斯特恩-格拉赫装置是量子测量的典范。我们按照玻色子之字形动力学将电子轨迹可视化。这种动力学是为了处理粒子的基本无质量特性(质量来自布鲁特-恩格勒特-希格斯机制)而开发的。由于左手和右手手性韦尔态之间的耦合,相应的轨迹呈现出随机的之字形。这种 "之 "字形变化在非相对论极限中持续存在,这里将考虑非相对论极限,它由非均匀外部磁场的保利方程描述。我们的结果澄清了 "自旋 "作为波函数属性和作为斯特恩-格拉赫设置中随机变量的不同含义,并说明了有效坍缩的概念。我们还研究了 EPR 对的情况。让其中一个纠缠粒子通过斯特恩-格拉赫装置,对另一个粒子的非局部影响(远距离作用)就会在它的轨迹上表现出来,例如,启动它的 "之 "字形运动。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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