Analysis of the Stern-Gerlach Measurement

TL;DR

This paper presents a dynamical model for quantum measurement collapse using a dissipative Stern-Gerlach setup, demonstrating how decoherence leads to classical behavior and correlates particle momentum with spin for measurement.

Contribution

It introduces a dissipative, environment-interacting model for wave function collapse in a Stern-Gerlach measurement, linking decoherence with classical measurement outcomes.

Findings

Density matrix becomes diagonal due to decoherence

Momentum correlates with spin operator after interaction

Measurement probabilities align with quantum principles

Abstract

A dynamical model for the collapse of the wave function in a quantum measurement process is proposed by considering the interaction of a quantum system (spin-1/2) with a macroscopic quantum apparatus interacting with an environment in a dissipative manner. The dissipative interaction leads to decoherence in the superposition states of the apparatus, making its behaviour classical in the sense that the density matrix becomes diagonal with time. Since the apparatus is also interacting with the system, the probabilities of the diagonal density matrix are determined by the state vector of the system. We consider a Stern-Gerlach type model, where a spin- 1/2 particle is in an inhomogeneous magnetic field, the whole set up being in contact with a large environment. Here we find that the density matrix of the combined system and apparatus becomes diagonal and the momentum of the particle becomes correlated with a spin operator, selected by the choice of the system-apparatus interaction. This allows for a measurement of spin via a momentum measurement on the particle with associated probabilities in accordance with quantum principles.