A Unified Scheme of Measurement and Amplification Processes based on Micro-Macro Duality -- Stern-Gerlach experiment as a typical example

TL;DR

This paper presents a unified mathematical framework for quantum measurement and amplification processes based on Micro-Macro duality, exemplified through the Stern-Gerlach experiment, highlighting the quantum-classical correspondence.

Contribution

It introduces a novel scheme that unifies measurement and amplification processes using Micro-Macro duality, with a detailed model of the Stern-Gerlach experiment.

Findings

The scheme naturally incorporates amplification in quantum measurements.

Helgason duality and Radon transform are key mathematical tools.

The model successfully describes the quantum-classical transition in measurement.

Abstract

A unified scheme for quantum measurement processes is formulated on the basis of Micro-Macro duality as a mathematical expression of the general idea of quantum-classical correspondence. In this formulation, we can naturally accommodate the amplification processes necessary for magnifying quantum state changes at the microscopic end of the probe system into the macroscopically visible motion of the measuring pointer. Its essence is exemplified and examined in the concrete model of the Stern-Gerlach experiment for spin measurement, where the Helgason duality controlling the Radon transform is seen to play essential roles.