A theory of quantum (statistical) measurement

TL;DR

This paper develops a comprehensive theory of quantum measurement that incorporates finite-time, finite-region measurements, avoiding collapse postulates and paradoxes, and aligns with decoherence and classical observables.

Contribution

It introduces a finite-time, finite-region measurement model extending Hepp's decoherence-based approach, and mathematically avoids the collapse postulate and related paradoxes.

Findings

Measurement can be modeled without collapse postulate

No irreversibility is inherent in the measurement process

The theory aligns with decoherence and classical observables

Abstract

We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp's theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and apply it to a model of the Stern-Gerlach experiment. The number N of degrees of freedom of the measuring apparatus is such that $N \to \infty$, justifying the adjective "statistical", but, in addition, and in contrast to Hepp's approach, we make a three-fold assumption: the measurement is not instantaneous, it lasts a finite amount of time and is, up to arbitrary accuracy, performed in a finite region of space, in agreement with the additional axioms proposed by Basdevant and Dalibard. It is then shown how von Neumann's "collapse postulate" may be avoided by a mathematically precise formulation of an argument of Gottfried, and, at the same time, Heisenbeg's "destruction of knowledge" paradox is eliminated. The fact that no irreversibility is attached to the process of measurement is shown to follow from the author's theory of irreversibility, formulated in terms of the mean entropy, due to the latter's property of affinity.