Stationary Phase and the Theory of Measurement -- 1/N expansion --

TL;DR

This paper analyzes the measurement process involving a large number of particles, demonstrating how fluctuations diminish as N increases and providing a 1/N expansion to quantify corrections to ideal measurement outcomes.

Contribution

It introduces a model that captures the measurement process with a finite number of particles and derives correction terms in powers of 1/N, linking stationary phase to measurement theory.

Findings

Fluctuations vanish as N approaches infinity.

Correction terms are systematically calculated in powers of 1/N.

The model reproduces ideal measurement results in the infinite N limit.

Abstract

The measuring process is studied, where a macroscopic number N of particles in the detector interact with the object. The macrovariable accompanies the stationary phase in the path-integral form, which is in one-to-one correspondence with the eigen-value of the object operator O to be measured. When N goes to infinity, the fluctuation of the object between different eigenvalues of O is suppressed, frozen to one the same state while the detector is on. A model is studied which produces the ideal result when N is infinite, and the correction terms are calculated in powers of 1/N. It is identical to the expansion including the fluctuation of the object successively.