Physics and the measurement of continuous variables

TL;DR

This paper discusses the measurement of continuous variables in quantum mechanics, arguing that the concept of a geometrical point remains meaningful in quantum physics when considering recent solutions to the measurement problem.

Contribution

It extends Sewell's resolution of the measurement problem to continuous spectra, demonstrating the continued relevance of geometrical points in quantum mechanics.

Findings

The notion of a geometrical point is valid in quantum mechanics.

Sewell's approach helps reconcile measurement issues with continuous variables.

Quantum and classical mechanics share similar conceptual foundations regarding points.

Abstract

Wigner had expressed the opinion that the impossibility of exact measurements of single operators like position operators rendered the notion of geometrical points somewhat dubious in physics. Using Sewell's recent resolution of the measurement problem (collapse of the wave packet) in quantum mechanics and extending it to the measurement of operators with continuous spectra, we are able to compare the situation in quantum mechanics with that in quantum mechanics. Our conclusion is that the notion of a geometrical point is as meaningful in quantum mechanics as it is in classical mechanics.