Measurement theory in classical mechanics

TL;DR

This paper explores measurement theory within classical mechanics using the Koopman-von Neumann Hilbert space formulation, highlighting differences from quantum measurement and deriving a classical uncertainty relation.

Contribution

It introduces a Hilbert space framework for classical measurement theory and compares it to quantum measurement, revealing fundamental differences.

Findings

Classical and quantum measurements have different interpretative frameworks.

A classical uncertainty relation analogous to quantum uncertainty is derived.

The Hilbert space formulation provides new insights into classical measurement processes.

Abstract

Measurement theory in classical mechanics is investigated in the formulation of classical mechanics by Koopman and von Neumann (KvN), using Hilbert space. It is shown that the classical and the quantum measurements give different "relative interpretations" of the measurement state and the recording state of the measurement device. The uncertainty relation in classical mechanics is also derived.