Non-ideal classical measurements and quantum measurements: a comparative study

TL;DR

This paper compares non-ideal classical measurements with quantum measurements, showing that classical systems are affected by measurement similarly to quantum systems and deriving classical analogs of quantum measurement rules.

Contribution

It introduces a framework for non-ideal classical measurements using a finite-resolution probe and derives classical counterparts to quantum measurement postulates.

Findings

Classical measurements influence systems similarly to quantum measurements.

Derived classical equivalents of L"uders' rule, collapse postulate, and Lindblad equation.

Finite resolution in classical measurements affects system states in a quantifiable manner.

Abstract

Measurements on classical systems are usually idealized and assumed to have infinite precision. In practice, however, any measurement has a finite resolution. We investigate the theory of non-ideal measurements in classical mechanics using a measurement probe with finite resolution. We use the von Neumann interaction model to represent the interaction between system and probe. We find that in reality classical systems are affected by measurement in a similar manner as quantum systems. In particular, we derive classical equivalents of L\"uders' rule, the "collapse postulate", and the Lindblad equation.