An abstract theory of physical measurements

TL;DR

This paper develops a mathematical framework for understanding physical measurements, distinguishing quantum and classical types, and deriving the concept of an observer from algebraic and topological principles.

Contribution

It introduces an abstract algebraic and topological model of measurement that formalizes the production of classical information and differentiates quantum from classical measurements.

Findings

Defines measurement space with algebraic and topological structures

Provides a formal distinction between quantum and classical measurements

Derives the notion of an observer within the measurement framework

Abstract

The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced. This translates into an algebraic and topological definition of measurement space that caters for the distinction between quantum and classical measurements and allows a notion of observer to be derived.