The Axiomatisation of Physics

TL;DR

This paper proposes an axiomatic framework for quantum measurement by analyzing amplification and probability as multi-scale phenomena, leading to a logical foundation for quantum mechanics and classical observables.

Contribution

It introduces a new axiomatic approach to quantum measurement, defining probability as a multi-scale concept and deriving classical observables as limits of quantum ones.

Findings

Quantum probability is a multi-scale phenomenon.

Classical observables are limits of quantum observables.

Provides a logical axiomatization of quantum mechanics.

Abstract

Analysing Quantum Measurement requires analysing the physics of amplification since amplification of phenomena from one scale to another scale is essential to measurement. There still remains the task of working this into an axiomatic logical structure, what should be the foundational status of the concepts of measurement and probability. We argue that the concept of physical probability is a multi-scale phenomenon and as such, can be explicitly defined in terms of more fundamental physical concepts. Thus Quantum Mechanics can be given a logically unexceptionable axiomatisation. We introduce a new definition of macroscopic observable which implements Bohr's insight that the observables of a measurement apparatus are classical in nature. In particular, we obtain the usual non-abelian observables as limits of abelian, classical, observables. This is the essential step in Hilbert's Sixth Problem.