2007/05/17 by Joseph F. Johnson, Johnson, Joseph F.
Arts and Humanities · Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Philosophy and History of Science #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.0705.2554
for larger context and other links, see http://euclid.unh.edu/~jjohnson
arxiv created 2007/05/17 · openalex publication_date 2007/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.