An Abstract Theory of Physical Measurements

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.

Causality in Schwinger’s Picture of Quantum Mechanics

“…A space equipped with a measurable structure satisfying the previous conditions will also be called a Borel space and the elements Borel sets (Borel sets are often referred, more restrictively, as the sets in the -algebra generated by a given topology on ). This constitutes a crude axiomatic setting for a proper algebraic description of measurement processes as described, for instance, by Resende using the notion of quantals in the context of topology in “pointless” spaces [ 24 , 25 ], even though using Borel structures is sufficient for the situations that will be met in this work.…”

“…The high level of abstraction involved in the groupoidal picture of quantum mechanics makes it well adapted to discuss these issues. Indeed, there is a relevant stream of investigative efforts which focuses on considering the foundational aspects of quantum mechanics on a more abstract level as a way to better understand their nature (see, for instance, the recent works [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]).…”