On the geometry of physical measurements: topological and algebraic aspects
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Publication:6339891
DOI10.1016/J.GEOMPHYS.2022.104730zbMATH Open1519.81040arXiv2005.00933MaRDI QIDQ6339891
Publication date: 2 May 2020
Abstract: We study the mathematical structure of the notion of measurement space, which extends aspects of noncommutative topology that are based on quantale theory. This yields a geometric model of physical measurements that provides a realist picture, yet also operational, such that measurements and classical information arise interdependently as primitive concepts. A derived notion of classical observer caters for a mathematical formulation of Bohr's classical/quantum divide. Two important classes of measurement spaces are obtained, respectively from C*-algebras and from second-countable locally compact open sober topological groupoids. The latter yield measurements of classical type and relate to Schwinger's notion of selective measurement. We show that the measurement space associated to the reduced C*-algebra of any second-countable locally compact Hausdorff 'etale groupoid is canonically equipped with a classical observer, and we establish a correspondence between properties of the observer and properties of the groupoid.
General and philosophical questions in quantum theory (81P05) General theory of (C^*)-algebras (46L05) Quantum measurement theory, state operations, state preparations (81P15) Topological groupoids (including differentiable and Lie groupoids) (22A22) Contextuality in quantum theory (81P13) Quantales (18F75)
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