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Algebras of Measurements: the logical structure of Quantum Mechanics

Daniel Lehmann·Kurt Engesser·Dov M. Gabbay
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Abstract

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic. PACS: 02.10.-v.

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Daniel Lehmann, Kurt Engesser, Dov M. Gabbay. 2005-12-08. Algebras of Measurements: the logical structure of Quantum Mechanics. https://doi.org/10.1007/s10773-006-9062-y

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