Algebras of Measurements: the logical structure of Quantum Mechanics

Details Algebras of Measurements: the logical structure of Quantum Mechanics Algebras of Measurements: the logical structure of Quantum Mechanics

2005-07-24

arxiv.org/abs/quant-ph/0507231v2

International Journal of Theoretical Physics, 45(4) April 2006, pages 698-723

Physics

Quantum Physics

Submitted, 30 pages

Scientific paper

10.1007/s10773-006-9062-y

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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