Algebras of Measurements: the logical structure of Quantum Mechanics
arXiv:quant-ph/0507231 · doi:10.1007/s10773-006-9062-y
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.
Submitted, 30 pages