SpringerLink - Journal Article

Algebras of Measurements: The Logical Structure of Quantum Mechanics

Daniel Lehmann¹, Kurt Engesser² and Dov M. Gabbay²

(1)	School of Engineering, Hebrew University, Jerusalem, 91904, Israel

(2)	Department of Computing, King’s College, London, U.K.

Received: 21 July 2005 Accepted: 26 January 2006 Published online: 23 May 2006

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.

Key Words quantum measurements - measurement algebras - quantum logic

PACS: 02.10.-V.

Daniel Lehmann (Corresponding author)
Email: lehmann@cs.huji.ac.il

Kurt Engesser
Email: Kurt.Engesser@uni-konstanz.de

Dov M. Gabbay
Email: dg@dcs.kcl.ac.uk

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