Tuesday, 29 November 2011
The New Quantum Logic
Robert B. Griffiths, Department of Physics
Carnegie Mellon University
12:05 pm, 817R Cathedral of Learning
Abstract: The structure of the quantum Hilbert space, in particular von Neumann's notion that properties and their negations are associated with subspaces and their orthogonal complements, was the motivation for the Birkhoff and von Neumann quantum logic. It is an internally consistent replacement for ordinary propositional logic, but suffers from a serious problem: it has not resolved the conceptual difficulties of quantum mechanics. The new quantum logic, developed by Omnes and the speaker (with important contributions from Gell-Mann and Hartle) is also based on Hilbert space, but is more successful in taming quantum paradoxes. It has no measurement problem, is consistent with special relativity (no action at a distance), can make sense of Schrodinger's cat, etc.
The talk will focus on the central logical issues, which are not difficult to understand even if one is not already acquainted with the older quantum logic. Their consistent resolution by means of a principle known as the Single Framework Rule leads to a strange and counterintuitive quantum ontology. However, the new logic itself provides an explanation, in fully quantum mechanical terms, of why ordinary (classical) logic works very well for the everyday world of macroscopic objects.