The Interpretation of Quantum Mechanics

Description

This book is a contribution to a problem in foundational studies, the problem of the interpretation of quantum mechanics, in the sense of the theoretical significance of the transition from classical to quantum mechanics. The obvious difference between classical and quantum mechanics is that quantum mechanics is statistical and classical mechanics isn't. Moreover, the statistical character of the quantum theory appears to be irreducible: unlike classical statistical mechanics, the probabilities are not generated by measures on a probability space, i. e. by distributions over atomic events or classical states. But how can a theory of mechanics be statistical and complete? Answers to this question which originate with the Copenhagen inter­ pretation of Bohr and Heisenberg appeal to the limited possibilities of measurement at the microlevel. To put it crudely: Those little electrons, protons, mesons, etc. , are so tiny, and our fingers so clumsy, that when­ ever we poke an elementary particle to see which way it will jump, we disturb the system radically - so radically, in fact, that a considerable amount of information derived from previous measurements is no longer applicable to the system. We might replace our fingers by finer probes, but the finest possible probes are the elementary particles them­ selves, and it is argued that the difficulty really arises for these. Front Matter....Pages I-IX The Statistical Algorithm of Quantum Mechanics....Pages 1-31 The Problem of Completeness....Pages 32-48 Von Neumann’s Completeness Proof....Pages 49-54 Lattice Theory: The Jauch and Piron Proof....Pages 55-64 The Imbedding Theorem of Kochen and Specker....Pages 65-71 The Bell-Wigner Locality Argument....Pages 72-83 Resolution of the Completeness Problem....Pages 84-91 The Logic of Events....Pages 92-107 Imbeddability and Validity....Pages 108-118 The Statistics of Non-Boolean Event Structures....Pages 119-127 The Measurement Problem....Pages 128-141 The Interpretation of Quantum Mechanics....Pages 142-150 Back Matter....Pages 151-155