Foundations of Quantum Mechanics, an Empiricist Approach

Willem M. de Muynck (auth.)1402009321, 9781402009327, 9780306480478

Old and new problems of the foundations of quantum mechanics are viewed from the new perspective provided by a generalization of the mathematical formalism encompassing positive operator-valued measures. One objective is to demonstrate the crucial role the generalized formalism plays in fundamental issues as well as in practical applications, and to contribute to the development of the operational approach.

A second objective is the development of an empiricist interpretation of this approach, duly taking into account the role played by the measuring instrument in quantum mechanical measurements. Copenhagen and anti-Copenhagen interpretations are critically assessed, and found to be wanting due to insufficiently taking into account the measurement interaction.

The Einstein-Podolsky-Rosen problem and the problem of the Bell inequalities are discussed, starting from this new perspective. An explanation of violation of the Bell inequalities is developed, providing an alternative to the usual explanation on the basis of non-locality. This treatise is based on lecture notes of an advanced course on the foundations of quantum mechanics.

Table of contents :
Standard and generalized formalisms of quantum mechanics….Pages 1-71
Empiricist and realist interpretations of quantum mechanics….Pages 73-112
Quantum mechanical description of measurement, and the “measurement problem”….Pages 113-170
The Copenhagen interpretation….Pages 171-237
The Einstein-Podolsky-Rosen problem….Pages 239-273
Individual-particle and ensemble interpretations of quantum mechanics….Pages 275-330
Generalized quantum mechanics….Pages 331-406
Applications of generalized quantum mechanics….Pages 407-469
The Bell inequality in quantum mechanics….Pages 471-533
Subquantum or hidden-variables theories….Pages 535-608