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.
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