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**The quantum theory of measurement.
2nd rev. ed.**
*(German)*
Zbl 0868.46051

Lecture Notes in Physics. New Series m: Monographs. m2. Berlin: Springer. xiii, 181 p. (1996).

The book under review is devoted to the quantum theory of measurement, i.e. to the investigation of the semantical consistency of quantum mechanics. Depending on the interpretation of quantum theory the measuring process is studied as a mutual relation between measured objects, measuring apparatus, environment and observables. The main mathematical language, exposed in Chapter II, is given by traditional Hilbert space mechanics in which observables (selfadjoint operators) are replaced by more general POV (positive operator valued) measures. This approach provides an appropriate means for dealing with unsharpness inherent in any real measurement. Also, the problem of measurement leads to a ‘non-unitary dynamics’ on the Hilbert structure. In the third chapter the basic elements of the quantum measurement theory are summarized. The underlying issue is the objectification problem, i.e. the question of how definite measurement outcomes are obtained. Various solutions to the measurement problem proposed in various interpretations of quantum mechanics are reviewed in Chapter IV. Concluding Chapter V contains general conclusions.

In the second edition the central chapters of the monography have been substantially rewritten so that they reflect the rapidly developing current research into numerous areas of quantum mechanics. The most important changes concern the elucidation of the various necessary objectification requirements such as pointer definiteness and pointer mixture conditions. The book is a well written account of one area of the foundations of quantum mechanics and can be recommended for mathematicians, physicists, and philosophers interested in this intriguing field.

In the second edition the central chapters of the monography have been substantially rewritten so that they reflect the rapidly developing current research into numerous areas of quantum mechanics. The most important changes concern the elucidation of the various necessary objectification requirements such as pointer definiteness and pointer mixture conditions. The book is a well written account of one area of the foundations of quantum mechanics and can be recommended for mathematicians, physicists, and philosophers interested in this intriguing field.

Reviewer: J.Hamhalter (Praha)

### MSC:

46N50 | Applications of functional analysis in quantum physics |

81P15 | Quantum measurement theory, state operations, state preparations |