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A Theory of Quantum (Statistical) Measurement

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Abstract

We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp’s theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and apply it to a model of the Stern-Gerlach experiment. The number N of degrees of freedom of the measuring apparatus is such that \(N \rightarrow \infty \), justifying the adjective “statistical”, but, in addition, and in contrast to Hepp’s approach, we make a three-fold assumption: the measurement is not instantaneous, it lasts a finite amount of time and is, up to arbitrary accuracy, performed in a finite region of space, in agreement with the additional axioms proposed by Basdevant and Dalibard. It is then shown how von Neumann’s “collapse postulate” may be avoided by a mathematically precise formulation of an argument of Gottfried, and, at the same time, Heisenberg’s “destruction of knowledge” paradox is eliminated. The fact that no irreversibility is attached to the process of measurement is shown to follow from the author’s theory of irreversibility, formulated in terms of the mean entropy, due to the latter’s property of affinity.

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Acknowledgements

We should like to thank Pedro L. Ribeiro for discussions, the late Derek W. Robinson for a correspondence in which he stressed the importance of the property of affinity, and Professor R. B. Griffiths for an enlightening correspondence on related matters. This paper owes very much to the remarks of both referees, which resulted in truly substantial improvements regarding the previous version.

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  1. Instituto de Fisica, Universidade de São Paulo (USP), Sao Paulo, Brazil

    Walter F. Wreszinski

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  1. Walter F. Wreszinski
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Correspondence to Walter F. Wreszinski.

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Communicated by Hal Tasaki.

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Wreszinski, W.F. A Theory of Quantum (Statistical) Measurement. J Stat Phys 190, 64 (2023). https://doi.org/10.1007/s10955-023-03071-0

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