Many-Hilbert-spaces approach to the wave-function collapse

Abstract

The many-Hilbert-spaces approach to the measurement problem in quantum mechanics is reviewed, and the notion of wave function collapse by measurement is formulated as a dephasing process between the two branch waves of an interfering particle. Following the approach originally proposed in Ref. 1, we introduce a “decoherence parameter,” which yields aquantitative description of the degree of coherence between the two branch waves of an interfering particle. By discussing the difference between the wave function collapse and the orthogonality of the apparatus' wave functions, we analyze critically two proposals, recently appeared in the literature,^{(2, 3)} and argue that neither one describes a dephasing process. We conclude that the concept of “wave function collapse,” according to the conventional Copenhagen interpretation, is to be replaced by that of a statisticallydefined dephasing process.