QUANTUM-THEORY OF MEASUREMENT BASED ON THE MANY-HILBERT-SPACE APPROACH

We review and develop the quantum theory of measurement along the line of thought of the many-Hilbert-space approach, originally proposed by Machida and Namiki some years ago. Our main interest is to analyze the mechanism of the wave-function collapse by measurement. We start by discussing the wave-particle dualism of quantum mechanical particles, as observed in a typical interference experiment of the Young type, and then analyze the quantum measurement process from a physical point of view. On the basis of these arguments, we reformulate the notion of wave-function collapse by measurement: We view the collapse as a dephasing process among the branch waves after they have undergone spectral decomposition, in opposition to the conventional Copenhagen interpretation. One of the most important points of the present approach is the introduction of an order parameter epsilon (named decoherence parameter) that ranges from 0 to 1 and quantitatively represents the degree of decoherence. In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus: The case of perfect decoherence, epsilon = 1, describes an apparatus by which we can perform perfect measurement, while the case of perfect coherence, epsilon = 0, describes an instrument by which we observe perfect interference. The intermediate values between 1 and 0 correspond to imperfect measurements or mesoscopic phenomena. From this point of view, we briefly give a critical review of some famous measurement theories. The present theory of measurement is also theoretically formulated in terms of density matrices within the mathematical framework of the continuous direct sum of many Hilbert spaces (the continuous-superselection-rule space). In order to show the characteristics of the theory, we introduce several solvable detector models and perform numerical simulations. Finally we analyze, by means of similar order parameters, miscellaneous related problems, including neutron and photon interference phenomena.