WAVE-FUNCTION COLLAPSE BY MEASUREMENT AND ITS SIMULATION

The many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ''yes-no'' experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ''wave-function collapse'' is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter epsilon that quantitatively describes the degree of decoherence. Its value ranges from epsilon = 0 (which describes the case in which the two waves are perfectly coherent) to epsilon = 1 (which describes the case in which coherence is totally lost); for this reason epsilon is named the ''decoherence parameter.'' In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex delta-potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit epsilon = 1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed.