Problem of Measurement Within the Operator Formulation of Hybrid Systems

The basic concepts of classical mechanics are given in operator form. Then ahybrid systems approach with the operator formulation of both quantum andclassical sectors is applied to the case of an ideal nonselective measurement. Itis found that the dynamical equation, consisting of the Schrödinger and Liouvilledynamics, produces noncausal evolution when the initial state of the measured(quantum mechanical) system and measuring apparatus=nclassical mechanicalsystem is chosen to be as demanded in discussions regarding the problem ofmeasurement. Nonuniqueness of possible realizations of the transition from apure noncorrelated to a mixed correlated state is analyzed in detail. It is concludedthat the state of the quantum mechanical system instantaneously collapses becauseof the nonnegativity of probabilities, and a dynamical model of this reductionis proposed.