A stochastic model for quantum measurement

Abstract: We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always have a definite configuration all the time as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wave function and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wave function of the whole system+apparatus evolves according to a Schr\"odinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wave function collapse. We will also show that while the result of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurement is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system.