Combining stochastic dynamical statevector reduction with spontaneous localization

A linear equation of motion for the statevector is presented, in which an anti-Hamiltonian that fluctuates randomly is added to the usual Hamiltonian of the Schroedinger equation. It is shown how the resulting theory describes the continuous evolution of a statevector to an ensemble of reduced statevectors while retaining important physical features of the Ghirardi, Rimini, Weber theory of Spontaneous Localization, in which the statevector reduction occurs discontinuously. A novel aspect, compared with ordinary quantum theory, is that the statevector norm changes with time. The squared norm of each statevector is interpreted as proportional to the probability possessed by that statevector in the ensemble of statevectors. This interpretation is shown to be consistent with the independent Markovian evolution of each statevector. (author). 25 refs