Experimental tests of dynamical state-vector reduction

We consider theories in which the Schrödinger equation is modified so that the reduction of the state vector becomes a dynamical process characterized by a mean reduction time ${\tau }_R$. It is generally believed that such a theory and quantum theory differently predict the outcome of any two experiments performed in rapid enough succession (separated by a time interval $\lesssim {\tau }_R$), such as Papaliolios's successive measurements of a photon's polarization. It is shown that the predictions of a plausible class of dynamical reduction theories (for which the ensemble average of ${\left|〈{\phi }_n\right|\psi 〉|}^2$ remains constant during the reduction process, where $|\psi 〉$ is the state vector, and $|{\phi }_n〉$ is any one of the basis states to which it may reduce) and quantum theory do not differ for any Papaliolios-type experiment. However, there are deviations from the predictions of quantum theory if the second experiment measures interference between the superposed states created by the first measurement. As an example, the result of a recent two-slit neutron interference experiment by Zeilinger et al. is applied to the theory of Pearle, placing an upper limit ${\tau }_R\gtrsim 5$ sec on the neutron self-reduction time.