Proposed Photon Interference Experiment for Test of Quantum Measurement Theories

Machida and one of the present authors (M.N.)1) have proposed a parallel run of double Stern-Gerlach experiments, in order to discriminate the many-Hilbert-spaces theory2) from the environment-induced-superselection-rule theory given by Zurek.) However, this type of experiment would not be so easy for particles with spin one-half. In this paper we propose a similar type of experiment using a photon beam. The proposed experiment is also used to examine the many-worlds interpretation.) Consider a measurement of an observable, F, of an object system, Q, in a superposed state ¢Q= 2.;.iCiUirp, Ui being an eigenstate of F belonging to an eigenvalue Ai and Ci=(Uirp, ¢Q). rp stands for a wave function with respect to observables other than F, for example, for a wave packet function of position variables in case F is spin or polarization. The Stern-Gerlach type of experiment is divided into two steps, the first being responsible for spectral decomposition and the second for detection. In the first step the wave function changes as