We show that there is essentially only one way to construct a stochastic Schrödinger equation that gives a dynamical account of the transformation of entangled into factorized states and is consistent with both quantum mechanics and required symmetries. The noisy, nonlinear term is a unimodular scalar multiple of the time-reversal operator that must be present whenever a Hamiltonian term in the Schrödinger equation can distinguish the factorized constituents of an entangled state. The dynamical mechanism involved in the transformation of entangled into factorized states provides an explanation for the fact that Einstein-Podolsky-Rosen correlations appear in a time determined by the response of the measuring device and independent of the distance between the particles. The dependence on the response time of the measuring device may be testable through a delay in observing the collapse of mesoscopic “Schrödinger cat” states in ion traps. It is further shown that there are situations where a two-particle interaction can induce a nonlinear term by virtue of coupling to decay modes that distinguish factorized constituents of an entangled state. We show that this should happen in the neutral $K$-meson system where the entangled $K_L$ state is pushed slightly in the direction of a factorized constituent ${(K}_0$ or $\overline{K_0})$ as a consequence of the fact that these can be distinguished via the sign of the charged lepton in a semileptonic decay mode. The result is a $\mathrm{CP}$ violation that is within 20% of the experimental value.

• Received 15 October 1996

DOI:https://doi.org/10.1103/PhysRevA.56.146