Abstract

We investigate and develop further two models, the GRW model and the K model, in which the Schrödinger evolution of the wave function is spontaneously and repeatedly interrupted by random, approximate localizations, also called “self-reductions” below. In these models the center of mass of a macroscopic solid body is well localized even if one disregards the interactions with the environment. The motion of the body shows a small departure from the classical motion. We discuss the prospects and the difficulties of observing this anomaly. As far a the influence of the surroundings on submacroscopic objects (like dust particles) is concerned, we show that the estimates obtained recently in the theory of continuous measurements and in the K model are compatible. Also, we elaborate upon the relationship between the models. Firstly, borrowing a line of thought from the K model, we find the transition region between macroscopic and microscopic behaviors in the GRW model. Secondly, we refine the propagation rule of the wave function in the K model with the help of the time-evolution equation proposed in the GRW model