Quantum dynamical reduction and reality: Replacing probability densities with densities in real space

Consideration is given to recent attempts to solve the objectification problem of quantum mechanics by considering nonlinear and stochastic modifications of Schrödinger's evolution equation. Such theories agree with all predictions of standard quantum mechanics concerning microsystems but forbid the occurrence of superpositions of macroscopically different states. It is shown that the appropriate interpretation for such theories is obtained by replacing the probability densities of standard quantum mechanics with mass densities in real space. Criteria allowing a precise characterization of the idea of similarity and difference of macroscopic situations are presented and it is shown how they lead to a theoretical picture which is fully compatible with a macrorealistic position about natural phenomena.