Modified Sch\"odinger dynamics with attractive densities

Abstract

The linear Schr\"{o}dinger equation does not predict that macroscopic bodies should be located at one place only. Quantum mechanics textbooks generally solve the problem by introducing the projection postulate, which forces definite values to emerge during position measurements; many other interpretations have also been proposed.\ Here, in the same spirit as the GRW and CSL theories, we modify the Schr\"{o}dinger equation in a way that efficiently cancels macroscopic density fluctuations in space.\ Instead of introducing the stochastic dynamics of GRW or CSL, we assume a deterministic dynamics that includes an attraction term towards the density in space of the de Broglie-Bohm position of particles. This automatically ensures macroscopic uniqueness, so that the state vector can be considered as a direct representation of physical reality.