Schrodinger-Newton equation as a possible generator of quantum state   reduction
  It has been suggested by Diosi and Penrose that the occurrence of quantum state reduction in macroscopic objects is related to a manifestation of gravitational effects in quantum mechanics. Although within Penrose's framework the dynamics of the quantum state reduction is not prescribed, it was suggested that the so called Schrodinger-Newton equation can be used to at least identify the resulting classical end states. Here we analyze the extent to which the Schrodinger-Newton equation can be used as a model to generate a full, time dependent description of the quantum state reduction process. We find that when supplied with an imaginary gravitational potential, the Schrodinger-Newton equation offers a rationalisation for some of the hitherto unexplained characteristics of quantum state reduction. The description remains incomplete however, because it is unclear how to fully recover Born's rule. 
Jasper van Wezel and Jeroen van den Brink