The Schrödinger–Newton equation as a possible generator of quantum state reduction

Abstract\n It has been suggested by Penrose that the occurrence of quantum state reduction in macroscopic objects is related to a manifestation of gravitational effects in quantum mechanics. Although within his 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 Schr?odinger-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 Schr?odinger-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.