Investigation of Gravity-Related Spontaneous Wave Function Collapse for Non-static Gravitational Field

Abstract

Diosi and Penrose have suggested a criterion for spontaneous wave function collapse. According to Penrose the profound conflict between the principle of superposition and general covariance entails the existence of reduction of quantum states, e.g. a quantum superposition of two different space–time geometries will collapse onto one of them. In his proposal, collapse time has an inverse relationship with ill-definedness in the gravitational self-energy, for the static gravitational fields. Anandan obtained the same result using the fluctuations of the connection of gravitational field. We show that in Newtonian limit of the superposition of a static and non-static gravitational field the results of the methods of Anandan and Penrose are different, but the numerical value of the extra term in Anandan’s approach, involving angular velocity, is not even considered in a case of practical interest. Then, we investigate the collapse time of the superposition of a static and non-static gravitational field.