On the role of gravitation in the possible breakdown of the quantum superposition principle for macroscopic systems

Abstract

A model for the time evolution of wave packets is developed, in which the gravitational effects of a «particle» on its own wave function are taken into account. Upon suitably combining quantum (wave) mechanics and general relativity, we deal with the stochastic effects, coming from the former, on the space-time metric described by the latter. In turn, the fact that the metric is not well defined affects the evolution of the wave function, then allowing for a «natural» breakdown of the quantum superposition principle for macroscopic systems and helping to clarify the classical limit of quantum mechanics. We also analysed the question of the relevance of these ideas in the everlasting «measurement problem» in quantum mechanics.