Ghirardi-Rimini-Weber model with massive flashes

I introduce a modification of the Ghirardi-Rimini-Weber (GRW) model in which the flashes (or collapse space-time events) source a classical gravitational field. The resulting semi-classical theory of Newtonian gravity preserves the statistical interpretation of quantum states of matter in contrast with mean field approaches. It can be seen as a discrete version of recent proposals of consistent hybrid quantum classical theories. The model is in agreement with known experimental data and introduces new falsifiable predictions: (1) single particles do not self-interact, (2) the $1/r$ gravitational potential of Newtonian gravity is cut-off at short ($\lesssim 10^{-7}$m) distances, and (3) gravity makes spatial superpositions decohere at a rate inversely proportional to that coming from the vanilla GRW model. Together, the last two predictions make the model experimentally falsifiable for \emph{all} values of its parameters.