Poissonian Spontaneous Localization process

The Tilloy-Diósi (TD) prescription allows to turn any Markovian spontaneous collapse model that can be formally regarded as a continuous measurement process of the mass density into a hybrid classical-quantum theory in which the classical system is the gravitational Newtonian field. We present the application of a similar idea to the Poissonian Spontaneous Localization (PSL) process. As in the TD case, the Newtonian field is again recovered upon averaging and additional decoherence appears due to the gravitational back-reaction. However, the PSL model present some advantages: absence of long-range decoherence due to the gravitational back-reaction noise, no negative mass measurements, stability of the gravitational field in empty space, and clarity of the so-called primitive ontology.