Gravitational Poissonian Spontaneous Localization Model of Hybrid Quantum-Classical Newtonian Gravity: Energy Increase and Experimental Bounds

The Gravitational Poissonian Spontaneous Localization (GPSL) model is a hybrid classical-quantum framework in which Newtonian gravity emerges from stochastic collapses of a smeared mass-density operator. Consistency of the hybrid dynamics entails momentum diffusion and, hence, spontaneous heating. Without smearing, which enters both the collapse (measurement) and gravitational-feedback components of the dynamics, the heating rate would be divergent. Previous work assumed identical smearings for both components. Here, we treat the general case of distinct spatial smearings $g_{r_C}(\mathbf{x})$ and $g_{r_G}(\mathbf{x})$, characterized, respectively, by length scales $r_C$ and $r_G$. We characterize the spontaneous heating rate for arbitrary $g_{r_C}(\mathbf{x})$ and $g_{r_G}(\mathbf{x})$, and then discuss which smearing profiles minimize the spontaneous heating rate in relevant physical situations. Remarkably, there are situations in which, while the measurement noise remains the same, allowing $g_{r_G}(\mathbf{x})\mathrm{\ne }{g}_{r_C}(\mathbf{x})$ may reduce the feedback-induced spontaneous heating by more than 60 orders of magnitude already for $r_G=10r_C$. Finally, we use our results to estimate the spontaneous heating rate of neutron stars and to set new lower bounds on the model’s parameters by comparing the theoretical predictions with astronomical data on temperature, radius, and mass of neutron stars.