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We investigate the Di\'osi-Penrose (DP) proposal for connecting the collapseof the wave function to gravity. The DP model needs a free parameter, acting asa cut-off to regularize the dynamics, and the predictions of the model highlydepend on the value of this cut-off. The Compton wavelength of a nucleon seemsto be the most reasonable cut-off value since it justifies the non-relativisticapproach. However, with this value, the DP model predicts an unrealistic highrate of energy increase. Thus, one either is forced to choose a much largercut-off, which is not physically justified and totally arbitrary, or one needsto include dissipative effects in order to tame the energy increase. Taking theanalogy with dissipative collisional decoherence seriously, we develop adissipative generalization of the DP model. We show that even with dissipativeeffects, the DP model contradicts known physical facts, unless either thecut-off is kept artificially large, or one limits the applicability of themodel to massive systems. We also provide an estimation for the mass range ofthis applicability.

Gravity and the Collapse of the Wave Function: a Probe into Di\'osi-Penrose model