Gravity and the Collapse of the Wave Function: a Probe into Diósi-Penrose model

Abstract

We investigate the Diósi-Penrose (DP) proposal for connecting the collapse of the wave function to gravity. The DP model needs a free parameter, acting as a cut-off to regularize the dynamics, and the predictions of the model highly depend on the value of this cut-off. The Compton wavelength of a nucleon seems to be the most reasonable cut-off value since it justifies the non-relativistic approach. However, with this value, the DP model predicts an unrealistic high rate of energy increase. Thus, one either is forced to choose a much larger cut-off, which is not physically justified and totally arbitrary, or one needs to include dissipative effects in order to tame the energy increase. Taking the analogy with dissipative collisional decoherence seriously, we develop a dissipative generalization of the DP model. We show that even with dissipative effects, the DP model contradicts known physical facts, unless either the cut-off is kept artificially large, or one limits the applicability of the model to massive systems. We also provide an estimation for the mass range of this applicability.

15 pages, 1 figure; v2 updated references and fixed minor mistakes in Eqs.(18) and (31)-(34), thanks to Marko Toros for pointing them out

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• Dissipative extension of the Ghirardi-Rimini-Weber model
• Experimental bounds on linear-friction dissipative collapse models from levitated optomechanics
• Seven non-standard models coupling quantum matter and gravity
• Collapse models and gravitational decoherence at test: How far can we push the limits of quantum mechanics?