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

TL;DR

This paper critically examines the Díosi-Penrose gravity-induced collapse model, highlighting issues with its parameter choices and proposing a dissipative extension that still faces physical consistency challenges.

Contribution

It introduces a dissipative generalization of the DP model and analyzes its limitations and applicability constraints.

Findings

The DP model's predictions depend heavily on the cut-off parameter.

Using the nucleon Compton wavelength as cut-off leads to unrealistic energy increases.

Dissipative effects do not fully resolve the model's physical inconsistencies.

Abstract

We investigate the Di\'osi-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.