On the effectiveness of the collapse in the Di\'osi-Penrose model

TL;DR

This paper investigates the Díosi-Penrose gravity-induced collapse model, providing bounds on its parameters and analyzing its effectiveness in explaining the quantum-to-classical transition at macroscopic scales.

Contribution

It derives new bounds on the model's parameters, showing that not all macroscopic systems necessarily undergo collapse, guiding future experimental tests.

Findings

Current experiments exclude some model versions

Not all macroscopic systems collapse effectively

Proposes a parameter bound of R_0 ≲ 10^{-4} m

Abstract

The possibility that gravity plays a role in the collapse of the quantum wave function has been considered in the literature, and it is of relevance not only because it would provide a solution to the measurement problem in quantum theory, but also because it would give a new and unexpected twist to the search for a unified theory of quantum and gravitational phenomena, possibly overcoming the current impasse. The Di\'osi-Penrose model is the most popular incarnation of this idea. It predicts a progressive breakdown of quantum superpositions when the mass of the system increases; as such, it is susceptible to experimental verification. Current experiments set a lower bound $R_0\gtrsim 4 \times 10^{-10}$ m for the free parameter of the model, excluding some versions of it. In this work we search for an upper bound, coming from the request that the collapse is effective enough to guarantee classicality at the macroscopic scale: we find out that not all macroscopic systems collapse effectively. If one relaxes this request, a reasonable (although to some degree arbitrary) bound is found to be: $R_0\lesssim 10^{-4}$ m. This will serve to better direct future experiments to further test the model.