Diffusion Minimization via Optimal Smearing in Collapse and Hybrid Classical-Quantum Gravitational Models

Abstract

Spontaneous diffusion (i.e., non-conservation of energy) is a prominent, testable prediction of collapse and hybrid classical-quantum gravitational models. Without smearing of the mass density operator, the associated heating (or energy increase) rate diverges, yet the smearing distribution is arbitrary and, on scales much larger than the smearing length $r_C$, much of the phenomenology is expected to be insensitive to this choice. We propose to resolve this arbitrariness as follows: for a fixed $r_C$, select the distribution that minimizes the heating rate. Conceptually, this should identify the minimal deviation from standard quantum mechanics and provide models that, once experimentally refuted, would strongly disfavor all variants with different distributions. We apply this approach to the most investigated collapse models: GRW (for Ghirardi-Rimini-Weber), CSL (for Continuous Spontaneous Localization), and DP (for Di\'osi-Penrose). Notably, the Gaussian is optimal only for the GRW case. Finally, we apply it to the Tilloy-Di\'osi hybrid classical-quantum model of Newtonian gravity, leading to the minimally deviating variant of it. This version of the model is entirely determined by only one free parameter $r_C$ and, if experimentally refuted, would strongly disfavor any other version of it.