Curator's Take
AI Commentary
This article shows that for a wide class of levitated‑mass superposition protocols the relative strength of mass‑proportional CSL and Diósi–Penrose decoherence depends only on geometry, not on mass or interrogation time, providing a clean “shape factor” that can be measured experimentally. By proving that the point‑particle CSL kernel admits an exact random‑unitary (Gaussian kick) representation, it clarifies that identical ensemble decoherence does not uniquely imply objective collapse, sharpening the theoretical criteria for discriminating competing models. The result gives experimentalists a concrete target—designing superpositions with separations around 2 nm—to directly compare CSL and DP predictions without needing extreme masses or long coherence times, while also warning that any observed loss of contrast alone cannot confirm a specific collapse mechanism.
— Mark Eatherly
Summary
We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi--Penrose (DP) self-energy exponent $E_Gτ/\hbar$. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is $x_*\approx1.91\,\mathrm{nm}$. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.