Quantum mechanics allows a particle to be in two places at once: this is called superposition. But massive objects, like a dust grain or a ball, don't behave that way: their position is always definite. Why? One idea is that it's an illusion: the particle is constantly "jittering" from random environmental kicks, and the blurred picture averages out. Another, more radical idea is that nature itself occasionally "clicks" and picks one position, like an invisible referee.
The authors compared two such mechanisms. The first, continuous spontaneous localization (CSL), posits that particles receive random kicks that destroy superposition. The second, the Diósi–Penrose effect (DP), ties the loss of quantumness to the object's own gravitational energy. It turns out that in a point-particle model, both processes give the same damping of quantum ripples, but the nature of the damping is different. In the CSL model, the kicks can be written as random momentum "shakes," and if we knew the history of all kicks, the state would remain pure. This means that the damping rate alone is not proof of collapse.
Then the researchers moved from point particles to solid spheres with arbitrary mass distributions along the radius. Here, masses, densities, and observation time cancel out, leaving only a dimensionless geometric factor. This paves the way for a decisive experiment: you need to catch three conditions — a noticeable absolute effect, a controlled comparison of CSL and DP scales, and observable quantities that see the difference in physics even if the decoherence looks the same externally.
as written by the authors arXiv:2608.05972v1
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 Di\'osi--Penrose (DP) self-energy exponent $$E_G\tau/\hbar$$. 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.
The 1.91 nm threshold is surprisingly close to the size of a protein molecule. It turns out that "quantumness" may vanish at scales where life begins.