Geometry-Only CSL/DP Ratios and the Nonuniqueness of Decoherence Kernels

Abstract: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 $E_G\tau/\hbar$. 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.

arXiv:2608.05972 [quant-ph]

(or arXiv:2608.05972v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.05972 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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