Gravity-Linked Collapse Models Predict Intrinsic Time Uncertainty Far Below Atomic Clock Limits

Bortolotti and colleagues at CREF and INFN-LNF quantified the Diósi-Penrose and Continuous Spontaneous Localization models under the assumption that collapse is sourced by gravitational self-energy. They derived an effective metric fluctuation whose integrated effect appears as a stochastic phase noise in any time-evolution operator. The resulting timing uncertainty scales with the fourth root of the system mass and remains below 10^-30 s for macroscopic objects, consistent with the absence of observed decoherence in current interferometers.

The result supplies a concrete, falsifiable bridge between collapse phenomenology and quantum gravity. Unlike purely interpretive frameworks, these models already predict measurable excess heating or radiation; adding a temporal jitter observable gives a second, independent channel that could be probed with future matter-wave clocks or optomechanical resonators once sensitivities cross the predicted threshold.

Standard coverage overlooked the explicit mapping from collapse rate to metric variance and therefore understated the models' testability. The calculation also shows that any detection would require not higher precision alone but correlated measurements of both spatial decoherence and timing noise on the same system, a protocol not yet implemented.

Next steps include proposals for levitated nanoparticles or atomic ensembles in free fall that could reach the required mass-time regime within a decade if vibration and thermal noise are further suppressed.