Fundamental Limits on Clock Precision from Spacetime Uncertainty in Quantum Collapse Models

Models of spontaneous wavefunction collapse explain the quantum-to-classical transition without invoking the von Neumann measurement postulate. Prominent frameworks, such as the Di\'osi-Penrose (DP) and Continuous Spontaneous Localization (CSL) models, propose a continuous, spontaneous measurement of the mass density field of quantized matter. We show that this mechanism could link both models - not just DP - to fundamental uncertainties in Newtonian gravity. Despite their non-relativistic nature, these models suggest an induced uncertainty in the flow of time due to fluctuations in the Newtonian potential. We calculate the ultimate limit on time uncertainty and demonstrate that the resulting clock-time uncertainty remains negligible for all contemporary time-keeping devices, including atomic clocks.