Current experimental upper bounds on spacetime diffusion

A consistent theory describing the dynamics of quantum systems interacting on a classical space-time was recently put forward by Oppenheim et al..1, 2. Quantum states may retain their coherence, at the cost of some amount of stochasticity of the spacetime metric, characterized by a spacetime diffusion parameter. Here, we report existing experimental upper bounds on such space-time diffusion, based on a review of several types of experiments with very low force noise over a broad range of test masses from single atoms to several kilograms. We find an upper bound at least 15 orders of magnitude lower as compared to the initial bounds for explicit models presented by Oppenheimn et al. The results presented here provide a path forward for future experiments that can help evaluate classical-quantum theories