  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
