Table-top quantum gravity (TTQG) experiments promise to probe the non-classical nature of spacetime. However, establishing precisely what can be inferred from such experiments, independently of a particular theory of quantum gravity, remains an open problem. Existing no-go theorems face fundamental difficulties, due to relying on concepts related to radiative phemomena while these experiments are to operate in a non-radiative regime.
In this talk, I will discuss an alternative approach based on geometrical invariants, taking background independence as a foundational premise. I will review recent results on how global invariants can encode local geometrical correlations, and discuss preliminary work on quantum graphs and non-classical geometrical observables. The broader aim is to develop theory-independent criteria for establishing what TTQG experiments can tell us about the quantum nature of spacetime.