Apart from the quantization of gravity as an effective field theory, one can also approach quantum gravity by considering the spacetime to be of quantum nature, i.e., quantizing spacetime itself. This approach is what is commonly referred to as noncommutative geometry, and various different methods are taken under this umbrella....
... the field-dependent dynamical coordinates that are needed to construct gauge-invariant
observables in the relational approach define a noncommutative geometry.
https://arxiv.org/pdf/2305.01517
In other words, what the relational approach shows is that physical events in a gravitational theory cannot be described using coordinates on the background manifold, but instead one must use a fully dynamical coordinate system.
In other words, relational observables constructed with curvature scalars as dynamical coordinates only measure the average over all points where the curvature scalars are constant and thus cannot describe localized measurements in such background spacetimes.
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