Limits of a non-local quantum spacetime

A generic implication of incorporating gravitational effects in the analysis of quantum measurements is the existence of a zero-point length of spacetime. This requires an inherently non-local description of spacetime, beyond the usual one based on metric $g_{ab}(x)$ etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form ${\mathcal{G}}_{ab\dots i^{\mathrm{\prime }}{j}^{\mathrm{\prime }}\dots }(x,x^{\mathrm{\prime }})$. A deeper look then reveals a subtle interplay interplay between non-locality and the limit $G\mathrm{\hslash }\mathrm{/}{c}^3\to 0$. In particular, the so called emergent gravity paradigm – in which gravitational dynamics/action/spacetime are emergent and characterised by an entropy functional – arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This essay describes the flow of metric with respect to Planck length, and proposes a novel action for the same.