Limits of a non-local quantum spacetime

Abstract

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 [Formula: see text] etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form [Formula: see text]. A deeper look then reveals a subtle interplay between non-locality and the limit [Formula: see text]. In particular, the so-called emergent gravity paradigm — in which gravitational dynamics/action/spacetime are emergent and characterized by an entropy functional — arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This paper describes the flow of metric with respect to Planck length, and proposes a novel action for the same.