Limits of a non-local quantum spacetime

TL;DR

This paper explores the non-local nature of quantum spacetime influenced by gravity, proposing a new action and analyzing the interplay between non-locality and classical limits within an emergent gravity framework.

Contribution

It introduces a non-local description of quantum spacetime using bi-tensors and proposes a novel action, advancing the understanding of emergent gravity from quantum non-locality.

Findings

Quantum spacetime exhibits non-locality due to gravitational effects.

Emergent gravity can be derived from non-local quantum spacetime structures.

A new action for quantum spacetime is proposed.

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 $g_{ab}(x)$ etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form $\mathscr{G}_{ab \ldots i'j' \ldots}(x,x')$. A deeper look then reveals a subtle interplay interplay between non-locality and the limit $G\hbar/c^3 \to 0$. 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.