# Locality from Quantum Gravity: All or Nothing

## TL;DR

This paper demonstrates that in quantum gravity, locality emerges abruptly rather than gradually, with local information appearing all at once when a sufficient boundary region is accessed, highlighting a fundamental 'all or nothing' nature of emergent locality.

## Contribution

It reveals that emergent locality in holographic quantum gravity is inherently 'all or nothing', contrasting with intuitive gradual emergence, under broad assumptions.

## Key findings

- Local data appears only when a large enough boundary region is accessed.
- Emergent locality is an all-or-nothing phenomenon in holographic theories.
- Special case of AdS/CFT confirms this abrupt emergence of locality.

## Abstract

In a full theory of quantum gravity, local physics is expected to be approximate rather than innate. It is therefore important to understand how approximate locality emerges in the semiclassical limit. Here we show that any notion of locality emergent from a holographic theory of quantum gravity is "all or nothing": local data is not obtained gradually from subregions of the boundary, but is rather obtained all at once when enough of the boundary is accessed. Our assumptions are mild and thus this feature is quite general; in the special case of AdS/CFT, a slightly different manifestation follows from well-known and familiar properties.