Spacetime equals entanglement

Yasunori Nomura,Fabio Sanches,Nico Salzetta,Sean J Weinberg

doi:10.1016/j.physletb.2016.10.045

Abstract

We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.

Highlights

How does the semiclassical picture arise from the fundamental theory of quantum gravity? Recently it has become increasingly clear that quantum entanglement in holographic [1,2] descriptions plays an important role in the emergence of the classical spacetime of general relativity [3,4,5,6,7,8]
We show that despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large
In the context of Friedmann– Robertson–Walker (FRW) universes, we find an interesting “Russian

Summary

Introduction

How does the semiclassical picture arise from the fundamental theory of quantum gravity? Recently it has become increasingly clear that quantum entanglement in holographic [1,2] descriptions plays an important role in the emergence of the classical spacetime of general relativity [3,4,5,6,7,8]. In this letter we take the view that entanglement in holographic theories determines gravitational spacetimes at the semiclassical level Rather than proving this statement, we adopt it as a guiding principle and explore its consequences. We show that despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. To illustrate these concepts, we use a putative holographic theory for cosmological spacetimes, in which the effects appear cleanly. See Ref. [11] for related discussion

Holographic theory on screens

Holography for FRW universes

Qubit model

Superpositions