Microscopic wormholes and the geometry of entanglement

D Rubiera-Garcia,Francisco S N Lobo,Gonzalo J Olmo

doi:10.1140/epjc/s10052-014-2924-1

Abstract

It has recently been suggested that Einstein–Rosen (ER) bridges can be interpreted as maximally entangled states of two black holes that form a complex Einstein–Podolsky–Rosen (EPR) pair. This relationship has been dubbed as the \(\textit{ER}=\textit{EPR}\) correlation. In this work, we consider the latter conjecture in the context of quadratic Palatini theory. An important result, which stems from the underlying assumptions as regards the geometry on which the theory is constructed, is the fact that all the charged solutions of the quadratic Palatini theory possess a wormhole structure. Our results show that spacetime may have a foam-like microstructure with wormholes generated by fluctuations of the quantum vacuum. This involves the spontaneous creation/annihilation of entangled particle–antiparticle pairs, existing in a maximally entangled state connected by a non-traversable wormhole. Since the particles are produced from the vacuum and therefore exist in a singlet state, they are necessarily entangled with one another. This gives further support to the \(\textit{ER}=\textit{EPR}\) claim.

Highlights

The Einstein– Rosen (ER) = Einstein– Podolsky–Rosen (EPR) claim received further support through specific models
The results presented above support the view that spacetime could have a foam-like microstructure with wormholes generated by fluctuations of the quantum vacuum involving the spontaneous creation/annihilation of entangled particlepairs
The fact that all the charged solutions of the quadratic Palatini theory possess a wormhole structure is an important result which stems from the underlying assumptions as regards the geometry on which the theory is constructed

Summary

Introduction

In the holographic dual the entanglement is encoded in a geometry of a non-traversable wormhole on the worldsheet of the flux tube connecting the pair In this context, it was pointed out that the proposed bulk dual of an entangled quark–anti-quark pair described above [8] corresponds to the Lorentzian continuation of the tunneling instanton describing a Schwinger pair creation in the dual field theory [10]. Wheeler used the source-free Maxwell equations, coupled to Einstein gravity, with the seasoning of nontrivial topology, to build models for classical electrical charges and all other particle-like entities in classical physics [11] This analysis culminated in the “geon” concept, coined by Wheeler to denote a “gravitational–electromagnetic entity”.

Palatini Ricci-squared theory

Geometry of entanglement

Discussion