Selected Honorable Mention EssaysNo Access

Entanglement entropy, scale-dependent dimensions and the origin of gravity

Michele Arzano

Dipartimento di Fisica and INFN, “Sapienza”, University of Rome, P.le A. Moro 2, 00185 Roma, Italy

E-mail Address: michele.arzano@roma1.infn.it

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and

Gianluca Calcagni

Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain

E-mail Address: g.calcagni@csic.es

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https://doi.org/10.1142/S0218271817430301Cited by:2 (Source: Crossref)

Abstract

We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If quantum geometry hinders diffusion, for instance, when its structure at some given scale is discrete or too rough, then the spectral dimension of spacetime vanishes at that scale and the entropy density blows up. A finite entanglement entropy is a key ingredient in deriving Einstein gravity in a semi-classical regime of a quantum-gravitational theory and, thus, our arguments strengthen the role of running dimensionality as an imprint of quantum geometry with potentially observable consequences.

This essay received an Honorable Mention in the 2017 Essay Competition of the Gravity Research Foundation.

Keywords:

PACS: 04.60.−m, 11.10.−z, 04.60.Bc

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