Entanglement entropy, scale-dependent dimensions and the origin of gravity
arXiv:1710.06164 · doi:10.1142/S0218271817430301
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.
arXiv comment8 pages, 1 figure. Received an Honorable Mention in the 2017 Essay Competition of the Gravity Research Foundation
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