Einstein–Hilbert action, with quantum corrections, from the Planck scale coarse-graining of the spacetime microstructure
Abstract
The gravitational dynamics of the coarse-grained spacetime geometry should emerge from extremizing the number of microscopic configurations, Ω, of the pre-geometric variables corresponding to a given geometry. This Ω will be the product over all events 𝒫 of the density, ρ(𝒫), of microscopic configurations associated with each event 𝒫. I show how ρ can be computed, in terms of the van Vleck determinant, and thus obtain directly the gravitational effective action ℒE at mesoscopic scales. The leading term of this, nonperturbative, effective action gives the Einstein–Hilbert action, thereby providing its microscopic derivation. The higher-order corrections are finite without any need for regularization and I demonstrate how they can be computed in a systematic manner.
This essay is awarded fourth prize in the 2021 Essay Competition of the Gravity Research Foundation.
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