Grin of the Cheshire cat: Entropy density of spacetime as a relic from quantum gravity

TL;DR

This paper proposes that the thermodynamic description of spacetime, including its entropy density, emerges as a low-energy relic of quantum gravity effects, specifically from a zero-point-length modification of geodesic distances.

Contribution

It demonstrates that the entropy density of spacetime can be derived as a nonperturbative low-energy limit of quantum gravity effects involving zero-point-length modifications.

Findings

Derivation of the entropy density from a zero-point-length spacetime model.

Connection between thermodynamic variational principles and quantum gravity.

Implications for the cosmological constant problem.

Abstract

There is considerable evidence to suggest that the field equations of gravity have the same status as, say, the equations describing an emergent phenomenon like elasticity. In fact, it is possible to derive the field equations from a thermodynamic variational principle in which a set of normalized vector fields are varied rather than the metric. We show that this variational principle can arise as a low energy ($L_P = (G\hbar/c^3)^{1/2} \to 0$) relic of a plausible nonperturbative effect of quantum gravity, viz. the existence of a zero-point-length in the spacetime. Our result is nonperturbative in the following sense: If we modify the geodesic distance in a spacetime by introducing a zero-point-length, to incorporate some effects of quantum gravity, and take the limit $L_P \to 0$ of the Ricci scalar of the modified metric, we end up getting a nontrivial, leading order ($L_P$ - independent) term. \textit{This term is identical to the expression for entropy density of spacetime used previously in the emergent gravity approach.} This reconfirms the idea that the microscopic degrees of freedom of the spacetime, when properly described in the full theory, could lead to an effective description of geometry in terms of a thermodynamic variational principle. This is conceptually similar to the emergence of thermodynamics from mechanics of, say, molecules. The approach also has important implications for cosmological constant which are briefly discussed.