The thermodynamics of quantum spacetime histories

TL;DR

This paper establishes a deep connection between the thermodynamics of causal diamonds in quantum spacetime, the simplicity constraints of spin foam models, and the emergence of Einstein's equations from quantum gravity principles.

Contribution

It demonstrates that the simplicity constraints in spin foam models are equivalent to the first law of thermodynamics for causal diamonds, linking quantum gravity, thermodynamics, and holography.

Findings

Simplicity constraints imply the first law of thermodynamics for causal diamonds.

Quantum spacetime geometries satisfying these constraints obey Einstein's equations.

The work suggests a quantum version of the equivalence principle.

Abstract

We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez and Bianchi. This allows us to apply a recent argument of Jacobson to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.