The Kinetic Theory of the Mesoscopic Spacetime

TL;DR

This paper develops a mesoscopic kinetic theory of spacetime, linking discrete geometric states to Einstein's equations and suggesting new avenues for understanding quantum gravity through fluctuation analysis.

Contribution

It introduces a mesoscopic kinetic framework for spacetime, connecting zero-point length, internal degrees of freedom, and Einstein's equations as an extremum of density of states.

Findings

Derives Einstein's equations from a density of states extremum.

Identifies internal degrees of freedom associated with spacetime events.

Proposes fluctuation analysis as a pathway to quantum gravity insights.

Abstract

At the mesoscopic scales --- which interpolate between the macroscopic, classical, geometry and the microscopic, quantum, structure of spacetime --- one can identify the density of states of the geometry which arises from the existence of a zero-point length in the spacetime. This spacetime discreteness also associates an internal degree of freedom with each event, in the form of a fluctuating vector of constant norm. The equilibrium state, corresponding to the extremum of the total density of states of geometry plus matter, leads precisely to Einstein's equations. In fact, the field equation can now be reinterpreted as a zero-heat dissipation principle. The analysis of fluctuations around the equilibrium state (described by Einstein's equations), will provide new insights about quantum gravity.