The Kinetic Theory of the Mesoscopic Spacetime

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.