Gravitation as a Statistical Theory on the Light Cone

TL;DR

This paper extends Padmanabhan's statistical approach to gravity by considering mixed states on the light cone, revealing connections to the cosmological constant and reformulating gravity within a statistical ensemble framework.

Contribution

It introduces a mixed state model for gravitational degrees of freedom on the light cone, linking variance to the cosmological constant and reinterpreting gravity as a statistical ensemble.

Findings

Variance on the light cone relates to the cosmological constant.

Mixed states prevent deriving gravitational equations from entropy functionals.

Reframes unimodular gravity as a statistical ensemble on the light cone.

Abstract

In this paper, we will explore Padmanabhan's mesoscopic, statistical approach to gravity [62] with a twist. The general picture of his approach is that spacetime is made of large numbers of localized quantum degrees of freedom. Padmanabhan assumed that the degrees of freedom of a given quantum state of geometry contribute, after averaging over fluctuations, a vector degree of freedom for space-time at a point. For null vectors, this can be regarded as corresponding to one single vector, i.e. a pure state, for the statistical ensemble on the light cone at every point. In the present paper, we consider instead the case where the states of the gravitational degrees of freedom are spread out and overlap, with only probabilistic information on which of them determines the actual spacetime at a point. In the continuum limit, this corresponds to a mixed state for the statistical ensemble on the light cone at every point. This change in assumptions leads to some interesting observations. When we define a statistical ensemble on the light cone, its variance "knows" about the interior of the light cone. As an intriguing consequence, we find that the cosmological constant can be related to the variance over the light cone. With a mixed state, we can no longer derive the gravitational field equations from an entropy functional. Here, instead, we show that a naive implementation of the measure of a mixed state on the light cone in the variation principle leads to modified measure theories (MMT) as the grand canonical ensemble and allows one to reframe unimodular gravity as the canonical ensemble of a statistical theory on the light cone.