Exploring gravitational statistics not based on quantum dynamical assumptions

TL;DR

This paper introduces a non-quantum dynamical approach to gravitational statistics that avoids traditional quantum assumptions and space-time splitting, recovering known physics in certain limits.

Contribution

It proposes a novel statistical framework (NDA) for gravity that does not rely on quantum dynamical assumptions or space-time splitting, expanding the conceptual landscape of quantum gravity.

Findings

Recovers general relativity at low curvature

Reproduces quantum field theory in flat space-time

Simplifies to a path integral model in 3+1 dimensions under thermal equilibrium

Abstract

Despite considerable progress in several approaches to quantum gravity, there remain uncertainties on the conceptual level. One issue concerns the different roles played by space and time in the canonical quantum formalism. This issue occurs because the Hamilton-Jacobi dynamics is being quantised. The question then arises whether additional physically relevant states could exist which cannot be represented in the canonical form or as a partition function. For this reason, the author has explored a statistical approach (NDA) which is not based on quantum dynamical assumptions and does not require space-time splitting boundary conditions either. For dimension 3+1 and under thermal equilibrium, NDA simplifies to a path integral model. However, the general case of NDA cannot be written as a partition function. As a test of NDA, one recovers general relativity at low curvature and quantum field theory in the flat space-time approximation. Related paper: arxiv:1505.03719.