The Information Geometry of Space and Time

TL;DR

This paper explores whether the geometry of space and gravity can be derived from principles of information theory and statistical inference, proposing a model that aligns with general relativity's structure.

Contribution

It introduces a novel model of geometrodynamics based on entropy and information geometry, linking microscopic statistical structures to macroscopic spacetime geometry.

Findings

Model exhibits similarities with 3+1 general relativity

Dynamical degrees of freedom relate to conformal geometry

The theory is time reversible and gauge symmetric

Abstract

Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics - the theory of gravity - derivable from general principles of inductive inference? Tentative answers are suggested by a model of geometrodynamics based on the statistical concepts of entropy, information geometry, and entropic dynamics. The model shows remarkable similarities with the 3+1 formulation of general relativity. For example, the dynamical degrees of freedom are those that specify the conformal geometry of space; there is a gauge symmetry under 3d diffeomorphisms; there is no reference to an external time; and the theory is time reversible. There is, in adition, a gauge symmetry under scale transformations. I conjecture that under a suitable choice of gauge one can recover the usual notion of a relativistic space-time.