The Information Geometry of Space-time

TL;DR

This paper models curved space-time using information geometry derived from maximum entropy principles, leading to a framework that reproduces Einstein's vacuum equations and introduces concepts like minimum length and space entropy.

Contribution

It introduces a novel approach to space-time geometry based on information geometry and maximum entropy, connecting it with Einstein's equations and quantum-like properties.

Findings

Reproduces Einstein's vacuum equations from information geometry.

Introduces a minimum length scale and finite volume for blurred points.

Proposes space volume as a measure of entropy.

Abstract

The method of maximum entropy is used to model curved physical space in terms of points defined with a finite resolution. Such a blurred space is automatically endowed with a metric given by information geometry. The corresponding space-time is such that the geometry of any embedded spacelike surface is given by its information geometry. The dynamics of blurred space, its geometrodynamics, is constructed by requiring that as space undergoes the deformations associated with evolution in local time, it sweeps a four-dimensional space-time. This reproduces Einstein's equations for vacuum gravity. We conclude with brief comments on some of the peculiar properties of blurred space: There is a minimum length and blurred points have a finite volume. There is a relativistic "blur dilation". The volume of space is a measure of its entropy.