Towards a Statistical Geometrodynamics

TL;DR

This paper explores whether the geometry of space and geometrodynamics can be derived from microscopic statistical principles using entropy and information geometry, proposing a new model based on inductive inference.

Contribution

It introduces a novel model of geometrodynamics grounded in statistical concepts like entropy and information geometry, linking microscopic structures to macroscopic space geometry.

Findings

Proposes a statistical model explaining spatial distances.

Suggests space geometry emerges from microscopic statistical structures.

Connects geometrodynamics with principles of inductive inference.

Abstract

Can the spatial distance between two identical particles be explained in terms of the extent that one can be distinguished from the other? Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics 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.