From Information Geometry to Newtonian Dynamics

TL;DR

This paper derives Newtonian dynamics from principles of information geometry and maximum entropy, showing that classical motion can emerge from probabilistic models without traditional physical postulates.

Contribution

It introduces a novel derivation of Newtonian mechanics using information geometry and entropic inference, eliminating the need for classical axioms.

Findings

Newtonian dynamics emerge from statistical manifold geometry.

Particle mass and interactions are explained as properties of the underlying information structure.

The approach reproduces classical trajectories without explicit physical postulates.

Abstract

Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by a probability distribution. The corresponding configuration space is a statistical manifold the geometry of which is defined by the information metric. The trajectory follows from a principle of inference, the method of Maximum Entropy. No additional "physical" postulates such as an equation of motion, or an action principle, nor the concepts of momentum and of phase space, not even the notion of time, need to be postulated. The resulting entropic dynamics reproduces the Newtonian dynamics of any number of particles interacting among themselves and with external fields. Both the mass of the particles and their interactions are explained as a consequence of the underlying statistical manifold.