Finite-State Classical Mechanics

TL;DR

This paper introduces classical mechanical models based on reversible lattice dynamics that incorporate finite resolution, locality, and information preservation, bridging discrete and continuous classical physics frameworks.

Contribution

It presents a family of models combining the informational realism of reversible lattice dynamics with classical mechanics' continuity.

Findings

Models embody finite state resolution and locality.

They link finite state change rates to energies and momenta.

These models clarify the informational foundations of classical mechanics.

Abstract

Reversible lattice dynamics embody basic features of physics that govern the time evolution of classical information. They have finite resolution in space and time, don't allow information to be erased, and easily accommodate other structural properties of microscopic physics, such as finite distinct state and locality of interaction. In an ideal quantum realization of a reversible lattice dynamics, finite classical rates of state-change at lattice sites determine average energies and momenta. This is very different than traditional continuous models of classical dynamics, where the number of distinct states is infinite, the rate of change between distinct states is infinite, and energies and momenta are not tied to rates of distinct state change. Here we discuss a family of classical mechanical models that have the informational and energetic realism of reversible lattice dynamics, while retaining the continuity and mathematical framework of classical mechanics. These models may help to clarify the informational foundations of mechanics.