One-dimensional relativistic particle as a movable cellular automaton

TL;DR

This paper explores a one-dimensional model combining particle and cellular automaton properties, demonstrating that the motion of a cluster leads to the Feynman chessboard model and the Dirac equation in the continuous limit.

Contribution

It introduces a novel one-dimensional discrete model that bridges cellular automata and relativistic quantum mechanics, deriving the Dirac equation from simple discrete dynamics.

Findings

Cluster motion reproduces Feynman chessboard model

Continuous limit yields Dirac equation

Model links cellular automata with relativistic quantum physics

Abstract

The one-dimensional dynamics of identical discrete elements that combine the properties of newtonian mechanical particles and cellular automata are investigated. It is shown that the motion of a cluster of combined discrete elements, which is the simplest observable object of the model, leads to the Feynman chessboard model whose continuous limit gives the Dirac equation.