Derivation of the Dirac Equation from Principles of Information Processing

TL;DR

This paper derives the Dirac equation from a quantum cellular automaton based on information processing principles, without relying on relativity, revealing scale-unifying properties and Lorentz covariance distortions at high energies.

Contribution

It introduces a novel derivation of the Dirac equation from quantum cellular automata principles, bypassing the need for relativity, and explores scale-unifying dynamics from Planck to Fermi scales.

Findings

Dirac equation emerges from quantum cellular automaton dynamics.

Lorentz covariance is distorted in the ultra-relativistic limit.

A dispersive Schrödinger equation describes narrow-band states at all scales.

Abstract

We show how the Dirac equation in three space-dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitariety, locality, homogeneity, and discrete isotropy, without using the relativity principle. The Dirac equation is recovered for small wave-vector and inertial mass, whereas Lorentz covariance is distorted in the ultra-relativistic limit. The automaton can thus be regarded as a theory unifying scales from Planck to Fermi. A simple asymptotic approach leads to a dispersive Schroedinger equation describing the evolution of narrow-band states at all scales.