Special Relativity in a Discrete Quantum Universe

TL;DR

This paper proposes a framework where special relativity is compatible with a discrete quantum universe by modeling fields with quantum cellular automata, recovering Lorentz invariance at low energies and revealing nonlinear distortions at the Planck scale.

Contribution

It introduces a novel approach to reconcile discrete quantum structures with special relativity using automata and symmetry-based transformations.

Findings

Lorentz group recovered at low energies

Nonlinear distortions of covariance at Planck scale

Relativity principle applied without reference to space-time

Abstract

The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e. the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted.