Bounds on QCA Lattice Spacing from Data on Lorentz Violation

TL;DR

This paper investigates how quantum cellular automata (QCA) models of quantum electrodynamics (QED) could imply Lorentz violation at high energies, and uses experimental data to constrain the possible discrete structure of spacetime.

Contribution

It provides bounds on the lattice spacing of QCA models of QED based on current experimental limits on Lorentz violation, linking discrete spacetime theories with observable physics.

Findings

QCA models of QED imply deviations from the speed of light and spatial anisotropies.

Current experimental data constrain the QCA lattice spacing to be below a certain threshold.

The results suggest that if spacetime is discrete, its lattice spacing must be extremely small.

Abstract

Recent work has demonstrated that discrete quantum walks, when extended to quantum cellular automata (QCA), can, in the continuum limit, reproduce relativistic wave equations and quantum field theories (QFTs), including free quantum electrodynamics (QED). This QCA/QFT correspondence bridges quantum information processing and high-energy physics, raising fundamental questions about the nature of spacetime: whether it is the continuum QFT or the discrete QCA that is fundamental. For while Lorentz invariance appears robust experimentally, it may only approximate a deeper discrete structure, particularly at Planck-scale energies. This high-energy Lorentz violation is potentially observable either through cumulative effects over cosmic distances or via small deviations at accessible energies. In this paper, we analyze the QCA corresponding to QED and show that it implies both a deviation from the speed of light and spatial anisotropies. Using current experimental and astrophysical constraints, we place upper bounds on the QCA lattice spacing, providing insight into the plausibility of a fundamentally discrete spacetime.