Quantum Cellular Automaton Theory of Light

TL;DR

This paper develops a quantum cellular automaton model of light that reproduces Maxwell's equations at large scales, predicts dispersive vacuum propagation, and suggests potential experimental tests using cosmological observations.

Contribution

It introduces a novel quantum cellular automaton framework for light, deriving Maxwell's equations and photon properties from informational principles, with testable predictions.

Findings

Derives Maxwell's equations from QCAs in the small wave-vector limit.

Predicts dispersive propagation of light in vacuum.

Suggests experimental tests via cosmological pulse observations.

Abstract

We present a quantum theory of light based on quantum cellular automata (QCA). This approach allows us to have a thorough quantum theory of free electrodynamics encompassing an hypothetical discrete Planck scale. The theory is particularly relevant because it provides predictions at the macroscopic scale that can be experimentally tested. We show how, in the limit of small wave-vector k, the free Maxwell's equations emerge from two Weyl QCAs derived from informational principles in Ref. [1]. Within this framework the photon is introduced as a composite particle made of a pair of correlated massless Fermions, and the usual Bosonic statistics is recovered in the low photon density limit. We derive the main phenomenological features of the theory, consisting in dispersive propagation in vacuum, the occurrence of a small longitudinal polarization, and a saturation effect originated by the Fermionic nature of the photon. We then discuss whether these effects can be experimentally tested, and observe that only the dispersive effects are accessible with current technology, from observations of arrival times of pulses originated at cosmological distances.