A 4D 24-Cell Quantum Cellular Automaton with Emergent Fermions, Gauge Fields, and Regge Gravity Abstract We investigate a discrete model of spacetime based on a four-dimensional lattice with 24-cell (icositetrachoron) adjacency, motivated by the search for a maximally symmetric and geometrically space-filling substrate without voids at the lattice scale underlying relativistic quantum field theory. We emphasize that this terminology refers strictly to the complete Euclidean tessellation of the spatial manifold and does not imply the absence of a spectral gap in the Hamiltonian. Unlike hypercubic lattices, the 24-cell lattice possesses self-duality, a kissing number of 24, and an associated 𝐹4 symmetry group, making it a natural candidate for suppressing anisotropies and Lorentz-violating artifacts in discrete formulations. Local degrees of freedom are taken to be quaternionic and evolve according to a discrete, self-dual update rule, defining a quantum cellular automaton. We show that, in the longwavelength limit, this construction admits effective Dirac fermions, with mass emerging from a local symmetry reduction of the lattice dynamics. Gauge fields arise naturally as holonomies associated with non-trivial loops around dual lattice centers, reproducing Maxwell electrodynamics in the continuum approximation. Gravitational dynamics are interpreted as a thermodynamic response of the lattice to defect density, closely related to Regge calculus. We further discuss cosmological implications, including the possibility of a parameterdependent phase transition beyond which the continuum spacetime description ceases to be valid. No claims of inevitability or specific cosmological timelines are made. The model provides a unified discrete framework in which matter, gauge interactions, and gravity emerge from lattice geometry and symmetry
Ken Croes (Wed,) studied this question.