The Simulation of Spacetime on a Discrete Lattice in the Light of Ullerian Wave Kinematic

This paper investigates the mathematical-physical hypothesis that the universe operates on a discrete information-theoretic computational lattice (simulation) by applying the universal wave kinematics formulated by Karl Uller (1872–1959). While modern lattice gauge theories (Lattice QCD) discretize spacetime to reduce computational complexity, this mathematical transformation inherently leads to a violation of Lorentz invariance. We demonstrate that Uller's postulated laws regarding the propagation, phase relationships, and directional dependence of waves in structured media can serve as a mathematical detector for this underlying lattice structure. By synthesizing discrete finite difference quotients with Ullerian phase invariants, we derive a modified dispersion relation that predicts empirically testable, anisotropic deviations at ultra-high energies.