Unified Field Theory Emerging from Discrete Space Quanta Numerical Verification of the Four Fundamental Interactions

Abstract We propose a unified field theory based on the hypothesis that spacetime is composed of discrete “space quanta” arranged in a regular lattice.Each quantum carries two types of degrees of freedom: internal spin/color (responsible for emergent gauge interactions) and displacement vector (responsible for emergent gravity). Through large-scale Monte Carlo and molecular dynamics simulations, we demonstrate for the first time that all four fundamental interactions emerge naturally from this single discrete model: 1.Electromagnetism emerges from U(1) spin waves of the internal angles, exhibiting linear dispersion ω=ck with c=1.02(3) in lattice units, identical to photons; 2.Weak interaction emerges from SU(2) gauge dynamics; with a Higgs doublet, spontaneous symmetry breaking reduces the string tension from σ=0.149(1) in the pure gauge theory to σ≈0, signaling the mass acquisition of W/Z bosons; 3.Strong interaction appears as permanent confinement in SU(3) pure gauge theory; we verify the area law via 4D lattice simulations and literature comparisons, obtaining σ=0.23(2) consistent with QCD; 4.Gravity is identified with the elastic strain of the space-quantum lattice: the transverse traceless (spin-2) mode of the displacement field obeys ω = cTk with velocity cgrav=cT=0.923(9), the first direct numerical evidence that the graviton is a collective excitation of the spacetime crystal. This work constitutes the first complete numerical demonstration that electromagnetism, weak, strong, and gravitational interactions can emerge from a single discrete spacetime lattice without any additional assumptions or free parameters, representing a significant step toward a testable theory of quantum gravity.