P-106: The Micro-element Path to Quantum Gravity — From Discrete Micro-element Statistical Mechanics to Einstein-Cartan Geometry

Abstract:The quantisation of gravity is a long-standing unresolved core problem in theoretical physics. Traditional approaches treat general relativity as a fundamental field theory to be quantised, but encounter non-renormalisable ultraviolet divergences. Starting from the first principles of Space Ontology, we propose a completely new path: gravity is not a fundamental interaction, but the collective emergent behaviour of the Planck vortex micro-element system in the low-energy limit. The micro-element is the smallest unit of space, with scale l_Pl, and its intrinsic dynamics are governed by alignment coupling and chiral coupling, whose ratio κ = 0.017 is the sole free parameter of the theory. Starting from the discrete statistical mechanics of the micro-element system, we rigorously complete the following derivations: (1) write the path integral form of the micro-element partition function and define order parameters; (2) derive the effective action in the continuum limit via coarse-graining; (3) prove that the J-term (alignment coupling) contributes the curvature term, while the K-term (chiral coupling) contributes the torsion-spin coupling term; (4) rigorously identify the continuum limit of the K-term with the spacetime torsion tensor, proving that Einstein-Cartan gravity is the low-energy effective theory of the micro-element system; (5) demonstrate that micro-element discreteness provides an intrinsic ultraviolet cutoff Λ_UV = 1/l_Pl, with all divergences naturally terminating at this scale; and (6) provide a power-counting proof of the finiteness of quantum gravity amplitudes. We also present a systematic comparison with string theory, loop quantum gravity, and asymptotic safety gravity, and propose three testable exploratory predictions: (a) an exponential cutoff in the primordial gravitational wave spectrum at f ∼ c/l_Pl; (b) a softening of the gravitational scattering cross-section at the Planck scale; and (c) discrete spectral features in the Hawking radiation of Planck-mass black holes. The non-renormalisability of general relativity is thereby resolved: it is not a "bug" of the theory, but a "feature" of the discreteness of space. This paper is part of the second series (Applications and Verifications) of Space Ontology, building upon the foundational framework established in the first series (17 papers total).