The Energy Scale Separation Explanation of Renormalization: A First-Principles Derivation of Quantum Field Theory Divergences in UD Theory

ABSTRACT Renormalization is the cornerstone of quantum field theory and also its Achilles' heel. To eliminate infinities, physicists invented the mathematical trick of "subtracting infinities from infinities. " Although the results agree remarkably with experiments, this process lacks physical intuition. Based on the fundamental axioms of UD theory, this paper demonstrates that renormalization is not a mathematical trick but a natural consequence of energy scale separation. In UD theory, all four components have masses of order the Planck scale, so at low energies they can only contribute through virtual processes, with their contributions suppressed by the enormous energy scale difference, of order (E/MP) ⁿ. Taking the electron anomalous magnetic moment as an example, the UD theory predicts corrections of order mₑ/MP ≈ 4. 2×10^-23, which is ten orders of magnitude below current experimental precision, fully consistent with 70 years of QED verification. The "mathematical monster" of renormalization is reduced to a simple physical fact. KEY FINDINGS 1. Divergences are not problems—they simply indicate that we have ignored high-energy physics. 2. Renormalization is not a mathematical trick—it is a natural consequence of scale separation. 3. In UD theory, all four components have masses of order the Planck scale MP, providing a natural cutoff without artificial introduction. 4. The electron anomalous magnetic moment receives UD corrections of order mₑ/MP ≈ 4. 2×10^-23, ten orders of magnitude below current experimental precision (2. 8×10^-13). 5. All low-energy QED processes are fully consistent with UD theory; deviations are completely unobservable at current precision. 6. This explains why QED has been so successful—the fundamental scale is the Planck scale, and all corrections are suppressed by E/MP. ELIMINATED ASSUMPTIONS - Infinities require subtraction → Scale separation naturally suppresses- Renormalization as mathematical trick → Physical scale separation- Need for artificial cutoff → MP natural cutoff- Renormalizability as special property → Low-energy approximation Keywords: renormalization, quantum field theory, scale separation, effective field theory, UD theory