General Relativity as the Classical Limit of the Unified Fractal Quantum Field Theory (UFQFT)

In this study, we demonstrate that Einstein’s General Relativity (GR) emerges as the classical geometric limit of the Unified Fractal Quantum Field Theory (UFQFT). Within UFQFT, spacetime is defined as a scale-dependent fractal manifold characterized by a local dimension D(x), and all physical interactions arise from the resonant dynamics of two unified fundamental fields: the energy field (Φ) and the charge field (Ψ). The macroscopic curvature of spacetime, expressed by Einstein’s field equations, is shown to result from the collective resonance geometry of these fields when D→3.0. Gravitation is reinterpreted as an emergent resonance curvature of the Φ-field, rather than a fundamental force. The classical energy–momentum tensor Tμν​ is replaced by a fractal energy tensor Tμν (Φ,Ψ,D) which depends explicitly on the local fractal dimension. This framework naturally incorporates dark matter as baryon-free, neutral resonance structures of the Φ–Ψ fields trapped in sub-fractal domains (D<3), and dark energy as non-material vacuum resonances (Φ₀ modes) that maintain constant phase and contribute to cosmic expansion. The results indicate that General Relativity is not an independent postulate but a macroscopic manifestation of a deeper fractal field dynamics. This correspondence provides a unified geometric interpretation of spacetime curvature, particle interactions, and cosmological acceleration within a single theoretical framework.