Ervin Goldfain. Emergence of Classical Gravity from Continuous Spacetime Dimensions
Natural Sciences / Physics / Mathematical Physics
Submitted on: Jan 20, 2026, 11:05:01
Description: We develop a geometric framework in which classical gravity emerges from spacetime endowed with continuous, non-integer effective dimensions. Spacetime is modeled as a fractal measure space, exemplified by Cantor-dust (CD) constructions, where the Hausdorff measure replaces ordinary volume. We point out that the notion of fractal measure plays the physical role of gravitational mass, leading to modified Poisson equations and nonlocal GreenâE™s functions without introducing additional matter components. The resulting gravitational kernel exhibits scale-dependent behavior determined solely by the effective dimension of spacetime. This approach provides a unified explanation for long-range gravitational anomalies and establishes a direct connection between Dimensional Regularization, nonlocal gravity, and emergent Dark-Matter phenomenology.