Fractal Time: A Scale-Dependent Framework for Reconciling Quantum Gravity and Cosmology

Fractal Time: A Scale-Dependent Framework for Reconciling Quantum Gravity and Cosmology Fractal Time: A Scale-Dependent Framework for Reconciling Quantum Gravity and Cosmology This paper introduces a groundbreaking concept—fractal time—which posits that time itself is scale dependent and possesses a fractal structure. By generalizing time derivatives to fractional order using the Caputo formalism, the framework naturally modifies classical and quantum dynamics. Key contributions include: Black Hole Resolution: The theory leads to non-singular black hole interiors by producing a scale-dependent mass distribution (M(r)∝r3M(r)∝r3), thereby resolving the traditional singularity problem. Quantum Field Theory Regularization: Fractal time alters dispersion relations and regularizes vacuum energy divergences, softening the standard Λ4Λ4 divergence to a milder Λ3+2βΛ3+2β behavior. Cosmological Implications: With a running fractal exponent β(ℓ)=1−Aℓγβ(ℓ)=1−Aℓγ, the model provides a mechanism to explain anomalies in the cosmic microwave background (CMB) and suggests modifications to inflationary dynamics, potentially addressing the Hubble tension. Testable Predictions: The paper outlines experimental strategies—including precision atomic clock comparisons, gamma-ray burst timing, and gravitational wave observations—to validate the fractal time framework. Perceptual Insights: It also explores how an observer’s scale can affect the perception of time, offering novel perspectives on the quantum-classical transition and consciousness. This unified approach bridges insights from quantum gravity, cosmology, and experimental physics, suggesting that our understanding of time is not absolute but scale dependent. The paper is of interest to researchers in theoretical physics, quantum gravity, and cosmology.