Exploring π-Dimensional Spacetime: A Fractal Framework for Addressing Singularities and Potentially Unifying Relativity with Quantum Mechanics

AbstractThe incompatibility between general relativity and quantum mechanicshas posed one of the greatest challenges in modern physics,particularly in addressing singularities and reconciling spacetime’s behaviorat large and small scales. In this paper, we explore a new modelof spacetime—π-dimensional spacetime—motivated by the observationthat, while we can move freely in the three spatial dimensions,time behaves asymmetrically, moving only forward. We intuitivelycan see π - 3 as a natural descriptor for time’s unidirectional, fractal,and infinite nature. By modifying key cosmological equations and incorporatingfractal structures, this model addresses singularities andsuggests new testable predictions for cosmic phenomena such as theCosmic Microwave Background, galaxy distribution, and gravitationalwaves. The π-dimensional spacetime could offer a promising frameworkfor unifying general relativity and quantum mechanics.