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

Abstract
The incompatibility between general relativity and quantum mechanics
has posed one of the greatest challenges in modern physics,
particularly in addressing singularities and reconciling spacetime’s behavior
at large and small scales. In this paper, we explore a new model
of spacetime—π-dimensional spacetime—motivated by the observation
that, while we can move freely in the three spatial dimensions,
time behaves asymmetrically, moving only forward. We intuitively
can see π - 3 as a natural descriptor for time’s unidirectional, fractal,
and infinite nature. By modifying key cosmological equations and incorporating
fractal structures, this model addresses singularities and
suggests new testable predictions for cosmic phenomena such as the
Cosmic Microwave Background, galaxy distribution, and gravitational
waves. The π-dimensional spacetime could offer a promising framework
for unifying general relativity and quantum mechanics.