Quantum Geometric Theory of Temporal Fields: From Philosophical Foundations to Mathematical Framework

This work presents a mathematical framework formalizing philosophical insights about the cyclic nature of time and universal evolution. Drawing from ancient philosophical traditions and modern physical theories, we develop a quantum geometric approach that treats time as an active field shaping cosmic evolution. By employing a minisuperspace approximation incorporating temporal degrees of freedom, we demonstrate how this framework naturally explains dark energy through graviton propagation in temporal dimensions. Our approach maintains consistency with current observational constraints from DES Y3 and gravitational wave observations [6, 14], while offering new insights into the quantum nature of spacetime. The theory makes specific predictions for next-generation experiments including Euclid, the Einstein Telescope, and pulsar timing arrays, providing multiple avenues for empirical verification of these fundamental ideas about the nature of time and reality.