Future Convergence Theory and Quantum Decoherence: A Unified Framework for Time Evolution and Probabilistic Reality

This paper extends the Future Convergence Theory (FCT) by integrating quantum decoherence into its mathematical framework. The theory suggests that the certainty of future states influences quantum systems, spacetime structure, and information theory. By incorporating future certainty into the density matrix formalism and modifying the Schrödinger equation, we demonstrate how quantum coherence is affected not only by environmental noise but also by the evolving certainty of future events.Key contributions of this study include:•A modified density matrix evolution equation, introducing future certainty F(T) as a key factor in quantum decoherence.•A refined Schrödinger equation, incorporating future certainty and environmental interactions E(T) to model the collapse of wavefunctions.•Implications for black hole information retention, dark matter emergence, and quantum gravitational effects.•Potential experimental validation, including quantum optics, gravitational lensing, and AI-driven simulations of future convergence.This work strengthens the mathematical foundation of FCT, linking it more explicitly with fundamental principles of quantum mechanics and general relativity. Future research should focus on empirical validation and computational simulations to further explore the implications of this theoretical framework.