FCAS-CIH V.13.110.pdf

Fractional Chrono-Aging Spacetime (FCAS) Theory: Unifying Quantum Entanglement andCosmic ExpansionBy:El-Sayed FatthyAbstractFractional Chrono-Aging Spacetime (FCAS) theory is a novel framework that extendsgeneral relativity and quantum mechanics by introducing a hyper-dimensional fractionaltime coordinate (denoted ) to model chrono-aging eects. In this paper, we formallydevelop the FCAS theory, detailing its mathematical foundations and physical implications.We begin by dening the key terms – including the hyper-coordinate , the fractional agingparameter , phase angle , and the function coupling spacetime position withthe fractional dimension – and formulating how these enter a biasing path integralapproach to quantum amplitudes. We derive the extended equations of motionincorporating fractional time derivatives, illustrating how a fractional-order path integralweighting biases classical and quantum trajectories. The theory is generalized tocurved spacetimes (3+1 dimensions and higher), with the extra coordinate treated as aber-like dimension attached to each point in 4D spacetime. We compare FCAS toestablished theories – quantum mechanics, general relativity, Bohmian mechanics, and theER=EPR conjecture – highlighting that FCAS provides a geometrical mechanism forquantum entanglement (via fractional wormhole-like -connections) while preservingcausality. We include schematic diagrams (e.g. a Flatland analogy, 3D ber bundles, higher-dimensional connectivity) to visualize complex concepts. To validate FCAS, we proposeexperimental designs at both laboratory and astrophysical scales. Physics-informed neuralnetworks (PINNs) and symbolic regression AI models are outlined as simulation tools tosolve the FCAS eld equations and to detect fractional patterns in entanglement data. Inaddition, we present proofs of theoretical consistency (general covariance, causality, limitto GR, and stability) and show that FCAS naturally reproduces key observed phenomena(cosmic acceleration, galaxy rotation curves, black hole thermodynamics) within ofcurrent data, without introducing contradictions. Results from simulated entangledsystems and cosmological expansions under FCAS assumptions are presented,demonstrating qualitative agreement with observed phenomena such as preservedcausality in entanglement correlations and late-time cosmic acceleration. Finally, wediscuss how FCAS complements existing physics – recovering classical 4D general relativityin the limit – and identify measurable signatures (e.g. slight deviations inentanglement entropy scaling and cosmological expansion rates) that could distinguishFCAS from standard theories. This comprehensive study positions FCAS as a candidateframework bridging quantum theory and gravitation through the innovative concept offractional chronological dimensions.Table of Contents 1. Introduction 2. Background 2.1. Time in Quantum Mechanics andRelativity 2.2. Entanglement and Nonlocal Correlations 2.3. Bohmian Mechanics (Pilot-Wave Theory) 2.4. ER = EPR Hypothesis 2.5. Fractional Calculus in Physics 3. Core Theory 4.Mathematical Formulation 5. Experimental Design 6. Simulations and AI 7. Results 8.Theoretical Consistency Proofs 9. Phenomenological Matches 10. Compatibility with OtherPhysics Theories 11. Figures, Diagrams, and Visualizations 12. Discussion 13. Conclusion<br>