FCAS-CIH V.13.110.pdf

Fractional Chrono-Aging Spacetime (FCAS) Theory: Unifying Quantum Entanglement and
Cosmic Expansion
By:El-Sayed Fatthy
Abstract
Fractional Chrono-Aging Spacetime (FCAS) theory is a novel framework that extends
general relativity and quantum mechanics by introducing a hyper-dimensional fractional
time coordinate (denoted ) to model chrono-aging eects. In this paper, we formally
develop the FCAS theory, detailing its mathematical foundations and physical implications.
We begin by dening the key terms – including the hyper-coordinate , the fractional aging
parameter , phase angle , and the function coupling spacetime position with
the fractional dimension – and formulating how these enter a biasing path integral
approach to quantum amplitudes. We derive the extended equations of motion
incorporating fractional time derivatives, illustrating how a fractional-order path integral
weighting biases classical and quantum trajectories. The theory is generalized to
curved spacetimes (3+1 dimensions and higher), with the extra coordinate treated as a
ber-like dimension attached to each point in 4D spacetime. We compare FCAS to
established theories – quantum mechanics, general relativity, Bohmian mechanics, and the
ER=EPR conjecture – highlighting that FCAS provides a geometrical mechanism for
quantum entanglement (via fractional wormhole-like -connections) while preserving
causality. We include schematic diagrams (e.g. a Flatland analogy, 3D ber bundles, higher-
dimensional connectivity) to visualize complex concepts. To validate FCAS, we propose
experimental designs at both laboratory and astrophysical scales. Physics-informed neural
networks (PINNs) and symbolic regression AI models are outlined as simulation tools to
solve the FCAS eld equations and to detect fractional patterns in entanglement data. In
addition, we present proofs of theoretical consistency (general covariance, causality, limit
to GR, and stability) and show that FCAS naturally reproduces key observed phenomena
(cosmic acceleration, galaxy rotation curves, black hole thermodynamics) within of
current data, without introducing contradictions. Results from simulated entangled
systems and cosmological expansions under FCAS assumptions are presented,
demonstrating qualitative agreement with observed phenomena such as preserved
causality in entanglement correlations and late-time cosmic acceleration. Finally, we
discuss how FCAS complements existing physics – recovering classical 4D general relativity
in the limit – and identify measurable signatures (e.g. slight deviations in
entanglement entropy scaling and cosmological expansion rates) that could distinguish
FCAS from standard theories. This comprehensive study positions FCAS as a candidate
framework bridging quantum theory and gravitation through the innovative concept of
fractional chronological dimensions.
Table of Contents 1. Introduction 2. Background 2.1. Time in Quantum Mechanics and
Relativity 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 Other
Physics Theories 11. Figures, Diagrams, and Visualizations 12. Discussion 13. Conclusion