A Rigorous Analysis of M31's Dynamics Using Surreal Mathematics and Category Theory
Joseph Spurway · HAL (Le Centre pour la Communication Scientifique Directe) · 2024
This paper presents a comprehensive mathematical framework that integrates surreal numbers, category theory, and quantum information theory to analyze the complex dynamics of the Andromeda galaxy (M31). By leveraging the Process of Quantum Information (PQI) framework, we apply these advanced mathematical constructs to empirical data, particularly the rotational velocities, mass distribution, and luminosity profiles derived from the seminal work of Vera Rubin and her collaborators. Surreal numbers, with their capacity to represent both infinitesimal and infinite values, offer a robust tool for capturing the full range of observed quantities and their inherent uncertainties. Category theory provides the structural foundation to generalize the relationships between these mathematical objects, ensuring consistency and coherence in the analysis. Furthermore, the integration of quantum information theory introduces a nuanced layer of interpretation, accounting for quantum effects that may influence large-scale astronomical observations. This interdisciplinary approach not only enhances our theoretical understanding of M31 but also contributes to the broader discourse in astrophysics by offering novel insights into the interplay between dark matter and baryonic matter in galaxies. The methodologies developed in this study have the potential to be applied to other cosmic systems, paving the way for future research in the intersection of quantum mechanics and cosmology.