2024/07/19 by Lu Chen, Chen, Lu
Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Origins and Evolution of Life #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2407.14234
openalex publication_date 2024/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous categorical strategy that formulate symmetries as isomorphisms between models and apply it to classical electromagnetism, and evaluate its philosophical significance in relation to the recent debate between `sophistication' and `reduction'. In addition to traditional spacetime models, I also consider algebraic models, in which case we can use the method of natural operators to address the problem of ontological nonperspicuity faced by the categorical strategy. Finally, I briefly expound on the significance of symmetries as isomorphisms in the framework of Univalent Foundations, in which isomorphic structures are formally identified.