Symmetry-Driven Renormalization in the Observer-Equivariance Framework

The idea for this article originates from an attempt to reconstruct the laws of physics from Leibniz’s ontology. In this ontology, the observer can be understood as a windowless monad. Leibniz’s ontology also includes the concept of the “pre-established harmony.” I realized that the symmetry principles in physics, within a Leibnizian ontology, can play a role analogous to the pre-established harmony. I also recognized that the relationship between the observer and the physical system can be expressed as a G-principal bundle p: O -> S, where O is the set of all observer perspectives and S is the physical system. For observers to share a coherent reality, the morphisms between any two observer perspectives must be invertible. In category-theoretic language, this implies isomorphism and G-equivariance. In this framework it is no longer "observers" in the classical sense, but abstract "observer perspectives". This leads to a kind of pan-monadology, with every small volume in the Planck-length scale acting as a monad. I realized this could be utilized in quantum gravity. The results of my diskussions with ChatGPT v o3 and Grok 4 are given in this article. The article is largely AI-generated based on my conceptual ideas. That is why it is shared as a "working article".