The Logical Structure of Physical Laws: A Fixed Point Reconstruction

TL;DR

This paper formalizes the self-referential nature of physical laws using fixed point theory, providing a logical framework that captures theories like QED and GR through their symmetry and locality principles.

Contribution

It introduces a novel logical structure based on fixed points to model physical laws, addressing previous set-theoretic issues and applying to fundamental theories.

Findings

QED and GR can be represented within this logical fixed point framework

The approach resolves pathologies of naive set-theoretic formulations

Physical theories are characterized as least fixed points of admissibility constraints

Abstract

We formalise the self-referential definition of physical laws using monotone operators on a lattice of theories, resolving the pathologies of naive set-theoretic formulations. By invoking Tarski fixed point theorem, we identify physical theories as the least fixed points of admissibility constraints derived from Galois connections. We demonstrate that QED and GR can be represented in such a logical structure with respect to their symmetry and locality principles.