Pushing Einstein's Principles to the Extreme

TL;DR

This paper explores the limits of Einstein's principle of coordinate independence to constrain fundamental physical equations, using minimal axioms and discretizations of key theories.

Contribution

It introduces a framework based on minimal axioms to analyze and restrict the form of fundamental equations in physics, including discretizations of Maxwell, Yang-Mills, and general relativity.

Findings

Discretizations of Maxwell and Yang-Mills theories fit the framework.

General relativity in Ashtekar variables is incorporated.

Minimal axioms can restrict possible fundamental equations.

Abstract

In these lectures I propose to push Einstein's principle of coordinate independence to the extreme in order to restrict the possible form of fundamental equations of motion in physics. I start from nearly tautological system theoretic axioms. They provide a minimal amount of a priori structure which is thought to be characteristic of human thinking in general. It is shown how formal discretizations of Maxwell and Yang Mills theory in flat space and of general relativity in Ashtekar variables fit into this frame work.