Heuristic rule for constructing physics axiomatization

TL;DR

This paper proposes a new heuristic rule to guide the axiomatization of physics, aiming to systematically derive fundamental principles and potentially achieve a complete Theory of Everything through rigorous mathematical proofs.

Contribution

It introduces a novel heuristic rule for physics axiomatization and derives key principles that lead to uniqueness results in various physical theories.

Findings

Identified three physical principles from the heuristic rule.

Generated uniqueness results for space, time, and quantum mechanics.

Suggested that axiomatization of the Standard Model may be feasible.

Abstract

Constructing the Theory of Everything (TOE) is an elusive goal of today's physics. Goedel's incompleteness theorem seems to forbid physics axiomatization, a necessary part of the TOE. The purpose of this contribution is to show how physics axiomatization can be achieved guided by a new heuristic rule. This will open up new roads into constructing the ultimate theory of everything. Three physical principles will be identified from the heuristic rule and they in turn will generate uniqueness results of various technical strengths regarding space, time, non-relativistic and relativistic quantum mechanics, electroweak symmetry and the dimensionality of space-time. The hope is that the strong force and the Standard Model axiomatizations are not too far out. Quantum gravity and cosmology are harder problems and maybe new approaches are needed. However, complete physics axiomatization seems to be an achievable goal, no longer part of philosophical discussions, but subject to rigorous mathematical proofs.