Numerical search for a fundamental theory

TL;DR

This paper introduces a numerical method to test fundamental physics by analyzing the complexity of functions related to physical constants, potentially revealing insights into the underlying theory and testing anthropic principles.

Contribution

It presents a novel numerical approach using Kolmogorov complexity to analyze fundamental constants and assess their typicality within physical theories.

Findings

The weak coupling constant appears atypical.

The Weinberg angle also shows atypical complexity.

The method can be applied broadly to scientific experiments.

Abstract

We propose a numerical test of fundamental physics based on the complexity measure of a general set of functions, which is directly related to the Kolmogorov (or algorithmic) complexity studied in mathematics and computer science. The analysis can be carried out for any scientific experiment and might lead to a better understanding of the underlying theory. From a cosmological perspective, the anthropic description of fundamental constants can be explicitly tested by our procedure. We perform a simple numerical search by analyzing two fundamental constants: the weak coupling constant and the Weinberg angle, and find that their values are rather atypical.