The Design of a Formal System of Science able to Prove Physics from Unhypothetical First Principles

Abstract

A method to prove the laws of physics from unhypothetical first principles is reported. The proof involves the construction of a formal system of science, then involves solving it for the laws of physics by applying a formalization of the scientific method to the system. That the method yields the right laws is perhaps initially surprising considering its purely mathematical origin, but can be understood as the simple consequence of the domain of the model, which is both universal in the computer theoretical sense (i.e. Turing complete) and complies with epistemology, thus is epistemologically-complete, and consequently is necessarily a superset of nature. Laws that apply to the system as a whole must cascade to its subsets, including nature, and these simply turn out to be (a familiar superset of) the laws of physics. To create the formal system, modern notions relating to mathematical undecidability are leveraged to create a 'trial and error' foundation to the discovery of mathematical knowledge, such that one is required to run programs to completion ---essentially to perform 'mathematical experiments'--- to acquire said knowledge, thereby permitting a re-formulation of mathematics conductive to experimental methods. The laws of physics are then derived as the probability measure that maximizes the entropy of a path in the space of all possible arrangements of experiments, leading precisely and uniquely to a generalization of quantum physics automatically supporting general relativity. Finally, applications of the system to fundamental open problems of physics as well as testable predictions are proposed.