Axiomatization of Mechanics

TL;DR

This paper addresses the longstanding problem of axiomatizing physics by exploring whether a consistent, integrated axiomatic framework can be developed without overhauling existing mathematical structures, to unify and generalize physical theories.

Contribution

It proposes a new approach to axiomatizing physics aimed at creating a consistent, unified, and generalized axiomatic system encompassing current theories.

Findings

Identifies inconsistencies in current physical axioms.

Suggests a pathway to unify physics through a generalized axiomatic framework.

Highlights the importance of axiomatization for the coherence of physical theories.

Abstract

The problem of axiomatization of physics formulated by Hilbert as early as 1900 and known as the Sixth Problem of Hilbert is nowadays even more topical than at the moment of its formulation. Axiomatic inconsistency of classic, quantum, and geometrized relativistic physics of the general relativistic theory does not in the least fade away, but on the contrary, becomes more pronounced each year. This naturally evokes the following questions: 1. Is it possible, without drastically changing the mathematics apparatus, to set up the axiomatics of physics so as to transform physics, being presently a multitude of unmatched theories with inconsistent axiomatics, into an integrated science? 2. Is it possible, maybe through expanding their scopes, to generalize of transform the existing axiomatics into an integral system of axioms in such a manner that existing axiomatics of inconsistent theories would follow there from as a particular case?