Probabilistic and Geometric Languages in the Context of the Principle of Least Action

TL;DR

This paper investigates unifying geometric and probabilistic languages of physics through the Principle of Least Action and Feynman's path integral, suggesting classical mechanics axioms emerge from quantum formulations.

Contribution

It proposes a framework linking geometric and probabilistic descriptions of physics via the Principle of Least Action and Feynman's path integral.

Findings

Equations in different physics languages derive from PLA

Feynman's path integral explains the meaning of PLA

Classical mechanics axioms follow from quantum mechanics

Abstract

This paper explores the issue of the unification of three languages of physics, the geometric language of forces, geometric language of fields or 4-dimensional space-time, and probabilistic language of quantum mechanics. On the one hand, equations in each language may be derived from the Principle of Least Action (PLA). On the other hand, Feynman's path integral method could explain the physical meaning of PLA. The axioms of classical and relativistic mechanics can be considered as consequences of Feynman's formulation of quantum mechanics.