Metaphysics of the Principle of Least Action

TL;DR

This paper explores the metaphysical foundations of the principle of least action, proposing a modal interpretation that considers all possible paths simultaneously, linking classical physics with contemporary metaphysics and quantum histories.

Contribution

It introduces a novel modal interpretation of the principle of least action, connecting possible paths with quantum histories and proposing a new ontological framework.

Findings

Possible paths in the principle of least action relate to quantum histories.

The action measures the essence of possible histories.

Only one history has maximal essence and minimal action.

Abstract

Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the contemporary metaphysics of modality and Leibniz's concept of essences or possibles striving for existence. I elaborate a modal interpretation of the principle of least action that replaces a classical representation of a system's motion along a single history in the actual modality by simultaneous motions along an infinite set of all possible histories in the possible modality. This model is based on an intuition that deep ontological connections exist between the possible paths in the principle of least action and possible quantum histories in the Feynman path integral. I interpret the action as a physical measure of the essence of every possible history. Therefore only one actual history has the highest degree of the essence and minimal action. To address the issue of necessity, I assume that the principle of least action has a general physical necessity and lies between the laws of motion with a limited physical necessity and certain laws with a metaphysical necessity.