Philosophical perspectives on the principle of least action

Abstract

The principle of least action (PLA) is a pivotal concept in theoretical physics, positing that when an object moves from one point to another, it minimizes a quantity called action. During its inception, the PLA was associated with theological and teleological notions as scholars sought to understand why particles followed such paths. Later, its wide applicability across different theories in physics and its utility in problem-solving led to its recognition as a significant principle. However, over the past century, due to the PLA yielding the same empirical predictions as the equations of motion (EOMs), the prevailing view in modern physics is that the PLA is merely a mathematical reformulation of the EOMs. In recent decades, philosophers have challenged this view, arguing that while the PLA is empirically equivalent to the EOMs, they are inequivalent in other respects. Some of these philosophers assign physical significance to the quantity of action, while others consider the PLA to be a meta-law. In this thesis, I will analyze these views. I will use the intriguing case of ‘alternative Lagrangians’ to argue against assigning physical significance to the action. I will then argue that the wide applicability of the PLA is not due to its modality as a meta-law but rather to the prevalence of second-order EOMs in the fundamental laws of physics.