Between Laws and Models: Some Philosophical Morals of Lagrangian Mechanics

TL;DR

This paper explores the philosophical implications of Lagrangian mechanics, highlighting its methodological and ontological aspects, and introduces foundational concepts like Routhian reduction and Noether's theorem for philosophical analysis.

Contribution

It offers a philosophical analysis of Lagrangian mechanics, emphasizing its methodological and ontological significance, and provides an accessible introduction to key concepts for philosophers.

Findings

Lagrangian mechanics occupies an overlooked intermediate level between laws and models.

The ontology of Lagrangian mechanics is more complex than traditionally assumed.

Includes an elementary presentation of Routhian reduction and Noether's theorem.

Abstract

I extract some philosophical morals from some aspects of Lagrangian mechanics. (A companion paper will present similar morals from Hamiltonian mechanics and Hamilton-Jacobi theory.) One main moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels--``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is both more subtle and more problematic than philosophers often realize. The treatment of Lagrangian mechanics provides an introduction to the subject for philosophers, and is technically elementary. In particular, it is confined to systems with a finite number of degrees of freedom, and for the most part eschews modern geometry. But it includes a presentation of Routhian reduction and of Noether's ``first theorem''.