Classical Mechanics Is Lagrangian; It Is Not Hamiltonian

Datos Bibliográficos

ID8399301
AutoresErik Curiel (0000-0002-5812-3033, Western University, autor de correspondencia)
Año2014
Volumen65
Número2
Páginas269-321
Fecha de publicación2014-06-01
Peer ReviewedSí
Open AccessNo
TipoARTICLE
RevistaThe British Journal for the Philosophy of Science (JOURNAL)
Identificadores de la revistaISSN: 0007-0882 • E-ISSN: 1464-3537
EditorialOxford University Press (PUBLISHER • GB)
DOI10.1093/bjps/axs034
OpenAlexW2120229085
IdiomaEN
Citas recibidas40
Referencias citadas15

One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question of whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and sketch proofs of two technical results—inspired by simple physical arguments about the generic properties of classical systems—to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none provided by Hamiltonian. The argument not only clarifies the conceptual structure of the two systems of mechanics, but also their relations to each other and their respective mechanisms for representing physical systems. It also shows why naïvely structural approaches to the representational content of physical theories cannot work. [Lagrange] grasped that he had gained a method of stating dynamical truths in a way, which is perfectly indifferent to the particular methods of measurement employed in fixing the positions of the various parts of the system. Accordingly, he went on to deduce equations of motion, which are equally applicable whatever quantitative measurements have been made, provided that they are adequate to fix positions. The beauty and almost divine simplicity of these equations is such that these formulae are worthy to rank with those mysterious symbols which in ancient times were held directly to indicate the Supreme Reason at the base of all things. (Whitehead [1948], p. 63) 1. Introduction 2. Abstract Classical Systems 3. The Possible Interactions of a Classical System and the Structure of Its Space of States 4. Classical Systems Are Lagrangian 5. Classical Systems Are Not Hamiltonian 6. How Lagrangian and Hamiltonian Mechanics Represent Classical Systems 7. The Conceptual Structure of Classical Mechanics

Algorithm · Analytical dynamics · Analytical mechanics · Classical mechanics · Epistemology · Geometry · Hamiltonian mechanics · Hamiltonian system · Mathematical analysis · Mathematical proof · Phase space · Physical system · Physics · Representation (politics) · Simple (philosophy) · Simplicity · Sketch · Mathematics · Philosophy and History of Science · Quantum Mechanics and Applications · Relativity and Gravitational Theory