Classical mechanics is Lagrangian; It is not Hamiltonian

Curiel, Erik (2014): Classical mechanics is Lagrangian; It is not Hamiltonian. In: British Journal for the Philosophy of Science, Bd. 65, Nr. 2: S. 269-321

Abstract

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 geo- metric 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.

• Dokumententyp: Zeitschriftenartikel
• Publikationsform: Publisher's Version
• Keywords: classical mechanics; Lagrangian mechanics; Hamiltonian mechanics; structure of theories
• Fakultät: Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) ; Philosophie, Wissenschaftstheorie und Religionswissenschaft > Lehrstuhl für Wissenschaftstheorie
• Themengebiete: 100 Philosophie und Psychologie > 100 Philosophie ; 100 Philosophie und Psychologie > 110 Metaphysik ; 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 0007-0882
• Sprache: Englisch