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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 4: Classical Mechanics and Causation

AGPhil 4.1: Invited Talk

Tuesday, March 16, 2010, 16:50–17:30, JUR G

Classical Mechanics Is Lagrangian; It Is Not Hamiltonian — •Erik Curiel — LSE London, Department of Philosophy, Houghton Street, London WC2A2AE

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 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 prove 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 that Hamiltonian mechanics does. The argument clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems.