Hamiltonian Privilege
Josh Hunt, Gabriele Carcassi, C. Aidala
Abstract
Abstract We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of a theory over another: ceteris paribus , a more general formulation is more fundamental. We illustrate this criterion through a novel interpretation of classical mechanics, based on three physical conditions. Two of these conditions suffice for recovering Hamiltonian mechanics. A third condition is necessary for Lagrangian mechanics. Hence, Lagrangian systems are a proper subset of Hamiltonian systems. Finally, we provide a geometric interpretation of the principle of stationary action and rebut arguments for privileging Lagrangian mechanics.