Equivalent and Inequivalent Formulations of Classical Mechanics

In this paper, I examine whether or not the Hamiltonian and Lagrangian formulations of classical mechanics are equivalent theories. I do so by applying a standard for equivalence that was recently introduced into philosophy of science by Halvorson and Weatherall. This case study yields three general philosophical payoffs. The first is a specific plea for clarity in our discussions of equivalence, while the second and third concern how we should interpret what our physical theories say about the world.