Classical Mechanics
This chapter applies our reasoning about structure in physics to two formulations of classical mechanics, Lagrangian and Newtonian mechanics, that are generally taken to be completely equivalent. It argues that these two formulations differ in both the type and amount of structure presupposed by their dynamical laws, as revealed by the invariances of the equations representing the laws as well as the theories’ statespace structures. This suggests that these are not fully equivalent theories: they differ in dynamical structure. There are also various metaphysical differences between them. The chapter goes on to argue that the minimize-structure rule tells us to choose one over the other. Along the way, the idea that preferred or natural coordinate systems indicate underlying structure is discussed.