Classical Mechanics from Energy Conservation or: Why not Momentum?

Abstract

It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and momentum in order to obtain the correct relativistic equations. Accordingly it is argued that not only quantum theory but also special relativity is intrinsically a Hamiltonian theory which requires a description of the dynamics using coordinate and momentum instead of velocity. Furthermore it is argued that the usual historical order of the ``formulations'' of mechanics, from Newtonian via Lagrangian to Hamiltonian mechanics, is illogical and misleading. We suggest that it should be reversed.