Bartosz Milewski on Nostr: Maybe the problem is that we teach about energy first, get used to the idea of ...

Maybe the problem is that we teach about energy first, get used to the idea of kinetic energy and potential energy, conservation of energy, etc. Then we spring up the Lagrangian in terms of energy and circle back to the Hamiltonian.

Maybe it would make more sense to think of the Lagrangian and the action as more fundamental and introduce energy (and momentum) as a result of Noether's theorem. After all, conservation of energy is not a fundamental law, as seen in General Relativity.