When Newton discovered ‘Newton’s law’ he was probably not aware that it could be viewed as a consequence of minimizing an ‘action integral’ (integral of some Lagrangian density).
Since the same is true in quantum physics as well, I am wondering why variation principles (VP) play such a pivotal role in physics. Why does nature seem to favour systems whose dynamics follow from a VP of some kind?
Are there dynamic systems that cannot be derived via a VP? If yes, what is a simple example?
