>>16711785Pop sci faggots are so tiresome.
>>16710842 (OP)Hamilton-Jacobi theory shows that the action can be interpreted as path length in phase space. Paths of least action are just geodesics on a symplectic manifold. In quantum mechanics, position and momentum are no longer commutative, which results in a much richer theory of Feynman path integrals. But path integrals always reduce to the least action picture in the limit of the Planck constant going to zero. In that sense, the Planck constant measures the degree of non-commutativity of quantum operators. Some mathematical theories, in particular AQFT, formalize this via Hopf algebras and nets of algebras.