This post reminds me of an anecdote I read in a biography of Feynman. As a young physics student, he avoided using the principle of least action to solve problems, preferring to solve the differential equations. The nonlocal nature of the variational optimization required by the principle of least action seemed non-physical to him, whereas the local nature of the differential equations seemed more natural. Being a genius, he then went on to resolve the problem when he developed the sum-over-paths approach. It turns out that the path of least action has stationary phase shifts relative to infinitesimally different paths, so only paths near the path of least action combine constructively. Far away from the path of least action, phase shifts vary rapidly with infinitesimal variations in path, so those paths cancel out. Voilà, no spooky nonlocality (although there’s plenty of wacky QM-ness).
This post reminds me of an anecdote I read in a biography of Feynman. As a young physics student, he avoided using the principle of least action to solve problems, preferring to solve the differential equations. The nonlocal nature of the variational optimization required by the principle of least action seemed non-physical to him, whereas the local nature of the differential equations seemed more natural. Being a genius, he then went on to resolve the problem when he developed the sum-over-paths approach. It turns out that the path of least action has stationary phase shifts relative to infinitesimally different paths, so only paths near the path of least action combine constructively. Far away from the path of least action, phase shifts vary rapidly with infinitesimal variations in path, so those paths cancel out. Voilà, no spooky nonlocality (although there’s plenty of wacky QM-ness).