There’s an aspect of path integrals that’s always bugged me. They rely on an underlying classical field configuration space to integrate over. But, this seems problematic to me, since properly the objects of classical physics should emerge as limits of quantum physics. Shouldn’t we be able to start with “pure” quantum mechanics (a state space, a Hamiltonian operator), with no mention even of “paths” and get out classical physics? I.e. it seems backward to speak of a particle trying out different paths since a “path” is a classical notion; it’s as though quantum mechanics is merely a superstructure on top of an underlying classical layer rather than the other way around. Know what I mean?
Quantum and Newtonian physics are both just conceptual models to help ourselves understand and predict the things around us. They're useful for describing reality but neither of them are accurate representations of the real deal. All models break down at some limits.
To imagine one model "being merely a superstructure" on another implies that the limit doesn't exist and the two models are, in fact, the same thing. If you expand that idea to all other models, they would all eventually merge into one grand unified theory that accurately explains every single occurrencence in the universe. A nice idea conceptually, but we're at best no where near that and at worst have brains that will find the nuance of the universe impossible to comprehend in totality.
Any model that is useful for understanding and predicting the universe is worth sticking with, as long as you understand the limits where it applies. If path integrals happen to unlock some new insight that seems evidentially correct, it doesn't really matter if it ties into other theories.
