They’re only syntactically equivalent. Their semantics are completely different. In my opinion, Feynman’s semantics is objectively correct regarding the ‘literal path’ of a particle through spacetime. Given we don’t officially know their paths, but we do know their end destinations (wave equation), we can figure all possible paths and have the practically impossible paths cancel each other out: leaving only the probable literal paths of a particle complete with a graph of their trajectories. Schrodinger’s equation is far behind semantically. I think Feynman’s path integrals are superior.
You’re drawing a philisophical distinction based on a particular ontology of the wavefunction. As simpler version arises in classical electromagnetism: we can integrate out the charges and describe the world entirely as an evolving state of the E&M field with the charges acting as weird source terms, or we can do the opposite and integrate out the E&M field to get a theory of charges moving with weird force laws. These are all equivalent descriptions in that they are observationally indistinguishable.
They’re only syntactically equivalent. Their semantics are completely different. In my opinion, Feynman’s semantics is objectively correct regarding the ‘literal path’ of a particle through spacetime. Given we don’t officially know their paths, but we do know their end destinations (wave equation), we can figure all possible paths and have the practically impossible paths cancel each other out: leaving only the probable literal paths of a particle complete with a graph of their trajectories. Schrodinger’s equation is far behind semantically. I think Feynman’s path integrals are superior.
You’re drawing a philisophical distinction based on a particular ontology of the wavefunction. As simpler version arises in classical electromagnetism: we can integrate out the charges and describe the world entirely as an evolving state of the E&M field with the charges acting as weird source terms, or we can do the opposite and integrate out the E&M field to get a theory of charges moving with weird force laws. These are all equivalent descriptions in that they are observationally indistinguishable.