Marco Forgione
In the present work I argue that the path integral formulation of quantum mechanics displays a holistic machinery that allows one to predict and explain the total amplitude of the quantum system.
The machinery shows that it is not the single path that counts, but rather, it is the whole ensemble that provides the total amplitude. In pursuing such interpretation, I refer to Healey's notion of holism and I show that -when applied to path integrals- it ultimately leads to a form of structural holism. To do so, I point out: (1) what the whole is composed of, (2) the non-supervenient relation the whole holds with its parts and (3) the mathematical object that instantiates such relation, i.e., the phase factor.
Concerning (1), I argue that while the parts correspond to the single possible paths, the whole is to be interpreted as the total ensemble posited by the theory. I show that the single possible trajectories play the role of mathematical tools, which do not represent real particle paths. They can be individuated mathematically by varying the phase factor, but they do not describe what actually happens: they remain mathematical possibilities devoid of ontological meaning.
Concerning (2), I will show that a strong reductionist account of the ensemble to the single paths is not possible. If that is the case, then the single paths will count as calculation tools, while it is the statistical representation of the whole that provides the description of the particle motion. In arguing for the irreducibility to single real paths of the total ensemble, I firstly take into consideration Wharton's realist account and secondly, I analyze the decoherent histories account of quantum mechanics. In the former case, I argue that even by parsing the total ensemble in sets of non-interfering paths and then mapping them into a space-time valued field, we cannot deny the holistic nature of the path integral formulation. Furthermore, although the decoherent histories account parses the total ensemble in coarse grained histories -where an history is a sequence of alternatives at successive times-, it ultimately fails in extrapolating the real history the particle undergoes.
Ultimately (3), I suggest that the phase factor is the mathematical object that instantiates the non-supervenient relation. It determines the cancellation of the destructively interfering paths and, in the classical limit, it explains the validity of the least action principle.
Once all these parts are addressed, I will argue that the holistic ensemble and the phase factor -which weights the probabilities for each trajectory- form a structural holism for which the distinction between particles and waves is no longer necessary.
