On the Principles That Serve as Guides to the Ontology of Quantum Mechanics

Abstract Is the ontology of non-relativistic quantum mechanics three dimensional 5
(3N) or high dimensional (3ND)? This paper discusses two principles, proposed in 6
North (The structure of a quantum world. The wave function: essays on the meta- 7
physics of quantum mechanics, pp 184–202, 2013) and Emery (Phil Phenomenol 8
Res 95(3):564–591, 2017), that are usually employed to answer this question. The 9
first, the dynamical matching principle (DMP), states that the fundamental structure 10
of the world should match the structure of the dynamical laws of the theory, in this 11
case, the Schrödinger equation. The second, the minimal divergence norm (MDN), 12
states that insofar as we have multiple empirically adequate theories, we ought to 13
choose the one that minimises the difference between what the theory says the world 14
is like and how the world appears. While the former is used to argue in favour of a 15
quantum 3ND ontology and the latter to argue in favour of a quantum 3D ontology, 16
I show that both principles can in fact be used to support either view. This casts 17
doubt on their role and legitimacy as meta-ontological principles that can guide us 18
in the decision between a commitment to a 3ND ontology or 3D ontology. I suggest 19
instead that they are best regarded as useful principles to construct and ‘regiment’ 20
the space of plausible quantum ontologies.