Abstract
The purpose of this article is to establish a connection between modelling practices and interpretive approaches in quantum mechanics, taking as a starting point the literature on scientific representation. Different types of modalities (epistemic, practical, conceptual and natural) play different roles in scientific representation. I postulate that the way theoretical structures are interpreted in this respect affects the way models are constructed. In quantum mechanics, this would be the case in particular of initial conditions and observables. I examine two formulations of quantum mechanics, the standard wave-function formulation and the consistent histories formulation, and show that they correspond to opposite stances, which confirms my approach. Finally, I examine possible strategies for deciding between these stances.
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Notes
This is at least the case for the theories of physics, which are the main focus of this paper.
This is consistent with the idea that epistemic possibilities are a subset of conceptual possibilities, which are a subset of logical possibilities, which, in this case, would correspond to the set of all mathematical structures.
Note that I am not trying to capture the process of model construction, but the final product. Presumably, scientists start from epistemic and practical constraints and then use conceptual inferences to construct an appropriate model. In retrospect, the constraints from which they started can be seen as restrictions on the space of available conceptual possibilities. Relations of necessity can be approached inferentially, or semantically, and the two approaches are complementary. Also note that this is a simplification, because models do not always strictly satisfy the laws of a theory, for example when approximations are used, and they often incorporate domain-specific postulates. However, I will neglect these complications here.
They can be replaced by final conditions in the case of retrodictions, or by any relevant input concerning the properties of the system at a particular time. In the following, I will only consider initial conditions, but my analyses can easily be transposed.
This observation cannot be generalised to unbounded systems. A counterexample (that I owe to an anonymous reviewer) is scattering theory, where the Hamiltonian is variable while initial conditions and observables are fixed. This could entail that the conclusions of this article are limited to the representation of some systems, notably bound systems. Further analyses beyond the scope of this paper would be required to address this potential limitation. However, the representation of bound systems remains canonical in physics, in particular when it comes to interpretive issues, and I hope that the analyses provided in what follows are still valuable as a demonstration of the fruitfulness of the methodological approach presented in this article.
I should note that another option consists in fixing a privileged observable at the conceptual level, and not at the practical or epistemic level. This option corresponds to Bohmian mechanics, which specifies that the positions of particles have definite values, whatever the model. In this case, the right observable could be considered a matter of natural (or even metaphysical) necessity, because it has nothing to do with the identification of the target. Note, however, that it is debatable whether fixing a “privileged basis” such as position at the conceptual level amounts to fixing observables: a distinct notion of observable that is independent from this privileged basis can be seen as supervening on the relation between a system and its environment.
The fact that the Hilbert space and algebra of observables are fixed, and potentially reflect a focus from the user of the model on particular properties of interest, could let us think that representation is perspectival in all cases. However, it is perspectival only in a weak sense, because of the selective interests of users, but properties of interest could still be objective. One can reasonably assume that the Hilbert space could be completed with new properties without affecting the initial content of the model. Fixing an observable makes the model perspectival in a stronger sense, insofar as observables are associated with the anthropocentric notion of measurement, and affect the content of the model.
Two more stances could have been considered: fixing everything, or fixing nothing at the basic level of abstraction (and perhaps still others considering unbounded systems: see footnote 5). However, they are less interesting because they do not specify a priority between observable and initial conditions, so I will leave them out.
This perspectivist stance could be compared to perspectivist positions in epistemology, such as Giere (2010b) and Massimi (2018)’s perspectival realism. The notion of perspective involved here is arguably more local, since it concerns a focus on some properties for a concrete target of representation, while perspectival realism puts emphasis on relativity to a conceptual scheme, a theoretical lexicon or epistemic norms of justification at a more general level. Nevertheless, there could be interesting connections between the two, notably because one of the motivations of perspectival realism is to account for the successful use of incompatible models to represent a single target system. There is no place to explore these connections here.
I am grateful to a reviewer for raising this objection.
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Ruyant, Q. On the Relationship Between Modelling Practices and Interpretive Stances in Quantum Mechanics. Found Sci 27, 387–405 (2022). https://doi.org/10.1007/s10699-020-09774-x
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DOI: https://doi.org/10.1007/s10699-020-09774-x