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Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics

Unitary inequivalence as a problem for structural realism

Steven French

Published Mar 20, 2012• 17 citations
Publisher
DOI
10.1016/j.shpsb.2011.09.001

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Abstract The standard claim that the Schrödinger and Heisenberg pictures of quantum mechanics are equivalent rests on the fact that they yield identical empirical predictions. This equivalence therefore assumes the instrumentalist worldview in which theories serve only as tools for prediction. Under scientific realism, by contrast, theories aim to describe reality. Whereas the Schrödinger picture posits a time-evolving wave function, the Heisenberg picture posits so-called descriptors, time-evolving generators of the algebra of observables. These two structures are non-isomorphic: descriptors surject onto but do not reduce to the Schrödinger state. Hence, under realism, the pictures are inequivalent. The chapter argues that this inequivalence marks an opening toward a richer, separable ontology for quantum theory. On explanatory grounds, descriptors provide genuinely local accounts of superdense coding, teleportation, branching, and Bell inequality violations—phenomena that the Schrödinger framework does not explain fully locally.
In this chapter the issue of unitarily inequivalent representations in QFT is examined. This has been raised as a fundamental problem for OSR. Here the issue of arriving at an appropriate ontology of QFT comes to the fore and in the context of recent debates in the foundations of QFT, the Lagrangian and Algebraic approaches are examined from a structuralist perspective. It us argued that the issue of unitarily inequivalent representations can be deflated in various ways, and in particular by adapting Ruetsche’s ‘Swiss Army Knife’ approach in the context of the view of primitive modality outlined in the previous chapter.