A New Argument for the Nomological Interpretation of the Wave Function: The Galilean Group and the Classical Limit of Nonrelativistic Quantum Mechanics

International Studies in the Philosophy of Science (2):177-188 (2017)
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In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function.

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Valia Allori
University of Bergamo

Citations of this work

Realism about the wave function.Eddy Keming Chen - 2019 - Philosophy Compass 14 (7):e12611.
The Wave-Function as a Multi-Field.Mario Hubert & Davide Romano - 2018 - European Journal for Philosophy of Science 8 (3):521-537.
Wave-functionalism.Valia Allori - 2021 - Synthese 199 (5-6):12271-12293.
Quantum mechanics, time and ontology.Valia Allori - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 66 (C):145-154.
A Puzzle for the Field Ontologists.Shan Gao - 2020 - Foundations of Physics 50 (11):1541-1553.

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