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The wave-function as a multi-field

Abstract

It is generally argued that if the wave-function in the de Broglie–Bohm theory is a physical field, it must be a field in configuration space. Nevertheless, it is possible to interpret the wave-function as a multi-field in three-dimensional space. This approach hasn’t received the attention yet it really deserves. The aim of this paper is threefold: first, we show that the wave-function is naturally and straightforwardly construed as a multi-field; second, we show why this interpretation is superior to other interpretations discussed in the literature; third, we clarify common misconceptions.

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Notes

  1. However, we will not enter here in the metaphysical issue concerning the nature of fields. As the notion of a classical field can be framed in different metaphysical frameworks (for example, Humean view, dispositional view, etc.), the same procedure is in principle applicable to the multi-field.

  2. Chen (2017b) challenges the view of defining the wave-function in mathematical terms; he instead proposes a nominalistic approach.

  3. The conditional wave-function ψt(x) of a particle is defined by the universal wave-function Ψ, once the positions of all the other particles in the universe Y (t) are fixed: ψt(x) := Ψ(x,Y (t)).

  4. Many arguments were given to criticize Albert’s ontology (for instance, Chen 2017a; Maudlin 2013; Monton 2013). We will focus on one argument that we think is the strongest with respect to the multi-field interpretation.

  5. More explicitly, there are two types of locality: ontological locality and dynamical locality. The former coincides with separability and is about local beables, while the latter is about the behavior of physical objects, for instance, Bell’s notion of local causality or Einstein’s locality.

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Acknowledgements

We wish to thank David Albert, Guido Bacciagaluppi, Michael Esfeld, Dustin Lazarovici, Tim Maudlin, Matteo Morganti, Travis Norsen, Andrea Oldofredi, Charles Sebens, and Tiziano Ferrando for many helpful comments on previous drafts of this paper. We also thank the audience of the 3rd Annual Conference of the Society for the Metaphysics of Science (SMS) and especially Lucas Dunlap for commenting on our paper at this event. We also thank two anonymous referees for their very detailed reviews. Davide Romano’s research was funded by the Swiss National Science Foundation (grant no. 105212_149650).

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Hubert, M., Romano, D. The wave-function as a multi-field. Euro Jnl Phil Sci 8, 521–537 (2018). https://doi.org/10.1007/s13194-017-0198-9

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Keywords

  • Bohmian mechanics
  • de Broglie–Bohm theory
  • Interpretation
  • Multi-field
  • Ontology
  • Wave-function