The wave-function as a multi-field

Original paper in Philosophy of Physics


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.


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



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).


  1. Albert, D.Z. (1994). Quantum mechanics and experience. Cambridge: Harvard University Press.Google Scholar
  2. Albert, D.Z. (1996). Elementary quantum metaphysics. In Cushing, J.T., Fine, A., & Goldstein, S. (Eds.) Bohmian mechanics and quantum theory: an appraisal (pp. 277–284). Netherlands: Springer.Google Scholar
  3. Albert, D.Z. (2015). After physics. Cambridge: Harvard University Press.CrossRefGoogle Scholar
  4. Allori, V. (2017). 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, forthcoming.Google Scholar
  5. Bell, J.S. (1987). Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.Google Scholar
  6. Belot, G. (2012). Quantum states for primitive ontologists. European Journal for Philosophy of Science, 2(1), 67–83.CrossRefGoogle Scholar
  7. Bhogal, H., & Perry, Z. (2017). What the Humean should say about entanglement. Noûs, 51(1), 74–94.CrossRefGoogle Scholar
  8. Bohm, D., & Hiley, B.J. (1993). The undivided universe: an ontological interpretation of quantum theory. London: Routledge.Google Scholar
  9. Callender, C. (2015). One world, one beable. Synthese, 192(10), 3153–3177.CrossRefGoogle Scholar
  10. Chen, E.K. (2017a). Our fundamental physical space: an essay on the metaphysics of the wave function. The Journal of Philosophy, 114(7), 333–365.Google Scholar
  11. Chen, E.K. (2017b). An intrinsic theory of quantum mechanics: progress in Field’s nominalistic program, part i. Preprint.
  12. Darby, G. (2012). Relational holism and Humean supervenience. The British Journal for the Philosophy of Science, 63(4), 773–788.CrossRefGoogle Scholar
  13. Dürr, D., Goldstein, S., & Zanghì, N. (2013). Quantum physics without quantum philosophy. Heidelberg: Springer.CrossRefGoogle Scholar
  14. Emery, N. (2017). Against radical quantum ontologies. Philosophy and Phenomenological Research. Advance access.
  15. Esfeld, M., Lazarovici, D., Hubert, M., & Dürr, D. (2014). The ontology of Bohmian mechanics. The British Journal for the Philosophy of Science, 65(4), 773–796.CrossRefGoogle Scholar
  16. Forrest, P. (1988). Quantum metaphysics. Oxford: Basil Blackwell.Google Scholar
  17. Goldstein, S., & Zanghì, N. (2013). Reality and the role of the wave function in quantum theory. In Ney, A., & Albert, D.Z. (Eds.) The wave function: essays on the metaphysics of quantum mechanics, chapter 4 (pp. 91–109). New York: Oxford University Press.Google Scholar
  18. Holland, P.R. (1993). The quantum theory of motion. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  19. Loewer, B. (1996). Humean supervenience. Philosophical Topics, 24(1), 101–127.CrossRefGoogle Scholar
  20. Maudlin, T. (2013). The nature of the quantum state. In Ney, A., & Albert, D.Z. (Eds.) The wave function: essays on the metaphysics of quantum mechanics, chapter 6, (pp. 126–153). New York: Oxford University Press.Google Scholar
  21. Maudlin, T. (2015). The universal and the local in quantum theory. Topoi, 34 (2), 349–58.CrossRefGoogle Scholar
  22. Miller, E. (2014). Quantum entanglement, Bohmian mechanics, and Humean supervenience. Australasian Journal of Philosophy, 92(3), 567–83.CrossRefGoogle Scholar
  23. Monton, B. (2013). Against 3N-dimensional space. In Ney, A., & Albert, D.Z. (Eds.) The wave function: essays on the metaphysics of quantum mechanics, chapter 7 (pp. 154–167). New York: Oxford University Press.Google Scholar
  24. Norsen, T. (2010). The theory of (exclusively) local beables. Foundations of Physics, 40(12), 1858–1884.CrossRefGoogle Scholar
  25. Norsen, T., Marian, D., & Oriols, X. (2015). Can the wave function in configuration space be replaced by single-particle wave functions in physical space? Synthese, 192(10), 3125–3151.CrossRefGoogle Scholar
  26. Schaffer, J. (2009). On what grounds what. In Chalmers, D.J., Manley, D., & Wasserman, R. (Eds.) Metametaphysics: new essays on the foundations of ontology, chapter 12 (pp. 347–383). New York: Oxford University Press.Google Scholar
  27. Sellars, W. (1963). Empiricism and the philosophy of mind. In Science perception and reality (pp. 127–196). Atascadero: Ridgeview Company.Google Scholar
  28. Suárez, M. (2015). Bohmian dispositions. Synthese, 192(10), 3203–28.CrossRefGoogle Scholar
  29. Valentini, A. (2010). De Broglie–Bohm pilot-wave theory: many worlds in denial? In Saunders, S., Barrett, J., Kent, A., & Wallace, D. (Eds.) Many worlds? Everett, quantum theory, and reality, chapter 16 (pp. 476–509). New York: Oxford University Press.Google Scholar
  30. Wald, R.M. (1984). General relativity. Chicago: The University of Chicago Press.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculté des Lettres, Section de PhilosophieUniversité de LausanneLausanneSwitzerland

Personalised recommendations