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Towards a Structuralist Elimination of Properties

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Quantum Mechanics and Fundamentality

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Abstract

Scientific realists investigate the ontology of the world and explain the observed phenomena by using our best fundamental physical theories. These theories describe the behavior of fundamental objects in terms of their fundamental properties, which determine their behavior. This paper is the natural companion of another paper in which I propose an alternative to this traditional account of metaphysics, according to which fundamental objects have no other fundamental property than the one needed to specify their nature. In that paper I argue that my view fares better than the traditional metaphysics both in the classical and in the quantum domain. In this paper I compare my view to structuralism. After discussing that my proposal shares many motivations with structuralism, I argue in which ways I think mine is superior.

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Notes

  1. 1.

    Allori (forthcoming).

  2. 2.

    Lewis (1986).

  3. 3.

    See Albert and Ney (2013), and then most notably Albert (1996, 2015), Lewis (2004, 2005, 2006, 2013), Ney (2012, 2013, 2015, 2017, 2021), North (2013).

  4. 4.

    In one approach, macroscopic objects can be functionally defined in terms of their role (Albert, 2015). In another approach three-dimensional objects exists as derivative when considering symmetry properties as fundamental facts about the world (Ney, 2021).

  5. 5.

    Dürr et al. (1992), Allori et al. (2008), Allori (2013a, b, 2015a, b, 2019a, b) and references therein.

  6. 6.

    Some have argued it is a property of matter (Monton, 2002; Lewis, 2013; Solé, 2013; Esfeld et al., 2014; Suàrez, 2015). Another approach is to take the wavefunction as a law (see Goldstein & Zanghì, 2013; Allori, 2018a, b, and references therein for a discussion), which seems particularly fitting to the Humean account of laws (Esfeld, 2014; Callender, 2015; Miller, 2014; Bhogal & Perry, 2017). For antirealism about the wavefunction see Healey (2012).

  7. 7.

    This view has been defended in Allori (2021b). Another structuralist perspective has also been defended by Lewis (2020), who writes: “the wave function describes the structure instantiated by whatever fundamental entities there may be in ordinary three-dimensional space: particles, fields, flashes, mass density, or something else entirely. A structure is not in itself an object, but rather a way that objects relate to each other.”

  8. 8.

    Allori (forthcoming).

  9. 9.

    For example, in case of a gravitational field, there is one effective law for the ‘electron,’ \( Eff\ {law}_1=\frac{H_1}{r^2} \) , where H 1 = Gm e M, one for the ‘proton,’ \( Eff\ {law}_2=\frac{H_2}{r^2} \) , where H 2 = Gm p M, and one for the ‘neutron,’ \( Eff\ {law}_3=\frac{H_3}{r^2} \) , where H 3 = Gm n M (where G is the gravitational constant, m e, m p, and m n are respectively the mass of the electron, proton and neutron as traditionally intended, while M is the reference mass, and r is the distance between the reference particle and the one under examination). See Allori (forthcoming) for more details.

  10. 10.

    Allori (2018a, b). See also Allori (2015c, 2019b, 2021a) for an argument that electromagnetic fields cannot be thought as fundamental objects otherwise they either would transform at odds with their nature, or we should stop thinking of classical electrodynamics as time-reversal invariant..

  11. 11.

    Dürr et al. (1992).

  12. 12.

    See Esfeld (2014) for a similar argument for his super Humeanism. See also Hall (2015).

  13. 13.

    For more details of this view, its objections and motivations, see Allori (forthcoming).

  14. 14.

    Worrall (1989).

  15. 15.

    Therefore, whenever I write ‘structuralism’ in the rest of the paper, I mean ‘ontic structuralism.’

  16. 16.

    See Ladyman (1998), French and Ladyman (2003), Ladyman and Ross (2007), French (2010, 2014) and references therein.

  17. 17.

    This view is defended most notably defended by Esfeld (2004) and refined in Esfeld and Lam (2008, 2010, 2012).

  18. 18.

    This view is inspired by Heil (2003) and Strawson (2008), who argue that the intrinsic properties of an object are the ways that object can be. See also Armstrong (1989).

  19. 19.

    Esfeld and Lam (2010).

  20. 20.

    French (2014) and references therein. See Saunders (2006), French and Krause (2006), Muller and Saunders (2008), Ladyman and Bigaj (2010) for further discussion.

  21. 21.

    Permutation invariance in many-particle quantum mechanics (Muller, 2009), gauge diffeomorphism invariance in general theory of relativity (Rickles, 2006, Esfeld & Lam, 2008).

  22. 22.

    See Bain (2006, 2009) in the context of the general theory of relativity; however, see Cao (2003), Pooley (2006).

  23. 23.

    For instance, a singlet state of two entangled spin ½ sub-systems is in a definite spin state, namely 0, but neither of the sub-systems has a definite spin state on its own. As such, it is argued that these sub-systems are best understood as relata of the fundamental entanglement relation they stand in, in this case: ‘has opposite spin to.’ For more on this argument, see Esfeld (2004).

  24. 24.

    See Teller (1986) for this argument. For discussion, see for instance Maudlin (2007), Ladyman and Ross (2007), Esfeld (2009), French (2014).

  25. 25.

    Ladyman (1998), French and Ladyman (2003), Esfeld (2004).

  26. 26.

    French (2014), and Esfeld (2014).

  27. 27.

    See for instance Busch (2003), Cao (2003), Chakravartty (2003), Morganti (2004), Psillos (2006).

  28. 28.

    Esfeld and Lam (2008).

  29. 29.

    Esfeld (2004).

  30. 30.

    Chakravartty (2007).

  31. 31.

    Ainsworth (2010).

  32. 32.

    See Castellani (1998) and references therein; see also Muller (2009). See Esfeld and Lam (2010) for criticisms.

  33. 33.

    Psillos (2006).

  34. 34.

    Russell (1912), Ladyman (2008).

  35. 35.

    Esfeld (2009), Esfeld and Sachse (2011), chapter 2.

  36. 36.

    Chakravartty (2004).

  37. 37.

    Allori (2019b).

  38. 38.

    Esfeld and Lam (2010).

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  1. Department of Philosophy, Northern Illinois University, Dekalb, IL, USA

    Valia Allori

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    Valia Allori

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Allori, V. (2022). Towards a Structuralist Elimination of Properties. In: Allori, V. (eds) Quantum Mechanics and Fundamentality . Synthese Library, vol 460. Springer, Cham. https://doi.org/10.1007/978-3-030-99642-0_10

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