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Fundamentality, Scale, and the Fractional Quantum Hall Effect

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Abstract

We examine arguments for distinguishing between ontological and epistemological concepts of fundamentality, focusing in particular on the role that scale plays in these concepts. Using the fractional quantum Hall effect as a case study, we show that we can draw a distinction between ontologically fundamental and non-fundamental theories without insisting that it is only the fundamental theories that get the ontology right: there are cases where non-fundamental theories involve distinct ontologies that better characterize real systems than fundamental ones do. In order to reconcile these distinct ontologies between fundamental and non-fundamental theories, we suggest that ontology must be understood as scale-dependent.

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Notes

  1. Also see Morrison (2006).

  2. The fractional quantum Hall effect is philosophically rich but has nevertheless received little attention from philosophers. Some recent notable exceptions include Bain (2016), Lancaster and Pexton (2015), and Shech (2015a, 2019a, b).

  3. Scale independent, i.e., “self-similar,” phenomenon notwithstanding.

  4. Admittedly, this point has been contested, for example, by Butterfield (2011), Norton (2012), Menon and Callender (2013), and Shech (2013, 2019a). Our goal here is not to take sides on this debate or other similar debates regarding infinite idealizations (but see Shech 2018 for an overview). Instead, we just note some ostensible examples in order to communicate to the reader what is meant by “epistemological fundamentality.”

  5. See, for instance, McGivern (2012). Of course, there are examples where the terms are used more or less interchangeably, but our focus is on the contrast between levels as understood on traditional philosophical accounts and scales as they are used in describing the application of theories and models to the world.

  6. Note that talk of ignoring or remaining indifferent to detail shouldn’t be taken to imply that a higher-scale or coarse-grained view is simplistic: discovering the right way of ignoring details—i.e., discovering an appropriate smoothing or averaging process—can take considerable work and involve careful attention to the system of interest. The point is simply that, however that process smoothing over details is achieved, variations in scale typically corresponds to variations detail.

  7. Working out the exact connection between variations in scale and variations in details is an issue that we leave for further study, but see McGivern (2012) for a discussion. Importantly, if our suggestion that ontology is scale dependent/relative is correct, then it will take some effort to work out the exact connection between variations in scale and variations in detail (as the latter is usually construed epistemically).

  8. That’s not to say that all explanatory questions are scale-specific. Some questions likely range across scales, or involve phenomena that are entirely “scale-free.” However, scale-relativity does seem to be important in the examples that have been the focus of discussion of epistemological fundamentality.

  9. Still, one may be unconvinced and worry that (1)–(3) and, correspondingly, (a–c) are not really different. For instance, one my object: what difference is there between saying that the molecular theory accurately characterizes the system at some fixed scale and saying that the system really consists of the molecules that the molecular theory talks about? In reply, and first, we agree that there may be no difference in claims about ontology if such claims match-up: e.g., fluids are composed of molecules-thought-of-as-particles (wherein this claim concerns (a) part-whole relations and corresponds to (1)), fluids just are particles at particular length-scales (wherein this claim concerns (b) scale and corresponds to (2)), and the theory that that most correctly characterizes fluids takes the basic ontology to be that of particles (wherein this claim concerns (c) matching accepted ontology and corresponds to (3)). However, and second, ostensible tension and inconsistencies may arise. Consider, for instance, the following situation: one holds that fluids are made up of molecules that we think of as particles, but that at high-energy scales the theory that most correctly characterizes the system of interest is quantum field theory (QFT) and that QFT is a theory about fields. In such a case there would be a difference between saying that fluids are composed of molecules-thought-of-as-particles and that molecules are “really” just excitations in a field. Similarly, such tension could also arise between talk of part-whole relations and the ontology that we accept based on our best sciences. Our point then is that, prima facie, and depending on the case at hand, (a–c) may correspond to different senses of ontological fundamentality.

  10. See Bain (2016, p. 36), Fradkin (2013, p. 502) and Zee (1995).

  11. See Lancaster and Blundell (2014, p. 419), Wen (2004, p. 298), and Zee (1995, p. 110).

  12. Accounts of Bose–Einstein condensate formation typically appeal to spontaneous symmetry breaking, viz., bosons condense and spontaneously break the global \( U\left( 1 \right) \) phase symmetry (Fradkin 2013, pp. 504–505).

  13. See Bain (2016, p. 32), Zee (1995, p. 113), and Fradkin (2013, p. 503). This is the Chern–Simons–Landau–Ginsburg formulation of the composite boson approach developed by Zhang et al. (1989).

  14. See Bain (2016, Section 4.2), Zee (1995, p. 113), and Fradkin (2013, p. 512). This is the Chern–Simons–Landau–Ginsburg formulation of the composite fermion approach developed by Lopez and Fradkin (1991).

  15. Note: we are not claiming that such an explanation is, in principle, impossible to give. Rather, we are claiming that if we take our current best theories and explanations seriously, RQFT is not the appropriate forum to look for explanations of the FQHE.

  16. See Zee (1995, p. 110) and Wen (2004, p. 298) for the details.

  17. See Shech (2019b) for a discussion of explanatory indispensability specifically in the case of anyons in the FQHE.

  18. Thanks to an anonymous reviewer for suggesting this.

  19. But for objections see, e.g., Azzouni (2012), Bangu (2008), Bueno (2012), Leng (2005, 2010, 2012), Liggins (2012), Yablo (2012).

  20. It is worthwhile to note that we are not saying that attaching flux to an electron is simply a convenient partitioning of degrees of freedom, since it causes a dramatic reconstruction of the system’s energy levels. Rather, the point is that we shouldn’t think about things like flux attachment as simple part-whole relations, where we take collections of smaller entities and process from a more fundamental theory and treat those collections as units.

  21. Even in cases of straightforward conflict, say, between two theories applying at the same scale, we can still regard explanatory success as good, though defeasible, evidence that a theory is getting the ontology right.

  22. We thank an anonymous reviewer for raising this objection.

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Acknowledgements

Thank you to Jonathan Bain, Alexander Franklin, Robin Hendry, James Ladyman, Tom Lancaster, and participants in the 2018 “26th Biennial Meeting of the Philosophy of Science Association” conference in Seattle for helpful discussion regarding earlier versions of this paper. This work began when the authors held Research Fellowships at Durham University, generously funded by the Institute for Advanced Study.

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  1. Department of Philosophy, Auburn University, Auburn, AL, USA

    Elay Shech

  2. School of Humanities and Social Inquiry, University of Wollongong, Wollongong, Australia

    Patrick McGivern

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Shech, E., McGivern, P. Fundamentality, Scale, and the Fractional Quantum Hall Effect. Erkenn 86, 1411–1430 (2021). https://doi.org/10.1007/s10670-019-00161-y

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