Emergence and mechanism in the fractional quantum Hall …

1 Emergence and mechanism in the fractional quantum hall effectJonathan BainTandon School of Engineering, New York University, Department of Technology, Culture and Society, 6 Metrotech Center, Brooklyn, NY 11201, United Statesarticle infoArticle history:Received 27 February 2016 Received in revised form24 August 2016 Accepted 29 September 2016 Available online 2 November 2016 Keywords:EmergenceMechanismQuantum hall effectCondensed matter physicsabstractFor some authors, an adequate notion of Emergence must include an account of a mechanism by meansof which emergent behavior is realized. This appeal to mechanism is problematic in the case of thefractional quantum hall effect (FQHE).

2 There is a consensus among physicists that the FQHE exhibitsemergent phenomena, but there are at least four alternative explanations of the latter that, arguably,appeal to ontologically distinct mechanisms , both at the microphysics level and at the level of generalorganizing principles. In light of this underdetermination of mechanism , one is faced with the followingoptions: (I) deny that Emergence is present in the FQHE; (II) argue for the priority of one mechanisticexplanation over the others; or (III) temper the desire for a mechanism -centric account of Emergence . Iwill argue that there are good reasons to reject (I) and (II) and accept (III).

3 In particular, I will suggest thata law-centric account of Emergence does justfine in explaining the emergent phenomena associatedwith the Elsevier Ltd. All rights citing this paper, please use the full journal titleStudies in History and Philosophy of Modern Physics1. IntroductionFor some authors, an adequate notion of Emergence must in-clude an account of a mechanism by means of which emergentbehavior is realized. These authors maintain that without such anaccount, Emergence risks becoming a trivial concept that is ap-pealed to whenever we lack epistemic access to a physical phe-nomenon, or the technical skill required to provide a completedescription of it.

4 According toMainwood (2006, 284), for instance, ..emergent properties are not a panacea, to be appealed towhenever we are puzzled by the properties of large systems. Ineach case, we must produce a detailed physical mechanism foremergence, which rigorously explains the qualitative differencethat we see with the microphysical . The mechanism of most in-terest to Mainwood in the context of condensed matter physics isspontaneous symmetry breaking (SSB).Morrison (2012, 160) si-milarly claims that Emergence in condensed matter systems mustbe underwritten by a physical mechanism , and in particular SSB: The important issue here is not just the elimination of irrelevantdegrees of freedom; rather it is the existence or Emergence ofcooperative behavior and the nature of the order parameter (as-sociated with symmetry breaking) that characterizes the differentkinds of systems.

5 Finally,Lancaster and Pexton (2015)note thatwhile the fractional quantum hall effect (FQHE) cannot be ex-plained in terms of SSB, nevertheless a physical mechanism can beassociated with it; namely, whatWen (2013)refers to as long-range entanglement , and it is in terms of this mechanism thatemergence in the FQHE should be aim of this essay is to question this mechanism -centricview of Emergence by considering Lancaster and Pexton s exampleof the FQHE in a bit more consensus among physicistsis that this effect exhibits Emergence , but there are at least fouralternative explanations of it that, arguably, appeal to distinctontological mechanisms , at both the microphysical level and thelevel of what have been called higher organizing principles.

6 Theseexplanations include (1) the Laughlin ground state account, (2) thecomposite fermion account, (3) the composite boson account, and(4) the topological order account. The FQHE is described by theseaccounts as (i) a many-body Coulomb effect of electrons, (ii) a one-body effect of composite fermions, (iii) a many-body effect ofcomposite bosons, and (iv) a many-body entangled effect of elec-trons, respectively. These ontologically distinct microphysicalContents lists available atScienceDirectjournal in History and Philosophyof Modern Elsevier Ltd. All rights addition toLancaster and Pexton (2015), recent philosophical discussionsof the FQHE includeShech (2015), andLederer (2015).

7 Studies in History and Philosophy of Modern Physics 56 (2016) 27 38mechanistic accounts are underwritten by the following ontolo-gically distinct high-level mechanistic accounts: (a) localization(accounts 1 and 2); (b) spontaneous symmetry breaking (account3), and (c) long-range entanglement (account 4).In light of this underdetermination of mechanism , one is facedwith the following options: (I) deny that Emergence is present inthe FQHE; (II) argue for the priority of one mechanistic explana-tion over the others; or (III) temper the desire for a mechanism -centric account of Emergence . I will argue that there are goodreasons to reject (I) and (II) and accept (III).

8 In particular, I willsuggest that Emergence in the FQHE is best described in terms of alaw-centric view of Emergence . According to this view, emergenceis characterized, in part, by novelty, and novelty is underwritten byan appeal to distinct laws, cashed out as the equations of motionassociated with formally distinct Lagrangian 2contrasts mechanism -centric and law-centric viewsby means of a particular notion of Emergence relevant to 3and4describe the quantum hall effect and al-ternative mechanistic accounts of the 5makes thecase for a law-centric view of Emergence in the Two versions of emergenceI will make the distinction between the mechanism -centric andlaw-centric views of Emergence in terms of a particular ontologicalaccount of Emergence .

9 The intent is to capture a sense of emer-gence that is relevant to the FQHE, on the one hand, and yetgeneral enough to underwrite the mechanism -centric/law-centricdistinction , on the other. The account I will consider is based ontwo conditions, inspired byMainwood (2006, 20):(a)Microphysicalism: An emergent system is composed of mi-crophysical systems that comprise the fundamental systemand that obey the fundamental system's laws.(b)Novelty: The properties of the emergent system aredynami-cally independentof, anddynamically robustwith respect to,the properties of the fundamental intended to capture the intuition that anemergent system does not float free of the fundamental systemfrom which it emerges; rather, there must be a sense in which thefundamental system ontologically determines the properties ofthe emergent system.

10 This sense cannot be too strong, however,and this is the motivation fornovelty. To say an emergent propertyisdynamically independentof a fundamental property is to say theformer is independent of the dynamics that governs the latter. Tosay an emergent property isdynamically robustwith respect to afundamental property is to say the former is dynamically in-dependent of the latter, and remains so, despite changes in thedynamics of the independence is supposed to guarantee that, whilethe emergent system is ontologically determined in a minimalsense by the fundamental system, insofar as it is ultimately com-posed of microphysical systems that comprise the fundamentalsystem and that obey the fundamental system s laws, it is notcompletely determined by the fundamental system, insofar as.