Missing the point in noncommutative geometry.
Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes se...
| Publicado en: | Synthese Vol. 199; no. 1/2; pp. 4695 - 4729 |
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| Autores principales: | , , |
| Formato: | Artículo |
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Springer Nature
Dec2021
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=153650982&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 153650982 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Dec2021 vid: 199 iid: 1/2 pid: 237 pub: Springer Nature artinfo: ui: 153650982 10.1007/s11229-020-02998-1 ppf: 4695 ppct: 34 formats: fmt: – @attributes: type: T – @attributes: type: P size: 884KB tig: atl: Missing the point in noncommutative geometry. aug: au: Huggett, Nick Lizzi, Fedele Menon, Tushar affil: Department of Philosophy, University of Illinois at Chicago, Chicago, IL, USA Dipartimento di Fisica "Ettore Pancini", Università di Napoli Federico II, Napoli, Italy INFN, Sezione di Napoli, Napoli, Italy Departament de Física Quàntica i Astrofìsica and Institut de Cìences del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, Spain Faculty of Philosophy, University of Cambridge, Cambridge, UK su: Geometry Scalar field theory Operational definitions Quantum field theory Noncommutative geometry sug: subj: Geometry Scalar field theory Operational definitions Quantum field theory Noncommutative geometry keyword: Emergent spacetime ab: Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes' spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2021. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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