Missing the point in noncommutative geometry
Journal article
Huggett, Nick, Lizzi, Fedele and Vasudev Menon, Tushar. (2021). Missing the point in noncommutative geometry. Synthese: an international journal for epistemology, methodology and philosophy of science. 199(1-2), pp. 4695-4728. https://doi.org/10.1007/s11229-020-02998-1
Authors | Huggett, Nick, Lizzi, Fedele and Vasudev Menon, Tushar |
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Abstract | 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. |
Keywords | Noncommutative geometry; Emergent spacetime; Quantum field theory |
Year | 01 Jan 2021 |
Journal | Synthese: an international journal for epistemology, methodology and philosophy of science |
Journal citation | 199 (1-2), pp. 4695-4728 |
Publisher | Springer |
ISSN | 0039-7857 |
Digital Object Identifier (DOI) | https://doi.org/10.1007/s11229-020-02998-1 |
Web address (URL) | https://link.springer.com/article/10.1007/s11229-020-02998-1 |
Open access | Published as non-open access |
Research or scholarly | Research |
Page range | 4695-4728 |
Publisher's version | License File Access Level Open |
Output status | Published |
Publication dates | |
Online | 18 Jan 2021 |
Publication process dates | |
Accepted | 10 Dec 2020 |
Deposited | 26 Aug 2024 |
Additional information | © The Author(s), 2021. |
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |
Place of publication | Germany |
https://acuresearchbank.acu.edu.au/item/90x0q/missing-the-point-in-noncommutative-geometry
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OA_Menon_2021_Missing_the_point_in_noncommutative_geometry.pdf | |
License: CC BY 4.0 | |
File access level: Open |
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