Synthese 199 (1-2):4695-4728 ()

Authors
Nick Huggett
University of Illinois, Chicago
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 the metaphysics of such a geometry, and how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.
Keywords spacetime  geometry   noncommutative geometry  quantum gravity
Categories (categorize this paper)
Reprint years 2021
ISBN(s)
DOI 10.1007/s11229-020-02998-1
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,959
Through your library

References found in this work BETA

The Metaphysics Within Physics.Tim Maudlin - 2007 - Oxford University Press.
Emergent Spacetime and Empirical (in) Coherence.Nick Huggett & Christian Wüthrich - 2013 - Studies in History and Philosophy of Modern Physics 44 (3):276-285.
What Price Spacetime Substantivalism? The Hole Story.John Earman & John Norton - 1987 - British Journal for the Philosophy of Science 38 (4):515-525.
Quantum Metaphysical Indeterminacy.Claudio Calosi & Jessica Wilson - 2019 - Philosophical Studies 176 (10):2599–2627.

View all 32 references / Add more references

Citations of this work BETA

Towards Noncommutative Quantum Reality.Otto C. W. Kong - 2022 - Studies in History and Philosophy of Science Part A 92:186-195.

Add more citations

Similar books and articles

Points. Lack Thereof.Fedele Lizzi - 2019 - Philosophical Problems in Science 66:35-60.
Revision of Phenomenology for Mathematical Physics.Masaki Hrada - 2008 - Proceedings of the Xxii World Congress of Philosophy 43:73-80.

Analytics

Added to PP index
2020-06-25

Total views
26 ( #438,695 of 2,504,809 )

Recent downloads (6 months)
2 ( #277,627 of 2,504,809 )

How can I increase my downloads?

Downloads

My notes