Maresca, Enrico (2026) Spacetime Models Without Points: The Case of Noncommutative Geometry. [Preprint]

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Abstract

Over the past decades, noncommutative geometry (NCG) has emerged as a prominent research project in quantum gravity (QG). This accounts for non-classical effects by introducing a noncommutative parameter and systematically deforming the relativistic spatiotemporal framework. In doing so, NCG challenges the definability of core geometric structures, including spacetime points (the so-called pointlessness problem). As a result, it threatens to undermine the foundations and viability of NCG as a candidate approach to QG. In this paper, I examine the pointlessness problem and characterise it as a breakdown of classical dualities between algebraic and geometric frameworks. This yields both the proliferation of inequivalent notions of points and the absence of standard differential-geometric models for noncommutative theories. By contrast, I argue that novel dualities can be recovered in the noncommutative setting, allowing for the identification of more sophisticated geometric models. I conclude that pointlessness alone is insufficient to support claims of non-spatiotemporality in NCG without further qualification.

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Item Type:	Preprint
Creators:	Creators Email ORCID Maresca, Enrico enrico.maresca@phd.unipi.it 0009-0006-5138-2530
Keywords:	Noncommutative geometry, Algebra, Points, Pointlessness, Dualities
Subjects:	Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories
Depositing User:	Mr Enrico Maresca
Date Deposited:	26 Mar 2026 22:49
Last Modified:	26 Mar 2026 22:49
Item ID:	28764
Subjects:	Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory General Issues > Structure of Theories
Date:	2026
URI:	https://philsci-archive.pitt.edu/id/eprint/28764

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