Maresca, Enrico (2026) Pointless Noncommutative Spacetime. [Preprint]
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Abstract
Noncommutative geometry is often taken to imply a radical departure from relativistic spacetime at the Planck scale. The structure it describes, noncommutaive spacetime (NCST), lacks spacetime points (pointlessness), thereby challenging its status as a genuine physical spatiotemporal structure, as opposed to a merely mathematical construct. This paper challenges that conclusion. First, I argue that claims of pointlessness presuppose an ambiguous criterion for distinguishing physical from merely mathematical structure: proposed specifications either generate conflicting interpretations or collapse into triviality in the noncommutative setting. Second, I contend that even granting pointlessness, non-spatiotemporality does not follow. The inference relies on an implicit constitution thesis (that spacetime is constituted by its points) which proves either insufficiently precise or too weak to sustain the conclusion. By analysing four functional roles of spacetime points in classical theories, I demonstrate that none requires their retention in NCST, thereby undermining claims that spacetime disappears in the noncommutative regime.
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| Item Type: | Preprint | ||||||
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| Keywords: | Noncommutative geometry, Noncommutative Spacetime, Pointlessness, Physicality, Criteria of Physicality | ||||||
| Subjects: | General Issues > Scientific Metaphysics General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory |
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| Depositing User: | Mr Enrico Maresca | ||||||
| Date Deposited: | 16 Apr 2026 12:30 | ||||||
| Last Modified: | 16 Apr 2026 12:30 | ||||||
| Item ID: | 29133 | ||||||
| Subjects: | General Issues > Scientific Metaphysics General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory |
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| Date: | 2026 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/29133 |
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