Maresca, Enrico (2025) Noncommutative Geometry and Chronogeometry in Quantum Gravity. [Preprint]

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Abstract

Chronogeometry is often conceived as a necessary condition for spatiotemporality, yet many theories of quantum gravity (QG) seem to challenge it. Applications of noncommutative geometry (NCG) to QG propose that spacetime exhibits noncommutative features at or beyond the Planck scale, thereby replacing relativistic symmetries with their deformations, known as quantum groups. This leads to an algebraic formulation of noncommutative structure that postulates a minimal length scale and deforms relativistic (commutative) physics, raising questions about whether noncommutative theories preserve spatiotemporal content,
and specifically, chronogeometry. I argue that noncommutative approaches can satisfy an appropriate definition of chronogeometry, thus attaining physical
significance within QG. In particular, I contend that noncommutativity is compatible with chronogeometricity, using κ-Minkowski spacetime as case study in NCG. In this algebraic setting, physical interpretation hinges on two crucial elements: a representation of the noncommutative algebra and a corresponding set of observers. I show how this framework enables the algebra to encode localisation
procedures for events in noncommutative spacetime, relative to a noncommutative reference frame, with frame transformations governed by the quantum group structure. By enriching the theory with noncommutative reference frames, NCG can satisfy the necessary representational principles to support chronogeometric content.

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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, Chronogeometry, Noncommutative reference frames, Interpretation, Quantum gravity
Subjects:	General Issues > Models and Idealization General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Quantum Gravity
Depositing User:	Mr Enrico Maresca
Date Deposited:	29 Jul 2025 14:04
Last Modified:	29 Jul 2025 14:04
Item ID:	26041
Subjects:	General Issues > Models and Idealization General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Quantum Gravity
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/26041

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