Noncommutative Geometry and Spacetime: A Philosophical Investigation

Quantum gravity (QG) seeks to elucidate physics at or beyond the Planck scale while remaining compatible with general relativity in low-energy regimes. The expected breakdown of the general relativistic framework at high energies suggests that spacetime may become ill-defined in such contexts and must be recovered as an emergent structure. Applications of noncommutative geometry (NCG) to QG propose that, in this regime, spacetime acquires a noncommutative algebraic structure. This structure characterises the fundamental object postulated by these theories, termed noncommutative spacetime (NCST). These proposals exacerbate key conceptual issues in QG by raising the question of whether spatiotemporal content can survive such deformations. In this thesis, I situate NCST approaches within the broader philosophical debate on the disappearance and emergence of spacetime, addressing the central question: can they provide a genuinely spatiotemporal framework for QG? To this end, I first develop the conceptual groundwork for analysing spatiotemporality in QG, characterising spacetime disappearance and assessing competing accounts of its emergence. I then present NCST as a case study by reconstructing its historical development. In particular, I examine the so-called pointlessness problem: the alleged elimination of spacetime points in noncommutative frameworks. I argue that pointlessness neither entails the disappearance of spacetime nor undermines the possibility of spatiotemporality. Finally, I explore whether NCST theories can sustain chronogeometric content. I demonstrate that, under suitable interpretative conditions, algebraic structures in NCG can indeed represent spatiotemporal relations. Overall, I contend that NCG can yield viable spatiotemporal models of QG when properly interpreted. By clarifying the intricate relationship between noncommutativity and spatiotemporality, this work aims to contribute both to the philosophy of QG and to broader debates concerning the status and reconstruction of spacetime in fundamental physics.