D'Esposito, Vittorio (2024) Spacetime, Symmetries, and Observers at the interface between Quantum Theory and Gravity. [Tesi di dottorato]

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Abstract

The incompatibility between Quantum Theory and General Relativity gives rise to several logical conundrums, and different approaches to the Quantum Gravity problem have arisen in trying to solve them. Most of these approaches share the expectation that the smooth spacetime of General Relativity, with local symmetries given by the Poincaré algebra, should be replaced by a fundamentally discretised structure, with a minimum localisation limit for spacetime events. The existence of such a scale requires a deformation of the local symmetries to retain the covariance of physical laws. Such deformations naturally arise as the symmetries of non-commutative spacetimes, which are models realising the idea of a quantum spacetime, where the transformations between reference frames become non-classical. Interestingly, similar features are found in a seemingly unrelated research area in the foundations of Quantum Theory: the quantum reference frames research programme, in which abstract reference frames are replaced by physical systems that act as reference for the description of physical laws. These systems can be quantum in nature and hence define reference frames with fuzzy properties. Additionally, both the deformation of symmetries and the quantisation of reference frames suggest that measurement apparatuses and observers should acquire non-classical features. Symmetries, reference frames, observers, and measurement apparatuses: Following the arguments above, it seems that all the pillars of General Relativity, and Physics in general, have to be thoroughly scrutinised in the quest for a theory of Quantum Gravity. This thesis aims to investigate such foundational issues and answer the following questions: How do quantum systems evolve in a spacetime with deformed symmetries? How does the quantisation of reference frames affect the observed physical properties of quantum systems? How do measurement apparatuses behave in a non-classical spacetime and how are communication protocols between observers affected? The relevance of these questions is rooted in the growing interest that has sparked in recent years in exploring the foundations of Quantum Gravity, independently of what the ultimate full theory will be, to advance the logical understanding of the fundamental principles on which such a theory should be built on. This thesis explores this sector of theoretical physics by focusing on how quantum systems are affected by the deformations of spacetime symmetries and the quantisation of the degrees of freedom describing reference frames. By employing innovative techniques and deriving some significant results, the research work presented in this thesis pushes the boundaries of the theoretical investigations and further stimulates discussions in the foundations of Quantum Gravity.

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