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Modular Theory, Non-Commutative Geometry and Quantum Gravity
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This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
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Spacetime granularity from finite-dimensionality of local observable algebras
Under finite-dimensionality of local observable algebras, the reconstructed operational spacetime topology is an atomistic Boolean algebra, implying a granular cellular spacetime.
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