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Defining a generic quantum system requires, together with a Hilbert space and a Hamiltonian, the introduction of an algebra of observables, or equivalently a tensor product structure. Assuming a background time variable, Cotler, Penington and Ranard showed that the Hamiltonian selects an almost-unique tensor product structure. This result has been advocated by Carrol and collaborators as supporting the Everettian interpretation of quantum mechanics and providing a pivotal tool for quantum gravity. In this talk I argue against this, on the basis of the fact that the Cotler-Penington-Ranard result does not hold in the generic background-independent case where the Hamiltonian is replaced by a Hamiltonian constrain. This reinforces the understanding that entropy and entanglement, that in the quantum theory depend on the tensor product structure, are quantities that are observable dependent. To conclude, I would like to pose the question of whether clocks can be thought as a resource, and how thinking of time in terms of physical clocks can inform our interpretation of quantum mechanics

I will describe how within eleven dimensional supergravity one can compute the logarithmic correction to the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS_4 black holes with arbitrary horizon topology.  The result perfectly agrees with the dual field theory computation of the topologically twisted index in  ABJM theory and in certain theories obtained from M5 wrapping a hyperbolic 3-manifold. The extension to rotating, electrically charged AdS_4 black holes and the dual superconformal index will also be discussed.