Gravitational entropy bounds suggest that any bounded quantum system should be describable by a finite-dimensional Hilbert space. I consider a formulation where the finite-dimensionality is implemented at the level of local operator algebras a la algebraic QFT. The requirement of local finite-dimensionality leads to modifications to the microscopic structure of spacetime, which I will explore. I will also discuss how local finite-dimensionality allows for spacetime geometry to be seen as an effective description of the statistical properties of quantum states, and for gravity to emerge as a statistical effect.
Hosted by Philipp Höhn