Quantum mechanics and observers for gravity in a closed universe

Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this be consistent with the complexity of our own experiences? In this paper we propose that the experiences of any observer Obin a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly eSOb, where SOb is the number of degrees of freedom of Ob. Moreover we argue that the errors in this description are exponentially small in SOb. We give evidence for this proposal using the gravitational path integral and the coding interpretation of holography, and we explain how similar effects arise in black hole physics in appropriate circumstances.