Quantum mechanics and observers for gravity in a closed universe

A bstract 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 Ob in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly e^S₎₁ e S Ob, where S Ob is the number of degrees of freedom of Ob. Moreover we argue that the errors in this description are exponentially small in S Ob. We give evidence for this proposal by incorporating it into the gravitational path integral and the coding interpretation of holography in simple models and seeing that it works, and we explain how similar effects arise in black hole physics in appropriate circumstances.