Closed Universe, Quantum Entanglement and Observers

Abstract: It has been argued that in quantum gravity the Hilbert space associated with any closed universe is trivially one-dimensional. To reconcile this argument with the richness of our own universe, it was suggested that a nontrivial Hilbert space will emerge once an observer" is included. Such anobserver" has been modeled in different ways. There are three concrete classes of models: $\textbf{1)}$ The observer" is modeled by a term in the full Hamiltonian of the system which is linear in a phase space variable; $\textbf{2)}$ Theobserver" is modeled in the quantum circuit model of holography as a subsystem in the closed universe which is entangled with an external non-gravitational system; $\textbf{3)}$ The observer" is argued to be described by the emergent Goldstone bosons when the diffeomorphisms are spontaneously broken. In fact, the third class was discovered by an attempt to physically realize the first class. In this paper, we will show that the second class can also be unified into the third class. Our result indicates that the emergence of theobserver" is a manifestation of the $\textit{Massive Islands}$ paradigm. It demonstrates that the graviton mass is a feature of the quantum state. One should think of the islands as closed universes and the Goldstone boson associated with the graviton mass as the observer", which is exactly the case at late-times for evaporating black holes. An implication of this work is that theobserver" can ``observe" global symmetries in quantum gravity.