Quantum equivalence, the second law and emergent gravity

Abstract: Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the intrinsic properties of space-time. At the same time, the precise relation between space-time and quantum mechanics is still one of the greatest problems of theoretical physics. This immediately raises the question on the completeness of our understanding of quantum mechanics. Here we address the problem by making an intrinsic analysis of observables in generic quantum systems. We show that there is an extreme fine tuning problem for the emergence of physics from the Hilbert space dynamics. However, for any initial condition and Hamiltonian, there exists a special set of observables. We show that these observables are intimately linked to the natural configuration space in which an area law for the entanglement is inevitable. We argue that this implies emergent gravity.