Recovering Einstein's equation from local correlations with quantum reference frames

Abstract

An observable spacetime can be viewed as a "continuum" of worldline coincidences (events) between a particle system and the observers of an ideal extended reference frame (RF). When this frame is absent, the metric encodes the infinitesimal proper intervals between those events that the ideal RF would assign if it were present. Extending this idea to the quantum domain -- where events arise from interactions that generate correlations -- we propose that, within a small spacelike region, the metric encodes local correlations with a quantum RF, thereby dispensing with its physical presence. This framework yields the full nonlinear Einstein equation in two scenarios: either recovering the maximal vacuum entanglement hypothesis in the first-order limit of state perturbations or producing a reference spacetime whose scalar curvature equals the cosmological constant.