Symmetry protected entanglement between gravity and matter
We show that gravity and matter fields are generically entangled, as a consequence of the local Poincare symmetry. First, within the covariant framework, we show explicitly that the Hartle-Hawking state in the Regge model of quantum gravity is necessarily entangled. Also, we present a general argument, applicable to any particular theory of quantum gravity with matter, by performing the analysis in the abstract nonperturbative canonical framework, demonstrating the nonseparability of the scalar constraint, thus promoting the entangled states as the physical ones. Our result is potentially relevant for the quantum-to-classical transition, taken within the framework of the decoherence programme: due to the symmetry requirements, the matter does not decohere, it is by default decohered by gravity. Generically, entanglement is a consequence of interaction. This new entanglement could potentially, in form of an "effective interaction", bring about corrections to the weak equivalence principle, further confirming that spacetime as a smooth four-dimensional manifold is an emergent phenomenon. Finally, the existence of the symmetry-protected entanglement between gravity and matter could be seen as a criterion for a plausible theory of quantum gravity, and in the case of perturbative quantisation approaches, a confirmation of the persistence of the manifestly broken symmetry.