Quantum wormholes at spatial infinity

We derive the interesting result that the two asymptotically flat Universes classically linked by the Einstein-Rosen bridge may also be quantum mechanically connected in their far out regions. This would be felt by the Newtonian potential far away from a black/white hole system, and raises the possibility of establishing communication via perturbations. We obtain our results by means of wavepackets with a small variance in the mass, solving the equations derived from a maximally symmetry-reduced canonical quantisation method. Mass and a proxy of the Newtonian potential appear as canonical duals, leading to a Heisenberg uncertainty relation between the two. Coherent states are then built, which become non-semiclassical only in two regions: asymptotic spatial infinity (where unitarity forces the packets to “feel” the other asymptotic spatial infinity), and inside the horizon at $r=Gm$ where there is ringing. Whilst the latter has been noted in the literature, the former—the quantum wormhole at spatial infinity—seems to have eluded past scrutiny. Even under a coherent state there is a free parameter determining the distance beyond which the states becomes non-semiclassical, given the ambiguity in defining quadratures and squeezing, with departures eventually becoming of order one and cutting off the Newtonian potential. Further studies are required to examine the stability of these conclusions beyond their symmetry-reduced test tube.