Bulk Locality and Infrared Entanglement in Quantum Field Theory and Quantum Gravity

The memory effect refers to the fact that in four dimensional asymptotically flat spacetimes, at order 1/r a massless field generically will not return to the same value at late retarded times as it had at early retarded times. In electromagnetism and gravity, when memory is present, the late retarded time field will differ from the early retarded time field by an asymptotic symmetry. There is a direct relationship between memory and the charges that generate the asymptotic symmetries. These charges must commute with any gauge invariant local observables in the bulk spacetime, thereby effectively decohering bulk states into superselection sectors of eigenstates of the large gauge charges. It can thereby be seen that in QED, states corresponding to "incoming bare electrons" from infinity (i.e., electron states with no incoming electromagnetic radiation) do not correspond to physical states in the bulk. The physical bulk states correspond at infinitely early and late times to Faddeev-Kulish states, in which the electrons are infinitely entangled with soft photons so as to produce eigenstates of the large gauge charges. However, for a physical bulk state, this entanglement will occur only logarithmically in time and should be completely negligible in the finite time required to do any realistic experiment in the bulk. In QED with massless charged particles, the Faddeev-Kulish construction yields singular states, and it does not appear that quantum scattering theory from infinity makes sense at all (even though classical scattering theory is well defined). In gravity, there are no eigenstates of the large gauge charges (apart from the vacuum), but there also are no gauge invariant local bulk observables, so it is not obvious what criteria should be imposed on scattering states so that they correspond to physically relevant bulk states. In all cases, the behavior of states at asymptotic infinity is very different from the behavior of states at the large but finite times relevant to experiments in the bulk spacetime. In contrast to the case of classical fields or massive quantum fields, bulk locality for any quantum theory interacting with massless fields arises entirely from entanglement with infinitley many low energy quanta.