Abstract:

We use asymptotic symmetry arguments to show that the only physical states in QED scattering theory are maximally entangled states, in which electron (or positron) momenta at timelike infinity are entangled with soft radiation with memory at null infinity. This radiation is in addition to the electron's Coulomb field, which is not radiation and accompanies the electron to timelike infinity. States lacking this soft, entangling radiation fail to localize in the bulk, due to superselection in the momentum basis. This has not obstructed collider predictions, because scattering cross sections in the plane wave approximation are insensitive to such delocalization. Nevertheless, this soft radiation is required for the consistency of the local theory.  Some resulting physical phenomena are discussed. In quantum gravity, an analogous argument suggests that all gauge-invariant observables of the theory should extend to the boundary of the spacetime, as would be consistent with a theory of "relational observables" or "extended objects."