From Newtonian to ultra-relativistic gravitational scattering at 3rd post-Minkowskian order

Using the eikonal approximation for quantum scattering I will argue that the non-relativistic (Newtonian) and ultra-relativistic (massless) limits of classical gravitational scattering are smoothly connected at 3rd post-Minkowskian (3PM) order provided radiation reaction effects are properly taken into account. This is how a two-year-old puzzle raised by the first 3PM result by Bern et al. was solved about a year ago. Extending the connection to the next PM order looks both important and non-trivial.