  In relativistic physics, angular momentum is paired with a lesser known
conserved quantity, the "mass moment", which appears as the time-space
components of the angular momentum tensor. Calculations of mass moment in
electromagnetic and gravitational scattering of point particles have led to
some puzzling behavior in which the radiated mass moment does not appear to
match the corresponding mechanical change. We review the issues and show how
the freedoms of time slicing and asymptotic frame may be used to bring all
known results into agreement. The key points are to use hyperboloidal time
slices and to allow the perturbative and asymptotic frames to differ by an
independent Bondi-Metzner-Sachs (BMS) transformation at early and late times.
The relevant BMS transformation involves a translation found recently by Riva,
Vernizzi, and Wong. Building on this work, we conjecture a flux balance law for
all orders in the post-Minkowski expansion.
