  In her Comment arXiv:1202.4066 [hep-th] Hossenfelder proposes a
generalization of the results we reported in Phys. Rev. D84 (2011) 087702 and
argues that thermal fluctuations introduce incurable pathologies for the
description of macroscopic bodies in the relative-locality framework. We here
show that Hossenfelder's analysis, while raising a very interesting point, is
incomplete and leads to incorrect conclusions. Her estimate for the
fluctuations did not take into account some contributions from the geometry of
momentum space which must be included at the relevant order of approximation.
Using the full expression here derived one finds that thermal fluctuations are
not in general large for macroscopic bodies in the relative-locality framework.
We find that such corrections can be unexpectedly large only for some choices
of momentum-space geometry, and we comment on the possibility of developing a
phenomenology suitable for possibly ruling out such geometries of momentum
space.
