Reply to "Comment on 'Relative locality and the soccer ball problem'"

In a Comment [S. Hossenfelder Phys. Rev. D 88, 028701 (2013)], Hossenfelder proposes a generalization of the results we reported in [Phys. Rev. D 84, 087702 (2011)] 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.