Relative locality and the soccer ball problem

We consider the behavior of macroscopic bodies within the framework of relative locality [G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman, and L. Smolin, arXiv:1101.0931]. This is a recent proposal for Planck scale modifications of the relativistic dynamics of particles which are described as arising from deformations in the geometry of momentum space. We consider and resolve a common objection against such proposals, which is that, even if the corrections are small for elementary particles in current experiments, they are huge when applied to composite systems such as soccer balls, planets, and stars, with energies $E_{\mathrm{macro}}$ much larger than $M_P$. We show that this soccer ball problem does not arise within the framework of relative locality because the nonlinear effects for the dynamics of a composite system with $N$ elementary particles appear at most of order $E_{\mathrm{macro}}/N·M_P$.