Relative locality and the soccer ball problem

TL;DR

This paper demonstrates that the relative locality framework resolves the soccer-ball problem by showing non-linear effects on macroscopic bodies are suppressed by the number of constituent particles, maintaining consistency with observed physics.

Contribution

The paper provides a resolution to the soccer-ball problem within relative locality, showing non-linear effects are negligible for macroscopic bodies due to suppression by particle number.

Findings

Non-linear effects are suppressed by the number of particles in composite systems.

The soccer-ball problem does not arise in relative locality.

Macroscopic bodies behave classically despite Planck scale modifications.

Abstract

We consider the behavior of macroscopic bodies within the framework of relative locality, which 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. These lead to the addition of non-linear terms to the energy-momentum relations and conservation laws, which are suppressed by powers of ratio between the energy E of the particles involved and the Planck mass M_P. 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_{macro} much larger than M_P. We show that this "soccer-ball problem" does not arise within the framework of relative locality, because the non-linear effects for the dynamics of a composite system with N elementary particles appear at most of order E_{macro}/ N M_{P}.