Noisy soccer balls

TL;DR

This paper refutes a previous claim that thermal fluctuations cause insurmountable issues for macroscopic bodies in the relative-locality framework, showing that such fluctuations are generally manageable with some exceptions.

Contribution

It corrects and extends prior analysis by including additional geometric contributions, demonstrating that thermal fluctuations are not inherently problematic in the framework.

Findings

Thermal fluctuations are not generally large for macroscopic bodies in the framework.

Some momentum-space geometries can lead to unexpectedly large fluctuations.

Potential for phenomenological tests to rule out certain geometries.

Abstract

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.