A solution to the soccer ball problem for generalised uncertainty relations

Abstract: We propose a new method for generating generalised uncertainty relations (GURs) including the generalised uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalised uncertainty principle (EGUP), previously proposed in the quantum gravity literature, without modifying the Heisenberg algebra. Our approach is compatible with the equivalence principle, and with local Poincar{\' e} invariance in the relativistic limit, thus circumventing many of the problems associated with GURs derived from modified commutation relations. In particular, it does not require the existence of a nonlinear additional law for momenta. This allows sensible multiparticle states to be constructed in which the total momentum is macroscopic, even if the momentum of an individual particle is bounded by the Planck momentum, thus providing a resolution of the "soccer ball problem" that plagues current approaches to GURs.