We propose a new method for generating generalized uncertainty relations (GURs) including the generalized uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalized 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 multi-particle 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.
Planck-Scale Soccer-Ball Problem: A Case of Mistaken Identity