  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.
