  Over the last decade it has been found that nonlinear laws of composition of
momenta are predicted by some alternative approaches to "real" 4D quantum
gravity, and by all formulations of dimensionally-reduced (3D) quantum gravity
coupled to matter. The possible relevance for rather different quantum-gravity
models has motivated several studies, but this interest is being tempered by
concerns that a nonlinear law of addition of momenta might inevitably produce a
pathological description of the total momentum of a macroscopic body. I here
show that such concerns are unjustified, finding that they are rooted in
failure to appreciate the differences between two roles for laws composition of
momentum in physics. Previous results relied exclusively on the role of a law
of momentum composition in the description of spacetime locality. However, the
notion of total momentum of a multi-particle system is not a manifestation of
locality, but rather reflects translational invariance. By working within an
illustrative example of quantum spacetime I show explicitly that spacetime
locality is indeed reflected in a nonlinear law of composition of momenta, but
translational invariance still results in an undeformed linear law of addition
of momenta building up the total momentum of a multi-particle system.
