  Over the last decade a growing number of quantum-gravity researchers has been
looking for opportunities for the first ever experimental evidence of a
Planck-length quantum property of spacetime. These studies are usually based on
the analysis of some candidate indirect implications of spacetime quantization,
such as a possible curvature of momentum space. Some recent proposals have
raised hope that we might also gain direct experimental access to quantum
properties of spacetime, by finding evidence of limitations to the
measurability of the center-of-mass coordinates of some macroscopic bodies.
However I here observe that the arguments that originally lead to speculating
about spacetime quantization do not apply to the localization of the center of
mass of a macroscopic body. And I also analyze some popular formalizations of
the notion of quantum spacetime, finding that when the quantization of
spacetime is Planckian for the constituent particles then for the composite
macroscopic body the quantization of spacetime is much weaker than Planckian.
These results show that finding evidence of spacetime quantization with studies
of macroscopic bodies is extremely unlikely. And they also raise some
conceptual challenges for theories of mechanics in quantum spacetime, in which
for example free protons and free atoms should feel the effects of spacetime
quantization differently.
