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Over the last decade a growing number of quantum-gravity researchers has beenlooking for opportunities for the first ever experimental evidence of aPlanck-length quantum property of spacetime. These studies are usually based onthe analysis of some candidate indirect implications of spacetime quantization,such as a possible curvature of momentum space. Some recent proposals haveraised hope that we might also gain direct experimental access to quantumproperties of spacetime, by finding evidence of limitations to themeasurability of the center-of-mass coordinates of some macroscopic bodies.However I here observe that the arguments that originally lead to speculatingabout spacetime quantization do not apply to the localization of the center ofmass of a macroscopic body. And I also analyze some popular formalizations ofthe notion of quantum spacetime, finding that when the quantization ofspacetime is Planckian for the constituent particles then for the compositemacroscopic body the quantization of spacetime is much weaker than Planckian.These results show that finding evidence of spacetime quantization with studiesof macroscopic bodies is extremely unlikely. And they also raise someconceptual challenges for theories of mechanics in quantum spacetime, in whichfor example free protons and free atoms should feel the effects of spacetimequantization differently.

Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry