Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry

TL;DR

This paper critically examines the feasibility of detecting quantum spacetime properties through macroscopic probes, arguing that such efforts are fundamentally limited and unlikely to succeed, thus challenging some recent experimental proposals.

Contribution

The paper demonstrates that the localization of macroscopic bodies does not reflect Planck-scale spacetime quantization, questioning the validity of certain experimental approaches.

Findings

Localization of macroscopic bodies is not Planck-scale quantized.

Spacetime quantization effects are much weaker for composite bodies.

Detecting spacetime quantization via macroscopic bodies is highly unlikely.

Abstract

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.