Uncertainty in measurements of distance

@article{Baez2002UncertaintyIM,
  title={Uncertainty in measurements of distance},
  author={John C. Baez and S. Jay Olson},
  journal={Classical and Quantum Gravity},
  year={2002},
  volume={19}
}
Ng and van Dam have argued that quantum theory and general relativity give a lower bound Δl l1/3lP2/3 on the uncertainty of any distance, where l is the distance to be measured and lP is the Planck length. Their idea is roughly that to minimize the position uncertainty of a freely falling measuring device, one must increase its mass, but if its mass becomes too large it will collapse to form a black hole. Here we show that one can go below the Ng–van Dam bound by attaching the measuring device… 
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