Uncertainty in Measurements of Distance

Details Uncertainty in Measurements of Distance Uncertainty in Measurements of Distance

2002-01-09

arxiv.org/abs/gr-qc/0201030v1

Class.Quant.Grav.19:L121-L126,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages LaTeX

Scientific paper

10.1088/0264-9381/19/14/101

Ng and van Dam have argued that quantum theory and general relativity give a lower bound of L^{1/3} L_P^{2/3} on the uncertainty of any distance, where L is the distance to be measured and L_P 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 to a massive elastic rod. Relativistic limitations on the rod's rigidity, together with the constraint that its length exceeds its Schwarzschild radius, imply that zero-point fluctuations of the rod give an uncertainty greater than or equal to L_P.

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