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Uncertainty in Measurements of Distance

John C. Baez·S. Jay Olson
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Abstract

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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John C. Baez, S. Jay Olson. 2002-01-09. Uncertainty in Measurements of Distance. https://doi.org/10.1088/0264-9381%2F19%2F14%2F101

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