Minimum Length from Quantum Mechanics and Classical General Relativity

Details Minimum Length from Quantum Mechanics and Classical General Relativity Minimum Length from Quantum Mechanics and Classical General Relativity

2004-05-04

arxiv.org/abs/hep-th/0405033v2

Phys.Rev.Lett. 93 (2004) 211101

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, latex, to appear in the Physical Review Letters

Scientific paper

10.1103/PhysRevLett.93.211101

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$. This suggests a Planck-size {\it minimum ball} of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order $l_P$. Our results imply a {\it device independent} limit on possible position measurements.

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