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Minimum Length from Quantum Mechanics and Classical General Relativity

Calmet, Xavier and Graesser, Michael and Hsu, Stephen D. H. (2004) Minimum Length from Quantum Mechanics and Classical General Relativity. Physical Review Letters, 93 (21). Art. No. 211101. ISSN 0031-9007. doi:10.1103/PhysRevLett.93.211101.

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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 lP. This suggests a Planck-size 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 lP. Our results imply a device independent limit on possible position measurements.

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Additional Information:©2004 The American Physical Society (Received 7 May 2004; published 15 November 2004) The authors would like to thank C. Bauer, V. Braginsky, Y. Chen, M. Perelstein, J. Preskill, K. S. Thorne, A. Weinstein, and M. Wise for discussions. C. Bauer contributed to this work at an early stage. This research supported in part under DOE Contracts No. DE-FG06-85ER40224 and No. DE-FG03-92ER40701.
Subject Keywords:quantum theory; general relativity
Issue or Number:21
Record Number:CaltechAUTHORS:CALprl04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1933
Deposited By: Archive Administrator
Deposited On:23 Feb 2006
Last Modified:08 Nov 2021 19:43

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