Minimum Length from Quantum Mechanics and Classical General Relativity

Xavier Calmet, Michael Graesser, and Stephen D. H Hsu
Phys. Rev. Lett. 93, 211101 – Published 15 November 2004

Abstract

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.

  • Received 7 May 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.211101

©2004 American Physical Society

Authors & Affiliations

Xavier Calmet*, Michael Graesser, and Stephen D. H Hsu

  • California Institute of Technology, Pasadena, California 91125, USA

  • *Email address: calmet@theory.caltech.edu
  • Email address: graesser@theory.caltech.edu
  • Permanent address: Institute of Theoretical Science and Department of Physics, University of OR, Eugene OR 97403. Email address: hsu@duende.uoregon.edu

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Issue

Vol. 93, Iss. 21 — 19 November 2004

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