Stability of Inverted Pendulum and Heisenberg Uncertainty Principle

ORAL

Abstract

Classical inverted pendulum can stay in the position of its unstable equilibrium (upside-down) indefinitely. However, due to the Heisenberg uncertainty principle no object can have both its position and its momentum to be absolutely certain at the same time. This fundamental principle applies to inverted pendulum resulting in impossibility to have even an unstable equilibrium. As a consequence, inverted pendulum has only a finite time to stay near its classical equilibrium position before it falls. Surprisingly, this time for a macroscopic-size pendulum (say, a pen on its tip) is only a few seconds long. In this presentation we analyze the time scales of ``quantum mechanical instability'' of inverted pendula of various lengths to see how quantum mechanics interferes with the behavior of classically-macroscopic objects.

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Authors

  • Andrew Polemi

    Utah State University, Brigham Young University, University of Pennsylvania, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, High Altitude Observatory, University of Colorado at Boulder, Massachutes Institute of Technology, Utah Valley University, University of New Hampshire, Applied Physics Laboratory, Johns Hopkins University, University of Montana, Southwest Research Institute, University of Southern California, Lockheed Martin Advanced Technology Center, University of Chicago, Massachusetts Institute of Technology, SciPrint.org, Centre National de la Recherche Scientifique, Colorado State University, V. Alecsandri College, Bacau, Romania, Colorado School of Mines, National Renewable Energy Laboratory, Utah State University, Department of Physics, Brigham Young University, Provo, Huntsman Cancer Institute, Brigham Young University - Idaho, University of Arizona, Florida State University, Weber State University, Brigham Young University - Provo, New Mexico State University, Colorado State University, Fort Collins, CO 80523

  • Alexander Panin

    Utah Valley University