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Statistical Predictions for the Dynamics of a Low-Speed System: Newtonian versus Special-Relativistic Mechanics

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  • Shiuan-Ni Liang
  • Boon Leong Lan

Abstract

The Newtonian and special-relativistic statistical predictions for the mean, standard deviation and probability density function of the position and momentum are compared for the periodically-delta-kicked particle at low speed. Contrary to expectation, we find that the statistical predictions, which are calculated from the same parameters and initial Gaussian ensemble of trajectories, do not always agree if the initial ensemble is sufficiently well-localized in phase space. Moreover, the breakdown of agreement is very fast if the trajectories in the ensemble are chaotic, but very slow if the trajectories in the ensemble are non-chaotic. The breakdown of agreement implies that special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to correctly calculate the statistical predictions for the dynamics of a low-speed system.

Suggested Citation

  • Shiuan-Ni Liang & Boon Leong Lan, 2012. "Statistical Predictions for the Dynamics of a Low-Speed System: Newtonian versus Special-Relativistic Mechanics," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-12, May.
    • Handle: RePEc:plo:pone00:0036430
    DOI: 10.1371/journal.pone.0036430
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    References listed on IDEAS

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    1. Lan, Boon Leong, 2009. "Implications of the disagreement between newtonian and relativistic low-speed trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 534-537.
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