Newtonian versus special-relativistic statistical predictions for low-speed scattering

• Published in: PloS one Vol. 7; no. 11; p. e48447
• Main Authors: Liang, Shiuan-Ni, Borondo, Florentino, Lan, Boon Leong
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 12.11.2012; Public Library of Science (PLoS)
• Subjects: Algorithms; Dwell time; Materials Science; Mathematics; Mechanics; Mechanics (physics); Models, Statistical; Motion; Nonlinear Dynamics; Physics; Relativism; Scattering; Standard deviation; Statistical prediction; Statistics; Theory of relativity; Selangor Malaysia; Malaysia
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0048447

The statistical predictions of Newtonian and special-relativistic mechanics, which are calculated from an initially Gaussian ensemble of trajectories, are compared for a low-speed scattering system. The comparisons are focused on the mean dwell time, transmission and reflection coefficients, and the position and momentum means and standard deviations. We find that the statistical predictions of the two theories do not always agree as conventionally expected. The predictions are close if the scattering is non-chaotic but they are radically different if the scattering is chaotic and the initial ensemble is well localized in phase space. Our result indicates that for low-speed chaotic scattering, special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to obtain empirically-correct statistical predictions from an initially well-localized Gaussian ensemble.