Mathematics  Physics

Newtonian versus SpecialRelativistic Statistical Predictions for LowSpeed Scattering
Published:
Monday, November 12, 2012
Author:
ShiuanNi Liang et al.
by ShiuanNi Liang, Florentino Borondo, Boon Leong Lan
The statistical predictions of Newtonian and specialrelativistic mechanics, which are calculated from an initially Gaussian ensemble of trajectories, are compared for a lowspeed 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 nonchaotic 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 lowspeed chaotic scattering, specialrelativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to obtain empiricallycorrect statistical predictions from an initially welllocalized Gaussian ensemble.
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