A Unification and Relativistic Correction for Boltzmann’s Law

Authors: Lloyd G. Allred

Abstract:

The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (E=mc²), then a relativistic correction is not required.

Keywords: Cosmology, EMP, Euclidean, plasma physics, relativity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3298852

References:

[1] M. Moisan, J. Pelletier, Physics of Collisional Plasmas. 2006 Springer Dondrecht: Heidelberg New York London. p 387. Full text available free online.
[2] University Physics – With Modern Physics (12th Edition), H. D. Young, R. A. Freedman (Original edition), Addison-Wesley (Pearson International), 1st Edition: 1949, 12th Edition: 2008, ISBN 978-0-321-50130-1. Full text available free online.
[3] Maxwell, J. C. (1860 A): Illustrations of the dynamical theory of gases. Part I. On the motions and collisions of perfectly elastic spheres. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 4th Series, vol.19, pp.19-32. Full text available free online.
[4] M. Abramowitz and I. Stegun, Irena A. Handbook of mathematical functions with formulas, graphs, and mathematical tables. 1964, U.S. Department of Commerce, National Bureau of Standards, p. 927. Full text available free online.
[5] Zwillinger, Daniel; Kokoska, Stephen (2010). CRC Standard Probability and Statistics Tables and Formulae, 2010. CRC Press. p. 49. ISBN 978-1-58488-059-2. Full text available free online.
[6] R. Weast, M. Astle, W Beyer. CRC Handbook of Chemistry and Physics 1922. Chemical Rubber Publishing Co. p A-85. Full text available free online.