On Consistency Issue of the Definition of Mean Free Path on the Basis of Measure Theoretic Probability and Speed of Light Postulate of Relativity
Debashis Chatterjee · 2013
There are many essential as well as very basic derivations in physics which requires rigorous mathematical review and explanation and at the same time new theoretical foundation not only for mere sake of completeness, but for both aesthetic and practical need. One such topic in physics is Mean free path of kinetic theory of gases which has been addressed in this paper. The aim of this paper is to strengthen the concept of Mean free path by restating it in terms of Probability space and to use some tools of measure theory to show the consistency of the new definition with the old one and also to answer the basic question about whether it is well defined. It will also be shown here that the truth of speed of light postulate of special theory of relativity brings about the consistency of the definition of mean free path after Probability space is taken into account.