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Author's self-defense

Why did I publish these lectures? The main reason was that I was not entirely happy with many of the texts which are already available, that is, the available texts didn't treat the topics I wanted to treat in the order which I wanted to use. First, most available books assume the primacy of quantum mechanics and the microcanonical ensemble over classical mechanics and the canonical ensemble. The superiority of quantum over classical mechanics, as a calculational tool on the submolecular level, is beyond dispute. In preferring to begin with the canonical rather than the microcanonical ensemble I follow Gibbs rather than Tolman. (Tolman says that his text is simply an expansion upon Gibbs' work, but this statement is difficult to square with his treatment of the basic ensembles, of which more below). Second, I wanted to say something of non-thermodynamic statistical mechanics, including proper treatments of the various ensembles and of the Liouville theorem, a matter handled most clearly by Gibbs. I also wanted to treat modern ideas, such as correlation functions and the Mori formalism, in a way which helps students to learn how to use these concepts. This final step is more easily said than done.

A few comments are in order:

1) The entire volume is based on the first few lectures. Everything else -- the remaining lectures - is only an illumination, showing what the early lectures mean.

2) The basic idea -- ``the fundamental equation of statistical mechanics''-- is simple but at first slightly obscure. After a few examples and some further discussion, the fog may tend to lift a trifle.

3) In my opinion, qualitative discussions enhance quantitative discussions, but are not a substitute for them. The physics is in the calculation, not in the words which can be used to describe the result. Words can be part of a proof, but are more often a mnemonic for the real arguments. The logic of a verbal handwaving argument is often not affected, except with respect to its rectitude, by replacing ``>'' with ``<'' at key stages. A famous example of an argument which sounds right, but in which ``>'' and ``<'' have been interchanged, is the usual schoolbook explanation as to why low- frequency sound waves involve the adiabatic rather than the isothermal compressibility. For many years the oft-quoted explanation, if analyzed, actually proved the wrong result. [See E. Condon [10] for the details.]

4) The objective of science is to explain all physical phenomena in a consistent axiomatic way. Correct natural laws are always correct. Momentum conservation cannot be suspended just because it is convenient to do so. Approximations have mathematical limits on their validity, and can only be used consistently within those limits.


next up previous
Next: Other readings Up: Chapter 1 Previous: Basic principles

Nicholas V Sushkin
Sat Jun 29 21:39:26 EDT 1996