Kuhn Losses Regained: Van Vleck from Spectra to Susceptibilities

TL;DR

This paper traces Van Vleck's work from 1926 to 1932, illustrating how quantum mechanics corrected classical predictions for electric susceptibilities, exemplifying a Kuhn loss that was regained, and discussing its pedagogical implications.

Contribution

It demonstrates the continuity of formalism from old quantum theory to quantum mechanics and shows how Van Vleck used the regained Kuhn loss pedagogically in his 1932 book.

Findings

Quantum mechanics restores the classical value of 1/3 for susceptibility.

Van Vleck's 1932 book effectively uses the Kuhn loss for teaching.

The historical analysis clarifies the evolution of susceptibility theory.

Abstract

We follow the trajectory of John H. Van Vleck from his 1926 Bulletin for the National Research Council (NRC) on the old quantum theory to his 1932 book, The Theory of Electric and Magnetic Susceptibilities. We highlight the continuity of formalism and technique in the transition from dealing with spectra in the old quantum theory to dealing with susceptibilities in the new quantum mechanics. Our main focus is on the checkered history of a numerical factor in the Langevin-Debye formula for the electric susceptibility of gases. Classical theory predicts that this factor is equal to 1/3. The old quantum theory predicted values up to 14 times higher. Van Vleck showed that quantum mechanics does away with this "wonderful nonsense" (as Van Vleck called it) and restores the classical value 1/3. The Langevin-Debye formula thus provides an instructive example of a Kuhn loss in one paradigm shift that was regained in the next. In accordance with Kuhn's expectation that textbooks sweep Kuhn losses under the rug, Van Vleck did not mention this particular Kuhn loss anywhere in his 1926 NRC Bulletin (though he prominently did flag a Kuhn loss in dispersion theory that had recently been regained). Contrary to Kuhn's expectations, however, he put the regained Kuhn loss in susceptibility theory to good pedagogical use in his 1932 book. Kuhn claimed that textbooks must suppress, truncate, and/or distort the prehistory of their subject matter if they are to inculcate the exemplars of the new paradigm in their readers. This claim is not borne out in this case. Because of the continuity of formalism and technique that we draw attention to that Van Vleck could achieve his pedagogical objectives in his 1932 book even though he devoted about a third of it to the treatment of susceptibilities in classical theory and the old quantum theory in a way that matches the historical record reasonably well.