Tatiana Ehrenfest-Afanassjewa’s Contributions to Dimensional Analysis

Abstract

Tatiana Ehrenfest-Afanassjewa was an important physicist, mathematician, and educator in 20th century Europe. While some of her work has recently undergone reevaluation, little has been said regarding her groundbreaking work on dimensional analysis. This, in part, reflects an unfortunate dismissal of her interventions in such foundational debates by her contemporaries. In spite of this, her work on the generalized theory of homogeneous equations provides a mathematically sound foundation for dimensional analysis and has found some appreciation and development. It remains to provide a historical account of Ehrenfest-Afanassjewa's use of the theory of homogeneous functions to ground (and limit) dimensional analysis. We take as a central focus Ehrenfest-Afanassjewa's contributions to a debate on the foundations of dimensional analysis started by physicist Richard Tolman in 1914. I go on to suggest an interpretation of the more thoroughgoing intervention Ehrenfest-Afanassjewa makes in 1926 based on this earlier context, especially her limited rehabilitation of a "theory of similitude" in contradistinction to dimensional analysis. It is shown that Ehrenfest-Afanassjewa has made foundational contributions to the mathematical foundations and methodology of dimensional analysis, our conception of the relation between constants and laws, and our understanding of the quantitative nature of physics, which remain of value