Mahmoud Jalloh, Caltech

Title: Tatiana Ehrenfest-Afanassjewa's Extension of the Erlanger Program to Dimensional Analysis and its Metaphysical Consequences

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. However, her work on the generalized theory of homogeneous equations provides a mathematically sound foundation for dimensional analysis and has found some appreciation and development. With it, Ehrenfest-Afanassjewa provides the first group-theoretic grounds for dimensional analysis. This, I argue, is a notable extension of Felix Klein's Erlanger Program into physics, befitting her Göttingen training. Providing such foundations to dimensional analysis was not only a mathematical advance but was also aimed at undercutting a metaphysically realist conception of dimensions. Ehrenfest-Afanassjewa showed rigorously for the first time that dimensional systems inherit some of the conventionality of unit systems. This metaphysical critique extends to another controversy of her times and ours: the role of the fundamental constants in physics. Ultimately, her stance towards dimensional analysis may be compared to Kant's stance towards metaphysics: providing rigorous foundations and critically determining limits.