The N-Stein Family

Abstract

The work of Newstein is now so familiar to us, thanks to Professor Stachel’s efforts, that it bears only the briefest recapitulation. Sometime after 1880 but before the advent of general relativity, Newstein brooded on the equality of inertial and gravitational mass. Through an ingenious thought experiment—the Newstein elevator—he hit upon the idea of an essential unity of gravitation and inertia. This was expressed in the indistinguishability of the effects of acceleration in a uniformly accelerated frame of reference from a homogeneous gravitational field in an inertial frame of reference. Now having to consider the behavior of the gravitational force as it is transformed from unaccelerated to accelerated frames of reference, Newstein found it no longer behaved like the familiar vector. Puzzled, he turned to his mathematician friend Weylmann, another neglected figure in history of mathematics. His extraordinary achievement, as revealed by Professor Stachel, was to formulate the notion of affine connection around 1880, decades before the much better known formulation of Levi-Civita of 1917. Weylmann recognized that the puzzling transformation behavior of gravitational force was simply that of the components of a four-dimensional affine connection.

With great pleasure, I join the contributors to this volume in honoring Professor Stachel and celebrating his many achievements. My debt to him is great. I learned the real craft of history of science at his elbow when he generously allowed me to visit the Einstein Papers Project in 1982 and 1983 in Princeton and my career owes a great deal to his generosity and kindness. We have all learned so much from Professor Stachel’s researches. However, when he revealed the hitherto unknown figure in history of physics, Newstein, in his (Stachel forthcoming) we may have learned somewhat more from him than even he intended, as this paper will demonstrate.