ESHS/HSS Annual Meeting

Similitude and Scalar Gravity: Tolman's Principle and Nordström's Theory

• In Event: Shifting Perspectives on Histories of Gravity and Mass 1

English Abstract

Published just prior to Einstein's perfected field equations in an internationally obscure Finnish journal, Gunnar Nordström's "R. C. Tolmans 'Prinzip der Ähnlichkeit und die Gravitation" is probably his most forgotten work. In this work, Nordström argues that his scalar theory of gravitation of 1913 (suitably adapted)---the first consistent theory of relativistic gravitation, promoted by none other than Einstein himself---was the only relativistic theory of gravity consistent with Tolman's so-called principle of similitude. Tolman, one of the earliest American relativists, inspired by Einstein's use of the principle of relativity, attempted to constrain the laws of physics by way of his principle of similitude, a relativity of size principle. This principle generated a large debate on the foundations of dimensional analysis, which has recently received renewed attention. Less remarked upon is the most consequential result of Tolman's principle: a constraint on future theories of gravity. As far as is known, only Nordström explicitly used this principle to discipline his theory of gravity. However, in correspondence with Ehrenfest regarding Nordström's use of Tolman's principle, Einstein breezily dismisses Tolman's principle as a special case of general covariance. Comparison of Einstein and Nordström's varying conceptions of Tolman's principle will shed some light on the relationship between the development of their two theories of gravity and the role of principles in the formation of theories more generally.

Author

• Mahmoud Jalloh, Caltech