Scott Walter

Minkowski’s Modern World

The phenomenal response to Minkowski’s 1908 lecture in Cologne has tested the historian’s capacity for explanation on rational grounds. What was it about Minkowki’s lecture that so schocked the sensibilities of his public? In this essay, Minkowski’s spacetime theory is considered as a solution in search of a problem. After physicists rejected his four-dimensional formalism, Minkowski made a point in Cologne of challenging their most cherished beliefs, piling provocation upon provocation in an effort to stir them from their torpor, in pure modernist style.

The Historical Origins of Spacetime

The idea of spacetime investigated in this chapter, with a view toward understanding its immediate sources and development, is the one formulated and proposed by Hermann Minkowski in 1908. Until recently, the principle source used to form historical narratives of Minkowski’s discovery of spacetime has been Minkowski’s own discovery account, outlined in the lecture he delivered in Cologne, entitled Space and time [1]. Minkowski’s lecture is usually considered as a bona fide first-person narrative of lived events. According to this received view, spacetime was a natural outgrowth of Felix Klein’s successful project to promote the study of geometries via their characteristic groups of transformations. Or as Minkowski expressed the same basic thought himself, the theory of relativity discovered by physicists in 1905 could just as well have been proposed by some late-nineteenth-century mathematician, by simply reflecting upon the groups of transformations that left invariant the form of the equation of a propagating light wave. Minkowski’s publications and research notes provide a contrasting picture of the discovery of spacetime, in which group theory plays no direct part. In order to relate the steps of Minkowski’s discovery, we begin with an account of Poincare’s theory of gravitation, where Minkowski found some of the germs of spacetime. Poincare’s geometric interpretation of the Lorentz transformation is examined, along with his reasons for not pursuing a four-dimensional vector calculus. In the second section, Minkowski’s discovery and presentation of the notion of a world line in spacetime is presented. In the third and final section, Poincare’s and Minkowski’s diagrammatic interpretations of the Lorentz transformation are compared.