The New Mechanics of Myron Mathisson and Its Subsequent Development

Abstract

In 1937, Myron Mathisson published a paper which initiated a program of work in general relativity that continues to the present day. The aim of this program was to obtain equations that determine the trajectory of an extended body in an external gravitational field. In Newtonian mechanics this is a straightforward task, but in general relativity even giving a precise meaning to the problem is fraught with difficulties. These difficulties are analysed, Mathisson’s approach is described and it is shown how his approach has been carried to fulfillment by subsequent authors in the years since Mathisson’s untimely death in 1940. This work, however, completes only a part of the overall program. The work is placed in context in this overall program and the issues remaining for that program are identified.