Putting Whitehead's theory of gravitation in its historical context (Q2910360)

Empirical tests justify to favor Einstein's general-relativistic theory of gravitation to its alternatives. Nevertheless, it is interesting to consider alternative approaches to a relativistic theory of gravitation since this makes the genuine content of general relativity more transparent and it helps to better judge the quality of its empirical basis. In this context, it is also clarifying to reveal the physical motivation and the historical circumstances that led and lead to such alternatives. In particular, this is also true for Whitehead's reformulation of general relativity.NEWLINENEWLINEThe author of the present paper puts Whitehead's theory in its historical context. First, he shows that, reading the special-relativistic writings of Wilson and Lewis, Silberstein, and Cunningham and discussing the matter with those authors, Whitehead was attracted by special relativity because of its Minkowskian unification of space and time, with a mathematics developed to formulate physical laws against this space-time background, and with the accordantly reformulated electromagnetic worldview. This is followed by a chapter devoted to Whitehead's search for a special-relativistic theory of gravitation. This endeavor was strongly inspired by Minkowski's attempt to bring gravitation in accordance with the relativity principle. The author reports on the works of Poincaré, de Sitter and again Wilson and Lewis, Silberstein, and Cunningham, who intended to express the gravitational force and potential analogues to the formulae expressing the corresponding electromagnetic quantities in the 4-tensor calculus, and he describes Whitehead's and other authors' frustration coming from that none of these attempts was satisfactory. Only in 1915, Einstein's theory of general relativity provided an empirically adequate relativistic treatment of gravitation, about which Whitehead first learned in September 1916. What follows is a report on Whitehead's study of general relativity, where the great meaning of the writings and other pro-general-relativity activities by Eddington and de Sitter for Whitehead's study is emphasized. Further, one finds an explanation of the seemingly surprising fact that Whitehead's first book on relativity, his 1919 ``Enquiry Concerning the Principles of Natural Knowledge'' [Cambridge: Cambridge University Press (1919; JFM 47.0049.02)], shows no trace of any Eddington or de Sitter impact. It is argued that this is caused by Whitehead's philosophical intention to avoid a bifurcation into the mathematical world and our day-to-day experience. Due to this intention, Whitehead (again strongly influenced by Silberstein) tried to show that the universe is Minkowskian and hence, as he believed, at one with our common experience. Therefore, he did not follow Einstein's insights, but separated by his interpretation of general relativity what Einstein had unified, space-time geometry and physics. This attitude implied the challenge to offer an alternative theory of gravitation. First time he presented this alternative in 1920 and, in a more elaborated version, 1922 in the book ``The Principle of Relativity''. The present paper ends with a brief outline of Whitehead's theory.