Whitehead's Philosophy of Mathematics and Relativity

In the early 1920s the British mathematician and philosopher Alfred North Whitehead (1861-1941) criticized Albert Einstein's general theory of relativity. Whitehead rejected Einstein's original interpretation of gravitation as published in the Annalen der Physik in 1916. In 1922 Whitehead bundled the majority of his lectures on an alternative and empirically almost equivalent theory in a book entitled The Principle of Relativity with Applications to Physical Science. This 1922 book and the Whitehead-Einstein-controversy concerning the relativistic theory of gravity was the starting point of the doctoral research that culminated in Whitehead's Philosophy of Mathematics and Relativity, and the ambitious aim of its author is to put an end to the ruling ignorance with regard to the philosophical, mathematical and scientific context from which Whitehead's critique and alternative theory emerged. At least three lessons can be retained from this doctoral research: (1) Whitehead's critique of Einstein is above all a philosophical, and no scientific critique. Whitehead did not want to surpass Einstein's general theory of relativity with respect to mathematical formulae and empirical success; his aim was to harmonize its interpretation with common sense. Einstein denies in theory what is inevitably presupposed by the commonsense practices of solving his equation and of measuring his predictions, whereas Whitehead's interpretation is coherent with the inevitable presupposition that the structure of space-time is uniform and independent from the field of gravitation. (2) Whitehead's distinction between Einstein's formulae and Einstein's interpretation, a distinction that frees the road that leads to alternative interpretations, was inspired by Whitehead's former work as a mathematician, which was focused on the emancipation of pure mathematics. From a purely mathematical point of view spatial intuition is logically irrelevant. Hence, Whitehead argued against the necessity of a spatio-temporal interpretation of the pure geometrical structure of Einstein's general theory of relativity. Freed from this necessity, Whitehead proposed a reinterpretation of Einstein's theory in terms of a physical quantity, the impetus of gravity. (3) Whitehead's reinterpretation and the ensuing reformulation of Einstein' theory of gravity should not only be studied in the light of his philosophical and mathematical work, but should also be put in the relevant scientific context. Without taking into account both Whitehead's training as a mathematical physicist in Cambridge, and the broader British reception history of Einstein's physics of relativity, Whitehead's alternative theory of gravity appears to be a creation out of nothing, and remains just as incomprehensible. Our understanding of his theory can only be furthered if we highlight the role of his training by Edward Routh and William Niven, his acquaintance with Hermann Minkowski's and Willem de Sitter's work via Ludwik Silberstein, Ebenezer Cunningham, and Arthur Eddington, and his awareness of Silberstein's earlier, unsuccessful attempt to undo Einstein's identification of gravity and space-time. Of course, the appropriate contextualization of Whitehead's theory does not imply its empirical superiority, and in 2008 Gary Gibbons and Clifford Will argued convincingly that it is not. Nonetheless, Whitehead's efforts in the domain of general relativity - together with comparable efforts by Richard Feynman in the same domain and by Ilya Prigogine in the domain of thermodynamics - can still inspire contemporary physicists and philosophers to seek interpretative coherence between scientific theory and com