D O C . 1 3 1 D I S C U S S I O N O N R E L A T I V I T Y 2 5 1 Published in Société française de Philosophie. Bulletin 22 (1922): 91–113. Dated 6 April 1922, pub- lished July 1922. [1]Xavier Léon. [2]Pierre Boutroux (1880–1922) was a French mathematician. [3]Winter 1911. [4]Langevin 1911a. The 4th International Congress on Philosophy took place on 6–11 April 1911. [5]Langevin 1911b. The lecture was delivered on 19 October 1911. [6]A meeting on philosophy was held at the Sorbonne on 26–28 December 1921 with American, Belgian, English, French, and Italian participants. Einstein was invited by M. P. Drosue on 30 Novem- ber 1921 (Vol. 12, Calendar). He declined Paul Painlevé’s invitation on 7 December 1921 (Vol. 12, Doc. 314). In its special session on “The More Recent Forms of the Theory of Relativity,” Dorothy Wrinch (1884–1976), lecturer in mathematics at University College, London, gave the introductory lecture. It was followed by a debate between Paul Langevin, adherent of the theory, and its opponent, Paul Painlevé. Federigo Enriques, Professor of Projective and Descriptive Geometry at the University of Bologna, did not participate in the debate. He delivered a lecture in another session on Kant and the historical development of contemporary science. For a review, see Bush 1922. [7]Poincaré 1901. [8]Einstein 1905r. [9]August Comte. [10]Jacques Hadamard. [11]In Doc. 120, Einstein proposed an open discussion with scholars rather than a formal lecture and referred to his meager command of French. Accordingly, after his lecture at the Collège de France, delivered on March 31 to a general audience, a discussion was arranged that consisted of three sessions. During the second session, on 5 April, Hadamard proposed a concrete example of a possible internal contradiction within general relativity. Specifically, he raised the question whether there could exist in nature sufficiently massive stars such that the radial coordinate at which a “singularity” existed (the Schwarzschild radius, now called the event horizon of a black hole) would actually lie outside the volume of the star such that the infinite term in the metric equation would apply in the physical world. “If … in fact this term could be cancelled somewhere in the universe,” Einstein replied, “this would constitute a terrible disaster for the theory and it would be very difficult a priori to say what would happen physically, because then the formula ceases to be applicable” (“Si … effectivement ce term pouvait quelque part dans l'Univers s’annuler, alors ce serait un malheur inimaginable pour la théorie et il est très difficile de dire a priori ce qui arriverait physiquement, car alors la formule cesse d’être applicable”). Einstein jokingly referred to the possibility that the singularity could manifest it- self in the real world as the “Hadamard catastrophe” (Nordmann 1922b, p. 156). Charles Nordmann observed that Eddington’s theory of stellar structure, as well as observation, seemed to suggest that stars of sufficient mass did not exist. Einstein replied that he would prefer that his theory not depend on any particular external model of the behavior of matter in order to escape from “the misfortune caused to the theory by the Hadamard catastrophe” (“au malheur que constituerait pour la théorie la catastrophe Hadamard” Nordmann 1922b, p. 155). At the third session of the discussion, on 7 April, Einstein returned with a calculation showing that, before a star could accumulate sufficient mass to be entirely contained within its own Schwarzschild radius, the pressure at the center of the star would become infinite. Under such conditions, clocks would not run and time would stop, preventing the Hadamard catastrophe from ever being realized. He stated that “the energy of matter is transformed into the energy of space” (“l’énergie de matière se transforme en énergie d’espace,” concluding by echoing Newton: “That’s all I can say, since I do not wish to make hypotheses” (“c’est tout ce que je peux dire, … car des hypothèses je ne veux pas en faire”). Hadamard declared himself satisfied that the catastrophe could not occur in nature (Nordmann 1922b, p. 156). [12]Elie Cartan (1869–1951) was Professor of Mathematics at the Sorbonne. [13]Langevin 1911a. [14]Paul Lévy (1886–1971) was Professor of Analysis at the École Polytechnique.