(1) The cosmological constants. Offprint from Nature 139. Kramers's copy. (2) A new basis for cosmology. Offprint from Proceedings of the Royal Society of London, series A, 165

1937. Dirac, Paul A. M. (1902-84). (1) The cosmological constants. Offprint from Nature 139 (1937). Single sheet. [2]pp. 215 x 134 mm. Corners a bit creased, light toning but very good. From the library of H. A. Kramers (1894-1952), with his stamp on the first page. (2) A new basis for cosmology. Offprint from Proceedings of the Royal Society of London, series A, 165 (1938). 199-208pp. 256 x 173 mm. Original printed wrappers. Faint creasing, light marginal toning but very good. Together 2 items. First Edition, Offprint Issue. Dirac’s brief 1937 paper (no. [1]) marks the announcement of his Large Number Hypothesis (LNH) relating ratios of size scales (truncated) in the Universe to those of force scales—in other words, positing a relationship between cosmic and atomic constants based on the then-new idea of an expanding universe. The following year Dirac published an expanded version of the LNH in “A new basis for cosmology” (no. [2]). Building on Arthur Eddington’s belief in “a grand unification of atomic physics and cosmology,” Dirac “focused on dimensionless numbers built from the fundamental constants of both atomic and cosmic phenomena; and he observed that there was a cluster of numbers around 1039, including the age of the universe in atomic time units and the ratio of electric forces to gravitational ones inside atoms. In 1937 he proposed the ‘large-number hypothesis,’ according to which numbers in the same cluster should be simply related. Consequently, the gravitation constant had to vary in time . . . contrary to general relativity” (Dictionary of Scientific Biography). “Dirac claimed that the regularity exhibited by these large dimensionless numbers was not purely fortuitous . . . [regarding] them to be contingent quantities, dependent on the history of the universe . . . Later, Dirac preferred to call this assumption the Large Number Hypothesis (LNH in what follows). In 1938 he named it the Fundamental Principle, emphasizing that it should be understood as a postulate of correlation between any two of the large dimensionless numbers, whether or not 0 [the age of the universe expressed in atomic units of time] was involved: ‘Any two of the very large dimensionless numbers occurring in Nature are connected by a simple mathematical relation, in which the coefficients are of the order of magnitude unity.’ Dirac thus accounted for the vastness of the ratio between electromagnetic and gravitational forces as a consequence of the age of our present universe” (Kragh, Dirac: A Scientific Biography, p. 228). Although Dirac’s cosmological theory was not well received on its publication, his Large Number Hypothesis has continued to stimulate scientific thought, inspiring—among other things—the idea of the “fine-tuned” universe. . (Inventory #: 50922)