Eddington number
In astrophysics, the Eddington number, , is the number of protons in the observable universe. Eddington originally calculated it as about ; current estimates make it approximately . The term is named for British astrophysicist Arthur Eddington, who in 1940 was the first to propose a value of and to explain why this number might be important for physical cosmology and the foundations of physics. History. Eddington argued that the value of the fine-structure constant, "α", could be obtained by pure deduction. He related "α" to the Eddington number, which was his estimate of the number of protons in the  universe. This led him in 1929 to conjecture that "α" was exactly 1/136. He devised a "proof" that N = 136 × 2, or about 1.57×10. Other physicists did not adopt this conjecture and did not accept his argument. In the late 1930s, the best experimental value of the fine-structure constant, "α", was approximately 1/137. Eddington then argued, from aesthetic and numerological considerations, that "α" should be exactly 1/137. Current estimates of "N" point to a value of about . These estimates assume that all matter can be taken to be hydrogen and require assumed values for the number and  size of galaxies and stars in the universe. Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. During a course of lectures that he delivered in 1938 as Tarner Lecturer at Trinity College, Cambridge, Eddington averred that: This large number was soon named the "Eddington number". Shortly thereafter, improved measurements of "α" yielded values closer to 1/137, whereupon Eddington changed his "proof" to show that "α" had to be exactly 1/137. Recent theory. The most precise value of "α" (obtained experimentally in 2012) is: Consequently, no reliable source any longer maintains that  α is the reciprocal of an integer. Nor does anyone take seriously a mathematical relationship between "α" and "N". On possible roles for "N" in contemporary cosmology, especially its connection with large number coincidences, see Barrow (2002) (easier) and Barrow and Tipler (1986: 224–31) (harder).