In astrophysics, the Eddington number, NEdd, is the number of protons in the observable universe. Eddington originally calculated it as about 1.57×1079; current estimates make it approximately 1080.
The term is named for British astrophysicist Arthur Eddington, who in 1940 was the first to propose a value of NEdd and to explain why this number might be important for physical cosmology and the foundations of physics.
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. [1] This led him in 1929 to conjecture that α was exactly 1/136. [2] He devised a "proof" that NEdd = 136 × 2256, or about 1.57×1079. Other physicists did not adopt this conjecture and did not accept his argument.[ citation needed]
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 NEdd point to a value of about 1080. [3] 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. [4]
During a course of lectures that he delivered in 1938 as Tarner Lecturer at Trinity College, Cambridge, Eddington averred that:
I believe there are 15747724136275002577605653961181555468044717914527116709366231425076185631031296 protons in the universe and the same number of electrons. [5]
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. [6]
As of 2012, the most precisely known value of α−1 was 137.035999174(35). [7]
Consequently, no reliable source maintains any longer that α is the reciprocal of an integer. Nor does anyone take seriously a mathematical relationship between α and NEdd.
On possible roles for NEdd in contemporary cosmology, especially its connection with large number coincidences, see Barrow (2002) (easier) and Barrow & Tipler (1986, pp. 224–231) (harder).