In astrophysics, the Eddington number, NEdd, is the number of protons in the observable universe. The term is named for British astrophysicist Arthur Eddington, who in 1938 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. This led him in 1929 to conjecture that α was exactly 1/137. 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 1/136. Eddington then argued, from aesthetic and numerological considerations, that α should be exactly 1/136. He devised a "proof" that NEdd = 136 × 2256, or about 1.57×1079. Some estimates of NEdd point to a value of about 1080. 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.
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.
The most precise value of α (obtained experimentally in 2012) is:
Consequently, no one 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 and Tipler (1986: 224–31) (harder).
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