In astrophysics, the Eddington number, NEdd, is the number of protons in the observable universe. The name honors the British astrophysicist Arthur Eddington who, in 1938, was the first to propose a calculation of NEdd, and to explain why this number could be important for cosmology and the foundations of physics.
In the late 1930s, the best experimental value of the fine structure constant, α, was about 1/136. Eddington began by arguing, from aesthetic and numerological considerations, that α should be exactly 1/136. He then gave a "proof" that NEdd = 136×2256, or about 1.57×1079. In the 1938 Tarner Lecture 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 – a feat for which Punch dubbed him "Sir Arthur Adding-One."
The most precise value of α obtained experimentally (as of 2012):
Hence no one maintains any longer that α is the reciprocal of an integer. Nor does anyone take seriously a mathematical connection between the value of α and NEdd. More defendable 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 numbers and sizes of galaxies and stars in the universe.
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