Eddington number

In astrophysics, the Eddington number, "N"_Edd, 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 "N"_Edd, 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 "N"_Edd = 136×2²⁵⁶, or about 1.57×10⁷⁹. In the 1938 Tarner Lecture at Trinity College, Cambridge, Eddington averred that:This large number was soon christened 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 [Eddington (1946)] - a feat for which "Punch" dubbed him "Sir Arthur Adding-One."

The best present-day estimate of the value of the fine structure constant is::$alpha\; =\; 7.297\; 352\; 568(24)\; imes\; 10^\{-3\}\; =\; frac\{1\}\{137.035\; 999\; 11(46)\}.$ [Mohr & Taylor (2002)] 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 "N"_Edd. More defendable estimates of "N"_Edd 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.

On possible roles for "N"_Edd in contemporary cosmology, especially its connection with the large number coincidences, see Barrow (2002) (easier) and Barrow and Tipler (1986: 224-31) (harder).

Notes

ee also

*Eddington-Dirac number
*Observable universe
* Eddington number (cycling)

Bibliography

*John D. Barrow, 2002. "The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe". Pantheon Books. ISBN 0-375-42221-8.
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*cite book | author=Arthur Eddington | title=The Nature of the Physical World | year=1928 | location=London | publisher=Cambridge University Press
*cite book | author=-------- | title=New Pathways in Science | year=1935 | location=London | publisher=Cambridge University Press
*cite book | author=-------- | title=The Philosophy of Physical Science | year=1939 | location=London | publisher=Cambridge University Press
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*cite book | author=Kilmister, C.W. & Tupper, B.O.J. | year=1962 | title=Eddington's Statistical Theory | location=London | publisher=Oxford University Press
*cite journal | author=Mohr, P.J. & Taylor, B.N. | title=CODATA recommended values of the fundamental physical constants: 2002 | journal=Reviews of Modern Physics | month=January | year=2005 | volume=77 | pages=1–107 | doi=10.1103/RevModPhys.77.1
*cite book | author=Slater, N.B. | year=1957 | title=Development and Meaning in Eddington's Fundamental Theory | location=London | publisher=Cambridge University Press
*cite book | author=Whittaker, E.T. | year=1951 | title=Eddington's Principle in the Philosophy of Science | publisher=Cambridge University Press | location=London
*cite book | author=-------- | year=1958 | title=From Euclid to Eddington | publisher=Dover | location=New York