Eddington number
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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:

I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 protons in the universe and the same number of electrons.¹

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 1/137² - 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:

³

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

1. ^ Eddington (1939), lecture titled "The Philosophy of Physical Science."
2. ^ Eddington (1946)
3. ^ Mohr & Taylor (2002)

See 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.
• -------- & Frank J. Tipler (1986). The Anthropic Cosmological Principle. London: Oxford University Press. 
• Dingle, H. (1954). The Sources of Eddington's Philosophy. London: Cambridge University Press. 
• Arthur Eddington (1928). The Nature of the Physical World. London: Cambridge University Press. 
• -------- (1935). New Pathways in Science. London: Cambridge University Press. 
• -------- (1939). The Philosophy of Physical Science. London: Cambridge University Press. 
• -------- (1946). Fundamental Theory. London: Cambridge University Press. 
• Kilmister, C.W. & Tupper, B.O.J. (1962). Eddington's Statistical Theory. London: Oxford University Press. 
• Mohr, P.J. & Taylor, B.N. (January 2005). "CODATA recommended values of the fundamental physical constants: 2002". Reviews of Modern Physics 77: 1–107. doi:10.1103/RevModPhys.77.1. 
• Slater, N.B. (1957). Development and Meaning in Eddington's Fundamental Theory. London: Cambridge University Press. 
• Whittaker, E.T. (1951). Eddington's Principle in the Philosophy of Science. London: Cambridge University Press. 
• -------- (1958). From Euclid to Eddington. New York: Dover. 

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