Eddington number explained

In astrophysics, the Eddington number,, is the number of protons in the observable universe. Eddington originally calculated it as about ; current estimates make it approximately .

The term is named for British astrophysicist Arthur Eddington, who in 1940 was the first to propose a value of and to explain why this number might be important for physical cosmology and the foundations of physics.

History

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, or about . Other physicists did not adopt this conjecture and did not accept his argument.

During a course of lectures that he delivered in 1938 as Tarner Lecturer 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.

Current estimates of N_Edd point to a value of about .^[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]

Recent theory

The modern CODATA recommended value of α is

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 N_Edd.

On possible roles for N_Edd in contemporary cosmology, especially its connection with large number coincidences, see (easier) and (harder).

See also

• Eddington–Dirac number
• The Sand Reckoner
• Universe

Bibliography

• Book: Barrow, John D. . John D. Barrow . The Constants of Nature from Alpha to Omega: The Numbers That Encode the Deepest Secrets of the Universe . Pantheon Books . 2002 . 978-0-375-42221-8 . New York . registration.
• Book: Barrow . John D. . John D. Barrow . The anthropic cosmological principle . Anthropic Principle . Tipler . Frank J. . Frank J. Tipler . . 1986 . 978-0-19-851949-2 . Oxford.
• Book: Dingle, Herbert . Herbert Dingle . The Sources of Eddington's Philosophy . . 1954 . London . 531389.
• Book: Eddington, Arthur Stanley . Arthur Eddington . The Nature of the Physical World . . 1928 . London . 645108.
• Book: Eddington, Arthur Stanley . New Pathways in Science . . 1935 . London . 522390.
• Book: Eddington, Arthur Stanley . The Philosophy of Physical Science . . 1939 . London . 669925.
• Book: Eddington, Arthur Stanley . Arthur Eddington . Fundamental Theory . . 1946 . Whittaker . E. T. . E. T. Whittaker . Cambridge . 2484474.
• Book: Kilmister . C.W. . Clive W. Kilmister . Eddington's Statistical Theory . Tupper . B.O.J. . . 1962 . London . 1294788.
• Book: Slater, Noel Bryan . Noel Slater . Development and Meaning in Eddington's Fundamental Theory . . 1957 . London . 843162.
• Book: Whittaker, E. T. . E. T. Whittaker . Eddington's Principle in the Philosophy of Science . . 1951 . London . 1453203.
• Book: Whittaker, E. T. . E. T. Whittaker . From Euclid to Eddington . . 1958 . New York . 8119156.

Notes and References

1. Book: Eddington, Arthur Stanley . The world of mathematics . . 2000 . 978-0-486-41150-7 . Newman . James R. . James R. Newman . 2 . Mineola, New York . 1074–1093 . The Constants of Nature . 1956.
2. Whittaker . Edmund . E. T. Whittaker . October 1945 . Eddington's Theory of the Constants of Nature . . 29 . 286 . 137–144 . 10.2307/3609461 . 0025-5572 . 3609461 . 125122360.
3. Web site: Munafo . Robert . Notable Properties of Specific Numbers . MROB . 19.
4. Kragh . Helge . Helge Kragh . July 2003 . Magic Number: A Partial History of the Fine-Structure Constant . . 57 . 5 . 395–431 . 10.1007/s00407-002-0065-7 . 0003-9519 . 118031104.