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.
In the late 1930s, the best experimental value of the fine-structure constant, α, was approximately 1/137. Eddington then argued, from aesthetic and numerological considerations, that α should be exactly 1/137.
Current estimates of NEdd 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]
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.[5]
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 NEdd.
On possible roles for NEdd in contemporary cosmology, especially its connection with large number coincidences, see (easier) and (harder).
See also
References
[6]
Bibliography
- Book: Barrow, J.D. . John D. Barrow . 2002 . The Constants of Nature from Alpha to Omega: The Numbers That Encode the Deepest Secrets of the Universe . registration . . 978-0-375-42221-8 .
- Book: Barrow . J.D. . John D. Barrow . Tipler . F.J. . Frank J. Tipler . The Anthropic Cosmological Principle . 1986 . London . Oxford University Press. Anthropic Principle .
- Book: Dingle, H. . 1954 . The Sources of Eddington's Philosophy . London . .
- Book: Arthur Eddington . The Nature of the Physical World . 1928 . London . Cambridge University Press . Arthur Eddington .
- Book: Arthur Eddington . New Pathways in Science . 1935 . London . Cambridge University Press .
- Book: Arthur Eddington . The Philosophy of Physical Science . 1939 . London . Cambridge University Press .
- Book: Arthur Eddington . Fundamental Theory . 1946 . London . Cambridge University Press .
- Book: Kilmister . C.W. . Clive W. Kilmister . Tupper . B.O.J. . 1962 . Eddington's Statistical Theory . London . Oxford University Press .
- Book: Slater, N.B. . 1957 . Development and Meaning in Eddington's Fundamental Theory . London . Cambridge University Press .
- Book: Whittaker, E.T. . E. T. Whittaker . 1951 . Eddington's Principle in the Philosophy of Science . Cambridge University Press . London .
- Book: Whittaker, E.T. . E. T. Whittaker. 1958 . From Euclid to Eddington . Dover . New York .
Notes and References
- Book: A. S. Eddington . 1956 . The World of Mathematics . The Constants of Nature . J. R. Newman . 2 . 1074–1093 . Simon & Schuster.
- Whittaker . Edmund . 1945 . Eddington's Theory of the Constants of Nature . The Mathematical Gazette . 29 . 286 . 137–144 . 10.2307/3609461 . 3609461 . 125122360.
- Web site: Notable Properties of Specific Numbers (page 19) at MROB.
- H. Kragh . 2003 . Magic Number: A Partial History of the Fine-Structure Constant . . 57 . 5 . 395–431 . 10.1007/s00407-002-0065-7 . 118031104.
- Eddington (1946)
- Book: Eddington, Arthur Stanley . Fundamental Theory . Cambridge University Press . 1946 . Cambridge.
