Eddington number
In astrophysics, the Eddington number, NEdd, is the number of protons in the observable universe. Eddington originally calculated it as about 1.57×1079; current estimates make it approximately 1080.
The term is named for British astrophysicist Arthur Eddington, who in 1940 was the first to propose a value of NEdd and to explain why this number might be important for physical cosmology and the foundations of physics.
History
[edit]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 NEdd = 136 × 2256, or about 1.57×1079. Other physicists did not adopt this conjecture and did not accept his argument.[citation needed]
During a course of lectures that he delivered in 1938 as Tarner Lecturer at Trinity College, Cambridge, Eddington averred that:
I believe there are 15747724136275002577605653961181555468044717914527116709366231425076185631031296 protons in the universe and the same number of electrons.[3]
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.[4]
Current estimates of NEdd point to a value of about 1080.[5] 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.[6]
Recent theory
[edit]The modern CODATA recommended value of α−1 is 137.035999177(21).[7]
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.[citation needed]
On possible roles for NEdd in contemporary cosmology, especially its connection with large number coincidences, see Barrow (2002) (easier) and Barrow & Tipler (1986, pp. 224–231) (harder).
See also
[edit]References
[edit]- ^ Eddington, Arthur Stanley (2000) [1956]. "The Constants of Nature". In Newman, James R. (ed.). The world of mathematics. Vol. 2. Mineola, New York: Dover Publications. pp. 1074–1093. ISBN 978-0-486-41150-7.
- ^ Whittaker, Edmund (October 1945). "Eddington's Theory of the Constants of Nature". The Mathematical Gazette. 29 (286): 137–144. doi:10.2307/3609461. ISSN 0025-5572. JSTOR 3609461. S2CID 125122360.
- ^ Eddington 1939, lecture titled "The Philosophy of Physical Science". The sentence appears in Chapter XI, "The Physical Universe". Eddington assumes that neutrons are composed of protons and electrons, and his number includes those as well.
- ^ Eddington 1946
- ^ Munafo, Robert. "Notable Properties of Specific Numbers". MROB. p. 19.
- ^ Kragh, Helge (July 2003). "Magic Number: A Partial History of the Fine-Structure Constant". Archive for History of Exact Sciences. 57 (5): 395–431. doi:10.1007/s00407-002-0065-7. ISSN 0003-9519. S2CID 118031104.
- ^ "2022 CODATA Value: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
Bibliography
[edit]- Barrow, John D. (2002). The Constants of Nature from Alpha to Omega: The Numbers That Encode the Deepest Secrets of the Universe. New York: Pantheon Books. ISBN 978-0-375-42221-8.
- Barrow, John D.; Tipler, Frank J. (1986). The anthropic cosmological principle. Oxford: Oxford University Press. ISBN 978-0-19-851949-2.
- Dingle, Herbert (1954). The Sources of Eddington's Philosophy. London: Cambridge University Press. OCLC 531389.
- Eddington, Arthur Stanley (1928). The Nature of the Physical World. London: Cambridge University Press. OCLC 645108.
- Eddington, Arthur Stanley (1935). New Pathways in Science. London: Cambridge University Press. OCLC 522390.
- Eddington, Arthur Stanley (1939). The Philosophy of Physical Science. London: Cambridge University Press. OCLC 669925.
- Eddington, Arthur Stanley (1946). Whittaker, E. T. (ed.). Fundamental Theory. Cambridge: Cambridge University Press. OCLC 2484474.
- Kilmister, C.W.; Tupper, B.O.J. (1962). Eddington's Statistical Theory. London: Oxford University Press. OCLC 1294788.
- Slater, Noel Bryan (1957). Development and Meaning in Eddington's Fundamental Theory. London: Cambridge University Press. OCLC 843162.
- Whittaker, E. T. (1951). Eddington's Principle in the Philosophy of Science. London: Cambridge University Press. OCLC 1453203.
- Whittaker, E. T. (1958). From Euclid to Eddington. New York: Dover. OCLC 8119156.