Errors and residuals in statistics: Difference between revisions

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{{About|astrophysics|the measure in cycling|Arthur_Eddington#Eddington_number_(cycling)}}
In [[astrophysics]], the '''Eddington number''', ''N''<sub>Edd</sub>, is the number of [[proton]]s in the [[observable universe]]. The name honors the [[United Kingdom|British]] astrophysicist [[Arthur Eddington]] who, in 1938, was the first to propose a calculation of ''N''<sub>Edd</sub>, 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''<sub>Edd</sub> = 136×2<sup>256</sup>, or about 1.57×10<sup>79</sup>. In the 1938 [[Tarner Lectures|Tarner Lecture]] at [[Trinity College, Cambridge]], Eddington averred that:


{{quotation |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 [[proton]]s in the universe and the same number of [[electron]]s.<ref>Eddington (1939), lecture titled "The Philosophy of Physical Science."</ref>}}
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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<ref>Eddington (1946)</ref> – a feat for which ''[[Punch (magazine)|Punch]]'' dubbed him "Sir Arthur Adding-One."
 
The most precise value of ''α'' obtained experimentally (as of 2012):<ref>
{{Cite journal
|author=Tatsumi Aoyama, Masashi Hayakawa, Toichiro Kinoshita, Makiko Nio
|year=2012
|title=Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant
|journal=[[Physical Review Letters]]
|volume=109
|issue=11 |page=111807
|doi=10.1103/PhysRevLett.109.111807
|url=http://link.aps.org/doi/10.1103/PhysRevLett.109.111807
|arxiv = 1205.5368v2 |bibcode = 2012PhRvL.109k1807A }}</ref>
: <math>\alpha^{-1} = 137.035\,999\,174(35).</math>
 
Hence no one maintains any longer that α is the [[unit fraction|reciprocal of an integer]]. Nor does anyone take seriously a mathematical connection between the value of α and ''N''<sub>Edd</sub>. [[Observable_universe#Matter_content|More defendable estimates]] of ''N''<sub>Edd</sub> point to a value of about 10<sup>80</sup>.{{Citation needed|date=February 2012}} These estimates assume that all matter can be taken to be [[hydrogen]], and require assumed values for the numbers and sizes of [[galaxie]]s and [[star]]s in the universe.
 
On possible roles for ''N''<sub>Edd</sub> in contemporary [[cosmology]], especially its connection with the [[Dirac large numbers hypothesis|large number coincidences]], see Barrow (2002) (easier) and Barrow and Tipler (1986: 224–31) (harder).
 
==Notes==
<!--See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
<references/>
 
==See also==
*[[Eddington–Dirac number]]
*[[Observable universe]]
*[[Arthur_Stanley_Eddington#Eddington_number_.28cycling.29|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.
*{{cite book | author=-------- & [[Frank J. Tipler]] | title=[[Anthropic Principle|The Anthropic Cosmological Principle]] | year=1986 | location=London | publisher=Oxford University Press}}
*{{cite book | author=Dingle, H. | year=1954 | title=The Sources of Eddington's Philosophy | location=London | publisher=Cambridge University Press }}
*{{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 }}
*{{cite book | author=-------- | title=Fundamental Theory | year=1946 | location=London | publisher=Cambridge University Press }}
*{{cite book | author=[[Clive W. Kilmister|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 phh | pages=1&ndash;107 | doi=10.1103/RevModPhys.77.1 | year=2005 | journal=Reviews of Modern Physics | volume=77 | bibcode=2005RvMP...77....1M}}
*{{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=[[E. T. Whittaker|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 }}
 
[[Category:Numerology]]
[[Category:Astrophysics]]

Latest revision as of 18:21, 12 January 2015


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