Eddington number

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.{{Cite book

|last=Eddington |first=Arthur Stanley

|url=https://books.google.com/books?id=se5iE4DMPioC

|title=The world of mathematics

|publisher=Dover Publications

|year=2000

|isbn=978-0-486-41150-7

|editor-last=Newman |editor-first=James R. |editor-link=James R. Newman

|volume=2

|location=Mineola, New York

|pages=1074–1093

|chapter=The Constants of Nature

|orig-date=1956

}} This led him in 1929 to conjecture that α was exactly 1/136.{{Cite journal

|last=Whittaker |first=Edmund |author-link=E. T. Whittaker

|date=October 1945

|title=Eddington's Theory of the Constants of Nature

|journal=The Mathematical Gazette

|volume=29 |issue=286 |pages=137–144

|doi=10.2307/3609461

|issn=0025-5572

|jstor=3609461

|s2cid=125122360

}} He devised a "proof" that {{nowrap|1=N_Edd = 136 × 2²⁵⁶}}, or about {{val|1.57|e=79}}. Other physicists did not adopt this conjecture and did not accept his argument. It even led to a major journal publishing a joke article making fun of the idea.{{cite web |last1=Appell |first1=David |title=Quark Soup |date=6 July 2012 |url=https://davidappell.blogspot.com/2012/07/making-fun-of-arthur-eddington.html}}

During a course of lectures that he delivered in 1938 as Tarner Lecturer at Trinity College, Cambridge, Eddington averred that:

{{quote |I believe there are {{gaps|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.{{harvnb|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.}}

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.{{harvnb|Eddington|1946}}

Current estimates of N_Edd point to a value of about {{val|e=80}}.{{Cite web

|last=Munafo |first=Robert

|title=Notable Properties of Specific Numbers

|url=http://mrob.com/pub/math/numbers-19.html

|website=MROB

|page=19

}} 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.{{Cite journal

|last=Kragh |first=Helge |author-link=Helge Kragh

|date=July 2003

|title=Magic Number: A Partial History of the Fine-Structure Constant

|journal=Archive for History of Exact Sciences

|volume=57 |issue=5 |pages=395–431

|doi=10.1007/s00407-002-0065-7

|issn=0003-9519

|s2cid=118031104

}}

The modern CODATA recommended value of α{{sup|−1}} is {{physconst|alphainv|after=.}}

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.{{cn|date=December 2024}}

On possible roles for N_Edd in contemporary cosmology, especially its connection with large number coincidences, see {{harvtxt|Barrow|2002}} (easier) and {{harvtxt|Barrow|Tipler|1986|pp=224–231}} (harder).

• Eddington–Dirac number
• The Sand Reckoner
• Universe

{{reflist|32em}}

• {{Cite book |last=Barrow |first=John D. |author-link=John D. Barrow |url=https://archive.org/details/constantsofnatur0000barr |title=The Constants of Nature from Alpha to Omega: The Numbers That Encode the Deepest Secrets of the Universe |publisher=Pantheon Books |year=2002 |isbn=978-0-375-42221-8 |location=New York |url-access=registration}}
• {{Cite book |last1=Barrow |first1=John D. |author-link1=John D. Barrow |title=The anthropic cosmological principle |title-link=Anthropic Principle |last2=Tipler |first2=Frank J. |author-link2=Frank J. Tipler |publisher=Oxford University Press |year=1986 |isbn=978-0-19-851949-2 |location=Oxford}}
• {{Cite book |last=Dingle |first=Herbert |author-link=Herbert Dingle |title=The Sources of Eddington's Philosophy |publisher=Cambridge University Press |year=1954 |location=London |oclc=531389}}
• {{Cite book |last=Eddington |first=Arthur Stanley |author-link=Arthur Eddington |url=https://archive.org/details/in.ernet.dli.2015.23480 |title=The Nature of the Physical World |publisher=Cambridge University Press |year=1928 |location=London |oclc=645108}}
• {{Cite book |last=Eddington |first=Arthur Stanley |title=New Pathways in Science |publisher=Cambridge University Press |year=1935 |location=London |oclc=522390}}
• {{Cite book |last=Eddington |first=Arthur Stanley |title=The Philosophy of Physical Science |publisher=Cambridge University Press |year=1939 |location=London |oclc=669925}}
• {{Cite book |last=Eddington |first=Arthur Stanley |author-link=Arthur Eddington |title=Fundamental Theory |publisher=Cambridge University Press |year=1946 |editor-last=Whittaker |editor-first=E. T. |editor-link=E. T. Whittaker |location=Cambridge |oclc=2484474}}
• {{Cite book |last1=Kilmister |first1=C.W. |author-link1=Clive W. Kilmister |title=Eddington's Statistical Theory |last2=Tupper |first2=B.O.J. |publisher=Oxford University Press |year=1962 |location=London |oclc=1294788}}
• {{Cite book |last=Slater |first=Noel Bryan |author-link=Noel Slater |title=Development and Meaning in Eddington's Fundamental Theory |publisher=Cambridge University Press |year=1957 |location=London |oclc=843162}}
• {{Cite book |last=Whittaker |first=E. T. |author-link=E. T. Whittaker |title=Eddington's Principle in the Philosophy of Science |publisher=Cambridge University Press |year=1951 |location=London |oclc=1453203}}
• {{Cite book |last=Whittaker |first=E. T. |author-link=E. T. Whittaker |title=From Euclid to Eddington |publisher=Dover |year=1958 |location=New York |oclc=8119156}}

{{Large numbers}}

Category:Large integers

Category:Proton

Category:Astrophysics

Category:Physical cosmology