Editing Fine-structure constant (section)

== Numerological explanations ==
As a dimensionless constant which does not seem to be directly related to any [[mathematical constant]], the fine-structure constant has long fascinated physicists.

[[Arthur Eddington]] argued that the value could be "obtained by pure deduction" and he related it to the [[Eddington number]], his estimate of the number of protons in the universe.<ref>
{{cite book
 |last=Eddington |first=A. S. |author-link=Arthur Eddington
 |year=1956
 |chapter=The constants of nature
 |editor-last=Newman |editor-first=J. R.
 |title=The World of Mathematics
 |volume=2 |pages=1074–1093
 |publisher=[[Simon & Schuster]]
}}</ref>
This led him in 1929 to conjecture that the reciprocal of the fine-structure constant was not approximately but precisely the [[integer]] [[137 (number)|137]].<ref>
{{cite journal
 |last=Whittaker |first=Edmund
 |date=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 |jstor=3609461 |s2cid=125122360
}}</ref>
By the 1940s experimental values for {{sfrac|1| {{mvar|α}} }} deviated sufficiently from 137 to refute Eddington's arguments.<ref name=Kragh-2003>
{{cite journal
 |last=Kragh |first=Helge
 |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
 |jstor=41134170 |s2cid=118031104
}}</ref>

Physicist [[Wolfgang Pauli]] commented on the appearance of [[Numerology#Related uses|certain numbers in physics]], including the fine-structure constant, which he also noted approximates reciprocal of the prime number [[137 (number)#Physics|137]].<ref>{{cite journal |url=https://www.newscientist.com/article/mg20227051.800-cosmic-numbers-pauli-and-jungs-love-of-numerology.html |title=Cosmic numbers: Pauli and Jung's love of numerology |first=Dan |last=Falk |issue=2705 |date=24 April 2009 |journal=New Scientist}}</ref> This constant so intrigued him that he collaborated with psychoanalyst [[Carl Jung]] in a quest to understand its significance.<ref>
{{cite journal
 |last1=Várlaki |first1=Péter
 |last2=Nádai   |first2=László
 |last3=Bokor   |first3=József
 |title=Number archetypes and 'background' control theory concerning the fine structure constant
 |journal=Acta Polytechica Hungarica
 |date=2008
 |volume=5 |issue=2 |pages=71–104
 |url=http://eprints.sztaki.hu/id/eprint/4822
}}</ref> Similarly, [[Max Born]] believed that if the value of {{mvar|α}} differed, the universe would degenerate, and thus that {{mvar|α}} = {{sfrac|1|137}} is a law of nature.<ref name=Miller-2009>
{{cite book
 |last = Miller |first=A. I.
 |year = 2009
 |title = Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung
 |page = [https://archive.org/details/isbn_9780393065329/page/253 253]
 |publisher = [[W. W. Norton & Co.]]
 |isbn = 978-0-393-06532-9
 |url = https://archive.org/details/isbn_9780393065329/page/253
}}</ref>{{efn|"If alpha were bigger than it really is, we should not be able to distinguish matter from ether [the vacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that alpha has just its value {{sfrac|1|137}} is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy." – [[Max Born]]<ref name=Miller-2009/>
}}

[[Richard Feynman]], one of the originators and early developers of the theory of [[quantum electrodynamics]] (QED), referred to the fine-structure constant in these terms:

{{blockquote|
There is a most profound and beautiful question associated with the observed coupling constant, {{math|''e''}} – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.)

Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans. You might say the "hand of God" wrote that number, and "we don't know how He pushed His pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out – without putting it in secretly!| [[Richard Feynman|R. P. Feynman]]<ref name=Feynman1985>
 {{cite book
  |last=Feynman |first=R. P. |author-link=Richard Feynman
  |year=1985
  |title=QED: The Strange Theory of Light and Matter
  |publisher=[[Princeton University Press]]
  |isbn=978-0-691-08388-9
  |title-link=QED: The Strange Theory of Light and Matter
  |page=[https://archive.org/details/qedstrangetheory00feyn_822/page/n133 129]
 }}</ref>
}}

Conversely, statistician [[I. J. Good]] argued that a numerological explanation would only be acceptable if it could be based on a good theory that is not yet known but "exists" in the sense of a [[Platonic Ideal]].{{efn|"There have been a few examples of numerology that have led to theories that transformed society: See the mention of [[Gustav Kirchhoff|Kirchhoff]] and [[Johann Balmer|Balmer]] in [[I. J. Good|Good]] (1962) p.&nbsp;316 ... and one can well include [[Johannes Kepler|Kepler]] on account of [[Kepler's third law|his third law]]. It would be fair enough to say that numerology was the origin of the theories of electromagnetism, quantum mechanics, gravitation. ... So I intend no disparagement when I describe a formula as numerological. When a numerological formula is proposed, then we may ask whether it is correct. ... I think an appropriate definition of correctness is that the formula has a good explanation, in a Platonic sense, that is, the explanation could be based on a good theory that is not yet known but 'exists' in the universe of possible reasonable ideas." — [[I. J. Good]] (1990)<ref>
 {{cite book
  |contributor-last=Good |contributor-first=I. J. |contributor-link=I. J. Good
  |year=1990
  |contribution=A quantal hypothesis for hadrons and the judging of physical numerology
  |last1=Grimmett |first1=G. R. 
  |last2=Welsh |first2=D. J. A. 
  |title=Disorder in Physical Systems
  |publisher=[[Oxford University Press]]
  |page=141
  |isbn=978-0-19-853215-6
  |chapter-url=https://www.statslab.cam.ac.uk/~grg/books/hammfest/9-jg.ps
 }}</ref>
}}

Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numerological explanation has ever been accepted by the physics community.

In the late 20th century, multiple physicists, including [[Stephen Hawking]] in his 1988 book ''[[A Brief History of Time]]'', began exploring the idea of a [[multiverse]], and the fine-structure constant was one of several universal constants that suggested the idea of a [[fine-tuned universe]].<ref name=Hawking-1988>
{{cite book
 |last=Hawking |first=S. |author-link=Stephen Hawking 
 |year=1988
 |title=A Brief History of Time
 |url=https://archive.org/details/briefhistoryofti00step_1
 |url-access=registration
 |publisher=Bantam Books
 |isbn=978-0-553-05340-1
 |pages=[https://archive.org/details/briefhistoryofti00step_1/page/7 7], 125
}}</ref>