Editing Dimensionless physical constant (section)

== History ==
In the 1920s and 1930s, [[Arthur Eddington]] embarked upon extensive mathematical investigation into the relations between the fundamental quantities in basic physical theories, later used as part of his effort to construct an [[Quantum cosmology|overarching theory unifying quantum mechanics and cosmological physics]]. For example, he speculated on the potential consequences of the ratio of the [[Classical electron radius|electron radius]] to its [[Electron rest mass|mass]]. Most notably, in a 1929 paper he set out an argument based on the [[Pauli exclusion principle]] and the [[Dirac equation]] that fixed the value of the reciprocal of the fine-structure constant as 𝛼<sup>−1</sup> = 16 + {{sfrac|1|2}} × 16 × (16–1) = '''136'''. When its value was discovered to be closer to 137, he changed his argument to match that value. His ideas were not widely accepted, and subsequent experiments have shown that they were wrong (for example, none of the measurements of the fine-structure constant suggest an integer value; the modern [[CODATA]] value is {{physconst|alphainv|symbol=yes|after=.}}

Though his derivations and equations were unfounded, Eddington was the first physicist to recognize the significance of universal dimensionless constants, now considered among the most critical components of major physical theories such as the [[Standard Model]] and [[Lambda-CDM model|ΛCDM cosmology]].<ref>[[:fr:Dina K. Prialnik|Prialnik, D. K.]], ''An Introduction to the Theory of Stellar Structure and Evolution'' ([[Cambridge]]: [[Cambridge University Press]], 2000), [https://books.google.com/books?id=TGyzlVbgkiMC&pg=PA82&redir_esc=y#v=onepage&q&f=false p. 82].</ref> He was also the first to argue for the importance of the [[cosmological constant]] Λ itself, considering it vital for explaining the [[expansion of the universe]], at a time when most physicists (including its discoverer, [[Albert Einstein]]) considered it an outright mistake or mathematical artifact and assumed a value of zero: this at least proved prescient, and a significant positive Λ features prominently in ΛCDM.

Eddington may have been the first to attempt in vain to derive the basic dimensionless constants from fundamental theories and equations, but he was certainly not the last. Many others would subsequently undertake similar endeavors, and efforts occasionally continue even today. None have yet produced convincing results or gained wide acceptance among theoretical physicists.<ref>{{Cite arXiv|last=Kragh|first=Helge|author-link=Helge Kragh|date=14 October 2015|title=On Arthur Eddington's Theory of Everything|eprint=1510.04046|class=physics.hist-ph}}</ref><ref>{{Cite journal|last=Gamow|first=G.|date=1 February 1968|title=Numerology of the Constants of Nature|journal=Proceedings of the National Academy of Sciences| language=en|volume=59| issue=2|pages=313–318| doi=10.1073/pnas.59.2.313| issn=0027-8424|pmid=16591598| pmc=224670|bibcode=1968PNAS...59..313G|doi-access=free}}</ref>

An [[Koide formula|empirical relation]] between the masses of the electron, muon and tau has been discovered by physicist [[Yoshio Koide]], but this formula remains unexplained.<ref>{{cite arXiv |last1=Rivero |first1=A. |last2=Gsponer |first2=A. |title=The strange formula of Dr. Koide |date=2 February 2008 |page=4 |eprint=hep-ph/0505220 }}</ref>