Editing Radian (section)

=== As an SI unit ===
{{see also|#Dimensional analysis}}

As Paul Quincey et al. write, "the status of angles within the [[International System of Units]] (SI) has long been a source of controversy and confusion."<ref>{{cite journal |last1=Quincey |first1=Paul |last2=Mohr |first2=Peter J. |last3=Phillips |first3=William D. |title=Angles are inherently neither length ratios nor dimensionless |journal=Metrologia |date=1 August 2019 |volume=56 |issue=4 |pages=043001 |doi=10.1088/1681-7575/ab27d7|arxiv=1909.08389|bibcode=2019Metro..56d3001Q |s2cid=198428043}}</ref> In 1960, the [[General Conference on Weights and Measures]] (CGPM) established the SI and the radian was classified as a "supplementary unit" along with the [[steradian]]. This special class was officially regarded "either as base units or as derived units", as the CGPM could not reach a decision on whether the radian was a base unit or a derived unit.<ref>{{citation|url=https://www.bipm.org/documents/20126/41483022/si_brochure_1.pdf/26bf12f9-1da7-e6c2-254b-c50fb978c01b|page=12|title=Le Système international d'unités|date=1970|language=fr|quote=Pour quelques unités du Système International, la Conférence Générale n'a pas ou n'a pas encore décidé s'il s'agit d'unités de base ou bien d'unités dérivées.|trans-quote=For some units of the SI, the CGPM still hasn't yet decided whether they are base units or derived units.}}</ref> Richard Nelson writes "This ambiguity [in the classification of the supplemental units] prompted a spirited discussion over their proper interpretation."<ref name=Nelson/> In May 1980 the [[Consultative Committee for Units]] (CCU) considered a proposal for making radians an SI base unit, using a constant {{math|1=''α''<sub>0</sub> = 1 rad}},<ref>{{citation |title=Report of the 7th meeting |publisher=Consultative Committee for Units |date=May 1980 |pages=6–7 |url=https://www.bipm.org/documents/20126/30132777/cc-publication-ID-422/cd7e3b5f-471c-4e5c-e4e1-eb998acb155f|language=fr}}</ref>{{sfn|Quincey|2021}} but turned it down to avoid an upheaval to current practice.{{sfn|Quincey|2021}}

In October 1980 the CGPM decided that supplementary units were dimensionless derived units for which the CGPM allowed the freedom of using them or not using them in expressions for SI derived units,<ref name=Nelson>{{cite journal |last1=Nelson |first1=Robert A. |title=The supplementary units |journal=The Physics Teacher |date=March 1984 |volume=22 |issue=3 |pages=188–193 |doi=10.1119/1.2341516|bibcode=1984PhTea..22..188N }}</ref> on the basis that "[no formalism] exists which is at the same time coherent and convenient and in which the quantities plane angle and solid angle might be considered as base quantities" and that "[the possibility of treating the radian and steradian as SI base units] compromises the internal coherence of the SI based on only seven base units".{{sfn|International Bureau of Weights and Measures|2019|pp=174-175}} In 1995 the CGPM eliminated the class of supplementary units and defined the radian and the steradian as "dimensionless derived units, the names and symbols of which may, but need not, be used in expressions for other SI derived units, as is convenient".{{sfn|International Bureau of Weights and Measures|2019|p=179}} Mikhail Kalinin writing in 2019 has criticized the 1980 CGPM decision as "unfounded" and says that the 1995 CGPM decision used inconsistent arguments and introduced "numerous discrepancies, inconsistencies, and contradictions in the wordings of the SI".<ref>{{cite journal |last1=Kalinin |first1=Mikhail I |title=On the status of plane and solid angles in the International System of Units (SI) |journal=Metrologia |date=1 December 2019 |volume=56 |issue=6 |pages=065009 |doi=10.1088/1681-7575/ab3fbf|arxiv=1810.12057|bibcode=2019Metro..56f5009K |s2cid=53627142 }}</ref>

At the 2013 meeting of the CCU, Peter Mohr gave a presentation on alleged inconsistencies arising from defining the radian as a dimensionless unit rather than a base unit. CCU President Ian M. Mills declared this to be a "formidable problem" and the ''CCU Working Group on Angles and Dimensionless Quantities in the SI'' was established.<ref>{{cite report|author=Consultative Committee for Units|author-link=Consultative Committee for Units|title=Report of the 21st meeting to the International Committee for Weights and Measures |date=11–12 June 2013|url=https://www.bipm.org/documents/20126/31581067/21st+meeting/99596189-a3f2-bc60-46bf-f7828b980a5c|pages=18–20}}</ref> The CCU met in 2021, but did not reach a consensus. A small number of members argued strongly that the radian should be a base unit, but the majority felt the status quo was acceptable or that the change would cause more problems than it would solve. A task group was established to "review the historical use of SI supplementary units and consider whether reintroduction would be of benefit", among other activities.<ref>{{cite report|author=Consultative Committee for Units|author-link=Consultative Committee for Units|title=Report of the 25th meeting to the International Committee for Weights and Measures |date=21–23 September 2021|url=https://www.bipm.org/documents/20126/68201438/CCU25.pdf/ab1be833-d656-ae2e-36fa-feb04948ed4c#page=16|pages=16–17}}</ref><ref>{{cite web |title=CCU Task Group on angle and dimensionless quantities in the SI Brochure (CCU-TG-ADQSIB) |url=https://www.bipm.org/en/committees/cc/ccu/wg/ccu-tg-adqsib |publisher=BIPM |access-date=26 June 2022}}</ref>