Fontem paginae Unitates Stoneyanae inspicere

{{Res|Unitates Stoneyanae}} sunt systema mensurae a physico [[Hibernia|Hibernico]] [[Georgius Johnstone Stoney|Georgio Johnstone Stoney]] anno [[1881]] creatum et primum exemplum
systematis {{Creanda|en|Natural units|d|Q3962243|unitates naturales|unitatum naturalium}} propositum – quod est grex unitatum sic excogitatum ut quaedam selectae {{Creanda|d|Q173227|quantitates physicae constantes}} et systema plene definiant et in ipso systemate includantur.

Georgius Stoney fuit primus qui intellexit [[onus electricum]] quantitates [[mechanica quantica|discretas]] tantum accipere posse; hoc ei suasit ut significationem universalem in minima unitate videret. Talis minima unitas ({{*ie}} onus electricum [[electron]]is), una cum aliis tribus [[quantitas constans|quantitatibus constantibus]] quas item ipse putavit universales (eae sunt [[celeritas lucis]], [[constans gravitationis]] et [[constans Coulombiana]]), sivit eum systema creare, quod hodie in honorem eius appellatur.

== Unitates ==
Ad novum systema mensurae definiendum, Georgius Stoney has quantitates constantes elegit:<ref>Ray, T. P. "Stoney's fundamental units." Irish Astronomical Journal, Vol. 15, P. 152, 1981 15 (1981): 152.</ref><ref>{{Cite journal 
	| last = Stoney 
	| first = G. Johnstone 
	| date = mense [[Maius|Maii]] [[1881]]
	| title = LII. On the physical units of nature 
	| url = https://www.tandfonline.com/doi/full/10.1080/14786448108627031 
	| journal = The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 
	| language = en 
	| volume = 11 
	| issue = 69 
	| pages = 381–390 
	| doi = 10.1080/14786448108627031 
	| issn = 1941-5982
}}</ref>

* {{mvar/c}}, [[celeritas lucis|celeritatem lucis]] in vacuo ({{Dimensiones|1|0|-1}})
* {{mvar/G}}, [[constans gravitatis|constantem gravitatis]] ({{Dimensiones|3|-1|-2}})
* {{mvar/k_e}}, [[constans Coulombiana|constantem Coulombianam]] ({{Dimensiones|3|1|-2|-2}})
* {{mvar/phye}}, onus electricum elementare ({{*ie}} onus [[proton]]is vel [[electron]]is – {{Dimensiones|0|0|0|1}})

Nonnulli auctores posteriores, praesertim post {{Creanda|en|2019 redefinition of the SI base units|d|Q3076763|reformatio unitatum primariarum Systematis Internationalis Unitatum anni 2019|reformationem unitatum primariarum systematis metrici}} anni [[2019]], in locum constantis Coulombianae ({{mvar/k_e}}) aliquando {{math|{{vfrac|1|4{{mvar|π}}{{mvar/epsilon_0}}}}}} substituunt (ubi {{mvar/epsilon_0}} est [[constans electrica|constans permittivitatis vacui]]).<ref>{{citation
	| last1 = Barrow
	| first1 = John D.
	| author-link1 = John D. Barrow
	| last2 = Tipler
	| first2 = Frank
	| author-link2 = Frank J. Tipler
	| year = [[1988]]
	| title = The anthropic cosmological principle
	| url = https://books.google.com/books?id=uSykSbXklWEC
	| publisher = Oxford University Press
	| page = 291
	| isbn = 978-0-192-82147-8
}}</ref><ref>{{citation
	| chapter = Constants, Units and Standards
	| first1 = Jeff
	| last1 = Flowers
	| first2 = Brian
	| last2 = Petley
	| page = 79
	| title = Astrophysics, clocks and fundamental constants
	| url = https://books.google.com/books?id=sGk05bF9KJEC&pg=PA79
	| editor-first1 = Savely G.
	| editor-last1 = Karshenboim
	| editor-first2 = Ekkehard
	| editor-last2 = Peik
	| publisher = Springer
	| year = [[2004]]
	| isbn = 978-3-540-21967-5
}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto;"
! Nomen
! Dimensio
! Aequatio
! Mensura ad [[Systema internationale unitatum|SI]] versa
|- style="text-align:left;"
| Longitudo Stoneyana
| [[longitudo]] (L)
| <math>l_\text{S} = \sqrt{\frac{G k_e e^2}{c^4}} = \sqrt{\frac{G e^2}{4\pi\epsilon_0 c^4}} = \sqrt{\frac{\alpha\hbar G}{c^3}}</math>
| 1.3807&thinsp;×&thinsp;10<sup>−36</sup> [[metrum|m]]
|-
| Massa Stoneyana
| [[massa]] (M)
| <math>m_\text{S} = \sqrt{\frac{k_e e^2}{G}} = \sqrt{\frac{e^2}{4\pi\epsilon_0 G}} = \sqrt{\frac{\alpha\hbar c}{G}}</math>
| 1.8592&thinsp;×&thinsp;10<sup>−9</sup> [[chiliogramma|kg]]
|-
| Tempus Stoneyanum
| [[tempus]] (T)
| <math>t_\text{S} = \sqrt{\frac{G k_e e^2}{c^6}} = \sqrt{\frac{G e^2}{4\pi\epsilon_0 c^6}} = \sqrt{\frac{\alpha\hbar G}{c^5}}</math>
| 4.6054&thinsp;×&thinsp;10<sup>−45</sup> [[secundum|s]]
|-
| Onus electricum Stoneyanum
| [[onus electricum]] (Q)
| <math>q_\text{S} = \sqrt{\frac{\alpha\hbar c}{k_e}} = \sqrt{4\pi\epsilon_0 \alpha\hbar c} = e</math>
| 1.6022&thinsp;×&thinsp;10<sup>−19</sup> [[coulomb (unitas)|C]]
|-
|}

Constantes quae systema Stoneyanum definiunt, cum per ipsas unitates Stoneyanas exprimantur, partem numeralem habent unius:

: <math>\begin{align}
c &= 1\ l_\text{S} \cdot t_\text{S}^{-1} \\
G &= 1\ l_\text{S}^3 \cdot t_\text{S}^{-2} \cdot m_\text{S}^{-1} \\
k_\text{e} &= 1\ l_\text{S}^3 \cdot t_\text{S}^{-2} \cdot m_\text{S} \cdot q_\text{S}^{-2}\\
e &= 1\ q_\text{S}
\end{align}</math>

Secundum ipsum systema pars numeralis [[Constans Planckiana#Constans Planckiana minuta|constantis Planckianae minutae]] est {{math|{{ofrac|1|{{mvar/phyalpha}}}}}}&hairsp;, i.e. ∼137:

: <math>\hbar = \frac{1}{\alpha} ~l_\text{S}^2 \cdot t_\text{S}^{-1} \cdot m_\text{S} \approx 137.036 ~l_\text{S}^2 \cdot t_\text{S}^{-1} \cdot m_\text{S}^{~},</math>

ubi {{mvar/phyalpha}} est [[constans structurae politae]].

Proportio inter [[unitates Planckianae]] et unitates Stoneyanas est <math>\sqrt{{1}/{\alpha}} \approx 11.7</math>.<ref>{{Citation
	| last1 = Duff
	| first1 = M. J.
	| author-link1 = Michael Duff (physicist)
	| last2 = Okun
	| first2 = L. B.
	| author-link2 = Lev Okun
	| last3 = Veneziano
	| first3 = G.
	| author-link3 = Gabriele Veneziano
	| date = [[3 Martii]] [[2002]]
	| title = Trialogue on the number of fundamental constants
	| journal = Journal of High Energy Physics
	| volume = 2002
	| issue = 3
	| page = 3
	| doi = 10.1088/1126-6708/2002/03/023
	| arxiv = physics/0110060
	| bibcode = 2002JHEP...03..023D
	| s2cid = 15806354
	| issn = 1029-8479
}}</ref> Idcirco: <math>l_\text{S} = \sqrt{\alpha}\,l_\text{P};</math> <math>m_\text{S} = \sqrt{\alpha}\,m_\text{P};</math> <math>t_\text{S} = \sqrt{\alpha}\,t_\text{P};</math> <math>q_\text{S} = \sqrt{\alpha}\,q_\text{P}.</math>

Nonnulli auctores, unitates Planckianas imitantes, unitatem Stoneyanam [[temperatura]]e ({{mvar/T_Stoney}}) systemati addunt,<ref>{{cite journal
	| last1 = Ievlev
	| first1 = Eugenius
	| last2 = Good
	| first2 = Michael
	| date = [[18 Iulii]] [[2023]]
	| title = Larmor Temperature, Casimir Dynamics, and Planck’s Law
	| url = https://arxiv.org/abs/2211.00946
	| journal = Physics
	| volume = 5
	| issue = 3
	| pages = 797–813
	| doi = 10.3390/physics5030050
}}</ref> cui 1.2103&thinsp;×&thinsp;10<sup>31</sup> [[kelvinus (unitas)|K]] congruunt.

== Notae ==
<references />

{{NexInt}}
* [[Constans Coulombiana]]
* [[Constans gravitationis]]
* [[Systema internationale unitatum]]
* [[Unitates Planckianae]]

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