Unitates Stoneyanae

Unitates Stoneyanae sunt systema mensurae a physico Hibernico Georgio Johnstone Stoney anno 1881 creatum et primum exemplum systematis unitatum naturalium^(en)(d) propositum – quod est grex unitatum sic excogitatum ut quaedam selectae quantitates physicae constantes^(d) et systema plene definiant et in ipso systemate includantur.

Georgius Stoney fuit primus qui intellexit onus electricum quantitates discretas tantum accipere posse; hoc ei suasit ut significationem universalem in minima unitate videret. Talis minima unitas (i.e. onus electricum electronis), una cum aliis tribus 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:^[1]^[2]

$c$ , celeritatem lucis in vacuo (L T⁻¹)
$G$ , constantem gravitatis (L³ M⁻¹ T⁻²)
$k e$ , constantem Coulombianam (L³ M T⁻² Q⁻²)
$e$ , onus electricum elementare (i.e. onus protonis vel electronis – Q)

Nonnulli auctores posteriores, praesertim post reformationem unitatum primariarum systematis metrici^(en)(d) anni 2019, in locum constantis Coulombianae ( $k e$ ) aliquando $.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1/4πε0$ substituunt (ubi $ε 0$ est constans permittivitatis vacui).^[3]^[4]

Nomen	Dimensio	Aequatio	Mensura ad SI versa
Longitudo Stoneyana	longitudo (L)	$l_{\text{S}}={\sqrt {\frac {Gk_{e}e^{2}}{c^{4}}}}={\sqrt {\frac {Ge^{2}}{4\pi \epsilon _{0}c^{4}}}}={\sqrt {\frac {\alpha \hbar G}{c^{3}}}}$	1.3807 × 10⁻³⁶ m
Massa Stoneyana	massa (M)	$m_{\text{S}}={\sqrt {\frac {k_{e}e^{2}}{G}}}={\sqrt {\frac {e^{2}}{4\pi \epsilon _{0}G}}}={\sqrt {\frac {\alpha \hbar c}{G}}}$	1.8592 × 10⁻⁹ kg
Tempus Stoneyanum	tempus (T)	$t_{\text{S}}={\sqrt {\frac {Gk_{e}e^{2}}{c^{6}}}}={\sqrt {\frac {Ge^{2}}{4\pi \epsilon _{0}c^{6}}}}={\sqrt {\frac {\alpha \hbar G}{c^{5}}}}$	4.6054 × 10⁻⁴⁵ s
Onus electricum Stoneyanum	onus electricum (Q)	$q_{\text{S}}={\sqrt {\frac {\alpha \hbar c}{k_{e}}}}={\sqrt {4\pi \epsilon _{0}\alpha \hbar c}}=e$	1.6022 × 10⁻¹⁹ C

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

{\begin{aligned}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{aligned}}

Secundum ipsum systema pars numeralis constantis Planckianae minutae est $.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1⁄α$ , i.e. ∼137:

\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}}^{~},

ubi $α$ est constans structurae politae.

Proportio inter unitates Planckianae et unitates Stoneyanas est ${\sqrt {{1}/{\alpha }}}\approx 11.7$ .^[5] Idcirco: $l_{\text{S}}={\sqrt {\alpha }}\,l_{\text{P}};$ $m_{\text{S}}={\sqrt {\alpha }}\,m_{\text{P}};$ $t_{\text{S}}={\sqrt {\alpha }}\,t_{\text{P}};$ $q_{\text{S}}={\sqrt {\alpha }}\,q_{\text{P}}.$

Nonnulli auctores, unitates Planckianas imitantes, unitatem Stoneyanam temperaturae ( $T S$ ) systemati addunt,^[6] cui 1.2103 × 10³¹ K congruunt.

Notae

↑ Ray, T. P. "Stoney's fundamental units." Irish Astronomical Journal, Vol. 15, P. 152, 1981 15 (1981): 152.
↑ Stoney, G. Johnstone (mense Maii 1881). "LII. On the physical units of nature". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 11 (69): 381–390
↑ Barrow, John D.; Tipler, Frank (1988), The anthropic cosmological principle, Oxford University Press, p. 291, ISBN 978-0-192-82147-8
↑ Flowers, Jeff; Petley, Brian (2004), "Constants, Units and Standards", Astrophysics, clocks and fundamental constants, Springer, p. 79, ISBN 978-3-540-21967-5
↑ Duff, M. J.; Okun, L. B.; Veneziano, G. (3 Martii 2002), "Trialogue on the number of fundamental constants", Journal of High Energy Physics 2002 (3): 3, arXiv:physics/0110060
↑ Ievlev, Eugenius; Good, Michael (18 Iulii 2023). "Larmor Temperature, Casimir Dynamics, and Planck’s Law". Physics 5 (3): 797–813

Nexus interni

[1] Ray, T. P. "Stoney's fundamental units." Irish Astronomical Journal, Vol. 15, P. 152, 1981 15 (1981): 152.

[2] Stoney, G. Johnstone (mense Maii 1881). "LII. On the physical units of nature". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 11 (69): 381–390

[3] Barrow, John D.; Tipler, Frank (1988), The anthropic cosmological principle, Oxford University Press, p. 291, ISBN 978-0-192-82147-8

[4] Flowers, Jeff; Petley, Brian (2004), "Constants, Units and Standards", Astrophysics, clocks and fundamental constants, Springer, p. 79, ISBN 978-3-540-21967-5

[5] Duff, M. J.; Okun, L. B.; Veneziano, G. (3 Martii 2002), "Trialogue on the number of fundamental constants", Journal of High Energy Physics 2002 (3): 3, arXiv:physics/0110060

[6] Ievlev, Eugenius; Good, Michael (18 Iulii 2023). "Larmor Temperature, Casimir Dynamics, and Planck’s Law". Physics 5 (3): 797–813

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