数理電子
微細構造定数アルファは無次元の物理定数である。α = 137.03599...
α = 2 h μ 0 e 2 c {\displaystyle \alpha ={\frac {2h}{\mu _{0}e^{2}c}}}
α = 2 ( 8 π 4 Ω 4 ) / ( α 2 11 π 5 Ω 4 ) ( 128 π 4 Ω 3 α ) 2 ( 2 π Ω 2 ) = α {\displaystyle \alpha =2({8\pi ^{4}\Omega ^{4}})/({\frac {\alpha }{2^{11}\pi ^{5}\Omega ^{4}}})({\frac {128\pi ^{4}\Omega ^{3}}{\alpha }})^{2}(2\pi \Omega ^{2})=\alpha }
スカラー = r 13 v 5 . 1 r 7 . v 6 r 6 . 1 v = 1 {\displaystyle ={\frac {r^{13}}{v^{5}}}.{\frac {1}{r^{7}}}.{\frac {v^{6}}{r^{6}}}.{\frac {1}{v}}=1}
単位 = u 19 u 56 ( u − 27 ) 2 u 17 = 1 {\displaystyle ={\frac {u^{19}}{u^{56}(u^{-27})^{2}u^{17}}}=1}
( μ 0 ∗ ) 3 = 3 6 h 3 c 5 α 13 R 2 2 π 10 , μ 0 ∗ = 1.256 637 251 88 10 − 6 {\displaystyle {(\mu _{0}^{*})}^{3}={\frac {3^{6}h^{3}c^{5}\alpha ^{13}R^{2}}{2\pi ^{10}}},\;\mu _{0}^{*}=1.256\;637\;251\;88\;10^{-6}}
( h ∗ ) 3 = 2 π 10 μ 0 3 3 6 c 5 α 13 R 2 , h ∗ = 6.626 069 149 10 − 34 {\displaystyle {(h^{*})}^{3}={\frac {2\pi ^{10}\mu _{0}^{3}}{3^{6}c^{5}\alpha ^{13}R^{2}}},\;h^{*}=6.626\;069\;149\;10^{-34}}
( e ∗ ) 3 = 4 π 5 3 3 c 4 α 8 R , e ∗ = 1.602 176 513 10 − 19 {\displaystyle {(e^{*})}^{3}={\frac {4\pi ^{5}}{3^{3}c^{4}\alpha ^{8}R}},\;e^{*}=1.602\;176\;513\;10^{-19}}
u , u n i t = L M T = u − 13 − 15 + 30 = 2 = u 1 {\displaystyle u,\;unit={\sqrt {\frac {L}{MT}}}={\sqrt {u^{-13-15+30=2}}}=u^{1}}
x , u n i t = M 9 T 11 L 15 = u 0 = 1 {\displaystyle x,\;unit={\sqrt {\frac {M^{9}T^{11}}{L^{15}}}}=u^{0}=1}
y , u n i t = M 2 T = u 0 = 1 {\displaystyle y,\;unit=M^{2}T=u^{0}=1}
結果;
u 3 = L 3 / 2 M 3 / 2 T 3 / 2 = A , {\displaystyle u^{3}={\frac {L^{3/2}}{M^{3/2}T^{3/2}}}=A,\;} (アンペア)
u 6 ( y ) = L 3 / T 2 M , ( G ) {\displaystyle u^{6}(y)=L^{3}/T^{2}M,\;(G)}
u 13 ( x y ) = 1 / L , ( 1 / l p ) {\displaystyle u^{13}(xy)=1/L,\;(1/l_{p})}
u 15 ( x y 2 ) = M , ( m P ) {\displaystyle u^{15}(xy^{2})=M,\;(m_{P})}
u 17 ( x y 2 ) = V , ( c ) {\displaystyle u^{17}(xy^{2})=V,\;(c)}