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TeX (original user input): 

\begin{align}
  & d{{s}^{2}}={{\eta }_{\mu \nu }}dx{{'}^{\mu }}dx{{'}^{\nu }} \\
 & d\tau =\frac{1}{c}\sqrt{{{\eta }_{\mu \nu }}dx{{'}^{\mu }}dx{{'}^{\nu }}}=\sqrt{1-{{\left( \frac{v'}{c} \right)}^{2}}}dt'=dt' \\
\end{align}

TeX (checked): 

{\begin{aligned}&d{{s}^{2}}={{\eta }_{\mu \nu }}dx{{'}^{\mu }}dx{{'}^{\nu }}\\&d\tau ={\frac {1}{c}}{\sqrt {{{\eta }_{\mu \nu }}dx{{'}^{\mu }}dx{{'}^{\nu }}}}={\sqrt {1-{{\left({\frac {v'}{c}}\right)}^{2}}}}dt'=dt'\\\end{aligned}}

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MathML (22.415 KB / 2.715 KB) :

d s 2 = η μ ⁢ ν d x d ′ μ x ν ′ d ⁢ τ = 1 c ⁢ η μ ⁢ ν d x d ′ μ x ν ′ = 1 - ( v ′ c ) 2 ⁢ d ⁢ t ′ = d ⁢ t ′ missing-subexpression fragments d superscript 𝑠 2 subscript 𝜂 𝜇 𝜈 d x superscript superscript 𝑑 𝜇 ′ x superscript superscript absent 𝜈 ′ missing-subexpression 𝑑 𝜏 1 𝑐 fragments subscript 𝜂 𝜇 𝜈 d x superscript superscript 𝑑 𝜇 ′ x superscript superscript absent 𝜈 ′ 1 superscript superscript 𝑣 ′ 𝑐 2 𝑑 superscript 𝑡 ′ 𝑑 superscript 𝑡 ′ {\displaystyle{\displaystyle\begin{aligned} &\displaystyle d{{s}^{2}}={{\eta}_% {\mu\nu}}dx{{{}^{\prime}}^{\mu}}dx{{{}^{\prime}}^{\nu}}\\ &\displaystyle d\tau=\frac{1}{c}\sqrt{{{\eta}_{\mu\nu}}dx{{{}^{\prime}}^{\mu}}% dx{{{}^{\prime}}^{\nu}}}=\sqrt{1-{{\left(\frac{v^{\prime}}{c}\right)}^{2}}}dt^% {\prime}=dt^{\prime}\\ \end{aligned}}}

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MathML (2.085 KB / 445 B) :

ds2=ημνdx'μdx'νdτ=1cημνdx'μdx'ν=1−(v′c)2dt′=dt′

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“