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Display information for equation id:math.1107.307 on revision:1107
* Page found: ART-Skript (eq math.1107.307)
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Hash: d922866dda79193780fab72ce4354d40
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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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>d</mi><msup><mi>s</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msub><mi>η</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msub><mi>d</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>d</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>d</mi><mi>τ</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><msub><mi>η</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow></msub><mi>d</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi>d</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup></mrow></msqrt></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>v</mi><mo>′</mo></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mi>d</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">=</mo><mi>d</mi><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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