Well we start out with(adsbygoogle = window.adsbygoogle || []).push({});

[tex]-\frac {d} {dt} \int_{V}^{} \sigma dV = \int_{\Pi}^{} \vec{J} \cdot d\vec{\Pi}[/tex]

Using the Gauss theorem

[tex]\int_{V}^{} (\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J}) dV = 0[/tex]

so

[tex]\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J} = 0[/tex]

and written in 4D..

[tex]\frac{ \partial {J^n}}{ \partial {x^n}} = 0 \qquad\quad\ (n = 0,1,2,3)[/tex]

I can't seem to get my head around that last step. How does it expand out?

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# Deriving the 4d continuity equation

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