= Four-gradient
{title2=$\partial_\mu=(c^{-1}\partial_t,\nabla)$}
For coordinates $x^\mu=(ct,x,y,z)$, the <four-gradient> of a scalar field is its <covector> of coordinate derivatives. Under a constant <Lorentz transformation>, $\partial'_\mu=(\Lambda^{-1})^\nu{}_{\mu}\partial_\nu$. In <metric signature> $(+,-,-,-)$, raising its index gives $\partial^\mu=(c^{-1}\partial_t,-\nabla)$. Contracting it with a <four-vector> field produces the <Lorentz scalar> <four-divergence>. In particular $\partial_\mu J^\mu=0$ is charge continuity in every <inertial frame>.
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