Editing Continuity equation (section)

===Special relativity===
{{see also|4-vector}}

The notation and tools of [[special relativity]], especially [[4-vector]]s and [[4-gradient]]s, offer a convenient way to write any continuity equation.

The density of a quantity {{math|''ρ''}} and its current {{math|'''j'''}} can be combined into a [[4-vector]] called a [[4-current]]:
<math display="block">J = \left(c \rho, j_x, j_y, j_z \right)</math>
where {{math|''c''}} is the [[speed of light]]. The 4-[[divergence]] of this current is:
<math display="block"> \partial_\mu J^\mu = c \frac{ \partial \rho}{\partial ct} + \nabla \cdot \mathbf{j}</math>
where {{math|∂<sub>''μ''</sub>}} is the [[4-gradient]] and {{math|''μ''}} is an [[index notation|index]] labeling the [[spacetime]] [[dimension]]. Then the continuity equation is:
<math display="block">\partial_\mu J^\mu = 0</math>
in the usual case where there are no sources or sinks, that is, for perfectly conserved quantities like energy or charge. This continuity equation is manifestly ("obviously") [[Lorentz invariant]].

Examples of continuity equations often written in this form include electric charge conservation
<math display="block">\partial_\mu J^\mu = 0</math>
where {{math|''J''}} is the electric [[4-current]]; and energy–momentum conservation
<math display="block">\partial_\nu T^{\mu\nu} = 0</math>
where {{math|''T''}} is the [[stress–energy tensor]].