In Feynman lectures vol 2 chapter 27 he says there is a theorem which says whenever there is a flow of energy per unit time per unit area the momentum density in the volume is found by multiplying it by $\frac{1}{c^2}$
$$\mathbf{g}=\frac{\mathbf{S}}{c^2}$$ where $\mathbf{g}$ is momentum density and $\mathbf{S}$ is Poynting vector
But where does this theorem come from?
In the Classical Electricity and Magnetism book of Panosfki and Philips , chapter 10 , at the end, they deal (used in the beginning of chapter 21)with the momentum balance in classical electromagnetism, and they show that in order for the law of conservation of momentum to still stand as a law including electromagnetic radiation it needs a momentum density given by
$g=N/c^2$
where $N$ is the Poynting vector.
So it is not really a theorem, but a necessity in order to keep conservation of momentum a general law.
For an isolated system angular momentum is conserved. Then the Noether theorem implies that the energy momentum tensor is symmetric, so $T^{0i}=T^{i0}$ .The first is the energy transport and the second the momentum density, up to a factor $1/c^2$.
