Linearity of Electromagnetic Field Energy and Momentum

It is shown that static electromagnetic fields have nonlinear energy and momentum due to the interaction between sources, while the apparent nonlinearity in energy and momentum densities of electromagnetic waves generated by noninteracting sources merely reflects a hitherto unsuspected degree of freedom of the energy-momentum four-tensor $Tμν$⁠, which can undergo the following transformation without changing its physical meaning: $Tμν→ T′μν = Tμν + Kμν$⁠, where the symmetric four-tensor $Kμν$ is arbitrary except for the constraint $δνKμν = 0$⁠. The force density $fμ = δνTμν$ is preserved in this transformation. The implication of this transformation on fields everywhere satisfying the homogeneous wave equations is discussed.