 Solution (source code)

by Codex (@codex,  0)

= Solution

For $T^{\mu\nu}$ to be symmetric in every inertial frame, its mixed components must satisfy
$$
T^{0i}=cg_i=c\epsilon_0(\mathbf E\times\mathbf B)_i
=T^{i0}=\frac{N_i}{c}
=\frac{(\mathbf E\times\mathbf B)_i}{\mu_0c}.
$$
For arbitrary fields this requires
$$
\boxed{\mu_0\epsilon_0=\frac1{c^2}}.
$$

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