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In the book “An Introduction To Mechanics”, by Daniel Kleppner and Robert J Kolenkow, at page 326 says that, the electromagnetic stress-energy tensor, giving its exact mathematical form, is trace-free because electromagnetism propagates at the invariant speed. Until now I understood that, the traceless character of this tensor, as also its vanishing covariant divergence were a direct result of its mathematical form (symmetries), which results from the application of the least action principle for writing it. Is it that propagation at invariant speed is enough for tracelessness and divergencelessness?

I was not able to work out an answer using tensor calculus, or intuition. I will very much appreciate any help.

Regards,

EagleH