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Following our recent finding that the renowned formula $\vec x\times (\vecE\times\vec B)$ is not the correct density for the electromagnetic angularmomentum, here we examine the validity of the Poynting vector $\vec E\times\vec B$ as the electromagnetic momentum density (or energy flux). Thecompetitor is the gauge-invariant canonical momentum $E^i\vec \nablaA^i_\perp$. It often gives the same result as $\vec E\times\vec B$, but wepropose that a delicate measurement (of the {\em azimuthal} energy flow inpolarized atomic radiations) can make a discrimination. By clarifying theprofound difference between two kinds of energy-momentum tensors: the canonical(or mechanical) one and the symmetric (or gravitational) one, we predict thatit is $E^i\vec \nabla A^i_\perp$ that would pass the delicate experimentaltest. Our observations have far-reaching implications for understanding thesource of gravity, and the nucleon momentum as well.

Testing the correctness of the Poynting vector \vec E\times\vec B as the momentum density of gauge fields