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

Abstract

Following our recent finding that the renowned formula $\vec{x}\times (\vec{E}\times \vec{B})$ is not the correct density for the electromagnetic angular momentum, here we examine the validity of the Poynting vector $\vec{E}\times \vec{B}$ as the electromagnetic momentum density (or energy flux). The competitor is the gauge-invariant canonical momentum $E^i\vec{\nabla }{A}_{\perp }^i$. It often gives the same result as $\vec{E}\times \vec{B}$, but we propose that a delicate measurement (of the {\em azimuthal} energy flow in polarized atomic radiations) can make a discrimination. By clarifying the profound difference between two kinds of energy-momentum tensors: the canonical (or mechanical) one and the symmetric (or gravitational) one, we predict that it is $E^i\vec{\nabla }{A}_{\perp }^i$ that would pass the delicate experimental test. Our observations have far-reaching implications for understanding the source of gravity, and the nucleon momentum as well.

3 pages, no figure