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arXiv · 0710.1427

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

Xiang-Song Chen·Xiang-Bai Chen·Wei-Min Sun·Fan Wang
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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 $E^i\vec \nabla A^i_\perp$. 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 $E^i\vec \nabla A^i_\perp$ 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.

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Xiang-Song Chen, Xiang-Bai Chen, Wei-Min Sun, Fan Wang. 2007-10-08. Testing the correctness of the Poynting vector \vec E\times\vec B as the momentum density of gauge fields. https://arxiv.org/abs/0710.1427

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