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

TL;DR

This paper critically examines whether the Poynting vector $oldsymbol{E} imes oldsymbol{B}$ accurately represents electromagnetic momentum density, proposing an alternative gauge-invariant canonical momentum that could be experimentally distinguished.

Contribution

It introduces a method to experimentally differentiate between the Poynting vector and the gauge-invariant canonical momentum as the true electromagnetic momentum density.

Findings

The gauge-invariant canonical momentum may be validated through specific measurements.

The Poynting vector might not be the correct energy flux in all contexts.

Implications for gravity and nucleon momentum are discussed.

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.