Question about Electromagnetic Energy

[lugita15]

In his Lectures on Physics, Feynman derives the electromagnetic energy density u and the electromagnetic energy flux $$\vec{S}$$. However, he states that there is an ambiguity in the field energy: the common expressions given for u and $$\vec{S}$$ are only the simplest known expressions. There are really an infinite number of possible expressions for u and $$\vec{S}$$ which are consistent with Maxwell's Equations, and as of the publication of the Feynman lectures, no one could figure out which one is correct.
Feynman even says, "People have guessed that the simplest one is probably the correct one, but we must say that we do not know for certain what is the actual location in space of the electromagnetic field energy." He later says, "It is interesting that there seems to be no unique way to resolve the indefiniteness in the location of the field energy."

My question is, since the publication of the Feynman Lectures, has there been any progress in proving that the commonly given expressions for u and $$\vec{S}$$ are ultimately correct?

Any help would be greatly appreciated.
Thank You in Advance.

 

[cesiumfrog]

I was recently reading a paper that attributes intrinsic spin to the rotating energy flux of an electron's probability wave function. It also noted a freedom in the definition of energy flux (and pointed out that only one choice cleanly gave rise to the elegant interpretation they were interested in), but said that their choice was the only covariant one (i.e., that basic consistency with relativity theory provides a suitable constraint to choose the expression).

 

[Meir Achuz]

arXiv:0707.3421

 

[cesiumfrog]

At any rate, in principle it seems to me that it should be possible to determine the location of energy by the fact that energy gravitates. I just don't imagine that such an experiment is practical.