Why Are Maxwell's Equations Preferred Before Those Proposed by H. Hertz?

Question

In a recent exchange it was pointed out that in certain situations Maxwell's equations need Lorentz force as a patch (the latter not being part of those equations neither is it derivable from them).

It appears that the equations proposed by H. Hertz lack that deficiency while retaining Lorentz invariance. What might be the reason for usng Maxwell's equations instead?

Answer 1

The content of the Maxwell equations are named after Maxwell because he derived their wave character, and theoretically predicted the induction of magnetic fields by changing electric fields (the Maxwell term). This is the reason they are named for Maxwell--- he took the known field relations from empirical laws and turned them into a comprehensive theory.

The motion of point charges was not so much of a concern at that time. I would assume that the discovery of the electron added an impetus to figuring out how points move. Bulk material properties are more interesting to physicists in Maxwell's time, and I wouldn't be surprised if bulk forces appear in Maxwell which reproduce the Lorentz force when you take the limit of a small charged sphere. I don't know, but it doesn't matter at all.

Any other system of equations is presumably equivalent in physical content to the Maxwell equations, predicting the same set of electric and magnetic fields in response to the same currents. If Hertz's theory predicts the same as Maxwell's, it is equivalent, and if it doesn't then it is a new theory, and probably a wrong one.

The question of which particular shape of symbols to express a physical law is a very inane one. It doesn't matter so long as the predictions for experimental quantities are the same. This prediction can be written as Maxwell's equations, as Hertz's equations, as differential forms, or as a C-code to give the fields from the sources. It really doesn't make any difference, it's still Maxwell's theory.

Answer 2

I have no personal opinion and I will report what I found interesting in the net about the subject.
The Hertz equations (I was not aware of them) had originally an error, here corrected by Pechenkov

A little error was eliminated from Hertz’s equations ... Therefore Hertz’s electrodynamics is the alternative to Einstein’s electrodynamics.

A discussion of Hertz versus Maxwell eqs can be seen here, by Petrovic Branko and the more interesting is his conclusions about 'Detectors' - 'Conformity to the first relativity postulate' - 'Denying Newton's Third Law'.

I will have to study more on this subject.