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On longitudinal electromagnetic waves

that noting (5) leads us to

In other words, reducing to zero the value of scalar potential, we thereby reduce to zero the value of vector potential, just lifting the very possibility of EM waves investigation in the considered region of space. Thereby we have proved the assertion expressed in the beginning of this item.

Returning to the above item of strongly transversal nature of EM waves, notice that the record of equality

in the form (9) is illegitimate too, because it is based on the above calibrating invariance of potentials. And using (9) in the form (20) even more aggravates the contradictions revealed here.

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2. Illegitimate equating to zero the divergence of vectors E and H

To prove this statement, recall the definition of divergence: "The divergence of vector function of the point  ()  is the scalar function of the point determined by the formula

[3. p. 166].

Notice that in (21), with the invariable S and   V, the vector function depends only on the integrated parameters. but in the wave process ()  depends not only on    but on time too. With it, should the wave processes in EM field obey the long-range postulates, the presence of the non-integrated parameter  t  anyway could not change (21). But the practice shows the field processes obeying to the short-range regularities. Consequently, the processes in a field propagate both in space and time. This causes the time delay phases between the space-distributed processes. The brought about phase shift can be compensated neither by varying the field lines density (because in this case we should leave the stationary region  V ) nor by the time average, as Levich tried to avoid this complication, because with this not only

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itself. Hence, (21) is true only for stationary processes where the phase shifts of time are absent.

To find the equivalent of (21) for electrodynamic processes in space, consider some flux of function (, t) propagating through a picked out source-free region  V  (see Fig. 2). To simplify the derivation, limit  V   from the sides by the surface coinciding with the filaments of current, and from the butts - by the equiphase surfaces. With it, as far as the EM waves velocity is constant, the relation

Fig. 2. General form of the time-variable field tube of the flux