36 - 37 - 38

S.B. Karavashkin

36

We can see that the claims to the accuracy of used mathematical tool are quite serious, and we cannot say that the shown calculations are super-complicated or super-original. We could obtain all these results with the mathematics of the beginning of 20th century and, indeed, with the wish to analyse scrupulously. And this is far from being all. We will analyse something in the further chapters, and not this is important. Important is that neither peremptory statements like "We see that the electromagnetic theory has led us at once to the conclusive elucidation of the problem that caused the extraordinary difficulties in the old wave theory of light. Actually, fine Fresnel's and Aragoe's experiments have proved the transverseness of light waves, but it was extremely difficult to interpret them in frames of conceptions of elastic waves propagation in the aether, it required to introduce a number of artificial assumptions which have extremely complicated the theory. For today this is of absolutely no importance, the light-carrying aether is inadmissible not only as a specific medium but also as an abstract reference system, and the absence of longitudinal component of a free electromagnetic wave proves to be a simple corollary of Maxwell equations" [4, p. 23] nor artificial restrictions introduced in theoretical studying of multi-polar radiation cannot and never will be able to delete out of scientists' brains the idea of factual existence of longitudinal EM waves. In a curtailed, overturned form it travels from book to book, and sometimes it is so obvious, how hard one is attempting again and again to disprove its wave nature.

37

As a worthy example, consider the analysis by Kugushev of a field of elementary electric radiator with the length  l <<   through which the current flows.

"Rewrite the equations in the form

In the induction zone, where

the expressions (2-3-8) may be rewritten as follows:

38

As we can see, this field has not the wave nature and fast falls with the distance. The average value of the Pointing vector … is zero, because     and    are out of phase by  90 . Thus in the field described by (2-3-10) there is no motion of energy and only the periodic exchange of the energy between the electric and magnetic components takes place " [5, p. 48].

Consider in details this transformation and conclusions made from it. Outwardly everything seems correct, except a trifle. In (2-3-10) the summand   r   has been eliminated from the time multiplier - probably, proceeding from an idea that if  r   is small, it will be also smaller than  t  - but this is incorrect. Actually,   cos (t - r) and  sin (t - r)  are the periodic functions, so we can take a summand equal to  2k  from the summand  t . Thus we can introduce

t ' = t - 2k

Now we have to compare  r  not with an arbitrarily large number  t  but with the quite limited number (32). May we neglect  r  in comparison with  t ' ? Of course, no, the more that, for example, at

but at