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S.B. Karavashkin

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To the point, in this derivation the commutation of taking the differential with respect to (t - (x/c))  and of the vector divergence took place, and this operation has been performed in full accordance with Landau's assumption, because if the operators are not commutative, the substitution

is also inadmissible, and we would have to substitute the variables in (15) in accordance with dependence of x on t . This last would lead us to the result = 0  that is not easier.

Thus we see that the derivation stating EM waves pure transversal, with all its obvious mathematical elegance, suffers from the important physical defects and has the only advantage - it is convenient. Just what we said in the beginning of the paper.

Several reasons lead the scientists to such results.

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1. Illegitimate equating the scalar potential to zero

"As we already know, as the potentials are not one-valued, we always (italicised by mine - S.K.) can impose on them some additional condition. On this grounds, choose the EM waves potentials so that the scalar potential be zero: = 0 " [2, p. 143]. The matter is here in the calibrating invariance

where f(, t)  means an arbitrary function of co-ordinates and time, and the prime marks the other co-ordinate system. However the vector and scalar EM potentials are not absolutely independent values spun from the thin air as, by a strange chance, the field theoreticians are interpreting. The above relation connects them unambiguously:

And this relation has been derived not as some abstract consideration but by formal transformation of the conventional system of the field theory basic equations with the use of standard formalism.

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Substituting (16) into (5), we yield the result non-identical to the conventional. Actually, if we multiply the second equation of (16) by   ()/c  and compare it with the first equality of this system, taking into account (5), we yield

This means, given the conservation regularities of the field theory for the transition  '  and  ' ,   f(, t) already cannot be an arbitrary function of co-ordinates and time, it has to satisfy definite differential equation.

Now imagine that by means of calibrating transformation we have reduced the field scalar potential to zero, i.e. ' = 0 . We can do it, introducing f(, t)   in the following form:

or in accordance with (17)

Substituting (18) into (16), we yield