As shown above, in paragraph §3, the geometrical model of §2.1 is built with a glance to constant amplitude, while Maxwell's equations require its change.

Now I shall give Pauli's opinion.

/Citation/ Because of (204)( the transformation formulae for the values of fields (4-2-1)..(4-2-2) - author's note) it is easy to write down, in addition, the transformation formulae for the amplitude A.

(253)

/end of citation/ [18] chapter III §32 page 94, the number of the formula corresponds to the source/

Pauli gives this formula for an electromagnetic wave, in addition to the relativistic Doppler effect formulae. It describes relativistic transformation for amplitude values of a light wave for going over to moving coordinate system. Pauli shows that this addition is made in terms of the requirement of the invariance of phase of a light wave and also it is the corollary of the transformation formulae for the values of fields (4-2-1)..(4-2-2).

And further..

/Citation /A comparison with (15)(the formula 4-4-3 - my commentary) shows that energy and amplitude transform in the same way as frequency; for the volume, on the other hand, the reverse is true,

(254a).

the first of these relations was stressed by Einstein as being of particular importance; Wien's law is connected with it./end of citation/ [18] chapter III §32 page 95, the number of the formula corresponds to the source/

Here there is in mind a volume, bounding from sides a finite wave train. Now we interpret these formulae. The higher the frequency of a light wave the greater its energy and amplitude. The higher the frequency the smaller volume a light wave occupies.

It means, according to Pauli, that relativistic Doppler effect varies both frequency and amplitude of a light wave, besides the one varies energy density of a light wave (the inverse proportionality for change of volume and energy).

For such result to satisfy the requirement of phase invariance is possible only with a glance to the relativistic length contraction of a light wave like the solid measuring rod, i.e. it is like the monolithic object for which its inner structure is left out of account and so there is supposed that any energy motion inside the structure of a light wave is absent or is ignored. It is conceptual restriction of the theory of relativity. Any attempt to allow for the inner structure motion leads to the necessity of revision of the fundamental postulates. But even such exotic model of a light wave does not reflect its basic relativistic features. Unlike the solid measuring rod, which can only shorten a light wave besides can lengthen (the Doppler red shift). This feature better is satisfied by model, which can be presented as pair of the solid rods combined by elastic link, for example, by a spring. It is interesting to note that just such model (the mechanical oscillator) mostly is used for illustrating of the undulate processes. It is necessary to mention also that in a series of modern works is considered the problem, whether the relativistic contraction is actual or imaginary effect.