This article discusses the relativistic Doppler effect and attempts to identify the misunderstandings in the current state of the theory of special relativity. The author's conclusion that he has found some "blue shift" that contradicts time dilation is wrong. The weakest feature of the article is that, although the formulas presented by the authors are in general correct, they do not support the conclusions drawn by the author from them, and the error hides in the interpretation. Let's focus on plane waves. In general, the transverse Doppler effect, as studied in the available literature, means that an observer (let's call him the 1st observer), who receives an electromagnetic wave coming from a distant source, moving with respect to the observer, will measure the wave frequency ν'=ν/γ, where γ=1/(sqrt(1-β²)), β²=u²/c², provided that the angle between the wave direction and the source motion vector , measured by the observer, is equal to π/2 (α'=π/2). So light from a moving source is redshifted. It is generally treated as a pure effect of the special theory of relativity, and is due to time dilation. The observer, in fact, can treat the wave crests like a clock, and the decrease in its frequency constitutes the effective dilation of time. This effect is called pure relativistic, since it is absent in classical theory. This is a fairly clear and well-known fact in special relativity. Note that the distance between the source and the first observer does not change over time, despite being measured by the first observer. All the issues raised by the author are due to the fact that the author decided not to use α', but α as an angle, i.e. equal to π/2, to define the transverse Doppler effect. It is obvious that α is the angle b... in the center of the paper... relativity, simultaneity is also relative. It is clear that in the case of uniform linear motion the time derivative of the distance between two objects is equal to 0 only once in time, at different times two objects converge or move apart. And in the case of non-inertial reference systems, special relativity is not applicable at all. I would also like to comment on the example with the spherical vias. The example should be treated carefully, since the reference system at the edge of the disk is not inertial. General relativity can handle this case correctly, okay. But direct, simplified conclusions should not be drawn from this example. And it won't help in our case with plane waves and inertial reference frames. To summarize: In my opinion the points raised by the author are incorrect. Therefore I would not recommend it for publication on Plos One.