This article discusses the relativistic Doppler effect and attempts to base misunderstandings in the current state of the special theory of relativity. The author's conclusion that he found a "blue shift" that contradicts time dilation is false. The weakest feature of the article is that although the formulas presented by the authors are generally correct, they do not support the conclusions extracted from the author. of them, and the error is hidden 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 from a distant source, moving relative to the observer, will measure the frequency of the wave ν'=ν/γ, where γ=1/(sqrt(1-β²)), β²=u²/c², provided that the angle between the direction of the The wave and the vector of the movement of the source, measured by the observer, is equal to π/2 (α'=π/2). Thus, light from a moving source is red-shifted. It is generally treated as a pure effect of the special theory of relativity and is due to time dilation. Indeed, the observer can treat wave crests like a clock, and the decrease in their frequency is the true dilation of time. This effect is described as purely relativistic, because it is absent from classical theory. This is a fairly clear and well-known fact in special relativity. Note that the distance between the source and the 1st observer does not change over time, when measured by the 1st observer. All the problems raised by the author are due to the fact that the author decided not to use α', but α as an angle, equal to π/2, in order to define the transverse Doppler effect. It is obvious that α is the angle b...... middle of paper ...... relativity simultaneity is also relative. It is clear that in 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 away. And in the case of non-inertial frames, special relativity is not applicable at all. Let me also comment on the spherical pathways example. The example must be treated with caution, because the frame on the edge of the disk is not inertial. General relativity can handle this case correctly, that's fine. But we should not draw direct and simplified conclusions from this example. And that won't help us in our case of plane waves and inertial frames. To summarize: in my opinion, the points raised by the author are not correct. Therefore, I would not recommend it for publication in Plos One..