Relativistic Doppler Effect and the Misunderstandings of...

The present paper discusses the relativistic Doppler effect and tries to found misunderstandings in the present state of the Special theory of relativity. The authors conclusion that he found some â€Å"blue shift† which contradicts with time dilation is wrong. The weakest feature of the paper is that although the formulas, presented by authors, are in general correct, but they do not support the conclusions the author extract from them, and mistake is hidden in the interpretation. Lets focus on the plane waves. In general, the transverse Doppler effect, as it is studied in the available literature, means that an observer (lets call him the 1st observer), that receive an electromagnetic wave from a distant source, moving relative to the†¦show more content†¦In case of author considerations, they are measured by different observers, situated at different reference frames. If one wants to use 2nd observer to find the Doppler effect, for 2nd observer, his ÃŽ ²=ÃŽ ²Ã¢â€šâ€š=0, and his ÃŽ ±=ÃŽ ±, formulas (1)-(2) will give ÃŽ ½=ÃŽ ½Ã¢â€šâ€š=ÃŽ ½. So there is no frequency shift for the 2nd observer. (as it should be for him, being in rest with the source). For the 1st observer, substituting the ÃŽ ² and ÃŽ ±=Ï€/2 will give correct result: ÃŽ ½=ÃŽ ½/ÃŽ ³, where ÃŽ ³=1/(sqrt(1-v ²/c ²)). One should not mix this two cases, as the author does. Lets look to the authors arguments, why one should use ÃŽ ±=Ï€/2 rather than ÃŽ ±=Ï€/2 to define transverse Doppler effect. The author calls ÃŽ ± as the proper angle and ÃŽ ± as apparent angle, in the analogy with the term proper length. This analogy seems to be not applicable. The proper length is the length of an item, measured in rest with this item. The term apparent length is for the length of an item, measured by another observer, moving relative to the item. For the angle between two items, it is not obvious, relative to what part of the system the observer should be in rest, in order to measure the angle to call the angle as proper angle. The authors idea, that using ÃŽ ±=Ï€/2 in order to compare with classical Doppler effect, also does not hold water, as in the classical theory