Authors: Teimuraz Bregadze
Spherical wave vs. plane wave approximation to the nature of the electromagnetic waves in regard to the Doppler shift and aberration is considered. The first approach is free from the blueshift – redshift transition paradox innate for the second one. For spherical electromagnetic waves, in contrast with the plane ones, we have to assume that not only the magnitude, but also the direction of the light velocity is the same in any inertial frame, which leads to the accepted expression for time dilation. The rest frame of the source of electromagnetic waves is unique among all inertial frames (in it the angles of emission and reception coincide, and there is no shift in wavelength in all directions). The spherical approximation to electromagnetic waves preserves this uniqueness without violating the principle of relativity of the uniform motion, while the planar approximation ignores the source completely. Both approximations give the same expression of the Lorentz–FitzGerald contraction. Both spherical and planar approaches give the same Doppler shift in the directions of the relative motion of the frames, but in the directions with perpendicular components there may be significant differences. A geometrical picture of the transformation of wavefronts of spherical electromagnetic waves, which differs from the one according to the Lorentz transformation, is suggested.
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