In reply to Di Francesco: The basic equation of the axial Doppler requires things have more than 4 dimensions. Because every thing with an axial Doppler shift has the viewing angle as a dimension or the dimensions and velocity determining the viewing angel. Also I gave on my question a proof that time itself is multidimensional. The axial Doppler shift exists and most the writers on relativity ignore it, because Lorentz assumed the axial effects of aether wind cancel. But Doppler shifts are not aether wind. See the two files below for more details.