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We first show that Doppler’s effect implies that the time runs identically in the frames of reference of the source of light and the observer. Furthermore, we then show that the frequency shift due to the (assumed) expansion of space, if any, is “indistinguishable” from that due to the motion of the source with respect to the observer; and that the shift does not depend on the distance to the source. Observed frequency shifts of cosmological sources then need to be interpreted as being only due to their motions with respect to us. This has important implications for our ideas in cosmology.