Doppler shift in this discussion will be defined as, the difference (distortion) between the the observed quality and original quality due to closing velocity between the two. All writers on relativity agree that the transverse shift changes observed time and space. Since frequency=1/time and axial shift happens even in a vacuum it too must do it. Also the first attached file shows any interval (A) a Fourier time series of any signal will be observed as A/k where k =observed frequncy/original frequency.
Therefore the observed half life of the emitter will be impacted by Doppler shifts. The observed number of emitters passing a point will likewise be changed. The mass of all particles in the beam or the emissions will change.
Not only that since the axial Doppler shift has a cos(B) factor (B=observation angle): The average over all B is zero, BUT the VARIANCE is not zero. Therefore disorder increases.
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